{"CFDocument":{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/23a8e45a-9d5a-11e7-81bc-064e21a83c7c","identifier":"23a8e45a-9d5a-11e7-81bc-064e21a83c7c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","creator":"Georgia Department of Education","title":"Mathematics - Georgia Standards of Excellence - Retired ","language":"en","adoptionStatus":"Deprecated","publisher":"Georgia Department of Education","licenseURI":{"title":"CC BY-NC-SA","identifier":"32aacbc3-4c71-49e7-a295-bab57f80dd6d","uri":"https://case.georgiastandards.org/uri/32aacbc3-4c71-49e7-a295-bab57f80dd6d"},"statusEndDate":"2023-07-31"},"CFItems":[{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707964bc-9d5a-11e7-85fe-c8bb8640d8b3","identifier":"707964bc-9d5a-11e7-85fe-c8bb8640d8b3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"fullStatement":"Standards for Mathematical Practice","notes":"The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \"processes and proficiencies\" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7079d6e0-9d5a-11e7-aaca-31e2c35a248c","identifier":"7079d6e0-9d5a-11e7-aaca-31e2c35a248c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \u201cDoes this make sense?\u201d They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7079efb8-9d5a-11e7-a02e-595e01e56db7","identifier":"7079efb8-9d5a-11e7-a02e-595e01e56db7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize\u2014to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents\u2014and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a07b4-9d5a-11e7-8748-c33fcafea48f","identifier":"707a07b4-9d5a-11e7-8748-c33fcafea48f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and\u2014if there is a flaw in an argument\u2014explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a1e48-9d5a-11e7-b0f5-c7b759c0c2e7","identifier":"707a1e48-9d5a-11e7-b0f5-c7b759c0c2e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.4","fullStatement":"Model with mathematics.","notes":"Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a3586-9d5a-11e7-9a36-be3cd37aebb6","identifier":"707a3586-9d5a-11e7-9a36-be3cd37aebb6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a4c92-9d5a-11e7-a0d9-e810927f2413","identifier":"707a4c92-9d5a-11e7-a0d9-e810927f2413","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.6","fullStatement":"Attend to precision.","notes":"Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a6344-9d5a-11e7-8f2a-80459324fbd8","identifier":"707a6344-9d5a-11e7-8f2a-80459324fbd8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 \u00d7 8 equals the well-remembered 7 \u00d7 5 + 7 \u00d7 3, in preparation for learning about the distributive property. In the expression *x*\u00b2 + 9*x* + 14, older students can see the 14 as 2 \u00d7 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 \u2013 3(*x* \u2013 *y*)\u00b2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers *x* and *y*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/707a7aaa-9d5a-11e7-9913-0723ae0b82d0","identifier":"707a7aaa-9d5a-11e7-9913-0723ae0b82d0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"humanCodingScheme":"MGSE.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (*y* \u2013 2)/(*x* \u2013 1) = 3. Noticing the regularity in the way terms cancel when expanding (*x* \u2013 1)(*x* + 1), (*x* \u2013 1)(*x*\u00b2 + x + 1), and (*x* \u2013 1)(*x*\u00b3 + *x*\u00b2 + *x* + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/677d8900-9d60-11e7-b9ca-2cca0bcdbd7d","identifier":"677d8900-9d60-11e7-b9ca-2cca0bcdbd7d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["01"],"humanCodingScheme":"27.01200","fullStatement":"Mathematics/Grade 1","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.  \r\n\r\nContent standards for Grade 1 are arranged within four domains and eleven clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/677dc42e-9d60-11e7-a855-27c8bc0e4c26","identifier":"677dc42e-9d60-11e7-a855-27c8bc0e4c26","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["01"],"humanCodingScheme":"1.NBT","fullStatement":"Number and Operations in Base Ten","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/677e06be-9d60-11e7-9d2d-4ecd9b2a0dd0","identifier":"677e06be-9d60-11e7-9d2d-4ecd9b2a0dd0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["01"],"fullStatement":"Measure lengths indirectly and by iterating length units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/677de062-9d60-11e7-96d2-4df0a90f1136","identifier":"677de062-9d60-11e7-96d2-4df0a90f1136","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["01"],"humanCodingScheme":"1.MD","fullStatement":"Measurement and Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/677e22de-9d60-11e7-8799-9bf311f36e6a","identifier":"677e22de-9d60-11e7-8799-9bf311f36e6a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["01"],"humanCodingScheme":"1.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6889a42-9d60-11e7-a07b-9f1682efbc9e","identifier":"d6889a42-9d60-11e7-a07b-9f1682efbc9e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["02"],"humanCodingScheme":"27.01300","fullStatement":"Mathematics/Grade 2","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.\r\n\r\nContent standards for Grade 2 are arranged within four domains and ten clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6890df6-9d60-11e7-9b3d-5af5ab91780c","identifier":"d6890df6-9d60-11e7-9b3d-5af5ab91780c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Represent and solve problems involving addition and subtraction.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d688db4c-9d60-11e7-a877-287faf01a48a","identifier":"d688db4c-9d60-11e7-a877-287faf01a48a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["02"],"humanCodingScheme":"2.OA","fullStatement":"Operations and Algebraic Thinking","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68927f0-9d60-11e7-af06-270f89da4cd3","identifier":"d68927f0-9d60-11e7-af06-270f89da4cd3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Add and subtract within 20.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6894b68-9d60-11e7-9b57-e184803e50e3","identifier":"d6894b68-9d60-11e7-9b57-e184803e50e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.OA.2","fullStatement":"Fluently add and subtract within 20 using mental strategies. (*See standard 1.OA.6 for a list of mental strategies.*) By end of Grade 2, know from memory all sums of two one-digit numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6896436-9d60-11e7-be19-7da9ba7d6208","identifier":"d6896436-9d60-11e7-be19-7da9ba7d6208","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Work with equal groups of objects to gain foundations for multiplication.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d689a824-9d60-11e7-992a-1ad8f6a8e759","identifier":"d689a824-9d60-11e7-992a-1ad8f6a8e759","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Understand place value.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6897cbe-9d60-11e7-8909-9b8c5aa4e841","identifier":"d6897cbe-9d60-11e7-8909-9b8c5aa4e841","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["02"],"humanCodingScheme":"2.NBT","fullStatement":"Number and Operations in Base Ten","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d689c1f6-9d60-11e7-a721-3923b963e1c6","identifier":"d689c1f6-9d60-11e7-a721-3923b963e1c6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Use place value understanding and properties of operations to add and subtract.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d689f892-9d60-11e7-b414-147971bfe0ba","identifier":"d689f892-9d60-11e7-b414-147971bfe0ba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.6","fullStatement":"Add up to four two-digit numbers using strategies based on place value and properties of operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68a1246-9d60-11e7-b7bd-817321011ac4","identifier":"d68a1246-9d60-11e7-b7bd-817321011ac4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.7","fullStatement":"Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68a298e-9d60-11e7-b5fc-d61fd3dca2ea","identifier":"d68a298e-9d60-11e7-b5fc-d61fd3dca2ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.8","fullStatement":"Mentally add 10 or 100 to a given number 100\u2013900, and mentally subtract 10 or 100 from a given number 100\u2013900.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68a4180-9d60-11e7-971b-2a8f68ecebeb","identifier":"d68a4180-9d60-11e7-971b-2a8f68ecebeb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.9","fullStatement":"Explain why addition and subtraction strategies work, using place value and the properties of operations.  *(Explanations may be supported by drawings or objects.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68ac0ec-9d60-11e7-8cad-d7631dc49334","identifier":"d68ac0ec-9d60-11e7-8cad-d7631dc49334","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.1","fullStatement":"Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68a878a-9d60-11e7-bf72-b97ffb725fe6","identifier":"d68a878a-9d60-11e7-bf72-b97ffb725fe6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Measure and estimate lengths in standard units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68a5a6c-9d60-11e7-85b6-163b71c09919","identifier":"d68a5a6c-9d60-11e7-85b6-163b71c09919","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["02"],"humanCodingScheme":"2.MD","fullStatement":"Measurement and Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b22d0-9d60-11e7-99b6-0dd343847cae","identifier":"d68b22d0-9d60-11e7-99b6-0dd343847cae","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["02"],"fullStatement":"Relate addition and subtraction to length.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b5354-9d60-11e7-802d-ba16407197fd","identifier":"d68b5354-9d60-11e7-802d-ba16407197fd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.5","fullStatement":"Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b6d08-9d60-11e7-8f05-ce64db756a94","identifier":"d68b6d08-9d60-11e7-8f05-ce64db756a94","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.6","fullStatement":"Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, \u2026, and represent whole-number sums and differences within 100 on a number line diagram.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b84be-9d60-11e7-9aa6-4e1dbdc79939","identifier":"d68b84be-9d60-11e7-9aa6-4e1dbdc79939","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.8","fullStatement":"Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and \u00a2 symbols appropriately.  *Example: If you have 2 dimes and 3 pennies, how many cents do you have?*","notes":"Example: If you have 2 dimes and 3 pennies, how many cents do you have?","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68ada82-9d60-11e7-8311-8f7b5bc6ab3a","identifier":"d68ada82-9d60-11e7-8311-8f7b5bc6ab3a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.2","fullStatement":"Measure the length of an object twice, using length units of different measurements; describe how the two measurements relate to the size of the unit chosen. Understand the relative size of units in different systems of measurement.  *For example, an inch is longer than a centimeter.*  (Students are not expected to convert between systems of measurements.)","notes":"For example, an inch is longer than a centimeter.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68af2ce-9d60-11e7-a0b9-bde0b374cde4","identifier":"d68af2ce-9d60-11e7-a0b9-bde0b374cde4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.3","fullStatement":"Estimate lengths using units of inches, feet, centimeters, and meters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b0a34-9d60-11e7-8836-946580656750","identifier":"d68b0a34-9d60-11e7-8836-946580656750","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.4","fullStatement":"Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d68b9d46-9d60-11e7-9d4e-2f52265f8c10","identifier":"d68b9d46-9d60-11e7-9d4e-2f52265f8c10","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["02"],"humanCodingScheme":"2.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8ad830-9d60-11e7-81e0-5650c391e261","identifier":"da8ad830-9d60-11e7-81e0-5650c391e261","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["03"],"humanCodingScheme":"27.01400","fullStatement":"Mathematics//Grade 3","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.  \r\n\r\nContent standards for Grade 3 are arranged within five domains and eleven clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8b83f2-9d60-11e7-99ea-48b99039d419","identifier":"da8b83f2-9d60-11e7-99ea-48b99039d419","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.2","fullStatement":"Interpret whole number quotients of whole numbers, e.g., interpret 56 \u00f7 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?).  *For example, describe a context in which a number of shares or a number of groups can be expressed as 56 \u00f7 8.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8b4f36-9d60-11e7-94ea-522f3267ce80","identifier":"da8b4f36-9d60-11e7-94ea-522f3267ce80","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["03"],"fullStatement":"Represent and solve problems involving multiplication and division.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8b193a-9d60-11e7-a782-00eb6a4b273b","identifier":"da8b193a-9d60-11e7-a782-00eb6a4b273b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["03"],"humanCodingScheme":"3.OA","fullStatement":"Operations and Algebraic Thinking","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8bd5aa-9d60-11e7-a5a4-851f08c6c2a8","identifier":"da8bd5aa-9d60-11e7-a5a4-851f08c6c2a8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["03"],"fullStatement":"Understand properties of multiplication and the relationship between multiplication and division.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8bfc60-9d60-11e7-9243-7abc15a84464","identifier":"da8bfc60-9d60-11e7-9243-7abc15a84464","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.6","fullStatement":"Understand division as an unknown-factor problem.  *For example, find 32 \u00f7 8 by finding the number that makes 32 when multiplied by 8.*","notes":"For example, find 32 \u00f7 8 by finding the number that makes 32 when multiplied by 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8c189e-9d60-11e7-8ff2-0ec29c8088d4","identifier":"da8c189e-9d60-11e7-8ff2-0ec29c8088d4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["03"],"fullStatement":"Multiply and divide within 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8ba008-9d60-11e7-b5ff-7078faefe334","identifier":"da8ba008-9d60-11e7-b5ff-7078faefe334","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.3","fullStatement":"Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (*See Mathematics Glossary, Table 2: Multiplication and Division Within 100.*)","notes":"See Mathematics Glossary, Table 2:  Multiplication and Division Within 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8bbad4-9d60-11e7-9fe4-b8e478f950e3","identifier":"da8bbad4-9d60-11e7-9fe4-b8e478f950e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.4","fullStatement":"Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division.  *For example, determine the unknown number that makes the equation true in each of the equations, 8 \u00d7 ? = 48, 5 = \u25a1 \u00f7 3, 6 \u00d7 6 = ?*.","notes":"For example, determine the unknown number that makes the equation true in each of the equations, 8 \u00d7 ? = 48, 5 = \u25a1 \u00f7 3, 6 \u00d7 6 = ?.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8c8928-9d60-11e7-84cd-21be93745d70","identifier":"da8c8928-9d60-11e7-84cd-21be93745d70","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NBT.1","fullStatement":"Use place value understanding to round whole numbers to the nearest 10 or 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8c5ae8-9d60-11e7-a1d9-0566620b1970","identifier":"da8c5ae8-9d60-11e7-a1d9-0566620b1970","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["03"],"fullStatement":"Use place value understanding and properties of operations to perform multi-digit arithmetic. (*A range of algorithms will be used.*)","notes":"A range of algorithms will be used.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8c34a0-9d60-11e7-8d01-d4e49c6530a6","identifier":"da8c34a0-9d60-11e7-8d01-d4e49c6530a6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["03"],"humanCodingScheme":"3.NBT","fullStatement":"Number and Operations in Base Ten","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8ca462-9d60-11e7-b1f2-ec7ae7c646d7","identifier":"da8ca462-9d60-11e7-b1f2-ec7ae7c646d7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NBT.3","fullStatement":"Multiply one-digit whole numbers by multiples of 10 in the range 10\u201390 (e.g., 9 \u00d7 80, 5 \u00d7 60) using strategies based on place value and properties of operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8cbfb0-9d60-11e7-8228-91a152559930","identifier":"da8cbfb0-9d60-11e7-8228-91a152559930","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["03"],"humanCodingScheme":"3.NF","fullStatement":"Number and Operations \u2013 Fractions","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8d2a4a-9d60-11e7-a725-c1ff8eb5b92e","identifier":"da8d2a4a-9d60-11e7-a725-c1ff8eb5b92e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.G.2","fullStatement":"Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.  *For example, partition a shape into 4 parts with equal area, and describe the area of each part as $\\frac{1}{4}$ of the area of the shape.*","notes":"For example, partition a shape into 4 parts with equal area, and describe the area of each part as $\\frac{1}{4}$ of the area of the shape.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8d0286-9d60-11e7-bf3c-e2315cb01305","identifier":"da8d0286-9d60-11e7-bf3c-e2315cb01305","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["03"],"fullStatement":"Reason with shapes and their attributes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8cdb3a-9d60-11e7-97a2-9de07b78f39a","identifier":"da8cdb3a-9d60-11e7-97a2-9de07b78f39a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["03"],"humanCodingScheme":"3.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc6b1fe-9d60-11e7-becf-b4a2d538eb97","identifier":"ddc6b1fe-9d60-11e7-becf-b4a2d538eb97","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["04"],"humanCodingScheme":"27.01500","fullStatement":"Mathematics/Grade 4","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.   \r\n\r\nContent standards for Grade 4 are arranged within five domains and twelve clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc74ad8-9d60-11e7-b433-2ec8da92252c","identifier":"ddc74ad8-9d60-11e7-b433-2ec8da92252c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.1","fullStatement":"Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to its right. *For example, recognize that 700 \u00f7 70 = 10 by applying concepts of place value and division.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc718f6-9d60-11e7-8b0e-89751e9945ea","identifier":"ddc718f6-9d60-11e7-8b0e-89751e9945ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Generalize place value understanding for multi-digit whole numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc6ec46-9d60-11e7-a9d9-cb6059698e41","identifier":"ddc6ec46-9d60-11e7-a9d9-cb6059698e41","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["04"],"humanCodingScheme":"4.NBT","fullStatement":"Number and Operations in Base Ten","notes":"Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc795c4-9d60-11e7-85f1-3f505bfcf996","identifier":"ddc795c4-9d60-11e7-85f1-3f505bfcf996","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Use place value understanding and properties of operations to perform multi-digit arithmetic.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc7c1ca-9d60-11e7-a066-d53c0315f5ba","identifier":"ddc7c1ca-9d60-11e7-a066-d53c0315f5ba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.4","fullStatement":"Fluently add and subtract multi-digit whole numbers using the standard algorithm.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc7db92-9d60-11e7-ae9f-d1e02283c14a","identifier":"ddc7db92-9d60-11e7-ae9f-d1e02283c14a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.5","fullStatement":"Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc764a0-9d60-11e7-8dda-cd747246e41d","identifier":"ddc764a0-9d60-11e7-8dda-cd747246e41d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.2","fullStatement":"Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc77d50-9d60-11e7-ac1f-31f3fe9fb2b2","identifier":"ddc77d50-9d60-11e7-ac1f-31f3fe9fb2b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.3","fullStatement":"Use place value understanding to round multi-digit whole numbers to any place.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc851d0-9d60-11e7-b58b-65a48ef38af2","identifier":"ddc851d0-9d60-11e7-b58b-65a48ef38af2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.1","fullStatement":"Explain why two or more fractions are equivalent $\\frac{a}{b} = \\frac{n \\times a}{n \\times b}$   ex: $\\frac{1}{4} = \\frac{3 \\times 1}{3 \\times 4}$ by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc825b6-9d60-11e7-ad1d-e2b4f4227653","identifier":"ddc825b6-9d60-11e7-ad1d-e2b4f4227653","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Extend understanding of fraction equivalence and ordering.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc7f3f2-9d60-11e7-9b70-2df98f096ed9","identifier":"ddc7f3f2-9d60-11e7-9b70-2df98f096ed9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["04"],"humanCodingScheme":"4.NF","fullStatement":"Number and Operations \u2013 Fractions","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8840c-9d60-11e7-9d10-1cc51a1a4d2b","identifier":"ddc8840c-9d60-11e7-9d10-1cc51a1a4d2b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8d5ce-9d60-11e7-8870-795b5404e3ab","identifier":"ddc8d5ce-9d60-11e7-8870-795b5404e3ab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.3a","fullStatement":"Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8a8ba-9d60-11e7-86f2-2e138d5b4aa5","identifier":"ddc8a8ba-9d60-11e7-86f2-2e138d5b4aa5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.3","fullStatement":"Understand a fraction $\\frac{a}{b}$ with a numerator > 1 as a sum of unit fractions $\\frac{1}{b}$.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8f004-9d60-11e7-84c3-23a46d78972f","identifier":"ddc8f004-9d60-11e7-84c3-23a46d78972f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.3c","fullStatement":"Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc90990-9d60-11e7-a137-71f37a0e7992","identifier":"ddc90990-9d60-11e7-a137-71f37a0e7992","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Understand decimal notation for fractions, and compare decimal fractions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc93af0-9d60-11e7-bf6b-ea74ee44ec17","identifier":"ddc93af0-9d60-11e7-bf6b-ea74ee44ec17","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.5","fullStatement":"Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.  *For example, express $\\frac{3}{10}$ as $\\frac{30}{100}$, and add $\\frac{3}{10}$ + $\\frac{4}{100}$ = $\\frac{34}{100}$.*  *(Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But, addition and subtraction with unlike denominators in general is not a requirement at this grade.)*","notes":"Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But, addition and subtraction with unlike denominators in general is not a requirement at this grade.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc95436-9d60-11e7-8202-14b6b60467bd","identifier":"ddc95436-9d60-11e7-8202-14b6b60467bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.6","fullStatement":"Use decimal notation for fractions with denominators 10 or 100.  *For example, rewrite 0.62 as $\\frac{62}{100}$; describe a length as 0.62 meters; locate 0.62 on a number line diagram.*","notes":"For example, rewrite 0.62 as $\\frac{62}{100}$; describe a length as 0.62 meters; locate 0.62 on a number line diagram.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc96c8c-9d60-11e7-a843-f167da22a7b8","identifier":"ddc96c8c-9d60-11e7-a843-f167da22a7b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.7","fullStatement":"Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or < , and justify the conclusions, e.g., by using a visual model.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc86bb6-9d60-11e7-9fbd-b01359d8fe9a","identifier":"ddc86bb6-9d60-11e7-9fbd-b01359d8fe9a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.2","fullStatement":"Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as $\\frac{1}{2}$.   Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or < , and justify the conclusions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc9d596-9d60-11e7-87ab-4aa92912ecf1","identifier":"ddc9d596-9d60-11e7-87ab-4aa92912ecf1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.G.1","fullStatement":"Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc9a9c2-9d60-11e7-903c-bcc81dfc6368","identifier":"ddc9a9c2-9d60-11e7-903c-bcc81dfc6368","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["04"],"fullStatement":"Draw and identify lines and angles, and classify shapes by properties of their lines and angles.","notes":"In Georgia resources and assessments, trapezoids are defined using the inclusive definition: At least one pair of parallel sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc985dc-9d60-11e7-ac16-954fa4b3e93b","identifier":"ddc985dc-9d60-11e7-ac16-954fa4b3e93b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["04"],"humanCodingScheme":"4.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc9eedc-9d60-11e7-8834-0e60f2580e97","identifier":"ddc9eedc-9d60-11e7-8834-0e60f2580e97","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.G.2","fullStatement":"Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.","notes":"In Georgia resources and assessments, trapezoids are defined using the inclusive definition: At least one pair of parallel sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e192b81e-9d60-11e7-91b3-2a5f5cc2b068","identifier":"e192b81e-9d60-11e7-91b3-2a5f5cc2b068","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["05"],"humanCodingScheme":"27.01600","fullStatement":"Mathematics/Grade 5","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.\r\n\r\nContent standards for Grade 5 are arranged within five domains and eleven clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e19343c4-9d60-11e7-b9e9-dbf8b9e8f6ec","identifier":"e19343c4-9d60-11e7-b9e9-dbf8b9e8f6ec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.OA.3","fullStatement":"Generate two numerical patterns using a given rule. Identify apparent relationships between corresponding terms by completing a function table or input/output table. Using the terms created, form and graph ordered pairs on a coordinate plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1931e30-9d60-11e7-b41a-18c9bd13cf01","identifier":"e1931e30-9d60-11e7-b41a-18c9bd13cf01","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Analyze patterns and relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e192f798-9d60-11e7-ac77-3f0af2f8ec9c","identifier":"e192f798-9d60-11e7-ac77-3f0af2f8ec9c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["05"],"humanCodingScheme":"5.OA","fullStatement":"Operations and Algebraic Thinking","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e193c2e0-9d60-11e7-9d76-f37887eb1bd5","identifier":"e193c2e0-9d60-11e7-9d76-f37887eb1bd5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.1","fullStatement":"Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1938ac8-9d60-11e7-8926-680da8a16457","identifier":"e1938ac8-9d60-11e7-8926-680da8a16457","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Understand the place value system.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1935f26-9d60-11e7-9626-31a1b74f2567","identifier":"e1935f26-9d60-11e7-9626-31a1b74f2567","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["05"],"humanCodingScheme":"5.NBT","fullStatement":"Number and Operations in Base Ten","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1946d30-9d60-11e7-b42c-383d06ac98a5","identifier":"e1946d30-9d60-11e7-b42c-383d06ac98a5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Perform operations with multi-digit whole numbers and with decimals to hundredths.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1949fda-9d60-11e7-8241-9bd2a4d35d97","identifier":"e1949fda-9d60-11e7-8241-9bd2a4d35d97","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.5","fullStatement":"Fluently multiply multi-digit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e194bab0-9d60-11e7-b671-6375aa075815","identifier":"e194bab0-9d60-11e7-b671-6375aa075815","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.6","fullStatement":"Fluently divide up to 4-digit dividends and 2-digit divisors by using at least one of the following methods: strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations or concrete models. (e.g., rectangular arrays, area models)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e194d324-9d60-11e7-8dca-e28dc6a048e8","identifier":"e194d324-9d60-11e7-8dca-e28dc6a048e8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.7","fullStatement":"Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e193dcc6-9d60-11e7-b985-c8f5e91e8956","identifier":"e193dcc6-9d60-11e7-b985-c8f5e91e8956","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.2","fullStatement":"Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e193f512-9d60-11e7-99b3-215eb97f167f","identifier":"e193f512-9d60-11e7-99b3-215eb97f167f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.3","fullStatement":"Read, write, and compare decimals to thousandths.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1942140-9d60-11e7-81bc-26bcad77986b","identifier":"e1942140-9d60-11e7-81bc-26bcad77986b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.3a","fullStatement":"Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 \u00d7 100 + 4 \u00d7 10 + 7 \u00d7 1 + 3 \u00d7 ($\\frac{1}{10}$) + 9 \u00d7 ($\\frac{1}{100}$) + 2 \u00d7 ($\\frac{1}{1000}$).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1943a40-9d60-11e7-ac1f-273a5f5f6ff5","identifier":"e1943a40-9d60-11e7-ac1f-273a5f5f6ff5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.3b","fullStatement":"Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e19453c2-9d60-11e7-9bd5-bf2be8630ece","identifier":"e19453c2-9d60-11e7-9bd5-bf2be8630ece","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NBT.4","fullStatement":"Use place value understanding to round decimals up to the hundredths place.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e195458e-9d60-11e7-afd8-b48150919c85","identifier":"e195458e-9d60-11e7-afd8-b48150919c85","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.1","fullStatement":"Convert among different-sized standard measurement units (mass, weight, length, time, etc.) within a given measurement system (customary and metric) (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real word problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1951f8c-9d60-11e7-997d-031ee2cae75f","identifier":"e1951f8c-9d60-11e7-997d-031ee2cae75f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Convert like measurement units within a given measurement system.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e194ed5a-9d60-11e7-a38b-bbaba7ce39b7","identifier":"e194ed5a-9d60-11e7-a38b-bbaba7ce39b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["05"],"humanCodingScheme":"5.MD","fullStatement":"Measurement and Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e195605a-9d60-11e7-a317-db1f4a36b98c","identifier":"e195605a-9d60-11e7-a317-db1f4a36b98c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Represent and interpret data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e195851c-9d60-11e7-8782-24d6d44613f3","identifier":"e195851c-9d60-11e7-8782-24d6d44613f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.2","fullStatement":"Make a line plot to display a data set of measurements in fractions of a unit ($\\frac{1}{2}$, $\\frac{1}{4}$, $\\frac{1}{8}$). Use operations on fractions for this grade to solve problems involving information presented in line plots.  *For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.*","notes":"For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1959f52-9d60-11e7-a17a-8bbe209d7bfa","identifier":"e1959f52-9d60-11e7-a17a-8bbe209d7bfa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["05"],"fullStatement":"Geometric measurement: understand concepts of volume and relate volume to multiplication and division.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e195cd10-9d60-11e7-bf89-3ea83df490e1","identifier":"e195cd10-9d60-11e7-bf89-3ea83df490e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.4","fullStatement":"Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1961bd0-9d60-11e7-b0b6-6c7b6fdbea86","identifier":"e1961bd0-9d60-11e7-b0b6-6c7b6fdbea86","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.5a","fullStatement":"Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e195e8b8-9d60-11e7-8721-edc3285b2340","identifier":"e195e8b8-9d60-11e7-8721-edc3285b2340","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.5","fullStatement":"Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e196358e-9d60-11e7-9c6d-c28026987117","identifier":"e196358e-9d60-11e7-9c6d-c28026987117","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.5b","fullStatement":"Apply the formulas V = l \u00d7 w \u00d7 h and V = b \u00d7 h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1964df8-9d60-11e7-883d-5bff2d84cc76","identifier":"e1964df8-9d60-11e7-883d-5bff2d84cc76","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.5c","fullStatement":"Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e196b932-9d60-11e7-a8f3-c51fc61f732e","identifier":"e196b932-9d60-11e7-a8f3-c51fc61f732e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.G.3","fullStatement":"Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.  *For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.*","notes":"In Georgia resources and assessments, trapezoids are defined using the inclusive definition: At least one pair of parallel 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one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities. *For example, given 1 in. = 2.54 cm, how many centimeters are in 6 inches?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e727f19a-9d60-11e7-bd2d-76be1b9939dc","identifier":"e727f19a-9d60-11e7-bd2d-76be1b9939dc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.1","fullStatement":"Write and evaluate numerical expressions involving whole-number 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Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7287ac0-9d60-11e7-a8e3-988b60aeb856","identifier":"e7287ac0-9d60-11e7-a8e3-988b60aeb856","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Reason about and solve one-variable equations and inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e728b350-9d60-11e7-bc01-237e8a4d2a4e","identifier":"e728b350-9d60-11e7-bc01-237e8a4d2a4e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.5","fullStatement":"Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e728cd68-9d60-11e7-8fcb-51d719e0d58d","identifier":"e728cd68-9d60-11e7-8fcb-51d719e0d58d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.6","fullStatement":"Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e728e528-9d60-11e7-95ac-dfd2d22d900b","identifier":"e728e528-9d60-11e7-95ac-dfd2d22d900b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.7","fullStatement":"Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e728fd38-9d60-11e7-981c-db1797aa0709","identifier":"e728fd38-9d60-11e7-981c-db1797aa0709","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.8","fullStatement":"Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e72914f8-9d60-11e7-9809-c97a7de3e9cd","identifier":"e72914f8-9d60-11e7-9809-c97a7de3e9cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Represent and analyze quantitative relationships between dependent and independent variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7293910-9d60-11e7-8d6d-4fd2e2c39aa2","identifier":"e7293910-9d60-11e7-8d6d-4fd2e2c39aa2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.9","fullStatement":"Use variables to represent two quantities in a real-world problem that change in relationship to another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7280bd0-9d60-11e7-a08a-73dfebf5f2fb","identifier":"e7280bd0-9d60-11e7-a08a-73dfebf5f2fb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.2","fullStatement":"Write, read, and evaluate expressions in which letters stand for numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7282ff2-9d60-11e7-8fe2-e8665f53399d","identifier":"e7282ff2-9d60-11e7-8fe2-e8665f53399d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.2a","fullStatement":"Write expressions that record operations with numbers and with letters standing for numbers.  *For example, express the calculation \u201cSubtract y from 5\u201d as 5\u2013 y.*","notes":"For example, express the calculation \"Subtract y from 5\" as 5 \u2013 y.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e72849ce-9d60-11e7-826b-23c62964cbbf","identifier":"e72849ce-9d60-11e7-826b-23c62964cbbf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.3","fullStatement":"Apply the properties of operations to generate equivalent expressions. *For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7286210-9d60-11e7-98e2-89438b74f8bb","identifier":"e7286210-9d60-11e7-98e2-89438b74f8bb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.4","fullStatement":"Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).  *For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e72999a0-9d60-11e7-95d3-9c1f5dd82d07","identifier":"e72999a0-9d60-11e7-95d3-9c1f5dd82d07","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["06"],"humanCodingScheme":"6.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef147630-9d60-11e7-b311-10950f516b35","identifier":"ef147630-9d60-11e7-b311-10950f516b35","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["07"],"humanCodingScheme":"27.02200","fullStatement":"Mathematics/Grade 7","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef1505aa-9d60-11e7-92a2-85c4c61c8fec","identifier":"ef1505aa-9d60-11e7-92a2-85c4c61c8fec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.1","fullStatement":"Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef14cfae-9d60-11e7-82a5-e5080a8a2f6d","identifier":"ef14cfae-9d60-11e7-82a5-e5080a8a2f6d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Analyze proportional relationships and use them to solve real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef14ab1e-9d60-11e7-a5ed-667e1033f00d","identifier":"ef14ab1e-9d60-11e7-a5ed-667e1033f00d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["07"],"humanCodingScheme":"7.RP","fullStatement":"Ratios and Proportional Relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef1526ac-9d60-11e7-8527-8e81df2d8f17","identifier":"ef1526ac-9d60-11e7-8527-8e81df2d8f17","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2","fullStatement":"Recognize and represent proportional relationships between quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef1562f2-9d60-11e7-b06f-4c2bbbf4f1c6","identifier":"ef1562f2-9d60-11e7-b06f-4c2bbbf4f1c6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2b","fullStatement":"Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef157f80-9d60-11e7-845d-29dbe2d6408b","identifier":"ef157f80-9d60-11e7-845d-29dbe2d6408b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2c","fullStatement":"Represent proportional relationships by equations. *For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef159a74-9d60-11e7-8574-a8b27fbff554","identifier":"ef159a74-9d60-11e7-8574-a8b27fbff554","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2d","fullStatement":"Explain what a point (*x,y*) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,*r*) where *r* is the unit rate.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef15b5ae-9d60-11e7-9df2-524690afd2fa","identifier":"ef15b5ae-9d60-11e7-9df2-524690afd2fa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.3","fullStatement":"Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef162c46-9d60-11e7-9b41-af878c344040","identifier":"ef162c46-9d60-11e7-9b41-af878c344040","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.2","fullStatement":"Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related.  *For example a + 0.05a = 1.05a means that adding a 5% tax to a total is the same as multiplying the total by 1.05.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef1602f2-9d60-11e7-a77b-2f3315823766","identifier":"ef1602f2-9d60-11e7-a77b-2f3315823766","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Use properties of operations to generate equivalent expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef15d282-9d60-11e7-a90e-5ee0323fd952","identifier":"ef15d282-9d60-11e7-a90e-5ee0323fd952","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["07"],"humanCodingScheme":"7.EE","fullStatement":"Expressions and Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef16496a-9d60-11e7-ba7e-d4168beb4365","identifier":"ef16496a-9d60-11e7-ba7e-d4168beb4365","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Solve real-life and mathematical problems using numerical and algebraic expressions and equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ef1670e8-9d60-11e7-ab76-64011a67a65d","identifier":"ef1670e8-9d60-11e7-ab76-64011a67a65d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.3","fullStatement":"Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.\r\n*For example:<ul><li>If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.</li><li>If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.</li></ul>*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5ce361e-9d60-11e7-b488-e4650695f4ea","identifier":"f5ce361e-9d60-11e7-b488-e4650695f4ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["08"],"humanCodingScheme":"27.02300","fullStatement":"Mathematics/Grade 8","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5ceccb4-9d60-11e7-bf5f-bd31286e65e7","identifier":"f5ceccb4-9d60-11e7-bf5f-bd31286e65e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.NS.1","fullStatement":"Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cea090-9d60-11e7-8429-9bffe858f20f","identifier":"f5cea090-9d60-11e7-8429-9bffe858f20f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Know that there are numbers that are not rational, and approximate them by rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5ce7b24-9d60-11e7-a8d6-56e1371d3abb","identifier":"f5ce7b24-9d60-11e7-a8d6-56e1371d3abb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["08"],"humanCodingScheme":"8.NS","fullStatement":"The Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cee5aa-9d60-11e7-ba5c-b2c458a8e104","identifier":"f5cee5aa-9d60-11e7-ba5c-b2c458a8e104","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.NS.2","fullStatement":"Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate *\u03c0*\u00b2 to the nearest tenth).  *For example, by truncating the decimal expansion of \u221a2 (square root of 2), show that \u221a2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cf68fe-9d60-11e7-ae6f-c77f4076fb65","identifier":"f5cf68fe-9d60-11e7-ae6f-c77f4076fb65","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.1","fullStatement":"Know and apply the properties of integer exponents to generate equivalent numerical expressions. *For example, $3^2 \\times 3^{(-5)} = 3^{(-3)} = \\frac{1}{(3^3)} = \\frac{1}{27}$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cf2fe2-9d60-11e7-8ebb-00cc687247f5","identifier":"f5cf2fe2-9d60-11e7-8ebb-00cc687247f5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Work with radicals and integer exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cefef0-9d60-11e7-8c3e-1044eb38c0d9","identifier":"f5cefef0-9d60-11e7-8c3e-1044eb38c0d9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["08"],"humanCodingScheme":"8.EE","fullStatement":"Expressions and Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cfcb82-9d60-11e7-8a68-1ea616788f6c","identifier":"f5cfcb82-9d60-11e7-8a68-1ea616788f6c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Understand the connections between proportional relationships, lines, and linear equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cfe388-9d60-11e7-ba93-6fcecfe23134","identifier":"f5cfe388-9d60-11e7-ba93-6fcecfe23134","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Analyze and solve linear equations and pairs of simultaneous linear equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d03cde-9d60-11e7-9a2e-f31d3d648e57","identifier":"f5d03cde-9d60-11e7-9a2e-f31d3d648e57","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7a","fullStatement":"Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form *x = a*, *a = a*, or *a = b* results (where *a* and *b* are different numbers).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d00fc0-9d60-11e7-ac04-9e9cce96948d","identifier":"f5d00fc0-9d60-11e7-ac04-9e9cce96948d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7","fullStatement":"Solve linear equations in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d056f6-9d60-11e7-a05d-4e3398ca7bcb","identifier":"f5d056f6-9d60-11e7-a05d-4e3398ca7bcb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7b","fullStatement":"Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d0a192-9d60-11e7-a07c-d7a63e4d8636","identifier":"f5d0a192-9d60-11e7-a07c-d7a63e4d8636","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8a","fullStatement":"Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d06f74-9d60-11e7-adac-a8b8e5a19ddd","identifier":"f5d06f74-9d60-11e7-adac-a8b8e5a19ddd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8","fullStatement":"Analyze and solve pairs of simultaneous linear equations (systems of linear equations).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d0bb0a-9d60-11e7-a342-d57bb6f7b30a","identifier":"f5d0bb0a-9d60-11e7-a342-d57bb6f7b30a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8b","fullStatement":"Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.  *For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d0d37e-9d60-11e7-b9d1-f9bb48dc3fb2","identifier":"f5d0d37e-9d60-11e7-b9d1-f9bb48dc3fb2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8c","fullStatement":"Solve real-world and mathematical problems leading to two linear equations in two variables.  *For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cf828a-9d60-11e7-9568-b427bfb3023a","identifier":"f5cf828a-9d60-11e7-9568-b427bfb3023a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.2","fullStatement":"Use square root and cube root symbols to represent solutions to equations. Recognize that x\u00b2 = p (where p is a positive rational number and |x| \u2264 25) has 2 solutions and x\u00b3 = p (where p is a negative or positive rational number and |x| \u2264 10) has one solution. Evaluate square roots of perfect squares \u2264 625 and cube roots of perfect cubes \u2265 -1000 and \u2264 1000.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cf9b30-9d60-11e7-a56c-98711938e5e9","identifier":"f5cf9b30-9d60-11e7-a56c-98711938e5e9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.3","fullStatement":"Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.  *For example, estimate the population of the United States as $3 \\times 10^8$ and the population of the world as $7 \\times 10^9$, and determine that the world population is more than 20 times larger.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5cfb340-9d60-11e7-bec2-075cf08ffe0d","identifier":"f5cfb340-9d60-11e7-bec2-075cf08ffe0d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.4","fullStatement":"Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g. use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g. calculators).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d14a2a-9d60-11e7-bf82-1d7216954ab9","identifier":"f5d14a2a-9d60-11e7-bf82-1d7216954ab9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.F.1","fullStatement":"Understand that a function is a rule that assigns to each input exactly one output. 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Determine the rate of change and initial value of the function from a description of a relationship or from two (*x,y*) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d1d7f6-9d60-11e7-91b6-8bc4e0067f14","identifier":"f5d1d7f6-9d60-11e7-91b6-8bc4e0067f14","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.F.5","fullStatement":"Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). 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give examples of functions that are not linear.  *For example, the function A = s\u00b2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d26090-9d60-11e7-8d5b-40212359c308","identifier":"f5d26090-9d60-11e7-8d5b-40212359c308","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.1","fullStatement":"Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d22256-9d60-11e7-93a6-7011880ccc69","identifier":"f5d22256-9d60-11e7-93a6-7011880ccc69","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Understand congruence and similarity using physical models, transparencies, or geometry software.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d1f0ce-9d60-11e7-a58b-79a2f83a4079","identifier":"f5d1f0ce-9d60-11e7-a58b-79a2f83a4079","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["08"],"humanCodingScheme":"8.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d2d8d6-9d60-11e7-b742-9804485fe1e0","identifier":"f5d2d8d6-9d60-11e7-b742-9804485fe1e0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Understand and apply the Pythagorean Theorem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d309b4-9d60-11e7-8f99-167fb50d6fb3","identifier":"f5d309b4-9d60-11e7-8f99-167fb50d6fb3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.6","fullStatement":"Explain a proof of the Pythagorean Theorem and its converse.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d32368-9d60-11e7-99e8-8e8955aa93ca","identifier":"f5d32368-9d60-11e7-99e8-8e8955aa93ca","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.7","fullStatement":"Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d33bbe-9d60-11e7-bf57-c65a7e5c6a63","identifier":"f5d33bbe-9d60-11e7-bf57-c65a7e5c6a63","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.8","fullStatement":"Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d354be-9d60-11e7-9f15-1f0e5192a47e","identifier":"f5d354be-9d60-11e7-9f15-1f0e5192a47e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d37822-9d60-11e7-bfd1-50e9b1110df1","identifier":"f5d37822-9d60-11e7-bfd1-50e9b1110df1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.9","fullStatement":"Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d27a76-9d60-11e7-99a6-3587251ad724","identifier":"f5d27a76-9d60-11e7-99a6-3587251ad724","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.2","fullStatement":"Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d29240-9d60-11e7-afd0-11ce649f735e","identifier":"f5d29240-9d60-11e7-afd0-11ce649f735e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.3","fullStatement":"Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d2a9c4-9d60-11e7-8064-92d49a083745","identifier":"f5d2a9c4-9d60-11e7-8064-92d49a083745","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.4","fullStatement":"Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d2c10c-9d60-11e7-9285-37eec92a2b6a","identifier":"f5d2c10c-9d60-11e7-9285-37eec92a2b6a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.G.5","fullStatement":"Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.  *For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d3e1b8-9d60-11e7-aef0-e61a16ec5fc9","identifier":"f5d3e1b8-9d60-11e7-aef0-e61a16ec5fc9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.3","fullStatement":"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.  *For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d3b594-9d60-11e7-a24f-4e5f76bcc717","identifier":"f5d3b594-9d60-11e7-a24f-4e5f76bcc717","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08"],"fullStatement":"Investigate patterns of association in bivariate data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d3928a-9d60-11e7-b277-6e3df4331f80","identifier":"f5d3928a-9d60-11e7-b277-6e3df4331f80","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["08"],"humanCodingScheme":"8.SP","fullStatement":"Statistics and Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d3fbda-9d60-11e7-b53d-e5f1b7c33bcd","identifier":"f5d3fbda-9d60-11e7-b53d-e5f1b7c33bcd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.4","fullStatement":"Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1556f6-9d60-11e7-979f-51f68417f642","identifier":"fc1556f6-9d60-11e7-979f-51f68417f642","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.1","fullStatement":"Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. *For example, we define $5^{(1/3)}$ to be the cube root of 5 because we want $[5^{(1/3)}]^3$ = $5^{[(1/3) x 3]}$ to hold, so $[5^{(1/3)}]^3$ must equal 5.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1531ee-9d60-11e7-981f-77370ed1120f","identifier":"fc1531ee-9d60-11e7-981f-77370ed1120f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Extend the properties of exponents to rational exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc150cfa-9d60-11e7-93c7-92820f4f87a3","identifier":"fc150cfa-9d60-11e7-93c7-92820f4f87a3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"The Real Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc14bf8e-9d60-11e7-a730-f2791a4efa0e","identifier":"fc14bf8e-9d60-11e7-a730-f2791a4efa0e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.09920","fullStatement":"Algebra II / Advanced Algebra","notes":"**Algebra II/Advanced Algebra** is the culminating course in a sequence of three high school courses designed to ensure career and college readiness. It is designed to prepare students for fourth course options relevant to their career pursuits. \r\n\r\nThe standards in the three-course high school sequence specify the mathematics that all students should study in order to be college and career ready. Additional mathematics content is provided in fourth credit courses and advanced courses including pre-calculus, calculus, advanced statistics, discrete mathematics, and mathematics of finance courses. High school course content standards are listed by conceptual categories including Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Conceptual categories portray a coherent view of high school mathematics content; a student\u2019s work with functions, for example, crosses a number of traditional course boundaries, potentially up through and including calculus. Standards for Mathematical Practice provide the foundation for instruction and assessment.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc157230-9d60-11e7-b5e3-464de27139ee","identifier":"fc157230-9d60-11e7-b5e3-464de27139ee","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"The Complex Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc15d234-9d60-11e7-a315-3461c6b7cac4","identifier":"fc15d234-9d60-11e7-a315-3461c6b7cac4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.CN.1","fullStatement":"Understand there is a complex number *i* such that *i\u00b2 = \u22121*, and every complex number has the form *a + bi* where *a* and *b* are real 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y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2) (x^2 + y^2)$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1ddc5e-9d60-11e7-93ac-70b660a17e8a","identifier":"fc1ddc5e-9d60-11e7-93ac-70b660a17e8a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1b","fullStatement":"Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e5efe-9d60-11e7-805c-315182e2a808","identifier":"fc1e5efe-9d60-11e7-805c-315182e2a808","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3a","fullStatement":"Factor any quadratic expression to reveal the zeros of the function defined by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e32ee-9d60-11e7-9a0a-aecc618d3dac","identifier":"fc1e32ee-9d60-11e7-9a0a-aecc618d3dac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3","fullStatement":"Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e0eae-9d60-11e7-ae04-86c07f0b72bd","identifier":"fc1e0eae-9d60-11e7-ae04-86c07f0b72bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Write expressions in equivalent forms to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e793e-9d60-11e7-a182-abb33768721d","identifier":"fc1e793e-9d60-11e7-a182-abb33768721d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3b","fullStatement":"Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e9414-9d60-11e7-a329-e195d7ef3c24","identifier":"fc1e9414-9d60-11e7-a329-e195d7ef3c24","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Arithmetic with Polynomials and Rational Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1eddf2-9d60-11e7-8477-7c79cebd90df","identifier":"fc1eddf2-9d60-11e7-8477-7c79cebd90df","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1eb8b8-9d60-11e7-bdfb-f760a424d84e","identifier":"fc1eb8b8-9d60-11e7-bdfb-f760a424d84e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Perform arithmetic operations on polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1ef864-9d60-11e7-9298-103adc862f5e","identifier":"fc1ef864-9d60-11e7-9298-103adc862f5e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Creating Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1f5a52-9d60-11e7-9d5d-908e71b04451","identifier":"fc1f5a52-9d60-11e7-9d5d-908e71b04451","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, ~~simple rational,~~ and exponential functions (integer inputs only).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1f1ca4-9d60-11e7-8105-0aa7d058760a","identifier":"fc1f1ca4-9d60-11e7-8105-0aa7d058760a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Create equations that describe numbers or relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1f769a-9d60-11e7-9462-cb99e0ef11d7","identifier":"fc1f769a-9d60-11e7-9462-cb99e0ef11d7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r/n)^{(nt)}$ has multiple variables.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1f8f90-9d60-11e7-81d5-8cfd035984d5","identifier":"fc1f8f90-9d60-11e7-81d5-8cfd035984d5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1fa976-9d60-11e7-af5c-adc13ab76911","identifier":"fc1fa976-9d60-11e7-af5c-adc13ab76911","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.4","fullStatement":"Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. *Examples: Rearrange Ohm's law V = IR to highlight resistance R; Rearrange area of a circle formula A = \u03c0 r\u00b2 to highlight the radius r.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1fc2ee-9d60-11e7-b699-2e5d98b78cae","identifier":"fc1fc2ee-9d60-11e7-b699-2e5d98b78cae","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Reasoning with Equations and Inequalities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc202130-9d60-11e7-8aa1-3a63abf6d963","identifier":"fc202130-9d60-11e7-8aa1-3a63abf6d963","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.1","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1ffb60-9d60-11e7-b564-cb81758b66b7","identifier":"fc1ffb60-9d60-11e7-b564-cb81758b66b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand solving equations as a process of reasoning and explain the reasoning","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc206852-9d60-11e7-a650-11d09c34ef46","identifier":"fc206852-9d60-11e7-a650-11d09c34ef46","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.3","fullStatement":"Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. *For example, given ax + 3 = 7, solve for x.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc203bde-9d60-11e7-8038-8f20ad4cfe8e","identifier":"fc203bde-9d60-11e7-8038-8f20ad4cfe8e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve equations and inequalities in one variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2081e8-9d60-11e7-896c-37af7192a630","identifier":"fc2081e8-9d60-11e7-896c-37af7192a630","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4","fullStatement":"Solve quadratic equations in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc20af2e-9d60-11e7-84e9-eb6d51c28674","identifier":"fc20af2e-9d60-11e7-84e9-eb6d51c28674","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4a","fullStatement":"Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x \u2013 p)\u00b2 = q that has the same solutions. 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(In the functions above, \u201cm\u201d and \u201cb\u201d are the parameters of the linear function, and \u201ca\u201d and \u201cd\u201d are the parameters of the exponential function.) 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Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc23bf3e-9d60-11e7-9d88-5d306aee80ba","identifier":"fc23bf3e-9d60-11e7-9d88-5d306aee80ba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.3","fullStatement":"Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc23d74e-9d60-11e7-87d6-19476b8f1e50","identifier":"fc23d74e-9d60-11e7-87d6-19476b8f1e50","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.4","fullStatement":"Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc23efb8-9d60-11e7-85c2-d3562c8b9dbc","identifier":"fc23efb8-9d60-11e7-85c2-d3562c8b9dbc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.5","fullStatement":"Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2434c8-9d60-11e7-a744-21e682174e65","identifier":"fc2434c8-9d60-11e7-a744-21e682174e65","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.6","fullStatement":"Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc24084a-9d60-11e7-b9ea-0d01d603d7bc","identifier":"fc24084a-9d60-11e7-b9ea-0d01d603d7bc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand congruence in terms of rigid motions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc244e40-9d60-11e7-be65-3081dd006475","identifier":"fc244e40-9d60-11e7-be65-3081dd006475","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.7","fullStatement":"Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc249922-9d60-11e7-a7eb-26aab3c31c8d","identifier":"fc249922-9d60-11e7-a7eb-26aab3c31c8d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.9","fullStatement":"Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc24670e-9d60-11e7-91ac-8e64638726a1","identifier":"fc24670e-9d60-11e7-91ac-8e64638726a1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Prove geometric theorems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc24b36c-9d60-11e7-978e-210cc8bc8107","identifier":"fc24b36c-9d60-11e7-978e-210cc8bc8107","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.10","fullStatement":"Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc24cbb8-9d60-11e7-85b9-951a3ca16391","identifier":"fc24cbb8-9d60-11e7-85b9-951a3ca16391","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.11","fullStatement":"Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc250fc4-9d60-11e7-9c2b-bc386a0c89cf","identifier":"fc250fc4-9d60-11e7-9c2b-bc386a0c89cf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.12","fullStatement":"Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc24e436-9d60-11e7-a5c7-5880ae8ea5a2","identifier":"fc24e436-9d60-11e7-a5c7-5880ae8ea5a2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Make geometric constructions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc252946-9d60-11e7-bae2-30f23b83eed3","identifier":"fc252946-9d60-11e7-bae2-30f23b83eed3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.13","fullStatement":"Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2542f0-9d60-11e7-8da6-92a749264f89","identifier":"fc2542f0-9d60-11e7-8da6-92a749264f89","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Similarity, Right Triangles, and Trigonometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc25a1aa-9d60-11e7-bf9e-c3139336c5b7","identifier":"fc25a1aa-9d60-11e7-bf9e-c3139336c5b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1","fullStatement":"Verify experimentally the properties of dilations given by a center and a scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc25750e-9d60-11e7-b801-17f3c1285e68","identifier":"fc25750e-9d60-11e7-b801-17f3c1285e68","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand similarity in terms of similarity transformations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc25e1a6-9d60-11e7-a3ca-352a5421c548","identifier":"fc25e1a6-9d60-11e7-a3ca-352a5421c548","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.3","fullStatement":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc262666-9d60-11e7-bac9-88cc82a3e4e1","identifier":"fc262666-9d60-11e7-bac9-88cc82a3e4e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.4","fullStatement":"Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, (and its converse); the Pythagorean Theorem using triangle similarity.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc25fa60-9d60-11e7-a44a-5ad5b6437296","identifier":"fc25fa60-9d60-11e7-a44a-5ad5b6437296","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Prove theorems involving similarity","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2640b0-9d60-11e7-8cd3-ad5b94d5d81e","identifier":"fc2640b0-9d60-11e7-8cd3-ad5b94d5d81e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.5","fullStatement":"Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc267eae-9d60-11e7-a12e-a9374b4359b6","identifier":"fc267eae-9d60-11e7-a12e-a9374b4359b6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.6","fullStatement":"Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc265a3c-9d60-11e7-959d-369f6fb097bc","identifier":"fc265a3c-9d60-11e7-959d-369f6fb097bc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Define trigonometric ratios and solve problems involving right triangles","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc269916-9d60-11e7-8115-20ceb6fedb9d","identifier":"fc269916-9d60-11e7-8115-20ceb6fedb9d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Categorical and Quantitative Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc26f172-9d60-11e7-894c-04385c41ccc9","identifier":"fc26f172-9d60-11e7-894c-04385c41ccc9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.3","fullStatement":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc26cb70-9d60-11e7-8b80-8e7a681fd4b1","identifier":"fc26cb70-9d60-11e7-8b80-8e7a681fd4b1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Summarize, represent, and interpret data on a single count or measurement variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc273740-9d60-11e7-a0ed-362feb89ac27","identifier":"fc273740-9d60-11e7-a0ed-362feb89ac27","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.5","fullStatement":"Summarize categorical data for two categories in two-way frequency tables. 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(For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the \"r\" value.) 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Additional mathematics content is provided in fourth credit courses and advanced courses including, calculus, advanced statistics, discrete mathematics, and mathematics of finance courses. High school course content standards are listed by conceptual categories including Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Conceptual categories portray a coherent view of high school mathematics content; a student\u2019s work with functions, for example, crosses a number of traditional course boundaries, potentially up through and including calculus. Standards for Mathematical Practice provide the foundation for instruction and assessment.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc291d1c-9d60-11e7-87a0-a47379880fce","identifier":"fc291d1c-9d60-11e7-87a0-a47379880fce","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"The Complex Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc297410-9d60-11e7-bb1c-aeb019afe261","identifier":"fc297410-9d60-11e7-bb1c-aeb019afe261","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.CN.7","fullStatement":"Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc294152-9d60-11e7-bb39-642647caf675","identifier":"fc294152-9d60-11e7-bb39-642647caf675","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use complex numbers in polynomial identities and equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2990d0-9d60-11e7-8347-793d2ee5ad4a","identifier":"fc2990d0-9d60-11e7-8347-793d2ee5ad4a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.CN.8","fullStatement":"Extend polynomial identities to include factoring with complex numbers. *For example, rewrite x\u00b2 + 4 as (x + 2i)(x \u2013 2i).*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc29ae6c-9d60-11e7-ad1b-91dbde8ab17e","identifier":"fc29ae6c-9d60-11e7-ad1b-91dbde8ab17e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.CN.9","fullStatement":"Use the Fundamental Theorem of Algebra to find all roots of a polynomial equation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc29cce4-9d60-11e7-8fab-f1a87eb9b1f7","identifier":"fc29cce4-9d60-11e7-8fab-f1a87eb9b1f7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Seeing Structure in Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2a28b0-9d60-11e7-8459-d77e460dc562","identifier":"fc2a28b0-9d60-11e7-8459-d77e460dc562","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.2","fullStatement":"Use the structure of an expression to rewrite it in different equivalent forms. *For example, see $x^4 - 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Include equations arising from linear, quadratic, simple rational, and exponential functions ~~(integer inputs only).~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2b01d6-9d60-11e7-af81-26262e2b510a","identifier":"fc2b01d6-9d60-11e7-af81-26262e2b510a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Create equations that describe numbers or relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2b5be0-9d60-11e7-b2f3-9c37160dfdf3","identifier":"fc2b5be0-9d60-11e7-b2f3-9c37160dfdf3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 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Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; ~~and periodicity.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2c9ff0-9d60-11e7-9fdb-75c522a90030","identifier":"fc2c9ff0-9d60-11e7-9fdb-75c522a90030","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret functions that arise in applications in terms of the context","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2cf3ec-9d60-11e7-998a-a1082292a0e6","identifier":"fc2cf3ec-9d60-11e7-998a-a1082292a0e6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.5","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2d1034-9d60-11e7-8cf0-fa7bd37ddbb8","identifier":"fc2d1034-9d60-11e7-8cf0-fa7bd37ddbb8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.6","fullStatement":"Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. 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using technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2d2d08-9d60-11e7-ac49-a563eb664635","identifier":"fc2d2d08-9d60-11e7-ac49-a563eb664635","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Analyze functions using different representations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2e10b0-9d60-11e7-99bd-68d181ec8a03","identifier":"fc2e10b0-9d60-11e7-99bd-68d181ec8a03","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8","fullStatement":"Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the 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period, midline, and amplitude.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2e728a-9d60-11e7-aecc-f21767eab547","identifier":"fc2e728a-9d60-11e7-aecc-f21767eab547","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Building Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2efa02-9d60-11e7-be9c-0ab1a1ccae00","identifier":"fc2efa02-9d60-11e7-be9c-0ab1a1ccae00","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1b","fullStatement":"Combine standard function types using arithmetic operations in contextual situations (Adding, subtracting, and multiplying functions of different 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quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2f165e-9d60-11e7-81df-79d8072e528c","identifier":"fc2f165e-9d60-11e7-81df-79d8072e528c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1c","fullStatement":"Compose functions. *For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc2f6924-9d60-11e7-ab8c-7d91a6f9f678","identifier":"fc2f6924-9d60-11e7-ab8c-7d91a6f9f678","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content 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working with typographic grid systems based on ratios).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc33a598-9d60-11e7-8171-dea743d06d69","identifier":"fc33a598-9d60-11e7-8171-dea743d06d69","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Conditional Probability and the Rules of Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc341802-9d60-11e7-bf5c-dd258c89ff39","identifier":"fc341802-9d60-11e7-bf5c-dd258c89ff39","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.1","fullStatement":"Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (*or, and, not*).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc33d55e-9d60-11e7-ad93-6735573b52c8","identifier":"fc33d55e-9d60-11e7-ad93-6735573b52c8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand independence and conditional probability and use them to interpret data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc3434fe-9d60-11e7-bd73-e7fa0d9ecd31","identifier":"fc3434fe-9d60-11e7-bd73-e7fa0d9ecd31","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.2","fullStatement":"Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc345088-9d60-11e7-a215-4cb67abe65c6","identifier":"fc345088-9d60-11e7-a215-4cb67abe65c6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.3","fullStatement":"Understand the conditional probability of A given B as P (A and B)/P(B). 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Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. *For example, use collected data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. 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Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4dbc26-9d60-11e7-8001-1836d28ad487","identifier":"fc4dbc26-9d60-11e7-8001-1836d28ad487","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.10","fullStatement":"Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4dd440-9d60-11e7-9743-5164b93c35e7","identifier":"fc4dd440-9d60-11e7-9743-5164b93c35e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.11","fullStatement":"Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4ded7c-9d60-11e7-89da-f0329266637f","identifier":"fc4ded7c-9d60-11e7-89da-f0329266637f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Make geometric constructions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4e18e2-9d60-11e7-a249-a3af04702ff2","identifier":"fc4e18e2-9d60-11e7-a249-a3af04702ff2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.12","fullStatement":"Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4e32be-9d60-11e7-91d3-2cd9f51755a4","identifier":"fc4e32be-9d60-11e7-91d3-2cd9f51755a4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.13","fullStatement":"Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc4c9116-9d60-11e7-ba7b-3866ace4128e","identifier":"fc4c9116-9d60-11e7-ba7b-3866ace4128e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.2","fullStatement":"Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. 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Additional mathematics content is provided in fourth credit courses and advanced courses including, calculus, advanced statistics, discrete mathematics, and mathematics of finance courses. High school course content standards are listed by conceptual categories including Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Conceptual categories portray a coherent view of high school mathematics content; a student\u2019s work with functions, for example, crosses a number of traditional course boundaries, potentially up through and including calculus. Standards for Mathematical Practice provide the foundation for instruction and assessment.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5ed0ec-9d60-11e7-ba71-57d581742683","identifier":"fc5ed0ec-9d60-11e7-ba71-57d581742683","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Seeing Structure in Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5f466c-9d60-11e7-882d-a8a167a9c2f3","identifier":"fc5f466c-9d60-11e7-882d-a8a167a9c2f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1a","fullStatement":"Interpret parts of an expression, such as terms, factors, and coefficients, in context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5f1a16-9d60-11e7-9224-e91a70444fc5","identifier":"fc5f1a16-9d60-11e7-9224-e91a70444fc5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1","fullStatement":"Interpret expressions that represent a quantity in terms of its context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5ef50e-9d60-11e7-ae53-5c7880d17fdc","identifier":"fc5ef50e-9d60-11e7-ae53-5c7880d17fdc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret the structure of expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5f5fbc-9d60-11e7-a111-07f5125a6e8b","identifier":"fc5f5fbc-9d60-11e7-a111-07f5125a6e8b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1b","fullStatement":"Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5f7a74-9d60-11e7-b161-2868cd6e69d4","identifier":"fc5f7a74-9d60-11e7-b161-2868cd6e69d4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Arithmetic with Polynomials and Rational Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5f9ea0-9d60-11e7-a43d-ed1a77159927","identifier":"fc5f9ea0-9d60-11e7-a43d-ed1a77159927","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Perform arithmetic operations on polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5fb926-9d60-11e7-aaae-2b568bdf8127","identifier":"fc5fb926-9d60-11e7-aaae-2b568bdf8127","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Creating Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc600fca-9d60-11e7-b285-66e79cf8324f","identifier":"fc600fca-9d60-11e7-b285-66e79cf8324f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, ~~quadratic, simple rational,~~ and exponential functions (integer inputs only).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5fdd8e-9d60-11e7-bb33-df143cd8e2b7","identifier":"fc5fdd8e-9d60-11e7-bb33-df143cd8e2b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Create equations that describe numbers or relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6029c4-9d60-11e7-9d7e-6d8daecdf1d0","identifier":"fc6029c4-9d60-11e7-9d7e-6d8daecdf1d0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, ~~quadratic,~~ and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r/n)^{(nt)}$ has multiple variables.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6041f2-9d60-11e7-a35a-b2e875669845","identifier":"fc6041f2-9d60-11e7-a35a-b2e875669845","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established 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x.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc608cd4-9d60-11e7-8104-f34a8ecc5f72","identifier":"fc608cd4-9d60-11e7-8104-f34a8ecc5f72","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve equations and inequalities in one variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc60f82c-9d60-11e7-b4fe-45a71bc698cd","identifier":"fc60f82c-9d60-11e7-b4fe-45a71bc698cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.5","fullStatement":"Show and explain why the elimination method works to solve a system of two-variable 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variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc615592-9d60-11e7-aad3-abf4b951d250","identifier":"fc615592-9d60-11e7-aad3-abf4b951d250","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.11","fullStatement":"Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc612a36-9d60-11e7-beba-fa5309648bd5","identifier":"fc612a36-9d60-11e7-beba-fa5309648bd5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Represent and solve equations and inequalities graphically","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc616ece-9d60-11e7-b005-d9f859ce1144","identifier":"fc616ece-9d60-11e7-b005-d9f859ce1144","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.12","fullStatement":"Graph the solution set to a linear inequality in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc61880a-9d60-11e7-9d41-ca0d96305ab2","identifier":"fc61880a-9d60-11e7-9d41-ca0d96305ab2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc61e4d0-9d60-11e7-8c59-853d675f6445","identifier":"fc61e4d0-9d60-11e7-8c59-853d675f6445","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.2","fullStatement":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc61b938-9d60-11e7-aa34-27f5d02f7051","identifier":"fc61b938-9d60-11e7-aa34-27f5d02f7051","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the concept of a function and use function notation","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc61fec0-9d60-11e7-834e-c7433b878c17","identifier":"fc61fec0-9d60-11e7-834e-c7433b878c17","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.3","fullStatement":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence $a_1$=7, $a_n=a_{(n-1)}$ +2; the sequence $s_n$ = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6249ca-9d60-11e7-af9f-1396d4e2af15","identifier":"fc6249ca-9d60-11e7-af9f-1396d4e2af15","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.4","fullStatement":"Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; ~~relative maximums and minimums; symmetries;~~ end behavior; ~~and periodicity.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc621784-9d60-11e7-94a6-9e7f3a8ef12e","identifier":"fc621784-9d60-11e7-94a6-9e7f3a8ef12e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret functions that arise in applications in terms of the context","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc626338-9d60-11e7-8932-8fbf826088c3","identifier":"fc626338-9d60-11e7-8932-8fbf826088c3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.5","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc627c92-9d60-11e7-a416-0b5d44058723","identifier":"fc627c92-9d60-11e7-a416-0b5d44058723","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.6","fullStatement":"Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. 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Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc63a45a-9d60-11e7-9431-2767779aadb7","identifier":"fc63a45a-9d60-11e7-9431-2767779aadb7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build new functions from existing functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc63bd50-9d60-11e7-b969-e87638f0447c","identifier":"fc63bd50-9d60-11e7-b969-e87638f0447c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Linear, Quadratic, and Exponential Models","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6440f4-9d60-11e7-acdb-f2891b271bfd","identifier":"fc6440f4-9d60-11e7-acdb-f2891b271bfd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1a","fullStatement":"Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. 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Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc65453a-9d60-11e7-ba13-a13ca0f705f6","identifier":"fc65453a-9d60-11e7-ba13-a13ca0f705f6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.3","fullStatement":"Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc659080-9d60-11e7-84c8-74274991cb9c","identifier":"fc659080-9d60-11e7-84c8-74274991cb9c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.6","fullStatement":"Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc655e76-9d60-11e7-a530-03f9011ca922","identifier":"fc655e76-9d60-11e7-a530-03f9011ca922","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand congruence in terms of rigid motions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc65aab6-9d60-11e7-a4d1-8f0229014216","identifier":"fc65aab6-9d60-11e7-a4d1-8f0229014216","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.7","fullStatement":"Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc65c2f8-9d60-11e7-ba28-5e421b091673","identifier":"fc65c2f8-9d60-11e7-ba28-5e421b091673","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.8","fullStatement":"Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc660ccc-9d60-11e7-8eba-f7012badf086","identifier":"fc660ccc-9d60-11e7-8eba-f7012badf086","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.9","fullStatement":"Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc65db80-9d60-11e7-a74d-b2e0af3299a9","identifier":"fc65db80-9d60-11e7-a74d-b2e0af3299a9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Prove geometric theorems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6626bc-9d60-11e7-a62b-11c81c0ffd4a","identifier":"fc6626bc-9d60-11e7-a62b-11c81c0ffd4a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.10","fullStatement":"Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc663eea-9d60-11e7-8e03-b6ccf3c056f7","identifier":"fc663eea-9d60-11e7-8e03-b6ccf3c056f7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.11","fullStatement":"Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc667c5c-9d60-11e7-8d4d-0d70455254d7","identifier":"fc667c5c-9d60-11e7-8d4d-0d70455254d7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.12","fullStatement":"Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc66581c-9d60-11e7-96d5-2149c9839262","identifier":"fc66581c-9d60-11e7-96d5-2149c9839262","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Make geometric constructions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc669778-9d60-11e7-9095-1c5d164edff2","identifier":"fc669778-9d60-11e7-9095-1c5d164edff2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Similarity, Right Triangles, and 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(For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the \"r\" value.) After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using \"r\".","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6bc82e-9d60-11e7-a638-a94061c76639","identifier":"fc6bc82e-9d60-11e7-a638-a94061c76639","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.9","fullStatement":"Distinguish between correlation and causation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc5dced6-9d60-11e7-94b0-4a7d96dee0b8","identifier":"fc5dced6-9d60-11e7-94b0-4a7d96dee0b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.3","fullStatement":"Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6c6c0c-9d60-11e7-80e9-4eb2f9827c62","identifier":"fc6c6c0c-9d60-11e7-80e9-4eb2f9827c62","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use properties of rational and irrational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6c4038-9d60-11e7-af30-2579f2a6d586","identifier":"fc6c4038-9d60-11e7-af30-2579f2a6d586","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"The Complex Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6be1ba-9d60-11e7-913d-9045156ca8f4","identifier":"fc6be1ba-9d60-11e7-913d-9045156ca8f4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.09770","fullStatement":"Accelerated Pre-Calculus","notes":"**Accelerated Pre-Calculus** is the third in a sequence of mathematics courses designed to ensure that students are prepared to take higher\u2010level mathematics courses during their high school career, including Advanced Placement Calculus AB, Advanced Placement Calculus BC, and Advanced Placement Statistics. \r\n\r\nThe standards in the three-course high school sequence specify the mathematics that all students should study in order to be college and career ready. 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find the expected value. *For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. 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use properties of this representation for computation. *For example, (-1 + \u221a3i)\u00b3 = 8 because (-1 + \u221a3i) has modulus 2 and argument 120\u00b0.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc6cfd3e-9d60-11e7-ada8-92842249639d","identifier":"fc6cfd3e-9d60-11e7-ada8-92842249639d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.CN.6","fullStatement":"Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7fcb62-9d60-11e7-ad29-9243779a79e0","identifier":"fc7fcb62-9d60-11e7-ad29-9243779a79e0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1a","fullStatement":"Apply properties of operations emphasizing when the commutative property applies.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7f82a6-9d60-11e7-b2ec-56d50c3d5ddc","identifier":"fc7f82a6-9d60-11e7-b2ec-56d50c3d5ddc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1","fullStatement":"Students will generate and interpret equivalent numeric and algebraic expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7f5290-9d60-11e7-9e7c-58a8c16e8e2b","identifier":"fc7f5290-9d60-11e7-9e7c-58a8c16e8e2b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will extend arithmetic operations to algebraic modeling.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7f29c8-9d60-11e7-9d25-fc8df69234fb","identifier":"fc7f29c8-9d60-11e7-9d25-fc8df69234fb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Arithmetic to Algebra","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7eeb84-9d60-11e7-b1d2-2100983a8dd1","identifier":"fc7eeb84-9d60-11e7-b1d2-2100983a8dd1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.04810","fullStatement":"Foundations of Algebra","notes":"Foundations of Algebra is a first year high school mathematics course option for students who have completed mathematics in grades 6\u20138 yet will need substantial support to bolster success in high school mathematics. The course is aimed at students who have reported low standardized test performance in prior grades and/or have demonstrated significant difficulties in previous mathematics classes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc813d94-9d60-11e7-8080-da2ceaad6a0b","identifier":"fc813d94-9d60-11e7-8080-da2ceaad6a0b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Proportional Reasoning","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc819622-9d60-11e7-aacf-85eb90a24817","identifier":"fc819622-9d60-11e7-aacf-85eb90a24817","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.1","fullStatement":"Students will explain equivalent ratios by using a variety of models. *For example, tables of 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quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc81e334-9d60-11e7-a78d-967647d42c75","identifier":"fc81e334-9d60-11e7-a78d-967647d42c75","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.2a","fullStatement":"Relate proportionality to fraction equivalence and division. *For example, $\\frac{3}{6}$ is equal to $\\frac{4}{8}$ because both yield a quotient of \u00bd and, in both cases, the denominator is double the value of the numerator.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc81fcd4-9d60-11e7-adb7-9f3661bc8754","identifier":"fc81fcd4-9d60-11e7-adb7-9f3661bc8754","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.2b","fullStatement":"Understand real-world rate/ratio/percent problems by finding the whole given a part and find a part given the whole.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8215c0-9d60-11e7-82a8-59b1ac634a0e","identifier":"fc8215c0-9d60-11e7-82a8-59b1ac634a0e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.2c","fullStatement":"Use proportional relationships to solve multistep ratio and percent problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc822e3e-9d60-11e7-8827-0a4fe03dbbf1","identifier":"fc822e3e-9d60-11e7-8827-0a4fe03dbbf1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.3","fullStatement":"Students will graph proportional 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plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc82a44a-9d60-11e7-aba6-ec8e65180a68","identifier":"fc82a44a-9d60-11e7-aba6-ec8e65180a68","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.PR.3c","fullStatement":"Compare two different proportional relationships represented in different ways. *For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc82bdea-9d60-11e7-a6e8-9d98489ea4bf","identifier":"fc82bdea-9d60-11e7-a6e8-9d98489ea4bf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Equations and Inequalities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc835444-9d60-11e7-badf-1cb2c3bf0dd3","identifier":"fc835444-9d60-11e7-badf-1cb2c3bf0dd3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1a","fullStatement":"Use variables to represent an unknown number in a specified set.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8315ec-9d60-11e7-9a1a-ad71e7ddb1da","identifier":"fc8315ec-9d60-11e7-9a1a-ad71e7ddb1da","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1","fullStatement":"Students will create and solve equations and inequalities in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc82e220-9d60-11e7-81ff-18b940ca68f1","identifier":"fc82e220-9d60-11e7-81ff-18b940ca68f1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will solve, interpret, and create linear models using equations and inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc83cfaa-9d60-11e7-a1a7-606365c9c14f","identifier":"fc83cfaa-9d60-11e7-a1a7-606365c9c14f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.2","fullStatement":"Students will use units as a way to understand problems and guide the solutions of multi-step problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc83e800-9d60-11e7-b8e4-fd8416992147","identifier":"fc83e800-9d60-11e7-b8e4-fd8416992147","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFAEI4","fullStatement":"Students will solve literal equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8412da-9d60-11e7-b5ba-3bbfbd503add","identifier":"fc8412da-9d60-11e7-b5ba-3bbfbd503add","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFAEI4.a","fullStatement":"Solve for any variable in a multi-variable equation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc842c98-9d60-11e7-8da2-f01ea2edca33","identifier":"fc842c98-9d60-11e7-8da2-f01ea2edca33","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFAEI4.b","fullStatement":"Rearrange formulas to highlight a particular variable using the same reasoning as in solving equations. *For example, solve for the base in A = \u00bd bh.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc836e7a-9d60-11e7-852d-5a33f30c6122","identifier":"fc836e7a-9d60-11e7-852d-5a33f30c6122","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1b","fullStatement":"Explain each step in solving simple equations and inequalities using the equality properties of numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8386a8-9d60-11e7-bdd0-8e28855ca809","identifier":"fc8386a8-9d60-11e7-bdd0-8e28855ca809","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1c","fullStatement":"Construct viable arguments to justify the solutions and methods of solving equations and inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc839f1c-9d60-11e7-a02c-d2ba4876f691","identifier":"fc839f1c-9d60-11e7-a02c-d2ba4876f691","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1d","fullStatement":"Represent and find solutions graphically.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc83b768-9d60-11e7-be0c-b8d12ba7817f","identifier":"fc83b768-9d60-11e7-be0c-b8d12ba7817f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.1e","fullStatement":"Use variables to solve real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc84464c-9d60-11e7-b86c-b33ac227a914","identifier":"fc84464c-9d60-11e7-b86c-b33ac227a914","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Quantitative Reasoning with Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc84cf9a-9d60-11e7-882d-efcbe7212fee","identifier":"fc84cf9a-9d60-11e7-882d-efcbe7212fee","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.1a","fullStatement":"Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc849d0e-9d60-11e7-b72d-27207c1e3c81","identifier":"fc849d0e-9d60-11e7-b72d-27207c1e3c81","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.1","fullStatement":"Students will understand characteristics of functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc846a50-9d60-11e7-bd3a-e5ea2540c31f","identifier":"fc846a50-9d60-11e7-bd3a-e5ea2540c31f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will create function statements and analyze relationships among pairs of variables using graphs, table, and equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc851ae0-9d60-11e7-8e05-9f38cf59904a","identifier":"fc851ae0-9d60-11e7-8e05-9f38cf59904a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2","fullStatement":"Students will compare and graph functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8561d0-9d60-11e7-afa4-af6d74740197","identifier":"fc8561d0-9d60-11e7-afa4-af6d74740197","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2a","fullStatement":"Calculate rates of change of functions, comparing when rates increase, decrease, or stay constant. *For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc857c74-9d60-11e7-bfd9-4ce58de34c83","identifier":"fc857c74-9d60-11e7-bfd9-4ce58de34c83","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2b","fullStatement":"Graph by hand simple functions expressed symbolically (use all four quadrants).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8595d8-9d60-11e7-8aec-fa6e4a0d9c26","identifier":"fc8595d8-9d60-11e7-8aec-fa6e4a0d9c26","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2c","fullStatement":"Interpret the equation y = mx + b as defining a linear function whose graph is a straight line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc85add4-9d60-11e7-943c-29d722383ab3","identifier":"fc85add4-9d60-11e7-943c-29d722383ab3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2d","fullStatement":"Use technology to graph non-linear functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc85c6ca-9d60-11e7-a200-c768ae8de47b","identifier":"fc85c6ca-9d60-11e7-a200-c768ae8de47b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2e","fullStatement":"Analyze graphs of functions for key features (intercepts, intervals of increase/decrease, maximums/minimums, symmetries, and end behavior) based on context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc85df7a-9d60-11e7-869e-37239f2877cd","identifier":"fc85df7a-9d60-11e7-869e-37239f2877cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.2f","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the great rate of change.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc85f7d0-9d60-11e7-bb14-f6b9d5af9483","identifier":"fc85f7d0-9d60-11e7-bb14-f6b9d5af9483","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.3","fullStatement":"Students will construct and interpret functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc862af2-9d60-11e7-b01c-69d3a5b9cf2f","identifier":"fc862af2-9d60-11e7-b01c-69d3a5b9cf2f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.3a","fullStatement":"Write a function that describes a relationship between two quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc86447e-9d60-11e7-8abe-b7204f2eae91","identifier":"fc86447e-9d60-11e7-8abe-b7204f2eae91","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.3b","fullStatement":"Use variables to represent two quantities in a real-world problem that change in relationship to one another (conceptual understanding of a variable).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc865cb6-9d60-11e7-b3c6-fad176781b28","identifier":"fc865cb6-9d60-11e7-b3c6-fad176781b28","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.3c","fullStatement":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc84e8ea-9d60-11e7-8c80-1453c72b719d","identifier":"fc84e8ea-9d60-11e7-8c80-1453c72b719d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.1b","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8501c2-9d60-11e7-a4ea-a25f7274ec6b","identifier":"fc8501c2-9d60-11e7-a4ea-a25f7274ec6b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.QR.1c","fullStatement":"Graph functions using sets of ordered pairs consisting of an input and the corresponding output.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8072e2-9d60-11e7-95fa-9a4c6a428e8c","identifier":"fc8072e2-9d60-11e7-95fa-9a4c6a428e8c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2","fullStatement":"Students will interpret and use the properties of exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc80b4a0-9d60-11e7-9ec0-d5a887e7cb5a","identifier":"fc80b4a0-9d60-11e7-9ec0-d5a887e7cb5a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2a","fullStatement":"Substitute numeric values into formulas containing exponents, interpreting units consistently.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc80d142-9d60-11e7-b7d5-a5e0667ea9a8","identifier":"fc80d142-9d60-11e7-b7d5-a5e0667ea9a8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2b","fullStatement":"Use properties of integer exponents to find equivalent numerical expressions. *For example, $3^2 \\times 3^{(-5)} = 3^{(-3)} = \\frac{1}{(3^3)} = \\frac{1}{27}$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc80ec90-9d60-11e7-a706-3eee5b51efb2","identifier":"fc80ec90-9d60-11e7-a706-3eee5b51efb2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2c","fullStatement":"Evaluate square roots of perfect squares and cube roots of perfect cubes","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8107b6-9d60-11e7-a98f-d84db9d5793d","identifier":"fc8107b6-9d60-11e7-a98f-d84db9d5793d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2d","fullStatement":"Use square root and cube root symbols to represent solutions to equations of the form x\u00b2 = p and x\u00b3 = p, where p is a positive rational number.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc812372-9d60-11e7-a438-8e87f62468ff","identifier":"fc812372-9d60-11e7-a438-8e87f62468ff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.2e","fullStatement":"Use the Pythagorean Theorem to solve triangles based on real-world contexts (Limit to finding the hypotenuse given two legs).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc7fe82c-9d60-11e7-891d-2abfb330eaad","identifier":"fc7fe82c-9d60-11e7-891d-2abfb330eaad","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1b","fullStatement":"Use area models to represent the distributive property and develop understandings of addition and multiplication (all positive rational numbers should be included in the models).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc800370-9d60-11e7-98c8-530d9d46249a","identifier":"fc800370-9d60-11e7-98c8-530d9d46249a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1c","fullStatement":"Model numerical expressions (arrays) leading to the modeling of algebraic expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc801ef0-9d60-11e7-b349-010d2e01d3f3","identifier":"fc801ef0-9d60-11e7-b349-010d2e01d3f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1d","fullStatement":"Add, subtract, and multiply algebraic expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc803ade-9d60-11e7-abec-4e92da4e4450","identifier":"fc803ade-9d60-11e7-abec-4e92da4e4450","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1e","fullStatement":"Generate equivalent expressions using properties of operations and understand various representations within context. *For example, distinguish multiplicative comparison from additive comparison. Students should be able to explain the difference between \"3 more\" and \"3 times\".*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc8056ae-9d60-11e7-a847-ee7fc7b31a46","identifier":"fc8056ae-9d60-11e7-a847-ee7fc7b31a46","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.AA.1f","fullStatement":"Evaluate formulas at specific values for variables. *For example, use formulas such as A = l x w and find the area given the values for the length and width.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1869888-9d61-11e7-9c3d-5fe436309e7a","identifier":"b1869888-9d61-11e7-9c3d-5fe436309e7a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.08500","fullStatement":"Advanced Mathematical Decision Making","notes":"This is a course designed to follow the completion of Algebra II, Advanced Algebra, Accelerated Geometry B/Algebra II or Accelerated Analytic Geometry B/Advanced Algebra. The course will give students further experiences with statistical information and summaries, methods of designing and conducting statistical studies, an opportunity to analyze various voting processes, modeling of data, basic financial decisions, and use network models for making informed decisions. (Prerequisite: Algebra II, Advanced Algebra, Accelerated Geometry B/Algebra II or Accelerated Analytic Geometry B/Advanced Algebra). \r\n\r\nInstruction and assessment should include the appropriate use of manipulatives and technology. Topics should be represented in multiple ways, such as concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be introduced and used, where appropriate, in the context of realistic phenomena.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1875d68-9d61-11e7-b800-d6a5088c6b55","identifier":"b1875d68-9d61-11e7-b800-d6a5088c6b55","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.N.1a","fullStatement":"Use proportional reasoning to solve problems involving ratios.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1872492-9d61-11e7-bc55-ded1eafe41ef","identifier":"b1872492-9d61-11e7-bc55-ded1eafe41ef","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.N.1","fullStatement":"Students will extend the understanding of proportional reasoning, ratios, rates, and percents by applying them to various settings to include business, media, and consumerism.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b186fe9a-9d61-11e7-a1f7-d9d0a670a78a","identifier":"b186fe9a-9d61-11e7-a1f7-d9d0a670a78a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will extend their understanding and use of ratios, proportions to solve problems involving in decision making.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b186d8a2-9d61-11e7-992f-2f6ab9c360d3","identifier":"b186d8a2-9d61-11e7-992f-2f6ab9c360d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Number and Operations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b187783e-9d61-11e7-9a30-cbed0706adeb","identifier":"b187783e-9d61-11e7-9a30-cbed0706adeb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.N.1b","fullStatement":"Understand and use averages, weighted averages, and indices.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18790ee-9d61-11e7-a085-be5cc4f3059b","identifier":"b18790ee-9d61-11e7-a085-be5cc4f3059b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.N.1c","fullStatement":"Solve problems involving large quantities that are not easily measured.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b187aa34-9d61-11e7-a12a-d8f92ce44bba","identifier":"b187aa34-9d61-11e7-a12a-d8f92ce44bba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.N.1d","fullStatement":"Understand how identification numbers, such as UPCs, are created and verified.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1884eee-9d61-11e7-9cbc-5d4b4ca107f0","identifier":"b1884eee-9d61-11e7-9cbc-5d4b4ca107f0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.1a","fullStatement":"Represent situations and solve problems using vectors in areas such as transportation, computer graphics, and the physics of force and motion.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18821ee-9d61-11e7-a7a4-3e71d90d6b26","identifier":"b18821ee-9d61-11e7-a7a4-3e71d90d6b26","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.1","fullStatement":"Students will use vectors and matrices to organize and describe problem situations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b187e936-9d61-11e7-b656-5e50432c02f2","identifier":"b187e936-9d61-11e7-b656-5e50432c02f2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will explore the applications of functions, their characteristics and their use in modeling. Vectors and matrices are employed for solving problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b187c4b0-9d61-11e7-9615-bcc216f4fe7d","identifier":"b187c4b0-9d61-11e7-9615-bcc216f4fe7d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Algebra","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1888260-9d61-11e7-a12f-c47a0b7e7202","identifier":"b1888260-9d61-11e7-a12f-c47a0b7e7202","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.2","fullStatement":"Students will use a variety of network models to organize data in quantitative situations, make informed decisions, and solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b188ba14-9d61-11e7-aa0f-23444591b2d9","identifier":"b188ba14-9d61-11e7-aa0f-23444591b2d9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.2a","fullStatement":"Solve problems represented by a vertex-edge graph, and find critical paths, Euler paths, and minimal spanning trees.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b188d4ae-9d61-11e7-b9d6-e9ae7a13f35f","identifier":"b188d4ae-9d61-11e7-b9d6-e9ae7a13f35f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.2b","fullStatement":"Construct, analyze, and interpret flow charts to develop an algorithm to describe processes such as quality control procedures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b188ed36-9d61-11e7-aa1f-1495d18971e1","identifier":"b188ed36-9d61-11e7-aa1f-1495d18971e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.2c","fullStatement":"Investigate the scheduling of projects using PERT.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18906fe-9d61-11e7-abab-ff1a111c0951","identifier":"b18906fe-9d61-11e7-abab-ff1a111c0951","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.2d","fullStatement":"Consider problems that can be resolved by coloring graphs.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b189208a-9d61-11e7-a06a-c59f144bcd6f","identifier":"b189208a-9d61-11e7-a06a-c59f144bcd6f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.3","fullStatement":"Students will create and analyze mathematical models to make decisions related to earning, investing, spending, and borrowing money.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1894ccc-9d61-11e7-81ca-2c67a43bdcfc","identifier":"b1894ccc-9d61-11e7-81ca-2c67a43bdcfc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.3a","fullStatement":"Use exponential functions to model change in a variety of financial situations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1896676-9d61-11e7-bbbb-edb641b74921","identifier":"b1896676-9d61-11e7-bbbb-edb641b74921","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.3b","fullStatement":"Determine, represent, and analyze mathematical models for income, expenditures, and various types of loans and investments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1898016-9d61-11e7-9237-9219d7248d98","identifier":"b1898016-9d61-11e7-9237-9219d7248d98","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.4","fullStatement":"Students will analyze and evaluate the mathematics behind various methods of voting and selection.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b189ac94-9d61-11e7-9483-f1e8e99b168e","identifier":"b189ac94-9d61-11e7-9483-f1e8e99b168e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.4a","fullStatement":"Evaluate various voting and selection processes to determine an appropriate method for a given situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b189c8f0-9d61-11e7-9330-95bbf517af39","identifier":"b189c8f0-9d61-11e7-9330-95bbf517af39","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.4b","fullStatement":"Apply various ranking algorithms to determine an appropriate method for a given situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18868b6-9d61-11e7-9374-ceac2dbf2f56","identifier":"b18868b6-9d61-11e7-9374-ceac2dbf2f56","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.A.1b","fullStatement":"Represent geometric transformations and solve problems using matrices in fields such as computer animations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18a3646-9d61-11e7-bbef-2aa02c83389f","identifier":"b18a3646-9d61-11e7-bbef-2aa02c83389f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.G.1","fullStatement":"Students will create and use two- and three-dimensional representations of authentic situations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18a093c-9d61-11e7-b2d1-19a5ee150b40","identifier":"b18a093c-9d61-11e7-b2d1-19a5ee150b40","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students apply tools to model geometric situations and solve problems. Students extend their knowledge of right triangle trigonometry.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b189e434-9d61-11e7-a83a-20eabb9a8155","identifier":"b189e434-9d61-11e7-a83a-20eabb9a8155","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18a4ffa-9d61-11e7-bcfe-1fad0f9ae3e4","identifier":"b18a4ffa-9d61-11e7-bcfe-1fad0f9ae3e4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.G.2","fullStatement":"Students will solve geometric problems involving inaccessible distances using basic trigonometric principles, including the Law of Sines and the Law of Cosines.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18afc52-9d61-11e7-8125-f2a76467a604","identifier":"b18afc52-9d61-11e7-8125-f2a76467a604","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.1a","fullStatement":"Determine conditional probabilities and probabilities of compound events to make decisions in problem situations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18ac7f0-9d61-11e7-a64b-bf5f158d6d1a","identifier":"b18ac7f0-9d61-11e7-a64b-bf5f158d6d1a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.1","fullStatement":"Students will determine probability and expected value to inform everyday decision making.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18a8efc-9d61-11e7-964c-e47891da7bf6","identifier":"b18a8efc-9d61-11e7-964c-e47891da7bf6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will explore representations of data and models of data as tools in the decision making.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18a6a58-9d61-11e7-a774-af339c9bee22","identifier":"b18a6a58-9d61-11e7-a774-af339c9bee22","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Data Analysis and Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18b48d8-9d61-11e7-bde2-6494cb966078","identifier":"b18b48d8-9d61-11e7-bde2-6494cb966078","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.2","fullStatement":"Students will build the skills and vocabulary necessary to analyze and critique reported statistical information, summaries, and graphical displays.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18b60de-9d61-11e7-8a91-3f43d08bb711","identifier":"b18b60de-9d61-11e7-8a91-3f43d08bb711","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.3","fullStatement":"Students will apply statistical methods to design, conduct, and analyze statistical studies.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18b79a2-9d61-11e7-951b-6fcb5b7854f2","identifier":"b18b79a2-9d61-11e7-951b-6fcb5b7854f2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.4","fullStatement":"Students will use functions to model problem situations in both discrete and continuous relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18ba5f8-9d61-11e7-85e6-27e0e2c30289","identifier":"b18ba5f8-9d61-11e7-85e6-27e0e2c30289","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.4a","fullStatement":"Determine whether a problem situation involving two quantities is best modeled by a discrete (pattern identification, population growth, compound interest) or continuous (medication dosage, climate change, bone decay) relationship.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18bc04c-9d61-11e7-becb-7501638a23c8","identifier":"b18bc04c-9d61-11e7-becb-7501638a23c8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.4b","fullStatement":"Use linear, exponential, logistic, piecewise and sine functions to construct a model.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18b167e-9d61-11e7-b0da-a17b8538f997","identifier":"b18b167e-9d61-11e7-b0da-a17b8538f997","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.1b","fullStatement":"Use probabilities to make and justify decisions about risks in everyday life.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b18b2f2e-9d61-11e7-b29c-5bc2f31aa034","identifier":"b18b2f2e-9d61-11e7-b29c-5bc2f31aa034","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAMDM.D.1c","fullStatement":"Calculate expected value to analyze mathematical fairness, payoff, and risk.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6d48f02-9d61-11e7-bea5-65d599b320c9","identifier":"b6d48f02-9d61-11e7-bea5-65d599b320c9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.08600","fullStatement":"Mathematics of Industry and Government","notes":"Modeled after operations research courses, Mathematics of Industry and Government allows students to explore decision making in a variety of 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Students learn to focus on the development of mathematical models that can be used to model, improve, predict, and optimize real-world systems. 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matrices.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0573ca0-9d61-11e7-9469-fdd521b515b4","identifier":"c0573ca0-9d61-11e7-9469-fdd521b515b4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.2a","fullStatement":"Find the determinant of 2-by-2 and 3-by-3 matrices.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05756c2-9d61-11e7-9972-81ebc8d509aa","identifier":"c05756c2-9d61-11e7-9972-81ebc8d509aa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.2b","fullStatement":"Represent a 3-by-3 system of linear equations as a matrix and solve the system in multiple ways: the inverse matrix, row operations, and Cramer's 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matrix.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c057a154-9d61-11e7-8cd9-48d61e9de2b7","identifier":"c057a154-9d61-11e7-8cd9-48d61e9de2b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.3","fullStatement":"Students will explore functions of two independent variables of the form *z = f(x, y)* and implicit functions of the form *f(x, y, z) = 0*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c057d39a-9d61-11e7-b864-09cee54f53a1","identifier":"c057d39a-9d61-11e7-b864-09cee54f53a1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.3a","fullStatement":"Evaluate such functions at a point in the plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c057ee48-9d61-11e7-af19-0ccb56a18a9e","identifier":"c057ee48-9d61-11e7-af19-0ccb56a18a9e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.3b","fullStatement":"Graph the level curves of such functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0580766-9d61-11e7-9b90-939ab695cd2a","identifier":"c0580766-9d61-11e7-9b90-939ab695cd2a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.3c","fullStatement":"Determine points or regions of discontinuity of such functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c056e85e-9d61-11e7-9f67-a82b23fb2774","identifier":"c056e85e-9d61-11e7-9f67-a82b23fb2774","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.A.1b","fullStatement":"Express analytic geometry of three dimensions (equations of planes, parallelism, perpendicularity, angles) in terms of the dot product and cross product of vectors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0587c8c-9d61-11e7-9720-2cc4df09a361","identifier":"c0587c8c-9d61-11e7-9720-2cc4df09a361","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.1","fullStatement":"Students will explore the continuity of functions of two independent variables in terms of the limits of such functions as (*x, y*) approaches a given point in the plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0584604-9d61-11e7-b5ff-1b6ed2a231c3","identifier":"c0584604-9d61-11e7-b5ff-1b6ed2a231c3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will investigate limits, continuity, and differentiation of functions of two independent variables; define and apply the gradient, the divergence, and the curl.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05820b6-9d61-11e7-abb1-97f53924337f","identifier":"c05820b6-9d61-11e7-abb1-97f53924337f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Derivatives","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c058965e-9d61-11e7-a9e8-8d6f753ddffb","identifier":"c058965e-9d61-11e7-a9e8-8d6f753ddffb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2","fullStatement":"Students will explore, find, use, and apply partial differentiation of functions of two independent variables of the form *z = f(x, y)* and implicit functions of the form *f(x, y, z) = 0*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c058da74-9d61-11e7-9521-8d15a6f8dff2","identifier":"c058da74-9d61-11e7-9521-8d15a6f8dff2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2a","fullStatement":"Approximate the partial derivatives at a point of a function defined by a table of data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c058f496-9d61-11e7-bd5d-25ab6460a9b1","identifier":"c058f496-9d61-11e7-bd5d-25ab6460a9b1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2b","fullStatement":"Find expressions for the first and second partial derivatives of a function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0590ca6-9d61-11e7-95c5-b55e9c086100","identifier":"c0590ca6-9d61-11e7-95c5-b55e9c086100","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2c","fullStatement":"Define and apply the total differential to approximate real-world phenomena.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0592560-9d61-11e7-8461-1bb4a64187e1","identifier":"c0592560-9d61-11e7-8461-1bb4a64187e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2d","fullStatement":"Represent the partial derivatives of a system of two functions in two variables using the Jacobian.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0593dd4-9d61-11e7-97a1-f956d82f482e","identifier":"c0593dd4-9d61-11e7-97a1-f956d82f482e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2e","fullStatement":"Find the partial derivatives of the composition of functions using the general chain rule.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0595562-9d61-11e7-836f-0d97f678b18b","identifier":"c0595562-9d61-11e7-836f-0d97f678b18b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.2f","fullStatement":"Apply partial differentiation to problems of optimization, including problems requiring the use of the Lagrange multiplier.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c0596e3a-9d61-11e7-a0ca-762d0a2d29cc","identifier":"c0596e3a-9d61-11e7-a0ca-762d0a2d29cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.D.3","fullStatement":"Students will define and apply the gradient, the divergence, and curl in terms of differential vector operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05a0a7a-9d61-11e7-8447-8739d82264b4","identifier":"c05a0a7a-9d61-11e7-8447-8739d82264b4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.1a","fullStatement":"Define, use, and interpret double and triple integrals in terms of volume and mass.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c059d7c6-9d61-11e7-b3ca-d5857586c5e2","identifier":"c059d7c6-9d61-11e7-b3ca-d5857586c5e2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.1","fullStatement":"Students will integrate functions of the form *z = f(x, y)* or *w = f(x, y, z)*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c059ab02-9d61-11e7-abcf-1c1dab97e554","identifier":"c059ab02-9d61-11e7-abcf-1c1dab97e554","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will explore double and triple integrals and integrals of vectors; use various methods of integration; understand and apply the theorems of Green, Stokes, and Gauss.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05986c2-9d61-11e7-81cc-1662fc98e4fe","identifier":"c05986c2-9d61-11e7-81cc-1662fc98e4fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Integration","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05a553e-9d61-11e7-a9e6-e6c3cd27a61b","identifier":"c05a553e-9d61-11e7-a9e6-e6c3cd27a61b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.2","fullStatement":"Students will apply and interpret the theorems of Green, Stokes, and Gauss.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05a8658-9d61-11e7-a640-4f61191ead2c","identifier":"c05a8658-9d61-11e7-a640-4f61191ead2c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.2a","fullStatement":"Apply line and surface integrals to functions representing real-world phenomena.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05aa066-9d61-11e7-8212-fff69c2ce6fd","identifier":"c05aa066-9d61-11e7-8212-fff69c2ce6fd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.2b","fullStatement":"Recognize, understand, and use line integrals that are independence of path.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05ab88a-9d61-11e7-85e8-f18ab5efe3b2","identifier":"c05ab88a-9d61-11e7-85e8-f18ab5efe3b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.2c","fullStatement":"Define and apply the gradient, the divergence, and the curl in terms of integrals of vectors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05a2406-9d61-11e7-b848-b74e9c317f6e","identifier":"c05a2406-9d61-11e7-b848-b74e9c317f6e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.1b","fullStatement":"Represent integrals of vectors as double and triple integrals.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05a3c34-9d61-11e7-8128-4e5b8a2fa8f3","identifier":"c05a3c34-9d61-11e7-8128-4e5b8a2fa8f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.I.1c","fullStatement":"Integrate functions through various techniques such as changing the order of integration, substituting variables, or changing to polar coordinates.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05b60d2-9d61-11e7-bf99-adc92c56b427","identifier":"c05b60d2-9d61-11e7-bf99-adc92c56b427","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1a","fullStatement":"Solve linear first-order differential equations of the form y' + p(x)y = q(x) with an integrating factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05b1be0-9d61-11e7-b678-a4b23748bcd3","identifier":"c05b1be0-9d61-11e7-b678-a4b23748bcd3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1","fullStatement":"Students will use, apply, and solve linear first-order differential equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05af6d8-9d61-11e7-8b69-e088774a7d07","identifier":"c05af6d8-9d61-11e7-8b69-e088774a7d07","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will explore solution methods of linear differential equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05ad284-9d61-11e7-b438-901dd0f745fc","identifier":"c05ad284-9d61-11e7-b438-901dd0f745fc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Differential Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05b7a72-9d61-11e7-b99f-a903c2f616b4","identifier":"c05b7a72-9d61-11e7-b99f-a903c2f616b4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1b","fullStatement":"Solve homogeneous linear first-order differential equations using a variable substitution.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05b9340-9d61-11e7-b75f-177c6f2ee266","identifier":"c05b9340-9d61-11e7-b75f-177c6f2ee266","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1c","fullStatement":"Solve Clairaut equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05babaa-9d61-11e7-9001-381bea5c496c","identifier":"c05babaa-9d61-11e7-9001-381bea5c496c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1d","fullStatement":"Explore the concepts of families of solutions and envelopes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05bc36a-9d61-11e7-ab3a-2c727bde3e9b","identifier":"c05bc36a-9d61-11e7-ab3a-2c727bde3e9b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1e","fullStatement":"Write linear first-order differential equations that represent real-world phenomena and solve them, such as those arising from Kirchhoff's Law and mixing problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c05bdbb6-9d61-11e7-bbea-fa0020172d9f","identifier":"c05bdbb6-9d61-11e7-bbea-fa0020172d9f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MMC.DE.1f","fullStatement":"Students will solve linear second-order differential equations of the form* y\" + p(x)y' + q(x)y = c* using the characteristic equation where the characteristic equation has two real roots, one real root, or no real roots.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ed6d3c-9d61-11e7-a4fc-9621c04e9568","identifier":"d5ed6d3c-9d61-11e7-a4fc-9621c04e9568","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.08800","fullStatement":"Statistical Reasoning","notes":"Statistical Reasoning is a fourth mathematics course option for students who have completed Algebra II, Advanced Algebra, Accelerated Geometry B/Algebra II, or Accelerated Analytic Geometry B/Advanced Algebra. The course provides experiences in statistics beyond the CCGPS sequence of courses, offering students opportunities to strengthen their understanding of the statistical method of inquiry and statistical simulations. Students will formulate statistical questions to be answered using data, will design and implement a plan to collect the appropriate data, will select appropriate graphical and numerical methods for data analysis, and will interpret their results to make connections with the initial question.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ee0044-9d61-11e7-bbc4-c7534d7e1477","identifier":"d5ee0044-9d61-11e7-bbc4-c7534d7e1477","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.FQ.1","fullStatement":"Students will apply the statistical method to real-world situations.<ol type=\"i\"><li>Formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.</li><li>Collect data by designing a plan to collect appropriate data and employ the plan to collect the data.</li><li>Analyze data by selecting appropriate graphical and numerical methods and using these methods to analyze the data.</li><li>Interpret results by interpreting the analysis and relating the interpretation to the original question.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5edd31c-9d61-11e7-9b78-9ad98bf3a4dd","identifier":"d5edd31c-9d61-11e7-9b78-9ad98bf3a4dd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5edad6a-9d61-11e7-9c0c-f209fa9ee9d4","identifier":"d5edad6a-9d61-11e7-9c0c-f209fa9ee9d4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Formulate Questions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ee9d10-9d61-11e7-a6f1-0506ed93d4f3","identifier":"d5ee9d10-9d61-11e7-a6f1-0506ed93d4f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.FQ.2","fullStatement":"Students will identify whether the data are categorical or quantitative (numerical).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ef877a-9d61-11e7-b661-1063da37a8d7","identifier":"d5ef877a-9d61-11e7-b661-1063da37a8d7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.1a","fullStatement":"Students will identify the three types of distributions. <ol type=\"i\"><li>Recognize a population distribution has fixed values of its parameters that are usually unknown</li><li>Recognize a sample data distribution is taken from a population distribution and the data distribution is what is seen in practice hoping it approximates the population distribution.</li><li>Recognize a sampling distribution is the distribution of a sample statistic (such as a sample mean or a sample proportion) obtained from repeated samples. The sampling distribution provides the key for determining how close to expect a sample statistic approximates the population parameter.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ef5a2a-9d61-11e7-8b96-6da3e5f76b23","identifier":"d5ef5a2a-9d61-11e7-8b96-6da3e5f76b23","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.1","fullStatement":"Students will distinguish between a population distribution, a sample data distribution, and a sampling distribution.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5ef2136-9d61-11e7-944e-ba4011489e2b","identifier":"d5ef2136-9d61-11e7-944e-ba4011489e2b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will design and implement a plan to collect the appropriate data to answer the statistical question.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5eefd64-9d61-11e7-8a79-9ee4c196c56c","identifier":"d5eefd64-9d61-11e7-8a79-9ee4c196c56c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Collect Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f060e6-9d61-11e7-a368-0066e71a2fcc","identifier":"d5f060e6-9d61-11e7-a368-0066e71a2fcc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.2","fullStatement":"Students will understand that randomness should be incorporated into a sampling or experimental procedure.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f08b0c-9d61-11e7-b3f5-b7d303ef6fab","identifier":"d5f08b0c-9d61-11e7-b3f5-b7d303ef6fab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.2a","fullStatement":"Students will be able to implement a reasonable random method for selecting a sample or for assigning treatments in an experiment.<ol type=\"i\"><li>Implement a simple random sample.</li><li>Randomly assign treatments to experimental subjects or objects.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f0be92-9d61-11e7-a53d-d042556501c5","identifier":"d5f0be92-9d61-11e7-a53d-d042556501c5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.3","fullStatement":"Students will distinguish between the three types of study designs for collecting data (sample survey, experiment, and observational study) and will know the scope of the interpretation for each design type.<ol type=\"i\"><li>Determine the type of study design appropriate for answering a statistical question.</li><li>Determine the appropriate scope of inference for the study design used.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f11c70-9d61-11e7-8c45-e576f5672e0c","identifier":"d5f11c70-9d61-11e7-8c45-e576f5672e0c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.4","fullStatement":"Students will distinguish between the role of randomness and the role of sample size with respect to using a statistic from a sample to estimate a population parameter.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f14da8-9d61-11e7-9584-12a6d82ddd33","identifier":"d5f14da8-9d61-11e7-9584-12a6d82ddd33","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.4a","fullStatement":"Students will be able to distinguish the roles of randomization and sample size with designing studies.<ol type=\"i\"><li>Recognize that randomization reduces bias where bias occurs when certain outcomes are systematically more likely to appear.</li><li>Recognize that random selection from a population plays a different role than random assignment in an experiment.</li><li>Recognize that sample size impacts the precision with which estimates of the population parameters can be made (larger the sample size the more precision).</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f00326-9d61-11e7-8456-929a8cb8f1b2","identifier":"d5f00326-9d61-11e7-8456-929a8cb8f1b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.CD.1b","fullStatement":"Students will create sample data distributions and a sampling distribution.<ol type=\"i\"><li>Create a sample data distribution by taking a sample from a defined population and summarizing the data in a distribution.</li><li>Create a sampling distribution of a statistic by taking repeated samples from a population (either hands-on or by simulation with technology).</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f21c10-9d61-11e7-8381-46b4f5e8fd91","identifier":"d5f21c10-9d61-11e7-8381-46b4f5e8fd91","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.1a","fullStatement":"Students will describe the distribution for quantitative data.<ol type=\"i\"><li>Describe and interpret the shape of the distribution.</li><li>Describe and interpret the measures of center for the distribution.</li><li>Describe and interpret the patterns in variability for the distribution.</li><li>Describe and interpret any outliers or gaps in the distribution.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f1ef74-9d61-11e7-890c-e2933e5fc668","identifier":"d5f1ef74-9d61-11e7-890c-e2933e5fc668","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.1","fullStatement":"Students will use distributions to identify the key features of the data collected.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f1bc84-9d61-11e7-957e-310adb0fa6b2","identifier":"d5f1bc84-9d61-11e7-957e-310adb0fa6b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will select appropriate graphical and numerical methods and use these methods to analyze the data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f19916-9d61-11e7-bdcf-35a33a51e51d","identifier":"d5f19916-9d61-11e7-bdcf-35a33a51e51d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Analyze Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f3137c-9d61-11e7-8392-62180a1355cc","identifier":"d5f3137c-9d61-11e7-8392-62180a1355cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.2","fullStatement":"Students will use distributions to compare two or more groups.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f33e88-9d61-11e7-8973-6b3fddb96aa8","identifier":"d5f33e88-9d61-11e7-8973-6b3fddb96aa8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.2a","fullStatement":"Students will compare two or more groups by analyzing distributions.<ol type=\"i\"><li>Construct appropriate graphical displays of distributions.</li><li>Use graphical and numerical attributes of distributions to make comparisons between distributions.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f37128-9d61-11e7-b4da-a54a93191fac","identifier":"d5f37128-9d61-11e7-b4da-a54a93191fac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.3","fullStatement":"Students will determine if an association exists between two variables (pattern or trend in bivariate data) and use values of one variable to predict values of another variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f3a2e2-9d61-11e7-86fa-58cfd54072ba","identifier":"d5f3a2e2-9d61-11e7-86fa-58cfd54072ba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.3a","fullStatement":"Students will analyze associations between variables and make predictions from one variable to another.<ol type=\"i\"><li>Analyze associations between two variables. 1) Create scatter plots for two-variable numerical data. 2) Create two-way tables for two-variable categorical data. 3) Analyze patterns and trends in data displays.</li><li>Make predictions and draw conclusions from two-variable data based on data displays.</li><li>Distinguish between association and causation.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f2b5f8-9d61-11e7-b540-21e0be288b0f","identifier":"d5f2b5f8-9d61-11e7-b540-21e0be288b0f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.AD.1b","fullStatement":"Students will describe the distribution for categorical data.<ol type=\"i\"><li>Describe and interpret the modal category for the distribution.</li><li>Describe and interpret patterns that exist for the distribution.</li><ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f4ce74-9d61-11e7-af56-89072e705ec4","identifier":"d5f4ce74-9d61-11e7-af56-89072e705ec4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.IR.1a","fullStatement":"Students will be able to determine if there are differences between two population parameters or treatment effects.<ol type=\"i\"><li>Using simulation, determine the appropriate model to decide if there is a significant difference between two population parameters.</li><li>Using simulation, determine the appropriate model to decide if there is a difference between two treatment effects.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f4a214-9d61-11e7-8a0b-3f592e55eecd","identifier":"d5f4a214-9d61-11e7-8a0b-3f592e55eecd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.IR.1","fullStatement":"Students will ask if the difference between two sample proportions or two sample means is due to random variation or if the difference is significant.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f475aa-9d61-11e7-8093-a2d2000939fc","identifier":"d5f475aa-9d61-11e7-8093-a2d2000939fc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will interpret results and make connections to the original question.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f4517e-9d61-11e7-b4a0-fdd02bbb0458","identifier":"d5f4517e-9d61-11e7-b4a0-fdd02bbb0458","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpret Results","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f50132-9d61-11e7-93c0-13293dcc85f1","identifier":"d5f50132-9d61-11e7-93c0-13293dcc85f1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.IR.2","fullStatement":"Students will understand that when randomness is incorporated into a sampling or experimental procedure, probability provides a way to describe the 'long-run' behavior of a statistic as described by its sampling distribution.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5f52c70-9d61-11e7-a4be-7bfa02444cb4","identifier":"d5f52c70-9d61-11e7-a4be-7bfa02444cb4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.IR.2a","fullStatement":"Students will be able to create simulated sampling distributions and understand how to use the sampling distribution to make predictions about a population parameter(s) or the difference in treatment effects.<ol type=\"i\"><li>Create an appropriate simulated sampling distribution (using technology) and develop a margin of error.</li><li>Create an appropriate simulated sampling distribution (using technology) and develop a p-value.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da7768a8-9d61-11e7-9f39-d8880c0185f8","identifier":"da7768a8-9d61-11e7-9f39-d8880c0185f8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.07800","fullStatement":"Calculus","notes":"Calculus is a fourth mathematics course option for students who have completed Pre- Calculus or Accelerated Pre-Calculus. It includes problem solving, reasoning and estimation, functions, derivatives, application of the derivative, integrals, and application of the integral.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da782a22-9d61-11e7-a748-dae7d02d2169","identifier":"da782a22-9d61-11e7-a748-dae7d02d2169","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.1a","fullStatement":"Use theorems and algebraic concepts in evaluating the limits of sums, products, quotients, and composition of functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da77fcdc-9d61-11e7-89dd-9601bf9ba5ab","identifier":"da77fcdc-9d61-11e7-89dd-9601bf9ba5ab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.1","fullStatement":"Students will demonstrate knowledge of both the definition and the graphical interpretation of limit of values of functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da77ca46-9d61-11e7-a3db-a68cfaf6892e","identifier":"da77ca46-9d61-11e7-a3db-a68cfaf6892e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will investigate properties of functions and use algebraic manipulations to evaluate limits and differentiate functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da77a4b2-9d61-11e7-8571-bec3de6a0ede","identifier":"da77a4b2-9d61-11e7-8571-bec3de6a0ede","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Algebra","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da785cae-9d61-11e7-b1dd-e404c8b67196","identifier":"da785cae-9d61-11e7-b1dd-e404c8b67196","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.2","fullStatement":"Students will demonstrate knowledge of both the definition and graphical interpretation of continuity of a function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da789548-9d61-11e7-a712-0e39da5b9d94","identifier":"da789548-9d61-11e7-a712-0e39da5b9d94","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.2a","fullStatement":"Evaluate limits of functions and apply properties of limits, including one-sided limits.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da78af1a-9d61-11e7-9924-5ae8cafb7d54","identifier":"da78af1a-9d61-11e7-9924-5ae8cafb7d54","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.2b","fullStatement":"Estimate limits from graphs or tables of data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da78c702-9d61-11e7-8811-e0639bb7b2c1","identifier":"da78c702-9d61-11e7-8811-e0639bb7b2c1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.2c","fullStatement":"Describe asymptotic behavior in terms of limits involving infinity.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da78dfda-9d61-11e7-bc39-134f6903d62b","identifier":"da78dfda-9d61-11e7-bc39-134f6903d62b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.2d","fullStatement":"Apply the definition of continuity to a function at a point and determine if a function is continuous over an interval.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da78f790-9d61-11e7-9ebe-e7591b415730","identifier":"da78f790-9d61-11e7-9ebe-e7591b415730","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.3","fullStatement":"Students will demonstrate knowledge of differentiation using algebraic functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da792a1c-9d61-11e7-b160-03f12a62cb35","identifier":"da792a1c-9d61-11e7-b160-03f12a62cb35","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.3a","fullStatement":"Use differentiation and algebraic manipulations to sketch, by hand, graphs of functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da79433a-9d61-11e7-94e6-f4035fd26651","identifier":"da79433a-9d61-11e7-94e6-f4035fd26651","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.3b","fullStatement":"Identify maxima, minima, inflection points, and intervals where the function is increasing and decreasing.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da795be0-9d61-11e7-a5b1-1a7e07a924ec","identifier":"da795be0-9d61-11e7-a5b1-1a7e07a924ec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MC.A.3c","fullStatement":"Use differentiation and algebraic manipulations to solve optimization (maximum \u2013 minimum problems) in a variety of pure and applied 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Calculate the number of permutations of *r* elements taken from a set of *n* elements.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3afec0f4-9d62-11e7-8d78-41cc478b66d3","identifier":"3afec0f4-9d62-11e7-8d78-41cc478b66d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use methods of counting.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aff0bc2-9d62-11e7-ad56-b3e02f4f46b3","identifier":"3aff0bc2-9d62-11e7-ad56-b3e02f4f46b3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.PC.6","fullStatement":"Calculate the number of subsets of size *r* that can be chosen from a set of *n* elements. Recognize this number as the number of combinations \"*n* choose *r*\".","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aff247c-9d62-11e7-9dbe-7b2f08d18e53","identifier":"3aff247c-9d62-11e7-9dbe-7b2f08d18e53","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.PC.7","fullStatement":"Calculate the number of combinations with repetitions of *r* elements from a set of *n* elements as *n* + *r* \u2013 1 choose *r*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aff6ef0-9d62-11e7-873d-3521d68dabd9","identifier":"3aff6ef0-9d62-11e7-873d-3521d68dabd9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.PC.8","fullStatement":"Prove combinatorial identities. For example, prove that *n* + 1 choose *r* is equal to n choose *r* \u2013 1 plus n choose *r*; prove that the sum of the entries in the *k*th row of Pascal's triangle is $2^k$ (where the first row is row 0).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aff3de0-9d62-11e7-8df8-36ad30113f62","identifier":"3aff3de0-9d62-11e7-8df8-36ad30113f62","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Prove statements involving combinatorics.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aff887c-9d62-11e7-a7e5-4a80110cce7f","identifier":"3aff887c-9d62-11e7-a7e5-4a80110cce7f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.PC.9","fullStatement":"Apply a combinatorial argument to prove the binomial theorem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3affa0f0-9d62-11e7-af2a-8c6d1482dd74","identifier":"3affa0f0-9d62-11e7-af2a-8c6d1482dd74","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.PC.10","fullStatement":"Use the pigeonhole principle to prove statements about counting.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b03b88e-9d62-11e7-bb75-a61829e32eb3","identifier":"3b03b88e-9d62-11e7-bb75-a61829e32eb3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Graph Theory","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b0424ea-9d62-11e7-926c-25a341885958","identifier":"3b0424ea-9d62-11e7-926c-25a341885958","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.1","fullStatement":"Identify simple graphs, complete graphs, complete bipartite graphs, and trees. Identify graphs that have Euler and Hamiltonian cycles.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b03ee9e-9d62-11e7-9b25-eab03c4b0156","identifier":"3b03ee9e-9d62-11e7-9b25-eab03c4b0156","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use and recognize graph properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b0441e6-9d62-11e7-a2d3-2e229f215431","identifier":"3b0441e6-9d62-11e7-a2d3-2e229f215431","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.2","fullStatement":"Determine the complement of a graph and the line graph of a graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b045d8e-9d62-11e7-860a-8752896437d3","identifier":"3b045d8e-9d62-11e7-860a-8752896437d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.3","fullStatement":"Use the adjacency matrix of a graph to determine the number of walks of length *n* in a graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b04a21c-9d62-11e7-be19-b0cdb8aebc96","identifier":"3b04a21c-9d62-11e7-be19-b0cdb8aebc96","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.4","fullStatement":"Prove statements about graph properties. For example, prove that a graph has an even number of vertices of odd degree; prove that a graph has an Euler cycle if and only if the graph is connected and every vertex has even degree; prove that any tree with *n* vertices has *n* \u2013 1 edges.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b047a62-9d62-11e7-8a57-100fab0ca915","identifier":"3b047a62-9d62-11e7-8a57-100fab0ca915","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Prove statements in graph theory.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b04eede-9d62-11e7-8216-67146e6425f7","identifier":"3b04eede-9d62-11e7-8216-67146e6425f7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.5","fullStatement":"Prove that every connected graph has a minimal spanning tree.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b04bfe0-9d62-11e7-a615-9c0e58125f76","identifier":"3b04bfe0-9d62-11e7-a615-9c0e58125f76","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Apply graph theory.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b050bda-9d62-11e7-a791-79615767c4ce","identifier":"3b050bda-9d62-11e7-a791-79615767c4ce","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.GT.6","fullStatement":"Use Kruskal's algorithm and Prim's algorithm to determine the minimal spanning tree of a weighted graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b084ee4-9d62-11e7-8014-bc13744b16f1","identifier":"3b084ee4-9d62-11e7-8014-bc13744b16f1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Methods of Proof","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b089124-9d62-11e7-96ed-e2dd2a1ef4fb","identifier":"3b089124-9d62-11e7-96ed-e2dd2a1ef4fb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.MP.1","fullStatement":"Use a counterexample to disprove a statement. For example, the statement \"there exists a positive integer *n* such that *n\u00b2* + 3*n* + 2 is prime\" is disproved by the counterexample n = 3.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b08ae3e-9d62-11e7-9847-1905c974e296","identifier":"3b08ae3e-9d62-11e7-9847-1905c974e296","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.MP.2","fullStatement":"Prove statements directly from definitions and previously proved statements. For example, using the definition of \"rational number\", prove that every integer is rational; using the definition of \"divides\", prove that if *a* divides *b* and *b* divides *a*, then *a* equals *b*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b08c9e6-9d62-11e7-95cb-7231d4085543","identifier":"3b08c9e6-9d62-11e7-95cb-7231d4085543","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.MP.3","fullStatement":"Prove statements indirectly by proving the contrapositive of the statement. For example, prove that if the square of an integer is even, then the integer is even, by instead proving that if an integer is odd, then its square is odd.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b08e5de-9d62-11e7-8c5c-4ddf80b4a738","identifier":"3b08e5de-9d62-11e7-8c5c-4ddf80b4a738","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.MP.4","fullStatement":"Apply the method of *reductio ad absurdum* (\"proof by contradiction\") to prove statements, such as proving that there are infinitely many prime numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b090172-9d62-11e7-a61d-29f88aab87fe","identifier":"3b090172-9d62-11e7-a61d-29f88aab87fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MAFM.MP.5","fullStatement":"Use the method of mathematical induction to prove statements involving the positive integers. For example, prove that 3 divides $2^{2n}$ \u2013 1 for all positive integers n; prove that 1 + 2 + 3 + \u2026 + *n* = *n*(*n* + 1)/2; prove that a given recursive sequence has a closed form expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5e9bc16a-9d62-11e7-a252-2622be78414e","identifier":"5e9bc16a-9d62-11e7-a252-2622be78414e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.09000","fullStatement":"Technical College Readiness Mathematics","notes":"**Technical College Readiness Mathematics** is designed to meet the needs of students who have passed Algebra I/Coordinate Algebra, have passed or are concurrently enrolled in Geometry/Analytic Geometry while taking this course, and intend to enroll in a technical college program. The course is aimed at students who have experienced difficulty in passing middle school mathematics End of Grade (EOG) assessments, have struggled significantly in the first two high school core mathematics courses, and have scored less than 34 on the ACCUPLACER Placement Assessment. The ACCUPLACER Placement Assessment will serve as the course post-test. \r\n\r\n**Technical College Readiness Mathematics** will examine numeracy, algebra, and geometry in a variety of contexts, including number sense, linear and non-linear relationships, functions and their graphs, and measurement and geometry. The course will provide an opportunity for students to review mathematics skills needed for success in Technical College and will extend students\u2019 understanding of mathematical concepts and skills by emphasizing topics from Foundations of Algebra, Coordinate Algebra/Algebra I, Analytic Geometry/Geometry, and Advanced Algebra/Algebra II.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f0ab94-9d62-11e7-886c-68bd18669003","identifier":"68f0ab94-9d62-11e7-886c-68bd18669003","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Number Sense","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f129f2-9d62-11e7-98dc-73a8f96ec4c9","identifier":"68f129f2-9d62-11e7-98dc-73a8f96ec4c9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content 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Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NS.4","fullStatement":"Students will extend their knowledge of positive, rational numbers to negative values, including comparisons and absolute values.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f18bfe-9d62-11e7-9adc-80d09a549613","identifier":"68f18bfe-9d62-11e7-9adc-80d09a549613","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NS.5","fullStatement":"Students will apply their knowledge of rational numbers to solve application problems involving all forms of these numbers, including the use of the mean, greatest common factor, and least common multiple.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f58ccc-9d62-11e7-95f7-6b271c14aa51","identifier":"68f58ccc-9d62-11e7-95f7-6b271c14aa51","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Linear Equations and Inequalities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f5fcc0-9d62-11e7-a124-9b06976e174f","identifier":"68f5fcc0-9d62-11e7-a124-9b06976e174f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.1","fullStatement":"Students will solve multi-step equations and inequalities, using all forms of rational numbers as coefficients.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f5b5f8-9d62-11e7-a590-166416e10055","identifier":"68f5b5f8-9d62-11e7-a590-166416e10055","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will solve equations and inequalities in one variable and then, extend this knowledge to two-variable linear equations and inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f61a0c-9d62-11e7-910a-dc41f7f526bd","identifier":"68f61a0c-9d62-11e7-910a-dc41f7f526bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.2","fullStatement":"Students will set-up and solve application problems including direct and inverse variations and proportions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f63640-9d62-11e7-b384-a21accc1bf4f","identifier":"68f63640-9d62-11e7-b384-a21accc1bf4f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.3","fullStatement":"Students will graph linear equations and inequalities using intercepts, slope and y-intercept, and tables of values.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f65206-9d62-11e7-a085-996ce70d9d74","identifier":"68f65206-9d62-11e7-a085-996ce70d9d74","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.4","fullStatement":"Students will determine and identify relationships between lines using slope.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f66dc2-9d62-11e7-b8fe-10b8ec267e07","identifier":"68f66dc2-9d62-11e7-b8fe-10b8ec267e07","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.5","fullStatement":"Students will solve systems of linear equations using graphing, substitution, and elimination, and then, apply these methods to set-up and solve application problems involving systems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f68a14-9d62-11e7-b74d-32837da72266","identifier":"68f68a14-9d62-11e7-b74d-32837da72266","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.LEI.6","fullStatement":"Students will set-up and graph problems involving systems of inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f95a8c-9d62-11e7-993e-7a0701d15a3e","identifier":"68f95a8c-9d62-11e7-993e-7a0701d15a3e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Non-Linear Relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f9cc24-9d62-11e7-8732-738fe3ba394a","identifier":"68f9cc24-9d62-11e7-8732-738fe3ba394a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.1","fullStatement":"Students will simplify and perform basic operations with square roots.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f983ae-9d62-11e7-833e-9e30249c39e3","identifier":"68f983ae-9d62-11e7-833e-9e30249c39e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will simplify square roots, rational expressions, and polynomial expressions, and then, solve equations involving these expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68f9e9a2-9d62-11e7-89dd-f615a8c2e2c3","identifier":"68f9e9a2-9d62-11e7-89dd-f615a8c2e2c3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.2","fullStatement":"Students will solve right triangle application problems by establishing and using the Pythagorean Theorem and right triangle relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fa05b8-9d62-11e7-a261-295ad6af68d1","identifier":"68fa05b8-9d62-11e7-a261-295ad6af68d1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.3","fullStatement":"Students will perform basic operations with polynomial expressions including the use of order of operations, substitution of rational numbers for variables, operations with exponents, and binomial expansion.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fa2192-9d62-11e7-b8fe-fb54c83db8cd","identifier":"68fa2192-9d62-11e7-b8fe-fb54c83db8cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.4","fullStatement":"Students will solve quadratic equations and corresponding application problems using square roots, factoring, completing the square, and the quadratic formula.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fa3d58-9d62-11e7-b3b8-31dcf8f7521e","identifier":"68fa3d58-9d62-11e7-b3b8-31dcf8f7521e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.5","fullStatement":"Students will perform basic operations with rational expressions, including simplification with factoring.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fa59dc-9d62-11e7-b870-af437b0e52ce","identifier":"68fa59dc-9d62-11e7-b870-af437b0e52ce","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.NLR.6","fullStatement":"Students will solve rational equations and corresponding application problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fd3bca-9d62-11e7-9849-5980d54e3897","identifier":"68fd3bca-9d62-11e7-9849-5980d54e3897","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Graphs and Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fd9ae8-9d62-11e7-9c07-7cef0b497cc7","identifier":"68fd9ae8-9d62-11e7-9c07-7cef0b497cc7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.GF.1","fullStatement":"Students will use the definition of functions to identify functions in various forms.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fd656e-9d62-11e7-8926-265f06b4d80b","identifier":"68fd656e-9d62-11e7-8926-265f06b4d80b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will identify and analyze functions using mappings, relations, graphs, and real-world applications.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fdb82a-9d62-11e7-9ac6-e6c5fd4dd046","identifier":"68fdb82a-9d62-11e7-9ac6-e6c5fd4dd046","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.GF.2","fullStatement":"Students will graph functions analyzing the important features of the graphs.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fdd4ae-9d62-11e7-b9e4-e65dfc0c79b8","identifier":"68fdd4ae-9d62-11e7-b9e4-e65dfc0c79b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.GF.3","fullStatement":"Students will analyze and solve application problems involving functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/68fffcca-9d62-11e7-b235-ffc0727c81f6","identifier":"68fffcca-9d62-11e7-b235-ffc0727c81f6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Measurement and Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/69005dd2-9d62-11e7-82a4-79efc1930597","identifier":"69005dd2-9d62-11e7-82a4-79efc1930597","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.MG.1","fullStatement":"Students will convert measurements within their same system of measurement including time.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/69002dbc-9d62-11e7-83fa-ff4f2dcf2db1","identifier":"69002dbc-9d62-11e7-83fa-ff4f2dcf2db1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will convert between measurements within the same systems and from metric to English/English to metric.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/69007b32-9d62-11e7-a52a-e292cf87b18a","identifier":"69007b32-9d62-11e7-a52a-e292cf87b18a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.MG.2","fullStatement":"Students will convert measurements from English to metric and metric to English, using given conversions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6900c7c2-9d62-11e7-be4a-c851e3189815","identifier":"6900c7c2-9d62-11e7-be4a-c851e3189815","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.MG.3","fullStatement":"Students will determine the characteristics and the relationships of 2-dimensional and 3-dimensional figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/69009856-9d62-11e7-aab7-6c50750b5587","identifier":"69009856-9d62-11e7-aab7-6c50750b5587","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will classify basic geometric shapes and then, calculate the perimeters, areas, volumes, and surface areas of figures extending this work into contextual problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6900e504-9d62-11e7-9fd3-759e49d9b576","identifier":"6900e504-9d62-11e7-9fd3-759e49d9b576","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MTCR.MG.4","fullStatement":"Students will use formulas to isolate unknowns and then calculate the perimeters, areas, volumes, and surface areas of the shapes including setting-up and solving contextual problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/88694a9e-9d62-11e7-a942-fc68508318cd","identifier":"88694a9e-9d62-11e7-a942-fc68508318cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.08900","fullStatement":"College Readiness Mathematics (Mathematics Capstone Course)","notes":"**College Readiness Mathematics** focuses on key content and practice standards to ensure that students will be ready for post-secondary academic courses and career preparation in non-STEM fields. The course will revisit and expand the understanding of content standards introduced in earlier mathematics courses and will emphasize numeracy, algebra and functions, geometry, and statistics in a variety of contexts. \r\n\nInstruction and assessment should include the appropriate use of manipulatives and technology. Mathematics concepts should be represented in multiple ways, such as concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be introduced and used, where appropriate, in the context of realistic experiences","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96af0634-9d62-11e7-a9f7-d902cf1f506c","identifier":"96af0634-9d62-11e7-a9f7-d902cf1f506c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96af4090-9d62-11e7-a6a5-745946e637bb","identifier":"96af4090-9d62-11e7-a6a5-745946e637bb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Reason quantitatively and use units to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96aff490-9d62-11e7-9c1c-88507e9fe910","identifier":"96aff490-9d62-11e7-9c1c-88507e9fe910","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.2","fullStatement":"Define appropriate quantities for the purpose of descriptive modeling. Given a situation, context, or problem, students will determine, identify, and use appropriate quantities for representing the situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b3c1d8-9d62-11e7-a1db-4c32d8b8676a","identifier":"96b3c1d8-9d62-11e7-a1db-4c32d8b8676a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Seeing Structure in Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b41ca0-9d62-11e7-964a-440ff991db72","identifier":"96b41ca0-9d62-11e7-964a-440ff991db72","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1","fullStatement":"Interpret expressions that represent a quantity in terms of its context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b3f004-9d62-11e7-8068-923949b72703","identifier":"96b3f004-9d62-11e7-8068-923949b72703","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret the structure of expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b43686-9d62-11e7-9b1c-7ee1b5a6c4ee","identifier":"96b43686-9d62-11e7-9b1c-7ee1b5a6c4ee","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.2","fullStatement":"Use the structure of an expression to rewrite it in different equivalent forms. *For example, see $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2) (x^2 + y^2)$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b472b8-9d62-11e7-8474-632f17899e7e","identifier":"96b472b8-9d62-11e7-8474-632f17899e7e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3","fullStatement":"Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b44f18-9d62-11e7-a8f8-29f412f6a84e","identifier":"96b44f18-9d62-11e7-a8f8-29f412f6a84e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Write expressions in equivalent forms to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b67158-9d62-11e7-99e5-d53f8725e272","identifier":"96b67158-9d62-11e7-99e5-d53f8725e272","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Creating Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b6cde2-9d62-11e7-a6e6-f8ae7d43c1a6","identifier":"96b6cde2-9d62-11e7-a6e6-f8ae7d43c1a6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b69674-9d62-11e7-9fb2-83f76a0a9a9e","identifier":"96b69674-9d62-11e7-9fb2-83f76a0a9a9e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Create equations that describe numbers or relationships","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b6e750-9d62-11e7-a5f2-6b2f11c66657","identifier":"96b6e750-9d62-11e7-a5f2-6b2f11c66657","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r/n)^{(nt)}$ has multiple variables.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b6ff10-9d62-11e7-9fd0-f9d9cd9a4b65","identifier":"96b6ff10-9d62-11e7-9fd0-f9d9cd9a4b65","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b716a8-9d62-11e7-b1aa-53eefb47403f","identifier":"96b716a8-9d62-11e7-b1aa-53eefb47403f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.4","fullStatement":"Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.  *Examples: Rearrange Ohm\u2019s law V = IR to highlight resistance R; Rearrange area of a circle formula A =  \u03c0 $r^2$ to highlight the radius r.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b91c3c-9d62-11e7-ab6e-0fb9b2d6ce7a","identifier":"96b91c3c-9d62-11e7-ab6e-0fb9b2d6ce7a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Reasoning with Equations and Inequalities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b98118-9d62-11e7-8960-529ce6974ec1","identifier":"96b98118-9d62-11e7-8960-529ce6974ec1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.1","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b95558-9d62-11e7-a5e1-30f98e53eebc","identifier":"96b95558-9d62-11e7-a5e1-30f98e53eebc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand solving equations as a process of reasoning and explain the reasoning","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b99b26-9d62-11e7-9282-a3f0285942b9","identifier":"96b99b26-9d62-11e7-9282-a3f0285942b9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.2","fullStatement":"Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b9de6a-9d62-11e7-ab1e-214429b282a1","identifier":"96b9de6a-9d62-11e7-ab1e-214429b282a1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.3","fullStatement":"Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. *For example, given ax +  3 = 7, solve for x.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b9b3c2-9d62-11e7-8863-d7609a8878ea","identifier":"96b9b3c2-9d62-11e7-8863-d7609a8878ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve equations and inequalities in one variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96b9f83c-9d62-11e7-b85f-1058f520cf7c","identifier":"96b9f83c-9d62-11e7-b85f-1058f520cf7c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4","fullStatement":"Solve quadratic equations in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96ba41e8-9d62-11e7-ab6f-a087c24fed70","identifier":"96ba41e8-9d62-11e7-ab6f-a087c24fed70","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.5","fullStatement":"Show and explain why the elimination method works to solve a system of two-variable equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96ba1146-9d62-11e7-b7f2-761ea653f254","identifier":"96ba1146-9d62-11e7-b7f2-761ea653f254","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve systems of equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96ba5bce-9d62-11e7-abd6-2c82a3fa09af","identifier":"96ba5bce-9d62-11e7-abd6-2c82a3fa09af","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.6","fullStatement":"Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96ba73ac-9d62-11e7-8687-0ae881426d4c","identifier":"96ba73ac-9d62-11e7-8687-0ae881426d4c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.7","fullStatement":"Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. *For example, find the points of intersection between the line y = - 3x and the circle x\u00b2 + y\u00b2 = 3.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96bab7fe-9d62-11e7-b5d1-68edb21c9bf4","identifier":"96bab7fe-9d62-11e7-b5d1-68edb21c9bf4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.11","fullStatement":"Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96ba8cf2-9d62-11e7-bd53-e4da4223f7c1","identifier":"96ba8cf2-9d62-11e7-bd53-e4da4223f7c1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Represent and solve equations and inequalities graphically","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96bad144-9d62-11e7-90d2-fea58298edd4","identifier":"96bad144-9d62-11e7-90d2-fea58298edd4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.12","fullStatement":"Graph the solution set to a linear inequality in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c018a2-9d62-11e7-b910-ddd68701a725","identifier":"96c018a2-9d62-11e7-b910-ddd68701a725","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c070f4-9d62-11e7-8231-38aeb3b7ad46","identifier":"96c070f4-9d62-11e7-8231-38aeb3b7ad46","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.1","fullStatement":"Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is y = f(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c04c64-9d62-11e7-ae23-1545c2bbb5f8","identifier":"96c04c64-9d62-11e7-ae23-1545c2bbb5f8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the concept of a function and use function notation","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c0bc30-9d62-11e7-940e-b047a7bedf5b","identifier":"96c0bc30-9d62-11e7-940e-b047a7bedf5b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.4","fullStatement":"Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c08ba2-9d62-11e7-806c-25ab5596e166","identifier":"96c08ba2-9d62-11e7-806c-25ab5596e166","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret functions that arise in applications in terms of the context","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c0d670-9d62-11e7-99f4-045c415d2039","identifier":"96c0d670-9d62-11e7-99f4-045c415d2039","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.5","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c0eee4-9d62-11e7-8b5d-32b07d450d3f","identifier":"96c0eee4-9d62-11e7-8b5d-32b07d450d3f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.6","fullStatement":"Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c137c8-9d62-11e7-a5cd-8ddf97742f91","identifier":"96c137c8-9d62-11e7-a5cd-8ddf97742f91","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7","fullStatement":"Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c106e0-9d62-11e7-a387-5befca6fa29b","identifier":"96c106e0-9d62-11e7-a387-5befca6fa29b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Analyze functions using different representations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c1510e-9d62-11e7-9fd0-18305cb5ec49","identifier":"96c1510e-9d62-11e7-9fd0-18305cb5ec49","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8","fullStatement":"Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c16978-9d62-11e7-8497-1a81c820908b","identifier":"96c16978-9d62-11e7-8497-1a81c820908b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.9","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example. given a graph of one function and an algebraic expression for another, say which has the larger maximum.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c4bdb2-9d62-11e7-ab31-66b59a56f4be","identifier":"96c4bdb2-9d62-11e7-ab31-66b59a56f4be","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Building Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c51730-9d62-11e7-a76c-e4f6777bca5c","identifier":"96c51730-9d62-11e7-a76c-e4f6777bca5c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1","fullStatement":"Write a function that describes a relationship between two quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c4eaee-9d62-11e7-975a-393cbfd1877d","identifier":"96c4eaee-9d62-11e7-975a-393cbfd1877d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build a function that models a relationship between two quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c5312a-9d62-11e7-9c28-0eb06b462498","identifier":"96c5312a-9d62-11e7-9c28-0eb06b462498","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.2","fullStatement":"Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c56d0c-9d62-11e7-8e6f-4f3367557a87","identifier":"96c56d0c-9d62-11e7-8e6f-4f3367557a87","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.3","fullStatement":"Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96c5498a-9d62-11e7-bc0d-e39414069667","identifier":"96c5498a-9d62-11e7-bc0d-e39414069667","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build new functions from existing functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b89d42-9d62-11e7-81e8-763cccbda963","identifier":"a1b89d42-9d62-11e7-81e8-763cccbda963","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Linear, Quadratic, and Exponential Models","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b908cc-9d62-11e7-a78a-3fdc343d3770","identifier":"a1b908cc-9d62-11e7-a78a-3fdc343d3770","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1","fullStatement":"Distinguish between situations that can be modeled with linear functions and with exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b8d690-9d62-11e7-8ae2-cf53f46c0f4e","identifier":"a1b8d690-9d62-11e7-8ae2-cf53f46c0f4e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Construct and compare linear, quadratic, and exponential models and solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b922b2-9d62-11e7-bb7e-e59b61b3b75a","identifier":"a1b922b2-9d62-11e7-bb7e-e59b61b3b75a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.2","fullStatement":"Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b93a2c-9d62-11e7-8451-40f416fb378c","identifier":"a1b93a2c-9d62-11e7-8451-40f416fb378c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.3","fullStatement":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b97668-9d62-11e7-b7ef-c5edcb8f2ce9","identifier":"a1b97668-9d62-11e7-b7ef-c5edcb8f2ce9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.5","fullStatement":"Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a\u2022$d^x$) function in terms of context.  (In the functions above, \u201cm\u201d and \u201cb\u201d are the parameters of the linear function, and \u201ca\u201d and \u201cd\u201d are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b952e6-9d62-11e7-a0f2-a0341fb1cf7a","identifier":"a1b952e6-9d62-11e7-a0f2-a0341fb1cf7a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret expressions for functions in terms of the situation they model","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1b9d478-9d62-11e7-aa40-8412bdf24e78","identifier":"a1b9d478-9d62-11e7-aa40-8412bdf24e78","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GPE.7","fullStatement":"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1bd4e46-9d62-11e7-bdc3-442a0dc705e1","identifier":"a1bd4e46-9d62-11e7-bdc3-442a0dc705e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Geometric Measurement and Dimension","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1bd74a2-9d62-11e7-a6cc-e20576bb6c04","identifier":"a1bd74a2-9d62-11e7-a6cc-e20576bb6c04","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Explain volume formulas and use them to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1be00e8-9d62-11e7-9f6b-43955256cedd","identifier":"a1be00e8-9d62-11e7-9f6b-43955256cedd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.3","fullStatement":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1bffaa6-9d62-11e7-af01-8371b81ec4fc","identifier":"a1bffaa6-9d62-11e7-af01-8371b81ec4fc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Modeling with Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c04baa-9d62-11e7-8983-d179f470bf19","identifier":"a1c04baa-9d62-11e7-8983-d179f470bf19","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.MG.2","fullStatement":"Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c01f9a-9d62-11e7-b19a-00401dcea3fd","identifier":"a1c01f9a-9d62-11e7-b19a-00401dcea3fd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Apply geometric concepts in modeling situations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c065c2-9d62-11e7-a0ff-f8d032832cde","identifier":"a1c065c2-9d62-11e7-a0ff-f8d032832cde","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.MG.3","fullStatement":"Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c21106-9d62-11e7-a591-a9fc932942e3","identifier":"a1c21106-9d62-11e7-a591-a9fc932942e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Categorical and Quantitative Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c2766e-9d62-11e7-a157-e50db068cd6f","identifier":"a1c2766e-9d62-11e7-a157-e50db068cd6f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.1","fullStatement":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c24428-9d62-11e7-9af9-38b8ded28045","identifier":"a1c24428-9d62-11e7-9af9-38b8ded28045","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Summarize, represent, and interpret data on a single count or measurement variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c28fd2-9d62-11e7-9924-fa4b66e7d647","identifier":"a1c28fd2-9d62-11e7-9924-fa4b66e7d647","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.2","fullStatement":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, mean absolute deviation, standard deviation) of two or more different data sets.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c2a8e6-9d62-11e7-aaca-a7d8beb06ae5","identifier":"a1c2a8e6-9d62-11e7-aaca-a7d8beb06ae5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.3","fullStatement":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c2ec66-9d62-11e7-9635-f7e384b3f500","identifier":"a1c2ec66-9d62-11e7-9635-f7e384b3f500","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.5","fullStatement":"Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c2c10a-9d62-11e7-b231-17ad503c482e","identifier":"a1c2c10a-9d62-11e7-b231-17ad503c482e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Summarize, represent, and interpret data on two categorical and quantitative variables","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c305de-9d62-11e7-8910-32d7eeb6f2d1","identifier":"a1c305de-9d62-11e7-8910-32d7eeb6f2d1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.6","fullStatement":"Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c35098-9d62-11e7-864c-da48fda20a29","identifier":"a1c35098-9d62-11e7-864c-da48fda20a29","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.7","fullStatement":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c31ef2-9d62-11e7-aaa6-d805d5af8aae","identifier":"a1c31ef2-9d62-11e7-aaa6-d805d5af8aae","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret linear models","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c36a60-9d62-11e7-b71f-c97de63bbada","identifier":"a1c36a60-9d62-11e7-b71f-c97de63bbada","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.8","fullStatement":"Compute (using technology) and interpret the correlation coefficient \"r\" of a linear fit. (For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the \"r\" value.) After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using \"r\".","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c3828e-9d62-11e7-9c0a-a8b7d89cc179","identifier":"a1c3828e-9d62-11e7-9c0a-a8b7d89cc179","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.9","fullStatement":"Distinguish between correlation and causation","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c75daa-9d62-11e7-87ff-547a334569c4","identifier":"a1c75daa-9d62-11e7-87ff-547a334569c4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Making Inferences and Justifying Conclusions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c7b07a-9d62-11e7-a1ba-18c2c44f5abb","identifier":"a1c7b07a-9d62-11e7-a1ba-18c2c44f5abb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.IC.1","fullStatement":"Understand statistics as a process for making inferences about population parameters based on a random sample from that population.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c78b54-9d62-11e7-8e84-d4afbd09f7eb","identifier":"a1c78b54-9d62-11e7-8e84-d4afbd09f7eb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand and evaluate random processes underlying statistical experiments","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c7ee64-9d62-11e7-a7bc-6c58f75c02dc","identifier":"a1c7ee64-9d62-11e7-a7bc-6c58f75c02dc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.IC.3","fullStatement":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1c7ca2e-9d62-11e7-a754-0245cc898c7d","identifier":"a1c7ca2e-9d62-11e7-a754-0245cc898c7d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Make inferences and justify conclusions from sample surveys, experiments, and observational studies","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/32f19f5c-9d63-11e7-a0b8-71e52e5326e7","identifier":"32f19f5c-9d63-11e7-a0b8-71e52e5326e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.09900","fullStatement":"Algebra I","notes":"**Algebra I** is the first course in a sequence of three required high school courses designed to ensure career and college readiness. The course represents a discrete study of algebra with correlated statistics applications. \r\n\r\nThe standards in the three-course high school sequence specify the mathematics that all students should study in order to be college and career ready. Additional mathematics content is provided in fourth credit courses and advanced courses including pre-calculus, calculus, advanced statistics, discrete mathematics, and mathematics of finance courses. High school course content standards are listed by conceptual categories including Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Conceptual categories portray a coherent view of high school mathematics content; a student\u2019s work with functions, for example, crosses a number of traditional course boundaries, potentially up through and including calculus. Standards for Mathematical Practice provide the foundation for instruction and assessment.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fe397e82-9d68-11e7-bcfb-e902a684e10d","identifier":"fe397e82-9d68-11e7-bcfb-e902a684e10d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["KG"],"humanCodingScheme":"27.01100","fullStatement":"Mathematics/Grade Kindergarten","notes":"The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings.\r\n\r\nIn Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.  \r\n\r\nContent standards for Kindergarten are arranged within five domains and nine clusters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2bbd8ec4-9d6a-11e7-ae97-276d0cabf52d","identifier":"2bbd8ec4-9d6a-11e7-ae97-276d0cabf52d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["KG"],"humanCodingScheme":"K.CC","fullStatement":"Counting and Cardinality","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/50674f44-9d6a-11e7-973f-9db41a69a9f1","identifier":"50674f44-9d6a-11e7-973f-9db41a69a9f1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["KG"],"humanCodingScheme":"K.OA","fullStatement":"Operations and Algebraic 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Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/75f7b71c-9d6a-11e7-8bee-9070ba71b5ef","identifier":"75f7b71c-9d6a-11e7-8bee-9070ba71b5ef","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["KG"],"humanCodingScheme":"K.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/48734e2c-9d6b-11e7-8f47-31d7b743ebd6","identifier":"48734e2c-9d6b-11e7-8f47-31d7b743ebd6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["01"],"humanCodingScheme":"1.OA","fullStatement":"Operations and Algebraic 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addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2bdb35a2-9d72-11e7-b938-ba62e27a6d6f","identifier":"2bdb35a2-9d72-11e7-b938-ba62e27a6d6f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.OA.3","fullStatement":"Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. *(Drawings need not include an equation).*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/36114188-9d72-11e7-920b-20677b5b2d89","identifier":"36114188-9d72-11e7-920b-20677b5b2d89","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.OA.4","fullStatement":"For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/41e60d22-9d72-11e7-8b41-e14396a609c9","identifier":"41e60d22-9d72-11e7-8b41-e14396a609c9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.OA.5","fullStatement":"Fluently add and subtract within 5.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/56602602-9d72-11e7-ac6d-e2b13555a98c","identifier":"56602602-9d72-11e7-ac6d-e2b13555a98c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.NBT.1","fullStatement":"Compose and decompose numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six , seven, eight, or nine ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7b88bf3e-9d72-11e7-bc35-68956228c67e","identifier":"7b88bf3e-9d72-11e7-bc35-68956228c67e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.MD.1","fullStatement":"Describe several measurable attributes of an object, such as length or weight.  *For example, a student may describe a shoe as, \u201cThis shoe is heavy! It is also really long!\u201d*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8a0b8d02-9d72-11e7-80d4-d1a864222bb0","identifier":"8a0b8d02-9d72-11e7-80d4-d1a864222bb0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.MD.2","fullStatement":"Directly compare two objects with a measurable attribute in common, to see which object has \u201cmore of\u201d/\u201cless of\u201d the attribute, and describe the difference.  *For example, directly compare the heights of two children and describe one child as taller/shorter.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a93fab18-9d72-11e7-800d-8d4f3f3aebec","identifier":"a93fab18-9d72-11e7-800d-8d4f3f3aebec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.MD.3","fullStatement":"Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.  *(Limit category counts to be less than or equal to 10.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f2977eb2-9d72-11e7-8336-ab1a89823475","identifier":"f2977eb2-9d72-11e7-8336-ab1a89823475","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.1","fullStatement":"Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as *above, below, beside, in front of, behind, and next to*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc9c2e08-9d72-11e7-b607-46cc09f779a1","identifier":"fc9c2e08-9d72-11e7-b607-46cc09f779a1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.2","fullStatement":"Correctly name shapes regardless of their orientations or overall size.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/078b439e-9d73-11e7-a1ea-1544810b85b5","identifier":"078b439e-9d73-11e7-a1ea-1544810b85b5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.3","fullStatement":"Identify shapes as two-dimensional (lying in a plane, \u201cflat\u201d) or three-dimensional (\u201csolid\u201d).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2398e820-9d73-11e7-a59f-970fc4c9c720","identifier":"2398e820-9d73-11e7-a59f-970fc4c9c720","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.4","fullStatement":"Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/\u201ccorners\u201d) and other attributes (e.g., having sides of equal length).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2cadb0da-9d73-11e7-8be9-c5e230f82289","identifier":"2cadb0da-9d73-11e7-8be9-c5e230f82289","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.5","fullStatement":"Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/398bb63a-9d73-11e7-8f09-f6f4bb8367b3","identifier":"398bb63a-9d73-11e7-8f09-f6f4bb8367b3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.G.6","fullStatement":"Compose simple shapes to form larger shapes.  *For example, \u201cCan you join these two triangles with full sides touching to make a rectangle?\u201d*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6bfb12e6-9d73-11e7-81f2-011a94318f1b","identifier":"6bfb12e6-9d73-11e7-81f2-011a94318f1b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.1","fullStatement":"Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.  *(Special note:  more details can be found in the Mathematics Glossary, Table 1)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/777ce7b6-9d73-11e7-a8c6-896c75dec0b9","identifier":"777ce7b6-9d73-11e7-a8c6-896c75dec0b9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.2","fullStatement":"Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9e78a3c8-9d73-11e7-831b-b1f891bbe83a","identifier":"9e78a3c8-9d73-11e7-831b-b1f891bbe83a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.3","fullStatement":"Apply properties of operations as strategies to add and subtract.  *(Students need not use formal terms for these properties. Problems should be within 20.)*\r\n\r\nExamples: \r\nIf 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/abd4724a-9d73-11e7-bdc1-f775a77d3008","identifier":"abd4724a-9d73-11e7-bdc1-f775a77d3008","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.4","fullStatement":"Understand subtraction as an unknown-addend problem. *For example, subtract 10 \u2013 8 by finding the number that makes 10 when added to 8.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/baa59254-9d73-11e7-b3ca-b3cf5c73d1d3","identifier":"baa59254-9d73-11e7-b3ca-b3cf5c73d1d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.5","fullStatement":"Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c8b8bdbc-9d73-11e7-9aa5-dcf53c398398","identifier":"c8b8bdbc-9d73-11e7-9aa5-dcf53c398398","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.6","fullStatement":"Add and subtract within 20.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fa3b5af2-9d73-11e7-aaaa-e5eeb589d403","identifier":"fa3b5af2-9d73-11e7-aaaa-e5eeb589d403","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.7","fullStatement":"Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. <i>For example, which of the following equations <b>are true</b> and which <b>are false</b>?</i>  6 = 6, 7 = 8 \u2013 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/18a9c8ac-9d74-11e7-9c06-6cc769fde936","identifier":"18a9c8ac-9d74-11e7-9c06-6cc769fde936","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.8","fullStatement":"Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. *For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = \u25a1 \u2013 3, 6 + 6 = \u2206.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2f269592-9d74-11e7-b1cf-42b0eb80dc78","identifier":"2f269592-9d74-11e7-b1cf-42b0eb80dc78","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.1","fullStatement":"Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3e61caae-9d74-11e7-8a99-9e7ecda202fe","identifier":"3e61caae-9d74-11e7-8a99-9e7ecda202fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.2","fullStatement":"Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/78047f90-9d74-11e7-877e-f977e4fbb5f0","identifier":"78047f90-9d74-11e7-877e-f977e4fbb5f0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.3","fullStatement":"Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, = , and < .","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/904cd3d6-9d74-11e7-bfce-cbeb99334806","identifier":"904cd3d6-9d74-11e7-bfce-cbeb99334806","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.4","fullStatement":"Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of ten (e.g., 24 + 9, 13 + 10, 27 + 40), using concrete models or drawings and strategies based on place value, properties of operations, and/or relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9bbbb0ac-9d74-11e7-b27b-217ab22e0913","identifier":"9bbbb0ac-9d74-11e7-b27b-217ab22e0913","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.5","fullStatement":"Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a5b197ac-9d74-11e7-a149-f604de793767","identifier":"a5b197ac-9d74-11e7-a149-f604de793767","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.6","fullStatement":"Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range of 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (e.g.,70 \u2013 30, 30 \u2013 10, 60 \u2013 60)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b16b321a-9d74-11e7-a441-6ffbc3c62a86","identifier":"b16b321a-9d74-11e7-a441-6ffbc3c62a86","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.7","fullStatement":"Identify dimes, and understand ten pennies can be thought of as a dime. (Use dimes as\r\nmanipulatives in multiple mathematical contexts.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c2a1b360-9d74-11e7-b7cc-3afafd97bb3b","identifier":"c2a1b360-9d74-11e7-b7cc-3afafd97bb3b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.MD.1","fullStatement":"Order three objects by length; compare the lengths of two objects indirectly by using a third object.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ce90429a-9d74-11e7-b696-1ba328e17ddc","identifier":"ce90429a-9d74-11e7-b696-1ba328e17ddc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.MD.2","fullStatement":"Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. (Iteration)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8d038a-9d74-11e7-ad0f-414c34aca1e7","identifier":"da8d038a-9d74-11e7-ad0f-414c34aca1e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.MD.3","fullStatement":"Tell and write time in hours and half-hours using analog and digital clocks.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e89adf56-9d74-11e7-8dc9-47a574c83a4e","identifier":"e89adf56-9d74-11e7-8dc9-47a574c83a4e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.MD.4","fullStatement":"Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff1e99d4-9d74-11e7-a60a-c140f4de34ff","identifier":"ff1e99d4-9d74-11e7-a60a-c140f4de34ff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.G.1","fullStatement":"Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1e82a6ee-9d75-11e7-99e0-759d7b907ede","identifier":"1e82a6ee-9d75-11e7-99e0-759d7b907ede","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.G.2","fullStatement":"Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.  *(Students do not need to learn formal names such as \u201cright rectangular prism.\u201d)  This is important for the future development of spatial relations which later connects to developing understanding of area, volume, and fractions.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/26ef39b4-9d75-11e7-954a-4cea15b7662b","identifier":"26ef39b4-9d75-11e7-954a-4cea15b7662b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.G.3","fullStatement":"Partition circles and rectangles into two and four equal shares, describe the shares using the words *halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of*.  Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4b1ee56e-9d75-11e7-bf09-7dc7cbab37ca","identifier":"4b1ee56e-9d75-11e7-bf09-7dc7cbab37ca","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.OA.1","fullStatement":"Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.  Problems include contexts that involve adding to, taking from, putting together/taking apart (part/part/whole) and comparing with unknowns in all positions.  *(More details can be found in the Mathematics Glossary, Table 1.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/75d66e30-9d75-11e7-accf-268558d66467","identifier":"75d66e30-9d75-11e7-accf-268558d66467","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.OA.3","fullStatement":"Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7ecfa614-9d75-11e7-9223-e088f4e8028f","identifier":"7ecfa614-9d75-11e7-9223-e088f4e8028f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.OA.4","fullStatement":"Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8f65cf8a-9d75-11e7-a43e-16336e81f47b","identifier":"8f65cf8a-9d75-11e7-a43e-16336e81f47b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.1","fullStatement":"Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ca4b8fc2-9d75-11e7-a711-31764381ce72","identifier":"ca4b8fc2-9d75-11e7-a711-31764381ce72","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.2","fullStatement":"Count within 1000; skip-count by 5s, 10s, and 100s.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/db913d7c-9d75-11e7-b6d1-6fa2c0b178c8","identifier":"db913d7c-9d75-11e7-b6d1-6fa2c0b178c8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.3","fullStatement":"Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eb0aab8a-9d75-11e7-81d7-bf864aa7b39a","identifier":"eb0aab8a-9d75-11e7-81d7-bf864aa7b39a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.4","fullStatement":"Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/029c233c-9d76-11e7-b5b5-3c80f975bf0c","identifier":"029c233c-9d76-11e7-b5b5-3c80f975bf0c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.5","fullStatement":"Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9e5521f2-9d76-11e7-a8ba-cb61cdeef6d2","identifier":"9e5521f2-9d76-11e7-a8ba-cb61cdeef6d2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.7","fullStatement":"Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cf11c96c-9d76-11e7-b866-4c022f252875","identifier":"cf11c96c-9d76-11e7-b866-4c022f252875","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.9","fullStatement":"Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e37eacb2-9d76-11e7-9038-857d6481236c","identifier":"e37eacb2-9d76-11e7-9038-857d6481236c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.MD.10","fullStatement":"Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.  *(See Mathematics Glossary, Table 1 for examples of  problems.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/17905280-9d77-11e7-aac7-65d93e5e185d","identifier":"17905280-9d77-11e7-aac7-65d93e5e185d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.G.1","fullStatement":"Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.  Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. *(Sizes are compared directly or visually, not compared by measuring.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2044f520-9d77-11e7-b646-020d649e2277","identifier":"2044f520-9d77-11e7-b646-020d649e2277","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.G.2","fullStatement":"Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2b7ac6b8-9d77-11e7-9cc6-492d41873519","identifier":"2b7ac6b8-9d77-11e7-9cc6-492d41873519","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.G.3","fullStatement":"Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words *halves, thirds, half of, a third of*, etc., and describe the whole as two halves, three thirds, four fourths.  Recognize that equal shares of identical wholes need not have the same shape.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/52302a78-9d77-11e7-a9b9-bc85102c73cc","identifier":"52302a78-9d77-11e7-a9b9-bc85102c73cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.1","fullStatement":"Interpret products of whole numbers, e.g., interpret 5 \u00d7 7 as the total number of objects in 5 groups of 7 objects each. *For example, describe a context in which a total number of objects can be expressed as 5 \u00d7 7.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/29a11328-9d78-11e7-885a-871584fb9874","identifier":"29a11328-9d78-11e7-885a-871584fb9874","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.5","fullStatement":"Apply properties of operations as strategies to multiply and divide. *(Students need not use formal terms for these properties.)* *Examples: If 6 \u00d7 4 = 24 is known, then 4 \u00d7 6 = 24 is also known. (Commutative property of multiplication.) 3 \u00d7 5 \u00d7 2 can be found by 3 \u00d7 5 = 15, then 15 \u00d7 2 = 30, or by 5 \u00d7 2 = 10, then 3 \u00d7 10 = 30. (Associative property of multiplication.) Knowing that 8 \u00d7 5 = 40 and 8 \u00d7 2 = 16, one can find 8 \u00d7 7 as 8 \u00d7 (5 + 2) = (8 \u00d7 5) + (8 \u00d7 2) = 40 + 16 = 56. (Distributive property.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4231b1b8-9d78-11e7-ae3d-8098dc27684e","identifier":"4231b1b8-9d78-11e7-ae3d-8098dc27684e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.7","fullStatement":"Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 \u00d7 5 = 40, one knows 40 \u00f7 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ba6ae7c-9d78-11e7-9141-abc139a1d475","identifier":"6ba6ae7c-9d78-11e7-9141-abc139a1d475","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.8","fullStatement":"Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.\r\n\r\n*This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order where there are no parentheses to specify a particular order (Order of Operations).*\r\n\r\n*See Mathematics Glossary, Table 2.*","notes":"This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order where there are no parentheses to specify a particular order (Order of Operations).\r\n\r\nSee Mathematics Glossary, Table 2.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8d38a1e4-9d78-11e7-b550-33bfece170d9","identifier":"8d38a1e4-9d78-11e7-b550-33bfece170d9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.OA.9","fullStatement":"Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.  *For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.*  (*See Mathematics Glossary, Table 3.*)","notes":"See Mathematics Glossary, Table 3.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b90a45e8-9d78-11e7-bb3b-969e7bf167b8","identifier":"b90a45e8-9d78-11e7-bb3b-969e7bf167b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NBT.2","fullStatement":"Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e66c4dba-9d78-11e7-93f8-8028a68ac90d","identifier":"e66c4dba-9d78-11e7-93f8-8028a68ac90d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.1","fullStatement":"Understand a fraction  $\\frac{1}{b}$  as the quantity formed by 1 part when a whole is partitioned into <i>**b**</i> equal parts (unit fraction); understand a fraction  $\\frac{a}{b}$  as the quantity formed by <i>*a*</i> parts of size $\\frac{1}{b}$.  <i>For example, $\\frac{3}{4}$ means there are three $\\frac{1}{4}$  parts, so  $\\frac{3}{4}$  =  $\\frac{1}{4}$  +  $\\frac{1}{4}$  +  $\\frac{1}{4}$.</i>","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/07c0bf1e-9d79-11e7-9161-cee7956c05b6","identifier":"07c0bf1e-9d79-11e7-9161-cee7956c05b6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.2","fullStatement":"Understand a fraction as a number on the number line; represent fractions on a number line diagram.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/17bce30c-9d79-11e7-ba73-fb0124d0eec9","identifier":"17bce30c-9d79-11e7-ba73-fb0124d0eec9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.3","fullStatement":"Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/29b85172-9d79-11e7-b353-939eb861dcfa","identifier":"29b85172-9d79-11e7-b353-939eb861dcfa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.3d","fullStatement":"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or < , and justify the conclusions, e.g., by using a visual fraction model.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3fc9289c-9d79-11e7-8b6e-e579a8459bd4","identifier":"3fc9289c-9d79-11e7-8b6e-e579a8459bd4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.1","fullStatement":"Tell and write time to the nearest minute and measure elapsed time intervals in minutes.  Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, drawing a pictorial representation on a clock face, etc.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/803dc0a4-9d79-11e7-b7af-79e2d55b9808","identifier":"803dc0a4-9d79-11e7-b7af-79e2d55b9808","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.2","fullStatement":"Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).  *(Excludes compound units such as cm\u00b3 and finding the geometric volume of a container.)*   Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.  *(Excludes multiplicative comparison problems (problems involving notions of \u201ctimes as much\u201d; see Mathematics Glossary, Table 2).*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8cae6eb0-9d79-11e7-b7d2-0fdc2d9699c5","identifier":"8cae6eb0-9d79-11e7-b7d2-0fdc2d9699c5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.3","fullStatement":"Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step \u201chow many more\u201d and \u201chow many less\u201d problems using information presented in scaled bar graphs. *For example, draw a bar graph in which each square in the bar graph might represent 5 pets.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/979c60ac-9d79-11e7-af7d-c0c29091fb0f","identifier":"979c60ac-9d79-11e7-af7d-c0c29091fb0f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.4","fullStatement":"Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units \u2014 whole numbers, halves, or quarters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a767af64-9d79-11e7-83cc-5672b8113422","identifier":"a767af64-9d79-11e7-83cc-5672b8113422","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.5","fullStatement":"Recognize area as an attribute of plane figures and understand concepts of area measurement.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc0a7bbe-9d79-11e7-8609-5792a3401339","identifier":"fc0a7bbe-9d79-11e7-8609-5792a3401339","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.6","fullStatement":"Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0a3efb92-9d7a-11e7-b6b9-bc6ed8b0c9e3","identifier":"0a3efb92-9d7a-11e7-b6b9-bc6ed8b0c9e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.7","fullStatement":"Relate area to the operations of multiplication and addition.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1392c368-9d7a-11e7-bb3c-850425420a23","identifier":"1392c368-9d7a-11e7-bb3c-850425420a23","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.7a","fullStatement":"Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/24db0fc2-9d7a-11e7-9dfa-1dace65899e4","identifier":"24db0fc2-9d7a-11e7-9dfa-1dace65899e4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.7b","fullStatement":"Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/30df991e-9d7a-11e7-a28a-241af9815617","identifier":"30df991e-9d7a-11e7-a28a-241af9815617","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.7c","fullStatement":"Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a \u00d7 b and a \u00d7 c.  Use area models to represent the distributive property in mathematical reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/415ad0f6-9d7a-11e7-b9ec-428f9c3a40d0","identifier":"415ad0f6-9d7a-11e7-b9ec-428f9c3a40d0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.8","fullStatement":"Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/51f59b12-9d7a-11e7-b2ee-63abd1343831","identifier":"51f59b12-9d7a-11e7-b2ee-63abd1343831","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.G.1","fullStatement":"Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).  Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.","notes":"In Georgia resources and assessments, trapezoids are defined using the inclusive definition:  At least one pair of parallel sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7577dd3e-9d7a-11e7-8afc-3bf067515729","identifier":"7577dd3e-9d7a-11e7-8afc-3bf067515729","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.1","fullStatement":"Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a2d70ca0-9d7a-11e7-9e2c-4e5761e55689","identifier":"a2d70ca0-9d7a-11e7-9e2c-4e5761e55689","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.2","fullStatement":"Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (*See Mathematics Glossary, Table 2.*)","notes":"See Mathematics Glossary, Table 2.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b248e2d0-9d7a-11e7-8f4e-9dc6197b922e","identifier":"b248e2d0-9d7a-11e7-8f4e-9dc6197b922e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.3","fullStatement":"Solve multistep word problems with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c42397b6-9d7a-11e7-a703-b2cc0d308e1c","identifier":"c42397b6-9d7a-11e7-a703-b2cc0d308e1c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.4","fullStatement":"Find all factor pairs for a whole number in the range 1\u2013100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1\u2013100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1\u2013100 is prime or composite.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4af2f03e-9d7b-11e7-8d7f-9548bbf49422","identifier":"4af2f03e-9d7b-11e7-8d7f-9548bbf49422","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.5","fullStatement":"Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Explain informally why the pattern will continue to develop in this way. *For example, given the rule \u201cAdd 3\u201d and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/804be6b4-9d7b-11e7-b2e4-5150ddaf1dbe","identifier":"804be6b4-9d7b-11e7-b2e4-5150ddaf1dbe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NBT.6","fullStatement":"Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e924c8fe-9d7b-11e7-b1d4-61c1b18ff56a","identifier":"e924c8fe-9d7b-11e7-b1d4-61c1b18ff56a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.3b","fullStatement":"Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. *Examples: $\\frac{3}{8}$ = $\\frac{1}{8}$ + $\\frac{1}{8}$ + $\\frac{1}{8}$ ; $\\frac{3}{8}$ = $\\frac{1}{8}$ + $\\frac{2}{8}$ ;  2$\\frac{1}{8}$ = 1 + 1 + $\\frac{1}{8}$ = $\\frac{8}{8}$ + $\\frac{8}{8}$ + $\\frac{1}{8}$.*","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/08d1cca6-9d7c-11e7-92a7-392595d24d8f","identifier":"08d1cca6-9d7c-11e7-92a7-392595d24d8f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.3d","fullStatement":"Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.","notes":"Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/20c85244-9d7c-11e7-a3fa-9c5e64b4db61","identifier":"20c85244-9d7c-11e7-a3fa-9c5e64b4db61","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.4","fullStatement":"Apply and extend previous understandings of multiplication to multiply a fraction by a whole number e.g., by using a visual such as a number line or area model.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2ee9ca06-9d7c-11e7-9b12-6fcfe38c5372","identifier":"2ee9ca06-9d7c-11e7-9b12-6fcfe38c5372","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.4a","fullStatement":"Understand a fraction a/b as a multiple of $\\frac{1}{b}$. *For example, use a visual fraction model to represent $\\frac{5}{4}$ as the product 5 \u00d7 ($\\frac{1}{4}$), recording the conclusion by the equation $\\frac{5}{4}$ = 5 \u00d7 ($\\frac{1}{4}$)*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3900111c-9d7c-11e7-be62-6085250858f3","identifier":"3900111c-9d7c-11e7-be62-6085250858f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.4b","fullStatement":"Understand a multiple of $\\frac{a}{b}$ as a multiple of $\\frac{1}{b}$, and use this understanding to multiply a fraction by a whole number. *For example, use a visual fraction model to express 3 \u00d7 ($\\frac{2}{5}$) as 6 \u00d7 ($\\frac{1}{5}$), recognizing this product as $\\frac{6}{5}$. (In general, n \u00d7 ($\\frac{a}{b}$) = $\\frac{(n \\times a)}{b}$.)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/45769902-9d7c-11e7-8ae4-a7004a37371b","identifier":"45769902-9d7c-11e7-8ae4-a7004a37371b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.NF.4c","fullStatement":"Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. *For example, if each person at a party will eat $\\frac{3}{8}$ of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a2fc9374-9d7c-11e7-b373-040522c8814c","identifier":"a2fc9374-9d7c-11e7-b373-040522c8814c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.1","fullStatement":"Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da664396-9d7c-11e7-aa9c-be75e3f78df8","identifier":"da664396-9d7c-11e7-aa9c-be75e3f78df8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.2","fullStatement":"Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.  Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e5f7117c-9d7c-11e7-955c-e8ec3307b349","identifier":"e5f7117c-9d7c-11e7-955c-e8ec3307b349","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.3","fullStatement":"Apply the area and perimeter formulas for rectangles in real world and mathematical problems. *For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/05afbd5c-9d7d-11e7-b0db-0baf5f8a18e6","identifier":"05afbd5c-9d7d-11e7-b0db-0baf5f8a18e6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.4","fullStatement":"Make a line plot to display a data set of measurements in fractions of a unit ($\\frac{1}{2}$, $\\frac{1}{4}$, $\\frac{1}{8}$). Solve problems involving addition and subtraction of fractions with common denominators by using information presented in line plots. *For example, from a line plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3310e104-9d7d-11e7-8ae8-0378fde7ac54","identifier":"3310e104-9d7d-11e7-8ae8-0378fde7ac54","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.6","fullStatement":"Measure angles in whole-number degrees using a protractor.   Sketch angles of specified measure.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3f4332ce-9d7d-11e7-939a-9e02e32817b3","identifier":"3f4332ce-9d7d-11e7-939a-9e02e32817b3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.7","fullStatement":"Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol or letter for the unknown angle measure.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/47b2f64c-9d7d-11e7-b2f3-31c9530a29a6","identifier":"47b2f64c-9d7d-11e7-b2f3-31c9530a29a6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.8","fullStatement":"Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dbfc58c-9d7d-11e7-bf12-ae50e3ca1c7d","identifier":"5dbfc58c-9d7d-11e7-bf12-ae50e3ca1c7d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.G.3","fullStatement":"Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7156395a-9d7d-11e7-8ad1-54f098aa83e9","identifier":"7156395a-9d7d-11e7-8ad1-54f098aa83e9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.OA.1","fullStatement":"Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/79d90c06-9d7d-11e7-ae2d-07883bf1a0ee","identifier":"79d90c06-9d7d-11e7-ae2d-07883bf1a0ee","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.OA.2","fullStatement":"Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation \u201cadd 8 and 7, then multiply by 2\u201d as 2 \u00d7 (8 + 7). Recognize that 3 \u00d7 (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e00ddf92-9d7d-11e7-ae31-9fdcc8db2303","identifier":"e00ddf92-9d7d-11e7-ae31-9fdcc8db2303","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.1","fullStatement":"Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ebfef566-9d7d-11e7-a891-b0c3d161c2bd","identifier":"ebfef566-9d7d-11e7-a891-b0c3d161c2bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.2","fullStatement":"Solve word problems involving addition and subtraction of fractions, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + \u00bd = 3/7, by observing that 3/7 < \u00bd.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/08bff524-9d7e-11e7-a11a-4990e2106051","identifier":"08bff524-9d7e-11e7-a11a-4990e2106051","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.3","fullStatement":"Interpret a fraction as division of the numerator by the denominator ($\\frac{a}{b}$ = a \u00f7 b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. *Example: $\\frac{3}{5}$ can be interpreted as \u201c3 divided by 5 and as 3 shared by 5\u201d.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/19eb7e90-9d7e-11e7-b806-911ac5133453","identifier":"19eb7e90-9d7e-11e7-b806-911ac5133453","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.4","fullStatement":"Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3adb6016-9d7e-11e7-87cc-cbbf6a9d7763","identifier":"3adb6016-9d7e-11e7-87cc-cbbf6a9d7763","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.4a","fullStatement":"Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction.  *Examples: $\\frac{a}{b}$ x q as $\\frac{a}{b}$ x $\\frac{q}{1}$  and $\\frac{a}{b}$ x $\\frac{c}{d}$ = $\\frac{ac}{bd}$*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4512d6cc-9d7e-11e7-b5b9-a4191bd92d24","identifier":"4512d6cc-9d7e-11e7-b5b9-a4191bd92d24","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.4b","fullStatement":"Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5634b2f4-9d7e-11e7-91a1-1b44345394bd","identifier":"5634b2f4-9d7e-11e7-91a1-1b44345394bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.5","fullStatement":"Interpret multiplication as scaling (resizing), by:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7a5e453c-9d7e-11e7-806a-2e322e11b709","identifier":"7a5e453c-9d7e-11e7-806a-2e322e11b709","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.6","fullStatement":"Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/929f5d2a-9d7e-11e7-8198-41afacd10c4c","identifier":"929f5d2a-9d7e-11e7-8198-41afacd10c4c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.7","fullStatement":"Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. *(Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)*","notes":"Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a0b6592c-9d7e-11e7-9001-98018d2b9ac1","identifier":"a0b6592c-9d7e-11e7-9001-98018d2b9ac1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.7a","fullStatement":"Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. <i>For example, create a story context for ($\\frac{1}{3}$) \u00f7 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that ($\\frac{1}{3}$) \u00f7 4 = $\\frac{1}{12}$ because ($\\frac{1}{12}$) \u00d7 4 = $\\frac{1}{3}$.<i/>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/adb72700-9d7e-11e7-a430-f46fc442494d","identifier":"adb72700-9d7e-11e7-a430-f46fc442494d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.7b","fullStatement":"Interpret division of a whole number by a unit fraction, and compute such quotients. <i>For example, create a story context for 4 \u00f7 ($\\frac{1}{5}$), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 \u00f7 ($\\frac{1}{5}$) = 20 because 20 \u00d7 ($\\frac{1}{5}$) = 4.</i>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b69b7a06-9d7e-11e7-b96d-224d5fd6623d","identifier":"b69b7a06-9d7e-11e7-b96d-224d5fd6623d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.7c","fullStatement":"Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual <i>fraction</i> models and equations to represent the problem. <i>For example, how much chocolate will each person get if 3 people share $\\frac{1}{2}$ lb of chocolate equally? How many $\\frac{1}{3}$-cup servings are in 2 cups of raisins?</i>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f2a92a5c-9d7e-11e7-ab64-84265e6881d5","identifier":"f2a92a5c-9d7e-11e7-ab64-84265e6881d5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.3","fullStatement":"Recognize volume as an attribute of solid figures and understand concepts of volume measurement.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/33423b94-9d7f-11e7-b54d-56f3e73b05cc","identifier":"33423b94-9d7f-11e7-b54d-56f3e73b05cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.G.1","fullStatement":"Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., *x*-axis and *x*-coordinate, *y*-axis and *y*-coordinate).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3c7e9fd6-9d7f-11e7-b7d4-373f6e8f061b","identifier":"3c7e9fd6-9d7f-11e7-b7d4-373f6e8f061b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.G.2","fullStatement":"Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/650f6ee2-9e2b-11e7-a114-5ec52accc1c1","identifier":"650f6ee2-9e2b-11e7-a114-5ec52accc1c1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.2a","fullStatement":"Represent a fraction $\\frac{1}{b}$ on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts.  Recognize that each part has size  $\\frac{1}{b}$.  Recognize that a unit fraction $\\frac{1}{b}$  is located $\\frac{1}{b}$ whole unit from 0 on the number line.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e6f0fa52-9e2b-11e7-b162-704f8259080a","identifier":"e6f0fa52-9e2b-11e7-b162-704f8259080a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.2b","fullStatement":"Represent a non-unit fraction $\\frac{a}{b}$  on a number line diagram by marking off  <i>*a*</i> lengths of  $\\frac{1}{b}$  (unit fractions) from 0.  Recognize that the resulting interval has size  $\\frac{a}{b}$   and that its endpoint locates the non-unit fraction  $\\frac{a}{b}$ on the number line.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7b345e16-9e2c-11e7-89c1-a43464efafd6","identifier":"7b345e16-9e2c-11e7-89c1-a43464efafd6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.3a","fullStatement":"Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ac5eeaba-9e2c-11e7-985b-52b26cff0496","identifier":"ac5eeaba-9e2c-11e7-985b-52b26cff0496","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.3b","fullStatement":"Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8, e.g., $\\frac{1}{2}$   =  $\\frac{2}{4}$ ,   $\\frac{4}{6}$  =  $\\frac{2}{3}$.  Explain why the fractions are equivalent, e.g., by using a visual fraction model.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eba1bce8-9e2c-11e7-8186-f892ffe10685","identifier":"eba1bce8-9e2c-11e7-8186-f892ffe10685","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.NF.3c","fullStatement":"Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.  *Examples:  Express 3 in the form 3 = $\\frac{6}{2}$ (3 wholes is equal to six halves); recognize that  $\\frac{3}{1}$ = 3; locate  $\\frac{4}{4}$  and 1 at the same point of a number line diagram*.","notes":"Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0f4f2e5e-9f0a-11e7-84ba-21ff9d678ba5","identifier":"0f4f2e5e-9f0a-11e7-84ba-21ff9d678ba5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"The Real Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/25d79198-9f0a-11e7-bec5-3466eb3805bc","identifier":"25d79198-9f0a-11e7-bec5-3466eb3805bc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b177852-9f0a-11e7-87fb-e83c545e9ede","identifier":"3b177852-9f0a-11e7-87fb-e83c545e9ede","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Seeing Structure in Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5f250f16-9f0a-11e7-b48e-97e8aa48680a","identifier":"5f250f16-9f0a-11e7-b48e-97e8aa48680a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Arithmetic with Polynomials and Rational Expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6d37bbb2-9f0a-11e7-b944-4ddcf1cf1eb8","identifier":"6d37bbb2-9f0a-11e7-b944-4ddcf1cf1eb8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Creating Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/83cfdae4-9f0a-11e7-8216-32d5fbe5d889","identifier":"83cfdae4-9f0a-11e7-8216-32d5fbe5d889","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Reasoning with Equations and Inequalities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c521ce4-9f0a-11e7-9476-b50adb67255a","identifier":"9c521ce4-9f0a-11e7-9476-b50adb67255a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a8c6056c-9f0a-11e7-8c1d-d9a98f466ed4","identifier":"a8c6056c-9f0a-11e7-8c1d-d9a98f466ed4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Building Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e2b33cc6-9f0b-11e7-af92-1ad976a9ac3d","identifier":"e2b33cc6-9f0b-11e7-af92-1ad976a9ac3d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Linear, Quadratic, and Exponential Models","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fec25ffa-9f0b-11e7-8232-88c34adc0102","identifier":"fec25ffa-9f0b-11e7-8232-88c34adc0102","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Categorical and Quantitative Data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3ea598d4-9f12-11e7-87b0-952ef8e2a426","identifier":"3ea598d4-9f12-11e7-87b0-952ef8e2a426","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use properties of rational and irrational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/70b8a65e-9f12-11e7-bac1-7f1b090d9195","identifier":"70b8a65e-9f12-11e7-bac1-7f1b090d9195","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Reason quantitatively and use units to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/95f402e2-9f12-11e7-afe1-1b9ac9079155","identifier":"95f402e2-9f12-11e7-afe1-1b9ac9079155","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret the structure of expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/be64fbb4-9f12-11e7-a000-b2e08971ce15","identifier":"be64fbb4-9f12-11e7-a000-b2e08971ce15","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Write expressions in equivalent forms to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eb372344-9fe7-11e7-91dd-3acb407267ad","identifier":"eb372344-9fe7-11e7-91dd-3acb407267ad","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.3","fullStatement":"Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a288cda4-9fe8-11e7-9751-2414843273ae","identifier":"a288cda4-9fe8-11e7-9751-2414843273ae","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1","fullStatement":"Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5570b4b8-9fe9-11e7-b39d-c606e5393d33","identifier":"5570b4b8-9fe9-11e7-b39d-c606e5393d33","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.2","fullStatement":"Define appropriate quantities for the purpose of descriptive modeling. Given a situation, context, or problem, students will determine, identify, and use appropriate quantities for representing the situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/70e2d82a-9fe9-11e7-acb9-a6c9bc9a59a6","identifier":"70e2d82a-9fe9-11e7-acb9-a6c9bc9a59a6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.3","fullStatement":"Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. *For example, money situations are generally reported to the nearest cent (hundredth).  Also, an answers\u2019 precision is limited to the precision of the data given.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bb761582-9fe9-11e7-834e-e60853ae2fb9","identifier":"bb761582-9fe9-11e7-834e-e60853ae2fb9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1","fullStatement":"Interpret expressions that represent a quantity in terms of its context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d4ac143e-9fe9-11e7-95dd-a1063590f785","identifier":"d4ac143e-9fe9-11e7-95dd-a1063590f785","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1a","fullStatement":"Interpret parts of an expression, such as terms, factors, and coefficients, in context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f21aeda6-9fe9-11e7-85b7-a864a95e8e5c","identifier":"f21aeda6-9fe9-11e7-85b7-a864a95e8e5c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1b","fullStatement":"Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0eb29a40-9fea-11e7-8a00-347de45fd4e0","identifier":"0eb29a40-9fea-11e7-8a00-347de45fd4e0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.2","fullStatement":"Use the structure of an expression to rewrite it in different equivalent forms. *For example, see $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2) (x^2 + y^2)$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2b9a24e8-9fea-11e7-8dfc-0ae1f8979f3b","identifier":"2b9a24e8-9fea-11e7-8dfc-0ae1f8979f3b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3","fullStatement":"Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5038b9cc-9fea-11e7-9881-4ee2f36b7651","identifier":"5038b9cc-9fea-11e7-9881-4ee2f36b7651","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3a","fullStatement":"Factor any quadratic expression to reveal the zeros of the function defined by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6787fd22-9fea-11e7-a5dc-af263e299a3a","identifier":"6787fd22-9fea-11e7-a5dc-af263e299a3a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.3b","fullStatement":"Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/82afdd68-9fea-11e7-b9a0-b6fae3e5762e","identifier":"82afdd68-9fea-11e7-b9a0-b6fae3e5762e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Perform arithmetic operations on polynomials.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c1f9752-9fea-11e7-96c3-230f8af849e6","identifier":"9c1f9752-9fea-11e7-96c3-230f8af849e6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d25e2f56-a1fa-11e7-8d7b-5ddbf5f6a866","identifier":"d25e2f56-a1fa-11e7-8d7b-5ddbf5f6a866","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Create equations that describe numbers or relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/03a48c22-a1fb-11e7-801b-bea2cddcf849","identifier":"03a48c22-a1fb-11e7-801b-bea2cddcf849","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, ~~simple rational,~~ and exponential functions (integer inputs only).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/23938614-a1fb-11e7-ac37-908de72b07ad","identifier":"23938614-a1fb-11e7-ac37-908de72b07ad","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r/n)^{(nt)}$ has multiple variables.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/376ad796-a1fb-11e7-9bf7-22ce43ef0c95","identifier":"376ad796-a1fb-11e7-9bf7-22ce43ef0c95","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3dd1fd38-a1fd-11e7-b4d0-9f946306d995","identifier":"3dd1fd38-a1fd-11e7-b4d0-9f946306d995","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.4","fullStatement":"Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.  *Examples: Rearrange Ohm\u2019s law V = IR to highlight resistance R; Rearrange area of a circle formula A =  \u03c0 $r^2$ to highlight the radius r.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/970bc21c-a1fd-11e7-b6c3-4c16d17c213d","identifier":"970bc21c-a1fd-11e7-b6c3-4c16d17c213d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand solving equations as a process of reasoning and explain the reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b2444e8c-a1fd-11e7-be76-7e65fcbe158f","identifier":"b2444e8c-a1fd-11e7-be76-7e65fcbe158f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.1","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c44538bc-a1fd-11e7-b421-f5b57a6fad25","identifier":"c44538bc-a1fd-11e7-b421-f5b57a6fad25","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve equations and inequalities in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e4f87e34-a1fd-11e7-82db-24034c3083f5","identifier":"e4f87e34-a1fd-11e7-82db-24034c3083f5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.3","fullStatement":"Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. *For example, given ax + 3 = 7, solve for x.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd822a7c-a1fd-11e7-be4a-eb82b5eb3aaf","identifier":"fd822a7c-a1fd-11e7-be4a-eb82b5eb3aaf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4","fullStatement":"Solve quadratic equations in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/981f4f9c-a1fe-11e7-83b3-aff5e59cea61","identifier":"981f4f9c-a1fe-11e7-83b3-aff5e59cea61","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4a","fullStatement":"Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x \u2013 p)\u00b2 = q that has the same solutions. Derive the quadratic formula from ax\u00b2 + bx + c = 0.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d14c20ec-a1fe-11e7-86ae-f1a8b690a73e","identifier":"d14c20ec-a1fe-11e7-86ae-f1a8b690a73e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4b","fullStatement":"Solve quadratic equations by inspection (e.g., for x\u00b2 = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0a284774-a1ff-11e7-b3fa-f82273acc22c","identifier":"0a284774-a1ff-11e7-b3fa-f82273acc22c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve systems of equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/26141c9c-a1ff-11e7-b00f-9fa1a2a3e9ee","identifier":"26141c9c-a1ff-11e7-b00f-9fa1a2a3e9ee","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.5","fullStatement":"Show and explain why the elimination method works to solve a system of two-variable equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/41a971fa-a1ff-11e7-907e-2a860cce7af7","identifier":"41a971fa-a1ff-11e7-907e-2a860cce7af7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.6","fullStatement":"Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/639fce26-a1ff-11e7-af1c-38c80448c04c","identifier":"639fce26-a1ff-11e7-af1c-38c80448c04c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Represent and solve equations and inequalities graphically.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/81751cc6-a1ff-11e7-8d0d-a8d8db590d1e","identifier":"81751cc6-a1ff-11e7-8d0d-a8d8db590d1e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.10","fullStatement":"Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9fe0714c-a1ff-11e7-9bbf-e5b5b185f9cd","identifier":"9fe0714c-a1ff-11e7-9bbf-e5b5b185f9cd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.11","fullStatement":"Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b69bc832-a1ff-11e7-b325-c156d79cf3b9","identifier":"b69bc832-a1ff-11e7-b325-c156d79cf3b9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.12","fullStatement":"Graph the solution set to a linear inequality in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d1c951d8-a1ff-11e7-904b-99707e94068f","identifier":"d1c951d8-a1ff-11e7-904b-99707e94068f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the concept of a function and use function notation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f0f8ebc2-a1ff-11e7-97b0-eb7af692da02","identifier":"f0f8ebc2-a1ff-11e7-97b0-eb7af692da02","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.1","fullStatement":"Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range).  Graphically, the graph is y = f(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/048023ea-a200-11e7-8a66-3b669ef08fa1","identifier":"048023ea-a200-11e7-8a66-3b669ef08fa1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.2","fullStatement":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/02c7ff54-a206-11e7-bb0f-1ced7508f0c9","identifier":"02c7ff54-a206-11e7-bb0f-1ced7508f0c9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.3","fullStatement":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence $a_1$=7, $a_n=a_{(n-1)}$ +2; the sequence $s_n$ = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/26115bb4-a20a-11e7-a2ad-ae1b4bff91d9","identifier":"26115bb4-a20a-11e7-a2ad-ae1b4bff91d9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret functions that arise in applications in terms of the context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/851fe5f8-a20a-11e7-b75a-26e1c2510104","identifier":"851fe5f8-a20a-11e7-b75a-26e1c2510104","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.4","fullStatement":"Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; ~~and periodicity.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9f18667e-a20a-11e7-aea7-f19ca308d294","identifier":"9f18667e-a20a-11e7-aea7-f19ca308d294","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.5","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1e4054c-a20a-11e7-b6ed-fdef7c590b21","identifier":"b1e4054c-a20a-11e7-b6ed-fdef7c590b21","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.6","fullStatement":"Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d3e23dda-a20a-11e7-b2ea-b9ce4ed9fd99","identifier":"d3e23dda-a20a-11e7-b2ea-b9ce4ed9fd99","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Analyze functions using different representations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/00ade2c4-a20b-11e7-87ec-0b48a00aa91c","identifier":"00ade2c4-a20b-11e7-87ec-0b48a00aa91c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7","fullStatement":"Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/25d0078a-a20b-11e7-a507-54aff85f6624","identifier":"25d0078a-a20b-11e7-a507-54aff85f6624","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7a","fullStatement":"Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7e2d47b2-a20b-11e7-a967-affe3ba4ca59","identifier":"7e2d47b2-a20b-11e7-a967-affe3ba4ca59","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7e","fullStatement":"Graph exponential ~~and logarithmic~~ functions, showing intercepts and end behavior, ~~and trigonometric functions, showing period, midline, and amplitude.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9abd40da-a20b-11e7-abde-ce7f1d539ef5","identifier":"9abd40da-a20b-11e7-abde-ce7f1d539ef5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8","fullStatement":"Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b7885524-a20b-11e7-90f1-4ef8485da350","identifier":"b7885524-a20b-11e7-90f1-4ef8485da350","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8a","fullStatement":"Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. *For example, compare and contrast quadratic functions in standard, vertex, and intercept forms.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d8883546-a20b-11e7-8def-d70d05ce1649","identifier":"d8883546-a20b-11e7-8def-d70d05ce1649","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.9","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f3c8d612-a20b-11e7-81a0-6afd43dea894","identifier":"f3c8d612-a20b-11e7-81a0-6afd43dea894","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build a function that models a relationship between two quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ef23b22-a20c-11e7-8543-fdc637b55d6e","identifier":"0ef23b22-a20c-11e7-8543-fdc637b55d6e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1","fullStatement":"Write a function that describes a relationship between two quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f1bc30e8-a20c-11e7-8f0d-f5d0dad17dde","identifier":"f1bc30e8-a20c-11e7-8f0d-f5d0dad17dde","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1a","fullStatement":"Determine an explicit expression and the recursive process (steps for calculation) from context. *For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression \u201c2x+15\u201d can be described recursively (either in writing or verbally) as \u201cto find out how much money Jimmy will have tomorrow, you add $2 to his total today.\u201d* $J_n$ = $J_{n-1}$ + 2, $J_0$ = 15","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/07ab0ba4-a20d-11e7-90a2-593fea3fe79b","identifier":"07ab0ba4-a20d-11e7-90a2-593fea3fe79b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.2","fullStatement":"Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/22d5a45c-a20d-11e7-bb6e-ddb81f32ed65","identifier":"22d5a45c-a20d-11e7-bb6e-ddb81f32ed65","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build new functions from existing functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4413c31a-a20d-11e7-93f0-0d9328f4b16f","identifier":"4413c31a-a20d-11e7-93f0-0d9328f4b16f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.3","fullStatement":"Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.  Experiment with cases and illustrate an explanation of the effects on the graph using technology.  Include recognizing even and odd functions from their graphs and algebraic expressions for them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6f05beca-a20d-11e7-a66f-d76cb40a2a8f","identifier":"6f05beca-a20d-11e7-a66f-d76cb40a2a8f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Construct and compare linear, quadratic, and exponential models and solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/80e27ad4-a20d-11e7-a6dc-12d98e9dac8e","identifier":"80e27ad4-a20d-11e7-a6dc-12d98e9dac8e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1","fullStatement":"Distinguish between situations that can be modeled with linear functions and with exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1ba5376-a20d-11e7-b924-1534f0ade996","identifier":"a1ba5376-a20d-11e7-b924-1534f0ade996","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1a","fullStatement":"Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/301129f6-a20e-11e7-8922-7f2bf39c7716","identifier":"301129f6-a20e-11e7-8922-7f2bf39c7716","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1b","fullStatement":"Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/42ada2b0-a20e-11e7-b7e9-c2eb5416f5cc","identifier":"42ada2b0-a20e-11e7-b7e9-c2eb5416f5cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1c","fullStatement":"Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dc5ad86-a20e-11e7-8dae-2e524b6f532d","identifier":"5dc5ad86-a20e-11e7-8dae-2e524b6f532d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.2","fullStatement":"Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8deabe7a-a20e-11e7-b2b0-9aeffdfe3cfa","identifier":"8deabe7a-a20e-11e7-b2b0-9aeffdfe3cfa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.3","fullStatement":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c9d759ca-a20e-11e7-8d11-d0ec38fe7cc6","identifier":"c9d759ca-a20e-11e7-8d11-d0ec38fe7cc6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret expressions for functions in terms of the situation they model","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/053803e8-a20f-11e7-8604-5f8f06131ec0","identifier":"053803e8-a20f-11e7-8604-5f8f06131ec0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.5","fullStatement":"Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a\u2022$d^x$) function in terms of context.  (In the functions above, \u201cm\u201d and \u201cb\u201d are the parameters of the linear function, and \u201ca\u201d and \u201cd\u201d are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/29310808-a20f-11e7-991d-5453ee384fac","identifier":"29310808-a20f-11e7-991d-5453ee384fac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Summarize, represent, and interpret data on a single count or measurement variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b9f425c-a20f-11e7-8c0e-f4b9ec7b78b0","identifier":"3b9f425c-a20f-11e7-8c0e-f4b9ec7b78b0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.1","fullStatement":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/514efe3a-a20f-11e7-9c37-3b9d8dd87333","identifier":"514efe3a-a20f-11e7-9c37-3b9d8dd87333","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.2","fullStatement":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, mean absolute deviation, ~~standard deviation~~) of two or more different data sets.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/64021148-a20f-11e7-9620-069ca74fc29c","identifier":"64021148-a20f-11e7-9620-069ca74fc29c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.3","fullStatement":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8323c440-a20f-11e7-85a7-9d5ac40270e7","identifier":"8323c440-a20f-11e7-85a7-9d5ac40270e7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Summarize, represent, and interpret data on two categorical and quantitative variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9cb09960-a20f-11e7-9f87-ebbb4aa63ba1","identifier":"9cb09960-a20f-11e7-9f87-ebbb4aa63ba1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.5","fullStatement":"Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c958a084-a20f-11e7-9576-6d8cefa02c25","identifier":"c958a084-a20f-11e7-9576-6d8cefa02c25","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.6","fullStatement":"Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e935c198-a20f-11e7-9b8a-d2a8709aa73c","identifier":"e935c198-a20f-11e7-9b8a-d2a8709aa73c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.6a","fullStatement":"Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit.  Use this function to solve problems in context.  Emphasize linear, quadratic and exponential models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/014eb5e6-a210-11e7-ab47-f03c21e93fff","identifier":"014eb5e6-a210-11e7-ab47-f03c21e93fff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.6c","fullStatement":"Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1cf5170e-a210-11e7-b738-56396072f11c","identifier":"1cf5170e-a210-11e7-b738-56396072f11c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret linear models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3334e68e-a210-11e7-809c-65aedb48ed52","identifier":"3334e68e-a210-11e7-809c-65aedb48ed52","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.7","fullStatement":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/52bd9d34-a210-11e7-b5fd-6edea78dd919","identifier":"52bd9d34-a210-11e7-b5fd-6edea78dd919","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.8","fullStatement":"Compute (using technology) and interpret the correlation coefficient \u201cr\u201d of a linear fit.  (For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the \u201cr\u201d value.)  After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using \u201cr\u201d.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/726f6aa4-a210-11e7-9350-3efa62af2198","identifier":"726f6aa4-a210-11e7-9350-3efa62af2198","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.9","fullStatement":"Distinguish between correlation and causation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/32282870-a83f-11e7-a36a-e587f2187fcf","identifier":"32282870-a83f-11e7-a36a-e587f2187fcf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["06"],"humanCodingScheme":"6.NS","fullStatement":"The Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4e446f28-a83f-11e7-8bad-73178941ca95","identifier":"4e446f28-a83f-11e7-8bad-73178941ca95","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["06"],"humanCodingScheme":"6.SP","fullStatement":"Statistics and Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7e93183c-a83f-11e7-8f5b-80da076ee1b7","identifier":"7e93183c-a83f-11e7-8f5b-80da076ee1b7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Apply and extend previous understandings of multiplication and division to divide fractions by fractions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/84d94b58-a83f-11e7-87e1-d6ff579b4991","identifier":"84d94b58-a83f-11e7-87e1-d6ff579b4991","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Compute fluently with multi-digit numbers and find common factors and multiples.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8bc0380a-a83f-11e7-860d-2278ce1c3b6b","identifier":"8bc0380a-a83f-11e7-860d-2278ce1c3b6b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Apply and extend previous understandings of numbers to the system of rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a41e10c0-a83f-11e7-a040-1aed9f30ce86","identifier":"a41e10c0-a83f-11e7-a040-1aed9f30ce86","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Solve real-world and mathematical problems involving area, surface area, and volume.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/abb816e6-a83f-11e7-85b2-99af57bd4b13","identifier":"abb816e6-a83f-11e7-85b2-99af57bd4b13","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Develop understanding of statistical variability.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b07fa20c-a83f-11e7-96b4-9c36a89d650d","identifier":"b07fa20c-a83f-11e7-96b4-9c36a89d650d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["06"],"fullStatement":"Summarize and describe distributions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bee778c4-a83f-11e7-89b2-ee3dbfd4ad8a","identifier":"bee778c4-a83f-11e7-89b2-ee3dbfd4ad8a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.4","fullStatement":"Display numerical data in plots on a number line, including dot plots (line plots), histograms, and box plots.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4806135e-a840-11e7-ae1a-3cd54504cb7a","identifier":"4806135e-a840-11e7-ae1a-3cd54504cb7a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.5","fullStatement":"Summarize numerical data sets in relation to their context, such as by:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/565bfc3e-a840-11e7-b691-671618187e3d","identifier":"565bfc3e-a840-11e7-b691-671618187e3d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.1","fullStatement":"Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. *For example, \u201cHow old am I?\u201d is not a statistical question, but \u201cHow old are the students in my school?\u201d is a statistical question because one anticipates variability in students\u2019 ages.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/628c17f0-a840-11e7-adf1-6bd92e4f9529","identifier":"628c17f0-a840-11e7-adf1-6bd92e4f9529","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.2","fullStatement":"Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6c5ffd64-a840-11e7-a36e-11fb924879e1","identifier":"6c5ffd64-a840-11e7-a36e-11fb924879e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.3","fullStatement":"Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/af4342e4-a840-11e7-b398-e614f077d063","identifier":"af4342e4-a840-11e7-b398-e614f077d063","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.G.1","fullStatement":"Find area of right triangles, other triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c103862e-a840-11e7-8737-ce0e21a78def","identifier":"c103862e-a840-11e7-8737-ce0e21a78def","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.G.2","fullStatement":"Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths (1/2 u), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = (length) x (width) x (height) and V= (area of base) x (height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ca4b665c-a840-11e7-aa50-a9fe0d823001","identifier":"ca4b665c-a840-11e7-aa50-a9fe0d823001","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.G.3","fullStatement":"Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d1c74838-a840-11e7-96bc-067b88799312","identifier":"d1c74838-a840-11e7-96bc-067b88799312","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.G.4","fullStatement":"Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ee0bf5f2-a840-11e7-81e3-eeee0fd476c2","identifier":"ee0bf5f2-a840-11e7-81e3-eeee0fd476c2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.2b","fullStatement":"Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. *For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddba078c-a92d-11e7-86b6-b94d03f8ad4d","identifier":"ddba078c-a92d-11e7-86b6-b94d03f8ad4d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.RP.3a","fullStatement":"Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e825f3e8-a92d-11e7-b9c4-1e5bc68f50dd","identifier":"e825f3e8-a92d-11e7-b9c4-1e5bc68f50dd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.RP.3b","fullStatement":"Solve unit rate problems including those involving unit pricing and constant speed. *For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b3d9be5c-a92e-11e7-83e9-4bed3236d852","identifier":"b3d9be5c-a92e-11e7-83e9-4bed3236d852","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.1","fullStatement":"Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, including reasoning strategies such as using visual fraction models and equations to represent the problem.\r\n*For example:*\r\n* *How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?*\r\n*  *How many 3/4-cup servings are in 2/3 of a cup of yogurt?*\r\n*  *How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?*\r\n*  *Three pizzas are cut so each person at the table receives \u00bc pizza. How many people are at the table?*\r\n*  *Create a story context for (2/3)\u00f7(3/4) and use a visual fraction model to show the quotient;*\r\n*  *Use the relationship between multiplication and division to explain that (2/3)\u00f7(3/4)=8/9 because 3/4 of 8/9 is 2/3. (In general, (?/?)\u00f7(?/?)=?d /?c .)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6a06404-a92e-11e7-8271-ee889b7f258a","identifier":"d6a06404-a92e-11e7-8271-ee889b7f258a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.2","fullStatement":"Fluently divide multi-digit numbers using the standard algorithm.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e676961e-a92e-11e7-ac5f-6a11b4c56a88","identifier":"e676961e-a92e-11e7-ac5f-6a11b4c56a88","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.3","fullStatement":"Fluently add, subtract, multiply, and divide multi-digit decimals using the standard\r\nalgorithm for each operation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0fbd6070-a92f-11e7-b1e4-9f4a452f3a94","identifier":"0fbd6070-a92f-11e7-b1e4-9f4a452f3a94","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.4","fullStatement":"Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/266d2f30-a92f-11e7-ae80-f69cb3657af5","identifier":"266d2f30-a92f-11e7-ae80-f69cb3657af5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.5","fullStatement":"Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2f3250d2-a92f-11e7-9bc7-9376bcdf89b1","identifier":"2f3250d2-a92f-11e7-9bc7-9376bcdf89b1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.6","fullStatement":"Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b64ff08-a92f-11e7-993f-f431f040d686","identifier":"3b64ff08-a92f-11e7-993f-f431f040d686","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.6a","fullStatement":"Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., \u2013(\u20133) = 3, and that 0 is its own opposite.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/43acb6ce-a92f-11e7-929f-1939018ebe54","identifier":"43acb6ce-a92f-11e7-929f-1939018ebe54","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.6b","fullStatement":"Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/60255ce8-a92f-11e7-9183-3a8275d96d1a","identifier":"60255ce8-a92f-11e7-9183-3a8275d96d1a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.6c","fullStatement":"Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6cad97c8-a92f-11e7-ab33-9eaa907d6460","identifier":"6cad97c8-a92f-11e7-ab33-9eaa907d6460","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.7","fullStatement":"Understand ordering and absolute value of rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/79ddcef4-a92f-11e7-9e4d-d39308e01b64","identifier":"79ddcef4-a92f-11e7-9e4d-d39308e01b64","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.7a","fullStatement":"Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. *For example, interpret \u2013 3 >\u2013 7 as a statement that \u20133 is located to the right of \u20137 on a number line oriented from left to right.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8634372e-a92f-11e7-8f25-c65b22a62f61","identifier":"8634372e-a92f-11e7-8f25-c65b22a62f61","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.7b","fullStatement":"Write, interpret, and explain statements of order for rational numbers in real-world contexts. *For example, write \u20133\u00b0C > \u20137\u00b0C to express the fact that \u20133\u00b0C is warmer than \u20137\u00b0C.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8f554532-a92f-11e7-abc8-f3428022f4b5","identifier":"8f554532-a92f-11e7-abc8-f3428022f4b5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.7c","fullStatement":"Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. *For example, for an account balance of \u201330 dollars, write |\u201330| = 30 to describe the size of the debt in dollars.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/98d98226-a92f-11e7-a3ae-8f5a9a37125e","identifier":"98d98226-a92f-11e7-a3ae-8f5a9a37125e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.7d","fullStatement":"Distinguish comparisons of absolute value from statements about order. *For example, recognize that an account balance less than \u201330 dollars represents a debt greater than 30 dollars.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a89800b6-a92f-11e7-ae0c-e15cbeb6e757","identifier":"a89800b6-a92f-11e7-ae0c-e15cbeb6e757","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.8","fullStatement":"Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/751ae264-a946-11e7-b751-c995a6dacb28","identifier":"751ae264-a946-11e7-b751-c995a6dacb28","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.2c","fullStatement":"Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  *For example, use the formulas V = s\u00b3 and A = 6s\u00b2 to find the volume and surface area of a cube with sides of length s = 1/2.*","notes":"For example, use the formulas V = s\u00b3 and A = 6s\u00b2 to find the volume and surface area of a cube with sides of length s = 1/2.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9d066c2e-a9d9-11e7-a1ca-a00e07a36f2d","identifier":"9d066c2e-a9d9-11e7-a1ca-a00e07a36f2d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2a","fullStatement":"Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d442186e-a9d9-11e7-b578-516a3e995f5f","identifier":"d442186e-a9d9-11e7-b578-516a3e995f5f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["07"],"humanCodingScheme":"7.NS","fullStatement":"The Number System","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e2195d12-a9d9-11e7-96a3-5c0769c96b8c","identifier":"e2195d12-a9d9-11e7-96a3-5c0769c96b8c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eda97d7e-a9d9-11e7-bee9-987b455a2447","identifier":"eda97d7e-a9d9-11e7-bee9-987b455a2447","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1","fullStatement":"Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd50ee7e-a9d9-11e7-aba1-3fded11ed7c5","identifier":"fd50ee7e-a9d9-11e7-aba1-3fded11ed7c5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1a","fullStatement":"Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. *For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2abb3004-a9da-11e7-8412-57017f43d63f","identifier":"2abb3004-a9da-11e7-8412-57017f43d63f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1b","fullStatement":"Understand *p + q* as the number located a distance |*q*| from *p*, in the positive or negative direction depending on whether *q* is positive or negative. Interpret sums of rational numbers by describing real-world contexts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5440637c-a9da-11e7-80ab-da102bc94dbe","identifier":"5440637c-a9da-11e7-80ab-da102bc94dbe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1c","fullStatement":"Understand subtraction of rational numbers as adding the additive inverse, *p - q* = *p + (-q)*. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6a98e2de-a9da-11e7-ae54-552b25fc3685","identifier":"6a98e2de-a9da-11e7-ae54-552b25fc3685","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1d","fullStatement":"Apply properties of operations as strategies to add and subtract rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/767ab352-a9da-11e7-8394-f9bf1708af61","identifier":"767ab352-a9da-11e7-8394-f9bf1708af61","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2","fullStatement":"Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/81f7b8e2-a9da-11e7-b31a-2f090d87b5a3","identifier":"81f7b8e2-a9da-11e7-b31a-2f090d87b5a3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2a","fullStatement":"Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (\u2013 1)(\u2013 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bbcb4ec6-a9da-11e7-a17a-fe26be6e8103","identifier":"bbcb4ec6-a9da-11e7-a17a-fe26be6e8103","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2b","fullStatement":"Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If *p* and *q* are integers then *\u2013(p/q) = (\u2013p)/q = p/(\u2013q)*. Interpret quotients of rational numbers by describing real-world contexts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c6465f94-a9da-11e7-8d91-df06232b8837","identifier":"c6465f94-a9da-11e7-8d91-df06232b8837","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2c","fullStatement":"Apply properties of operations as strategies to multiply and divide rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d2d9c674-a9da-11e7-95ee-9226c9b97163","identifier":"d2d9c674-a9da-11e7-95ee-9226c9b97163","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2d","fullStatement":"Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e05568d0-a9da-11e7-903d-1c2ccdd07b1e","identifier":"e05568d0-a9da-11e7-903d-1c2ccdd07b1e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.3","fullStatement":"Solve real-world and mathematical problems involving the four operations with rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f7171a50-a9da-11e7-9bd4-73a41dbbe7c7","identifier":"f7171a50-a9da-11e7-9bd4-73a41dbbe7c7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.1","fullStatement":"Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2af4ea78-a9db-11e7-b640-5bea71eae15b","identifier":"2af4ea78-a9db-11e7-b640-5bea71eae15b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4","fullStatement":"Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8075faa0-a9db-11e7-95e1-159a62b9f27a","identifier":"8075faa0-a9db-11e7-95e1-159a62b9f27a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4a","fullStatement":"Solve word problems leading to equations of the form *px + q = r and p(x + q) = r*, where *p*, *q*, and *r* are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. *For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bd4f9378-a9db-11e7-868a-23c436b575b9","identifier":"bd4f9378-a9db-11e7-868a-23c436b575b9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4b","fullStatement":"Solve word problems leading to inequalities of the form *px + q > r or px + q < r*, where *p*, *q*, and *r* are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. *For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d312eb1a-a9db-11e7-a9e4-c9fe4f7c7f8f","identifier":"d312eb1a-a9db-11e7-a9e4-c9fe4f7c7f8f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4c","fullStatement":"Solve real-world and mathematical problems by writing and solving equations of the form *x + p = q* and *px = q* in which *p* and *q* are rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e20b4f36-a9db-11e7-b8ba-d26c7bcbb249","identifier":"e20b4f36-a9db-11e7-b8ba-d26c7bcbb249","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["07"],"humanCodingScheme":"7.G","fullStatement":"Geometry","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eba24298-a9db-11e7-bc9f-18a72f8d919c","identifier":"eba24298-a9db-11e7-bc9f-18a72f8d919c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Draw, construct, and describe geometrical figures and describe the relationships between them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f6de3d60-a9db-11e7-80e7-62ad5c2dcea4","identifier":"f6de3d60-a9db-11e7-80e7-62ad5c2dcea4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/054ad34a-a9dc-11e7-872b-07ca9a04b6e1","identifier":"054ad34a-a9dc-11e7-872b-07ca9a04b6e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.1","fullStatement":"Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ecedaba-a9dc-11e7-9444-24b6881c0043","identifier":"0ecedaba-a9dc-11e7-9444-24b6881c0043","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.2","fullStatement":"Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/18a11788-a9dc-11e7-b6f9-1c3877c5ef9f","identifier":"18a11788-a9dc-11e7-b6f9-1c3877c5ef9f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.3","fullStatement":"Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/260115d6-a9dc-11e7-ad6a-869cbc64a8d1","identifier":"260115d6-a9dc-11e7-ad6a-869cbc64a8d1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.4","fullStatement":"Given the formulas for the area and circumference of a circle, use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/333e9124-a9dc-11e7-a134-3f2eac2877e9","identifier":"333e9124-a9dc-11e7-a134-3f2eac2877e9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.5","fullStatement":"Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b6c6420-a9dc-11e7-a2fe-164982890dab","identifier":"3b6c6420-a9dc-11e7-a2fe-164982890dab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.G.6","fullStatement":"Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/548b68b6-a9dc-11e7-9880-ff2806cb4b65","identifier":"548b68b6-a9dc-11e7-9880-ff2806cb4b65","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["07"],"humanCodingScheme":"7.SP","fullStatement":"Statistics and Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5eb5f6c6-a9dc-11e7-b020-c9e2eadccd87","identifier":"5eb5f6c6-a9dc-11e7-b020-c9e2eadccd87","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Use random sampling to draw inferences about a population.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/640f3a1a-a9dc-11e7-b119-dd97ddba9aa5","identifier":"640f3a1a-a9dc-11e7-b119-dd97ddba9aa5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Draw informal comparative inferences about two populations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6c9800a4-a9dc-11e7-966a-471648a9770f","identifier":"6c9800a4-a9dc-11e7-966a-471648a9770f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["07"],"fullStatement":"Investigate chance processes and develop, use, and evaluate probability models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7ac20efe-a9dc-11e7-b9cb-d4a5a9fc0691","identifier":"7ac20efe-a9dc-11e7-b9cb-d4a5a9fc0691","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.1","fullStatement":"Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/85857bf0-a9dc-11e7-ba79-66bac388e548","identifier":"85857bf0-a9dc-11e7-ba79-66bac388e548","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.2","fullStatement":"Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. *For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/91bf6188-a9dc-11e7-b03c-06315fb46881","identifier":"91bf6188-a9dc-11e7-b03c-06315fb46881","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.3","fullStatement":"Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the medians by expressing it as a multiple of the interquartile range.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9d7ab6d0-a9dc-11e7-a7dc-158d1be59a27","identifier":"9d7ab6d0-a9dc-11e7-a7dc-158d1be59a27","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.4","fullStatement":"Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. *For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a9e2bf76-a9dc-11e7-9adb-f7a852b3dbfd","identifier":"a9e2bf76-a9dc-11e7-9adb-f7a852b3dbfd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.5","fullStatement":"Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b3c5f9fe-a9dc-11e7-94d0-93af3863a10c","identifier":"b3c5f9fe-a9dc-11e7-94d0-93af3863a10c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.6","fullStatement":"Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency. Predict the approximate relative frequency given the probability. *For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bca537ba-a9dc-11e7-9f1e-6a043faf508a","identifier":"bca537ba-a9dc-11e7-9f1e-6a043faf508a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7","fullStatement":"Develop a probability model and use it to find probabilities of events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c8c31f62-a9dc-11e7-8f6d-4ef3f2cb7a6b","identifier":"c8c31f62-a9dc-11e7-8f6d-4ef3f2cb7a6b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7a","fullStatement":"Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. *For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d134f1d4-a9dc-11e7-960c-70549e3ef75b","identifier":"d134f1d4-a9dc-11e7-960c-70549e3ef75b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7b","fullStatement":"Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. *For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f0c48b5e-a9dc-11e7-aa16-23c8dadeac46","identifier":"f0c48b5e-a9dc-11e7-aa16-23c8dadeac46","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8","fullStatement":"Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff2f9576-a9dc-11e7-a8ab-fbdc9b31d0ff","identifier":"ff2f9576-a9dc-11e7-a8ab-fbdc9b31d0ff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8a","fullStatement":"Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0d4f5510-a9dd-11e7-819f-938fb926313e","identifier":"0d4f5510-a9dd-11e7-819f-938fb926313e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8b","fullStatement":"Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \u201crolling double sixes\u201d), identify the outcomes in the sample space which compose the event.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/152f7c2e-a9dd-11e7-ba8f-92f710289072","identifier":"152f7c2e-a9dd-11e7-ba8f-92f710289072","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8c","fullStatement":"Explain ways to set up a simulation and use the simulation to generate frequencies for compound events. *For example, if 40% of donors have type A blood, create a simulation to predict the probability that it will take at least 4 donors to find one with type A blood.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bfdc5aec-a9de-11e7-9f3c-4fd6881b5476","identifier":"bfdc5aec-a9de-11e7-9f3c-4fd6881b5476","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.5","fullStatement":"Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. *For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d9008638-a9de-11e7-800a-988e1fc78e6a","identifier":"d9008638-a9de-11e7-800a-988e1fc78e6a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.6","fullStatement":"Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation *y = mx* for a line through the origin and the equation *y = mx + b* for a line intercepting the vertical axis at *b*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/44a27bca-a9e0-11e7-a3ba-3d887d89ec76","identifier":"44a27bca-a9e0-11e7-a3ba-3d887d89ec76","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.1","fullStatement":"Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/611797a4-a9e0-11e7-a46c-8a89f9906ccc","identifier":"611797a4-a9e0-11e7-a46c-8a89f9906ccc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.2","fullStatement":"Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/429c5e8a-d475-11e7-96be-11018ae94b24","identifier":"429c5e8a-d475-11e7-96be-11018ae94b24","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Number Sense and Quantity","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddd41686-d475-11e7-bc7b-95bc99a26851","identifier":"ddd41686-d475-11e7-bc7b-95bc99a26851","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will compare different representations of numbers (i.e. fractions, decimals, radicals, etc.) and perform basic operations using these different representations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/37669c6e-d476-11e7-8999-1f2fb42f51c6","identifier":"37669c6e-d476-11e7-8999-1f2fb42f51c6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.1","fullStatement":"Students will analyze number relationships.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f3f20eec-d523-11e7-b908-7bbf4a8e9a71","identifier":"f3f20eec-d523-11e7-b908-7bbf4a8e9a71","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.1a","fullStatement":"Solve multi-step real world problems, analyzing the relationships between all four operations. *For example, understand division as an unknown-factor problem in order to solve problems. Knowing that 50 x 40 = 2000 helps students determine how many boxes of cupcakes they will need in order to ship 2000 cupcakes in boxes that hold 40 cupcakes each.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2be83100-d524-11e7-9ad4-85c26fdb1a1a","identifier":"2be83100-d524-11e7-9ad4-85c26fdb1a1a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.1b","fullStatement":"Understand a fraction *a/b* as a multiple of *1/b*. (MGSE4.NF.4)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd374a48-d524-11e7-ae1c-b13e77d2e561","identifier":"fd374a48-d524-11e7-ae1c-b13e77d2e561","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.1c","fullStatement":"Explain patterns in the placement of decimal points when multiplying or dividing by powers of ten.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/293fc840-d525-11e7-a7cc-af8c815ad4c1","identifier":"293fc840-d525-11e7-a7cc-af8c815ad4c1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.1d","fullStatement":"Compare fractions and decimals to the thousandths place. For fractions, use strategies other than cross multiplication. *For example, locating the fractions on a number line or using benchmark fractions to reason about relative size. For decimals, use place value.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f7f17684-d525-11e7-99e6-cbbc36910fb1","identifier":"f7f17684-d525-11e7-99e6-cbbc36910fb1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.2","fullStatement":"Students will conceptualize positive and negative numbers (including decimals and fractions).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1bbd6faa-d526-11e7-a7f8-cfd0d8f17b8d","identifier":"1bbd6faa-d526-11e7-a7f8-cfd0d8f17b8d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.2a","fullStatement":"Explain the meaning of zero.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6592cb98-d526-11e7-9af2-e978389cf80b","identifier":"6592cb98-d526-11e7-9af2-e978389cf80b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.2b","fullStatement":"Represent numbers on a number line.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/87e95da6-d526-11e7-aa6c-95db664628fd","identifier":"87e95da6-d526-11e7-aa6c-95db664628fd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.2c","fullStatement":"Explain meanings of real numbers in a real world context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a23f02a0-d526-11e7-8708-379b86cae613","identifier":"a23f02a0-d526-11e7-8708-379b86cae613","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.3","fullStatement":"Students will recognize that there are numbers that are not rational, and approximate them with rational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cf47b206-d526-11e7-a1de-19491efff67f","identifier":"cf47b206-d526-11e7-a1de-19491efff67f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.3a","fullStatement":"Find an estimated decimal expansion of an irrational number locating the approximations on a number line. *For example, for \u221a2, show that \u221a2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue this pattern in order to obtain better approximations.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e83f1286-d526-11e7-b383-3123e58efb72","identifier":"e83f1286-d526-11e7-b383-3123e58efb72","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.3b","fullStatement":"Explain the results of adding and multiplying with rational and irrational numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e60a31d4-d527-11e7-8983-9d6ad0ef9f94","identifier":"e60a31d4-d527-11e7-8983-9d6ad0ef9f94","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4","fullStatement":"Students will apply and extend previous understanding of addition, subtraction, multiplication, and division.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0e40b010-d528-11e7-8a54-65dc0ef6fe50","identifier":"0e40b010-d528-11e7-8a54-65dc0ef6fe50","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4a","fullStatement":"Find sums, differences, products, and quotients of multi-digit decimals using strategies based on place value, the properties of operations, and/or relationships between operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/38a61228-d528-11e7-8459-15aa0ef6ce84","identifier":"38a61228-d528-11e7-8459-15aa0ef6ce84","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4b","fullStatement":"Find sums, differences, products, and quotients of all forms of rational numbers, stressing the conceptual understanding of these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7251215c-d528-11e7-8cdd-f560209c2a73","identifier":"7251215c-d528-11e7-8cdd-f560209c2a73","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4c","fullStatement":"Interpret and solve contextual problems involving division of fractions by fractions. *For example, how many 3/4-cup servings are in 2/3 of a cup of yogurt?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a0c0cb5a-d528-11e7-86d6-97d380a7a616","identifier":"a0c0cb5a-d528-11e7-86d6-97d380a7a616","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4d","fullStatement":"Illustrate and explain calculations using models and line diagrams.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bc6c66de-d528-11e7-8217-a534f85906eb","identifier":"bc6c66de-d528-11e7-8217-a534f85906eb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.NSQ.4e","fullStatement":"Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using estimation strategies and graphing technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a0e10e4c-d5dc-11e7-88a0-4fa79ca5455e","identifier":"a0e10e4c-d5dc-11e7-88a0-4fa79ca5455e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.2a","fullStatement":"Choose and interpret units in formulas.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c6111bbc-d5dc-11e7-971e-f3efd254c3ec","identifier":"c6111bbc-d5dc-11e7-971e-f3efd254c3ec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.2b","fullStatement":"Choose and interpret graphs and data displays, including the scale and comparisons of data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e89707f0-d5dc-11e7-b99a-77a9f1e839a2","identifier":"e89707f0-d5dc-11e7-b99a-77a9f1e839a2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.2c","fullStatement":"Graph points in all four quadrants of the coordinate plane","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1f30fb7c-d5dd-11e7-8a7d-adf033f589f7","identifier":"1f30fb7c-d5dd-11e7-8a7d-adf033f589f7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.3","fullStatement":"Students will create algebraic models in two variables.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/36a109be-d5dd-11e7-9c6a-a16d99b675fb","identifier":"36a109be-d5dd-11e7-9c6a-a16d99b675fb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.3a","fullStatement":"Create an algebraic model from a context using two-variable equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5a0c5e62-d5dd-11e7-acc1-a5e5839b74fe","identifier":"5a0c5e62-d5dd-11e7-acc1-a5e5839b74fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.3b","fullStatement":"Find approximate solutions using technology to graph, construct tables of values, and find successive approximations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8640b9b0-d5dd-11e7-915c-03a2b8ad2b9f","identifier":"8640b9b0-d5dd-11e7-915c-03a2b8ad2b9f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.3c","fullStatement":"Represent solutions to systems of equations graphically or by using a table of values.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a77328a2-d5dd-11e7-a1e0-5d8a8bcffcac","identifier":"a77328a2-d5dd-11e7-a1e0-5d8a8bcffcac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MFA.EI.3d","fullStatement":"Analyze the reasonableness of the solutions of systems of equations within a given context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ba4d5b88-d5e1-11e7-b08c-939a72142ac3","identifier":"ba4d5b88-d5e1-11e7-b08c-939a72142ac3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Extend the properties of exponents to rational exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ef24bf2-d5e3-11e7-a639-5db70c552948","identifier":"0ef24bf2-d5e3-11e7-a639-5db70c552948","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.2","fullStatement":"Rewrite expressions involving radicals ~~and rational exponents using the properties of exponents.}~~ (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/aaa5842e-d606-11e7-8e5b-4bc2ad37c4d1","identifier":"aaa5842e-d606-11e7-8e5b-4bc2ad37c4d1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Extend the properties of exponents to rational exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddd6f7ce-d606-11e7-b542-3d8724772429","identifier":"ddd6f7ce-d606-11e7-b542-3d8724772429","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.2","fullStatement":"Rewrite expressions involving radicals ~~and rational exponents using the properties of exponents.~~ (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4d931de2-d60a-11e7-937b-f5ed6845a572","identifier":"4d931de2-d60a-11e7-937b-f5ed6845a572","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Interpreting Functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7c950aa6-d60a-11e7-8a61-1d4aec5c483b","identifier":"7c950aa6-d60a-11e7-8a61-1d4aec5c483b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the concept of a function and use function notation","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90f9ec00-d60a-11e7-98e7-db173876befd","identifier":"90f9ec00-d60a-11e7-98e7-db173876befd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret functions that arise in applications in terms of the context","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a2f550d4-d60a-11e7-a8df-f5714a5cb915","identifier":"a2f550d4-d60a-11e7-a8df-f5714a5cb915","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Analyze functions using different representations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ca4fea7c-d60a-11e7-9f4a-1ffe3fe1da64","identifier":"ca4fea7c-d60a-11e7-9f4a-1ffe3fe1da64","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.1","fullStatement":"Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is y = f(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e4f057e0-d60a-11e7-bd5a-b9b2c9e71dc7","identifier":"e4f057e0-d60a-11e7-bd5a-b9b2c9e71dc7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.2","fullStatement":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/12c79944-d60b-11e7-9b3f-195b8a9eaf7f","identifier":"12c79944-d60b-11e7-9b3f-195b8a9eaf7f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.3","fullStatement":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.  (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence $a_1$=7, $a_n=a_{(n-1)}$ +2; the sequence $s_n$ = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/45a4f244-d60b-11e7-8a29-7f9ccd5713e2","identifier":"45a4f244-d60b-11e7-8a29-7f9ccd5713e2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.4","fullStatement":"Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; ~~and periodicity.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6550d752-d60b-11e7-8b72-6de72ebc814a","identifier":"6550d752-d60b-11e7-8b72-6de72ebc814a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.5","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/837487a6-d60b-11e7-8412-57b4905471e3","identifier":"837487a6-d60b-11e7-8412-57b4905471e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.6","fullStatement":"Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a2d92cbe-d60b-11e7-85a0-fb40d7feb48d","identifier":"a2d92cbe-d60b-11e7-85a0-fb40d7feb48d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7","fullStatement":"Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c6de9612-d60b-11e7-bb83-97ca525523f6","identifier":"c6de9612-d60b-11e7-bb83-97ca525523f6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7a","fullStatement":"Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f3f8ce4c-d60b-11e7-b66f-dfa4396f1080","identifier":"f3f8ce4c-d60b-11e7-b66f-dfa4396f1080","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7e","fullStatement":"Graph exponential ~~and logarithmic~~ functions, showing intercepts and end behavior, ~~and trigonometric functions, showing period, midline, and amplitude.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/157dc3d8-d60c-11e7-a627-a1379cfaf0ce","identifier":"157dc3d8-d60c-11e7-a627-a1379cfaf0ce","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8","fullStatement":"Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3a49086c-d60c-11e7-aa9a-a7398f8395ab","identifier":"3a49086c-d60c-11e7-aa9a-a7398f8395ab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.8a","fullStatement":"Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. *For example, compare and contrast quadratic functions in standard, vertex, and intercept forms.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/60c85c0e-d60c-11e7-a14a-237a336f7e37","identifier":"60c85c0e-d60c-11e7-a14a-237a336f7e37","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.9","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d490c4e0-d60d-11e7-8db1-4121dc467646","identifier":"d490c4e0-d60d-11e7-8db1-4121dc467646","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.2","fullStatement":"Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fab52f1c-d60d-11e7-bdaa-1ddbb36d7232","identifier":"fab52f1c-d60d-11e7-bdaa-1ddbb36d7232","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.3","fullStatement":"Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/39807922-d60e-11e7-9535-21138b5f33df","identifier":"39807922-d60e-11e7-9535-21138b5f33df","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1","fullStatement":"Distinguish between situations that can be modeled with linear functions and with exponential functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/57aab1c4-d60e-11e7-9d42-0504966b9667","identifier":"57aab1c4-d60e-11e7-9d42-0504966b9667","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1a","fullStatement":"Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7a3a6ef0-d60e-11e7-ad98-1571d6876541","identifier":"7a3a6ef0-d60e-11e7-ad98-1571d6876541","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08","09","10","11"],"humanCodingScheme":"MGSE9-12.F.LE.1b","fullStatement":"Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d949be6e-d60e-11e7-a8ed-4dacc4985f9f","identifier":"d949be6e-d60e-11e7-a8ed-4dacc4985f9f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.1c","fullStatement":"Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0c8cf110-d60f-11e7-b3e3-5da79b434dfb","identifier":"0c8cf110-d60f-11e7-b3e3-5da79b434dfb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.2","fullStatement":"Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/18c36e4a-d610-11e7-b584-87603799bfbc","identifier":"18c36e4a-d610-11e7-b584-87603799bfbc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.8","fullStatement":"Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/29cbaf94-d611-11e7-ac12-53af643dab51","identifier":"29cbaf94-d611-11e7-ac12-53af643dab51","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.2","fullStatement":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/82303740-d611-11e7-8cbd-1fe9e5c1d579","identifier":"82303740-d611-11e7-8cbd-1fe9e5c1d579","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.7","fullStatement":"Explain and use the relationship between the sine and cosine of complementary angles.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/99373e20-d611-11e7-8994-d5f1c65a6fe9","identifier":"99373e20-d611-11e7-8994-d5f1c65a6fe9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.8","fullStatement":"Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e7cd5a88-d611-11e7-8f7c-8b75005022b0","identifier":"e7cd5a88-d611-11e7-8f7c-8b75005022b0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.1","fullStatement":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a10dac4-d612-11e7-888d-07bbe83cdc5e","identifier":"1a10dac4-d612-11e7-888d-07bbe83cdc5e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.2","fullStatement":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, mean absolute deviation, ~~standard deviation~~) of two or more different data sets.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3dc6fcf8-d6a5-11e7-a6f7-37c1e61e723c","identifier":"3dc6fcf8-d6a5-11e7-a6f7-37c1e61e723c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Extend the properties of exponents to rational exponents.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8b005406-d6a5-11e7-bca8-c52815ec6227","identifier":"8b005406-d6a5-11e7-bca8-c52815ec6227","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.RN.2","fullStatement":"Rewrite expressions involving radicals ~~and rational exponents using the properties of exponents.~~ (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1a0205e-d6a6-11e7-bf0a-2550ae9e5d20","identifier":"b1a0205e-d6a6-11e7-bf0a-2550ae9e5d20","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/592d759a-d6a9-11e7-aa0d-87f69bcb8540","identifier":"592d759a-d6a9-11e7-aa0d-87f69bcb8540","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.4","fullStatement":"Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.  *Examples: Rearrange Ohm\u2019s law V = IR to highlight resistance R; ~~Rearrange area of a circle formula A =  \u03c0 $r^2$ to highlight the radius r.~~*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3becf6da-d6aa-11e7-a951-855700672478","identifier":"3becf6da-d6aa-11e7-a951-855700672478","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand solving equations as a process of reasoning and explain the reasoning","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5ca4220e-d6aa-11e7-8b3a-2953d8f85f53","identifier":"5ca4220e-d6aa-11e7-8b3a-2953d8f85f53","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.1","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ca48edd0-d6aa-11e7-a4f0-5fb13ec37ae6","identifier":"ca48edd0-d6aa-11e7-a4f0-5fb13ec37ae6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.10","fullStatement":"Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1da7fd2c-d6ab-11e7-b681-f50e871e3191","identifier":"1da7fd2c-d6ab-11e7-b681-f50e871e3191","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.1","fullStatement":"Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is y = f(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5083fbbe-d6ac-11e7-8f0b-df2856b408c4","identifier":"5083fbbe-d6ac-11e7-8f0b-df2856b408c4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.9","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c01c0b38-d6ac-11e7-954d-7f05dac435d0","identifier":"c01c0b38-d6ac-11e7-954d-7f05dac435d0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.1a","fullStatement":"Determine an explicit expression and the recursive process (steps for calculation) from context. *For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression \u201c2x+15\u201d can be described recursively (either in writing or verbally) as \u201cto find out how much money Jimmy will have tomorrow, you add $2 to his total today.\u201d* $J_n$ = $J_{n-1}$ + 2, $J_0$ = 15","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/030bd414-d6ad-11e7-8aeb-5f2d35b4a6aa","identifier":"030bd414-d6ad-11e7-8aeb-5f2d35b4a6aa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.3","fullStatement":"Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. ~~Include recognizing even and odd functions from their graphs and algebraic expressions for them.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/855b3360-d6ad-11e7-96e4-8727cf7d9a1a","identifier":"855b3360-d6ad-11e7-96e4-8727cf7d9a1a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.3","fullStatement":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, ~~quadratically, or (more generally) as a polynomial function.~~","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b45bcf58-d6ad-11e7-b776-2bea634e9b4d","identifier":"b45bcf58-d6ad-11e7-b776-2bea634e9b4d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Interpret expressions for functions in terms of the situation they model","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/dc4cd03e-d6ad-11e7-8b8c-816fc197b2df","identifier":"dc4cd03e-d6ad-11e7-8b8c-816fc197b2df","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.LE.5","fullStatement":"Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a\u2022$d^x$) function in terms of context.  (In the functions above, \u201cm\u201d and \u201cb\u201d are the parameters of the linear function, and \u201ca\u201d and \u201cd\u201d are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3a3aeef6-d6ae-11e7-a194-ebbbe41c1aa3","identifier":"3a3aeef6-d6ae-11e7-a194-ebbbe41c1aa3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.4","fullStatement":"Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/536aef8e-d6ae-11e7-a6b6-8ff1195c4915","identifier":"536aef8e-d6ae-11e7-a6b6-8ff1195c4915","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.CO.5","fullStatement":"Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. 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Theorems include: a line parallel to one side of a triangle divides the other two proportionally, (and its converse); the Pythagorean Theorem using triangle similarity.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f98c3854-d6af-11e7-b219-079dbb709f4c","identifier":"f98c3854-d6af-11e7-b219-079dbb709f4c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.5","fullStatement":"Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/34e65d44-d6b0-11e7-918f-0533fe81094d","identifier":"34e65d44-d6b0-11e7-918f-0533fe81094d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.C.2","fullStatement":"Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4a6717b2-d6b0-11e7-b250-f76754aac527","identifier":"4a6717b2-d6b0-11e7-b250-f76754aac527","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.C.3","fullStatement":"Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1ec9f36-d6d0-11e7-af1f-dd63b3163083","identifier":"b1ec9f36-d6d0-11e7-af1f-dd63b3163083","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Conditional Probability and the Rules of Probability","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cce3ad3e-d6d0-11e7-900f-7f8921ba5cab","identifier":"cce3ad3e-d6d0-11e7-900f-7f8921ba5cab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand independence and conditional probability and use them to interpret data","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0bab468a-d6d1-11e7-ae6e-8d29a7a1c414","identifier":"0bab468a-d6d1-11e7-ae6e-8d29a7a1c414","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use the rules of probability to compute probabilities of compound events in a uniform probability model","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/315762e2-d6d1-11e7-9592-bb54e47220ea","identifier":"315762e2-d6d1-11e7-9592-bb54e47220ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.1","fullStatement":"Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/49c9e1a6-d6d1-11e7-9552-8f85088a1962","identifier":"49c9e1a6-d6d1-11e7-9552-8f85088a1962","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.2","fullStatement":"Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/61d7108e-d6d1-11e7-8d30-a395c6bfdc7f","identifier":"61d7108e-d6d1-11e7-8d30-a395c6bfdc7f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.3","fullStatement":"Understand the conditional probability of A given B as P (A and B)/P(B). 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Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. *For example, use collected data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. 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y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2) (x^2 + y^2)$.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a824b114-d90f-11e7-80a6-63caa2b466b0","identifier":"a824b114-d90f-11e7-80a6-63caa2b466b0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Perform arithmetic operations on polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b8169d8a-d90f-11e7-a1fb-b9f63b1f5be6","identifier":"b8169d8a-d90f-11e7-a1fb-b9f63b1f5be6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the relationship between zeros and factors of polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cc695fe8-d90f-11e7-8cf2-95f618343528","identifier":"cc695fe8-d90f-11e7-8cf2-95f618343528","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use polynomial identities to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/dd34a530-d90f-11e7-b347-2f576123bf3d","identifier":"dd34a530-d90f-11e7-b347-2f576123bf3d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Rewrite rational expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f935ea28-d90f-11e7-ac1a-f14dc500d164","identifier":"f935ea28-d90f-11e7-ac1a-f14dc500d164","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/125d40d2-d910-11e7-ac78-c5048e611536","identifier":"125d40d2-d910-11e7-ac78-c5048e611536","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.2","fullStatement":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x \u2013 a is p(a), so p(a) = 0 if and only if (x \u2013 a) is a factor of p(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3850ce6c-d910-11e7-b18f-c135706c1750","identifier":"3850ce6c-d910-11e7-b18f-c135706c1750","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.3","fullStatement":"Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eaf5bef6-d910-11e7-8b2d-95d7177b2832","identifier":"eaf5bef6-d910-11e7-8b2d-95d7177b2832","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.4","fullStatement":"Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2$ = $(x^2 - y^2)^2$ + $(2xy)^2$ can be used to generate Pythagorean triples.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1be592d4-d911-11e7-964b-c51932acf4fa","identifier":"1be592d4-d911-11e7-964b-c51932acf4fa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.5","fullStatement":"Know and apply that the Binomial Theorem gives the expansion of ${(x + y)}^n$ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal\u2019s Triangle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/35bba194-d911-11e7-bb0a-09c1a248199f","identifier":"35bba194-d911-11e7-bb0a-09c1a248199f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["08","09","10","11"],"humanCodingScheme":"MGSE9-12.A.APR.6","fullStatement":"Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/53fce5be-d911-11e7-87ba-41cb1f71bca7","identifier":"53fce5be-d911-11e7-87ba-41cb1f71bca7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.7","fullStatement":"Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/07a1dd36-d912-11e7-81bd-fd7d5a0207ea","identifier":"07a1dd36-d912-11e7-81bd-fd7d5a0207ea","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Solve equations and inequalities in one variable","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1ba054d4-d912-11e7-a01c-af9c94d1cfac","identifier":"1ba054d4-d912-11e7-a01c-af9c94d1cfac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Represent and solve equations and inequalities graphically","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/353a7c1c-d912-11e7-98f2-370aee2fd589","identifier":"353a7c1c-d912-11e7-98f2-370aee2fd589","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4","fullStatement":"Solve quadratic equations in one variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/66d73102-d912-11e7-9eca-59e883d141d8","identifier":"66d73102-d912-11e7-9eca-59e883d141d8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.REI.4a","fullStatement":"Use the method of completing the square to transform any quadratic equation in x into an equation of the form $(x - p)^2$ = q that has the same solutions. 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For example, f(x) =2($x^3$) or f(x) = (x+1)/(x-1) for x \u2260 1.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/afceca58-d923-11e7-8311-5d2260f01693","identifier":"afceca58-d923-11e7-8311-5d2260f01693","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use coordinates to prove simple geometric theorems algebraically","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ce5e52a4-d923-11e7-9ddb-572c2e7139ac","identifier":"ce5e52a4-d923-11e7-9ddb-572c2e7139ac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GPE.1","fullStatement":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2dec908c-d924-11e7-b387-39ecb90625e1","identifier":"2dec908c-d924-11e7-b387-39ecb90625e1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GPE.4","fullStatement":"Use coordinates to prove simple geometric theorems algebraically. *For example, ~~prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle;~~ prove or disprove that the point (1, \u221a3) lies on the circle centered at the origin and containing the point (0,2).* (Focus on ~~quadrilaterals, right triangles, and~~ circles.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/de86018a-d924-11e7-b349-15279d1ab272","identifier":"de86018a-d924-11e7-b349-15279d1ab272","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.ID.6a","fullStatement":"Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize ~~linear,~~ quadratic ~~and exponential~~ models.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5b3a31b0-d925-11e7-8843-3ba02a5b3884","identifier":"5b3a31b0-d925-11e7-8843-3ba02a5b3884","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.3","fullStatement":"Understand the conditional probability of A given B as P (A and B)/P(B). 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use the conjugate to find the ~~absolute value (modulus) and~~ quotient of complex numbers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f7af7e10-d92a-11e7-9f88-6f6249f2a049","identifier":"f7af7e10-d92a-11e7-9f88-6f6249f2a049","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1","fullStatement":"Interpret expressions that represent a quantity in terms of its context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/24a869ae-d92b-11e7-8609-6f20750a770f","identifier":"24a869ae-d92b-11e7-8609-6f20750a770f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1a","fullStatement":"Interpret parts of an expression, such as terms, factors, and coefficients, in context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/442b6c36-d92b-11e7-9e29-c98c9be2883a","identifier":"442b6c36-d92b-11e7-9e29-c98c9be2883a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.SSE.1b","fullStatement":"Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eaa14c66-d92b-11e7-975e-7bb3256952b8","identifier":"eaa14c66-d92b-11e7-975e-7bb3256952b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Perform arithmetic operations on polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/07958904-d92c-11e7-b458-d1290390be71","identifier":"07958904-d92c-11e7-b458-d1290390be71","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand the relationship between zeros and factors of polynomials","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/19c3198e-d92c-11e7-9e01-3b3b4d7185a1","identifier":"19c3198e-d92c-11e7-9e01-3b3b4d7185a1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use polynomial identities to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2e991f16-d92c-11e7-9e7b-017e6a835129","identifier":"2e991f16-d92c-11e7-9e7b-017e6a835129","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Rewrite rational expressions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4555fca6-d92c-11e7-a426-27d139b2c9a2","identifier":"4555fca6-d92c-11e7-a426-27d139b2c9a2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6225208c-d92c-11e7-a138-8fa7de5a5b3d","identifier":"6225208c-d92c-11e7-a138-8fa7de5a5b3d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.2","fullStatement":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x \u2013 a is p(a), so p(a) = 0 if and only if (x \u2013 a) is a factor of p(x).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7918ed78-d92c-11e7-9f11-f51ff8764171","identifier":"7918ed78-d92c-11e7-9f11-f51ff8764171","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.3","fullStatement":"Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a205e600-d92c-11e7-bb88-cf745fab4690","identifier":"a205e600-d92c-11e7-bb88-cf745fab4690","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.4","fullStatement":"Prove polynomial identities and use them to describe numerical relationships. 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Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/70bbb83e-dac8-11e7-a959-1d0ecea4e2fb","identifier":"70bbb83e-dac8-11e7-a959-1d0ecea4e2fb","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["08","09","10","11"],"fullStatement":"Perform operations on matrices and use matrices in applications.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8729b526-dac8-11e7-a322-c3b4e4cf064a","identifier":"8729b526-dac8-11e7-a322-c3b4e4cf064a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.6","fullStatement":"Use matrices to represent and manipulate data, e.g., transformations of vectors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d73219dc-dac8-11e7-a78e-5bb5b9d05675","identifier":"d73219dc-dac8-11e7-a78e-5bb5b9d05675","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.7","fullStatement":"Multiply matrices by scalars to produce new matrices.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e8357f44-dac8-11e7-bfa0-b5eef7fe529e","identifier":"e8357f44-dac8-11e7-bfa0-b5eef7fe529e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.8","fullStatement":"Add, subtract, and multiply matrices of appropriate dimensions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/77dca726-dac9-11e7-a4a7-7dd4022758e0","identifier":"77dca726-dac9-11e7-a4a7-7dd4022758e0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.9","fullStatement":"Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/87bc7a54-dac9-11e7-ad17-5109014dc414","identifier":"87bc7a54-dac9-11e7-ad17-5109014dc414","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.10","fullStatement":"Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9a1bdcb2-dac9-11e7-aa34-05d9ffa2a87d","identifier":"9a1bdcb2-dac9-11e7-aa34-05d9ffa2a87d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.11","fullStatement":"Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/abd06aea-dac9-11e7-9da0-bb578b63230e","identifier":"abd06aea-dac9-11e7-9da0-bb578b63230e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.VM.12","fullStatement":"Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1ac7b844-dacb-11e7-9170-4f9dbfd841e3","identifier":"1ac7b844-dacb-11e7-9170-4f9dbfd841e3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7","fullStatement":"Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3a3f2cca-dacb-11e7-9c44-91dc49465757","identifier":"3a3f2cca-dacb-11e7-9c44-91dc49465757","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.IF.7e","fullStatement":"Graph ~~exponential and logarithmic functions, showing intercepts and end behavior, and~~ trigonometric functions, showing period, midline, and amplitude.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/556d5c56-dacb-11e7-b496-a5a5ba043ed7","identifier":"556d5c56-dacb-11e7-b496-a5a5ba043ed7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Build new functions from existing functions","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/699f1c14-dacb-11e7-a562-91ebbc3cd834","identifier":"699f1c14-dacb-11e7-a562-91ebbc3cd834","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.4","fullStatement":"Find inverse functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/80137238-dacb-11e7-b9b3-5fb8a673db60","identifier":"80137238-dacb-11e7-b9b3-5fb8a673db60","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.BF.4d","fullStatement":"Produce an invertible function from a non-invertible function by restricting the domain.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5c29756-db64-11e7-ba15-152f40619566","identifier":"d5c29756-db64-11e7-ba15-152f40619566","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.TF.3","fullStatement":"Use special triangles to determine geometrically the values of sine, cosine, tangent for *\u03c0/3*, *\u03c0/4* and *\u03c0/6*, and use the unit circle to express the values of sine, cosine, and tangent for *\u03c0 - x*, *\u03c0 + x*, and *2\u03c0 - x* in terms of their values for *x*, where *x* is any real number.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e8207c4c-db64-11e7-a6a7-69abf167e7a7","identifier":"e8207c4c-db64-11e7-a6a7-69abf167e7a7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.F.TF.4","fullStatement":"Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/526496e2-db65-11e7-a7eb-97983c84d39e","identifier":"526496e2-db65-11e7-a7eb-97983c84d39e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.10","fullStatement":"Prove the Laws of Sines and Cosines and use them to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/43de3dac-db66-11e7-9df8-2fc12424d355","identifier":"43de3dac-db66-11e7-9df8-2fc12424d355","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use the rules of probability to compute probabilities of compound events in a uniform probability model","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5ac8a228-db66-11e7-8df5-b3b541ba8a07","identifier":"5ac8a228-db66-11e7-8df5-b3b541ba8a07","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.8","fullStatement":"Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the answer in terms of the model.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6f9b7e00-db66-11e7-af1d-893a1ea5e22d","identifier":"6f9b7e00-db66-11e7-af1d-893a1ea5e22d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.CP.9","fullStatement":"Use permutations and combinations to compute probabilities of compound events and solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d786b322-db66-11e7-9440-1d77b120e252","identifier":"d786b322-db66-11e7-9440-1d77b120e252","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.MD.5a","fullStatement":"Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fdfce864-db66-11e7-b685-7b562d72b4f3","identifier":"fdfce864-db66-11e7-b685-7b562d72b4f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.MD.6","fullStatement":"Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1603d562-db67-11e7-83a4-8b193fca2c0c","identifier":"1603d562-db67-11e7-83a4-8b193fca2c0c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.S.MD.7","fullStatement":"Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f19a5314-db74-11e7-b2ea-b9091bc4a6cc","identifier":"f19a5314-db74-11e7-b2ea-b9091bc4a6cc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Expressing Geometric Properties with Equations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/43a138e4-db75-11e7-9228-0fa18c728c3e","identifier":"43a138e4-db75-11e7-9228-0fa18c728c3e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Use coordinates to prove simple geometric theorems algebraically","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8cd74cba-db75-11e7-88e5-1f02c293af20","identifier":"8cd74cba-db75-11e7-88e5-1f02c293af20","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GPE.4","fullStatement":"Use coordinates to prove simple geometric theorems algebraically. *For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, \u221a3) lies on the circle centered at the origin and containing the point (0,2)*. (Focus on quadrilaterals, right triangles, and circles.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cbaf9212-db84-11e7-ae38-5dda92e13a95","identifier":"cbaf9212-db84-11e7-ae38-5dda92e13a95","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MSR.FQ.2a","fullStatement":"Students will be able to identify the difference between categorical and quantitative (numerical) data.<ol type=\"i\"><li>Determine the appropriate graphical display for each type of data.</li><li>Determine the type of data used to produce a given graphical display.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d41a4112-db8f-11e7-9b70-7957a659a29a","identifier":"d41a4112-db8f-11e7-9b70-7957a659a29a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Standards for Mathematical Practice Through a Statistical Lens","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a23366f0-db90-11e7-b835-1359b1ef44fe","identifier":"a23366f0-db90-11e7-b835-1359b1ef44fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Statistically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.\r\n\r\nOlder students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Statistically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Statistically proficient students check their answers to problems using a different method, and they continually ask themselves, \u201cDoes this make sense?\u201d They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/397646f4-db91-11e7-af81-4563900492db","identifier":"397646f4-db91-11e7-af81-4563900492db","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Statistically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize\u2014to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents\u2014and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/02c3b2b2-db92-11e7-b759-c9708bdb265a","identifier":"02c3b2b2-db92-11e7-b759-c9708bdb265a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Statistically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Statistically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and\u2014if there is a flaw in an argument\u2014explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8957bce2-db92-11e7-ba1b-f3d39005c692","identifier":"8957bce2-db92-11e7-ba1b-f3d39005c692","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.4","fullStatement":"Model with mathematics.","notes":"Statistically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Statistically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships statistically to draw conclusions. They routinely interpret their statistical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/db4be078-db92-11e7-9b59-2d94cb555d1a","identifier":"db4be078-db92-11e7-9b59-2d94cb555d1a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Statistically proficient students consider the available tools when solving a statistical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, statistically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making statistical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Statistically proficient students at various grade levels are able to identify relevant external statistical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0d637954-db93-11e7-b077-b9ecd1bc4bc0","identifier":"0d637954-db93-11e7-b077-b9ecd1bc4bc0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.6","fullStatement":"Attend to precision.","notes":"Statistically proficient students try to communicate precisely to others. They use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3e403bde-db93-11e7-8bd0-7df5f5416b06","identifier":"3e403bde-db93-11e7-8bd0-7df5f5416b06","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.7","fullStatement":"Look for and make use of structure.","notes":"Statistically proficient students look closely to discern a pattern or structure. Patterns are prevalent in statistics and can often be quantified. Randomization provides the foundation for identifying patterns in variability, thereby allowing students to quantify uncertainty.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/742bfb84-db93-11e7-af1c-19f288a85343","identifier":"742bfb84-db93-11e7-af1c-19f288a85343","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Statistically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. As they work to solve a problem, statistically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their results in the context of the statistical question.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f7f5dc2e-dc3c-11e7-8f9e-3bae47641570","identifier":"f7f5dc2e-dc3c-11e7-8f9e-3bae47641570","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Students will learn the basics of algebra and functions in two or more dimensions to\r\nprepare for the study of differentiation and integration of functions of several variables. In\r\naddition, students will explore and summarize the educational requirements and\r\nprofessional expectations associated with engineering career paths and solve problems\r\nrelated to various engineering disciplines.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8827c5be-dc3d-11e7-85f6-01acf0faffa1","identifier":"8827c5be-dc3d-11e7-85f6-01acf0faffa1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.1","fullStatement":"Students will apply knowledge of mathematics, science, and engineering design to\r\nsolve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a68c48b8-dc3d-11e7-8a3c-df8ab3eb27b2","identifier":"a68c48b8-dc3d-11e7-8a3c-df8ab3eb27b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.1a","fullStatement":"Determine the equations of lines and surfaces using vectors and 3D graphing.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c181b982-dc3d-11e7-ba2b-579da753fee7","identifier":"c181b982-dc3d-11e7-ba2b-579da753fee7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.1b","fullStatement":"Apply dot and cross products of vectors to express equations of planes, parallelism, perpendicularity, angles.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ded9911c-dc3d-11e7-9fe9-4d0dde133081","identifier":"ded9911c-dc3d-11e7-9fe9-4d0dde133081","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.1c","fullStatement":"Describe the role of vectors in engineering applications, such as modeling the velocity of moving objects or static forces on structures and objects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fbf10988-dc3d-11e7-9a19-7989c080625e","identifier":"fbf10988-dc3d-11e7-9a19-7989c080625e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.2","fullStatement":"Students will learn to evaluate matrices and apply their properties to solve engineering\r\nproblems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0f7dd940-dc3e-11e7-b9d2-ebd4e52ac5c3","identifier":"0f7dd940-dc3e-11e7-b9d2-ebd4e52ac5c3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.2a","fullStatement":"Calculate determinants of matrices.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/23ed29d0-dc3e-11e7-a2f1-e10979894374","identifier":"23ed29d0-dc3e-11e7-a2f1-e10979894374","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.2b","fullStatement":"Express systems of linear equations in matrix equation form.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3bf6088a-dc3e-11e7-a0a4-fb5a3f77e19c","identifier":"3bf6088a-dc3e-11e7-a0a4-fb5a3f77e19c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.2c","fullStatement":"Use Gaussian elimination to compute solution sets of linear systems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/553761ae-dc3e-11e7-94ed-abf9bb8892a9","identifier":"553761ae-dc3e-11e7-94ed-abf9bb8892a9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.3","fullStatement":"Students will investigate functions of two and three independent variables to model\r\nengineering systems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/694b6ee2-dc3e-11e7-bf3f-97608ceeecac","identifier":"694b6ee2-dc3e-11e7-bf3f-97608ceeecac","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.3a","fullStatement":"Compute limits of scalar and vector-valued functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8dc51908-dc3e-11e7-90a1-81462784783a","identifier":"8dc51908-dc3e-11e7-90a1-81462784783a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.3b","fullStatement":"Identify and graph level curves of multivariate functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a34c2b7c-dc3e-11e7-8fd4-a150a416f229","identifier":"a34c2b7c-dc3e-11e7-8fd4-a150a416f229","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.3c","fullStatement":"Calculate regions of continuity of such functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c76632dc-dc3e-11e7-aa4b-a5e1535be5d0","identifier":"c76632dc-dc3e-11e7-aa4b-a5e1535be5d0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.4","fullStatement":"Students will use visual and written communication to express basic design elements\r\nin the appropriate mathematics notation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e113d91e-dc3e-11e7-9524-990ee84096e6","identifier":"e113d91e-dc3e-11e7-9524-990ee84096e6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.4a","fullStatement":"Demonstrate fundamentals of technical sketching using computer-generated visuals by using the appropriate mathematics scale.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd03c38c-dc3e-11e7-836d-adaa3ecb3650","identifier":"fd03c38c-dc3e-11e7-836d-adaa3ecb3650","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.A.4b","fullStatement":"Present a technical design, using computer-generated model, for an assigned design project utilizing the appropriate scientific units (US standards and SI units).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1d477542-dc41-11e7-9fc8-0b9f416f97f4","identifier":"1d477542-dc41-11e7-9fc8-0b9f416f97f4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1","fullStatement":"Students will apply the techniques of double and triple integration to multivariable\r\nscalar- and vector-valued functions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3b426ed0-dc41-11e7-993b-2bf9518cc680","identifier":"3b426ed0-dc41-11e7-993b-2bf9518cc680","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1a","fullStatement":"Manipulate integrals by changing the order of integration, introducing variable substitutions, or changing to curvilinear coordinates.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/58a42b8a-dc41-11e7-995d-93de6d67b1c2","identifier":"58a42b8a-dc41-11e7-995d-93de6d67b1c2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1b","fullStatement":"Evaluate and apply line integrals that are independent of path.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6cad4ddc-dc41-11e7-9bb6-97c22bbc42ab","identifier":"6cad4ddc-dc41-11e7-9bb6-97c22bbc42ab","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1c","fullStatement":"Apply properties of integrals to calculate and represent area, volume, or mass.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/89c94326-dc41-11e7-b03d-436c19425005","identifier":"89c94326-dc41-11e7-b03d-436c19425005","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1d","fullStatement":"Use integrals of vectors to define and apply the gradient, divergence, or the curl.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9d457078-dc41-11e7-aab1-7fa1a1f5b716","identifier":"9d457078-dc41-11e7-aab1-7fa1a1f5b716","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MEC.I.1e","fullStatement":"Interpret the theorems of Green, Stokes, or Gauss and apply them to the study of real-world phenomena.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c4c91dfc-ab2b-11e8-b76a-15fb169fc09e","identifier":"c4c91dfc-ab2b-11e8-b76a-15fb169fc09e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.4a","fullStatement":"When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (one-to-one correspondence)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/dd7c434c-ab2b-11e8-b278-8fb9314bee92","identifier":"dd7c434c-ab2b-11e8-b278-8fb9314bee92","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.4b","fullStatement":"Understand that the last number name said tells the number of objects counted (cardinality). The number of objects is the same regardless of their arrangement or the order in which they were counted.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eec77e8c-ab2b-11e8-b479-53171d07b5d3","identifier":"eec77e8c-ab2b-11e8-b479-53171d07b5d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.4c","fullStatement":"Understand that each successive number name refers to a quantity that is one larger.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2d968428-ab2c-11e8-80c7-178cd0f5a4af","identifier":"2d968428-ab2c-11e8-80c7-178cd0f5a4af","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.5a","fullStatement":"Count to answer \u201chow many?\u201d questions about as many as 20 things arranged in a variety of ways (a line, a rectangular array, or a circle), or as many as 10 things in a scattered configuration.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4158ee2e-ab2c-11e8-a40b-a3fede276fad","identifier":"4158ee2e-ab2c-11e8-a40b-a3fede276fad","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.5b","fullStatement":"Given a number from 1-20, count out that many objects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/500495f4-ab2c-11e8-aa56-9d6ee5f2d620","identifier":"500495f4-ab2c-11e8-aa56-9d6ee5f2d620","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["KG"],"humanCodingScheme":"MGSEK.CC.5c","fullStatement":"Identify and be able to count pennies within 20. (Use pennies as manipulatives in multiple mathematical contexts.)","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fb917080-ab2d-11e8-a226-67dac41c2818","identifier":"fb917080-ab2d-11e8-a226-67dac41c2818","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.6a","fullStatement":"Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 \u2013 4 = 13 \u2013 3 \u2013 1 = 10 \u2013 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 \u2013 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0dd563b4-ab2e-11e8-943b-6db6eee5f994","identifier":"0dd563b4-ab2e-11e8-943b-6db6eee5f994","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["01"],"humanCodingScheme":"MGSE1.OA.6b","fullStatement":"Fluently add and subtract within 10.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4f59ff02-ab2e-11e8-8190-45b1f8cbc494","identifier":"4f59ff02-ab2e-11e8-8190-45b1f8cbc494","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.2a","fullStatement":"10 can be thought of as a bundle of ten ones \u2014 called a \u201cten.\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/615608ae-ab2e-11e8-85d4-214402870e84","identifier":"615608ae-ab2e-11e8-85d4-214402870e84","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.2b","fullStatement":"The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ee8b0f2-ab2e-11e8-a603-716eebdae864","identifier":"6ee8b0f2-ab2e-11e8-a603-716eebdae864","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["01"],"humanCodingScheme":"MGSE1.NBT.2c","fullStatement":"The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6b421950-ab30-11e8-b175-a3600b89c68b","identifier":"6b421950-ab30-11e8-b175-a3600b89c68b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.1a","fullStatement":"100 can be thought of as a bundle of ten tens \u2014 called a \u201chundred.\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7f7d2270-ab30-11e8-bc2f-17b3039e8fb4","identifier":"7f7d2270-ab30-11e8-bc2f-17b3039e8fb4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["02"],"humanCodingScheme":"MGSE2.NBT.1b","fullStatement":"The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/61e1f388-ab69-11e8-8ced-a11e414c1ccd","identifier":"61e1f388-ab69-11e8-8ced-a11e414c1ccd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.5a","fullStatement":"A square with side length 1 unit, called \u201ca unit square,\u201d is said to have \u201cone square unit\u201d of area, and can be used to measure area.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7de9dc94-ab69-11e8-b45c-e9997a135e33","identifier":"7de9dc94-ab69-11e8-b45c-e9997a135e33","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["03"],"humanCodingScheme":"MGSE3.MD.5b","fullStatement":"A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of *n* square units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/43fccc52-ab6a-11e8-8e66-15817186ea77","identifier":"43fccc52-ab6a-11e8-8e66-15817186ea77","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.1a","fullStatement":"Interpret a multiplication equation as a comparison e.g., interpret 35 = 5 \u00d7 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5c5265c8-ab6a-11e8-8023-5bcd6fe59821","identifier":"5c5265c8-ab6a-11e8-8023-5bcd6fe59821","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.OA.1b","fullStatement":"Represent verbal statements of multiplicative comparisons as multiplication equations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e0cfab48-ab6b-11e8-a4cb-7f8f7476f817","identifier":"e0cfab48-ab6b-11e8-a4cb-7f8f7476f817","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.1a","fullStatement":"Understand the relationship between gallons, cups, quarts, and pints.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f6b3bde6-ab6b-11e8-9b75-85b5bca5b94a","identifier":"f6b3bde6-ab6b-11e8-9b75-85b5bca5b94a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.1b","fullStatement":"Express larger units in terms of smaller units within the same measurement system.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0829162a-ab6c-11e8-bc34-db85f1453a25","identifier":"0829162a-ab6c-11e8-bc34-db85f1453a25","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.1c","fullStatement":"Record measurement equivalents in a two column table.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4c63dc4e-ab6c-11e8-be48-834709eb1126","identifier":"4c63dc4e-ab6c-11e8-be48-834709eb1126","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.5a","fullStatement":"An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a \u201cone-degree angle,\u201d and can be used to measure angles.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6153fdc8-ab6c-11e8-b89a-699cf4e6dabe","identifier":"6153fdc8-ab6c-11e8-b89a-699cf4e6dabe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["04"],"humanCodingScheme":"MGSE4.MD.5b","fullStatement":"An angle that turns through n one-degree angles is said to have an angle measure of *n* degrees.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab48d222-ab6d-11e8-b663-8fa96e5b7691","identifier":"ab48d222-ab6d-11e8-b663-8fa96e5b7691","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.5.a","fullStatement":"Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. *Example: 4 x 10 is twice as large as 2 x 10.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cdd380c6-ab6d-11e8-a658-91603fd6d1e4","identifier":"cdd380c6-ab6d-11e8-a658-91603fd6d1e4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.NF.5.b","fullStatement":"Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence <i> $\\frac{a}{b}$ = $\\frac{(n \\times a)}{(n \\times b)}$</i> to the effect of multiplying <i>$\\frac{a}{b}$</i> by 1.</li></ol>","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8c08b35e-ab6e-11e8-8c68-07161863eb4e","identifier":"8c08b35e-ab6e-11e8-8c68-07161863eb4e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.3.a","fullStatement":"A cube with side length 1 unit, called a \u201cunit cube,\u201d is said to have \u201cone cubic unit\u201d of volume, and can be used to measure volume.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a13b3440-ab6e-11e8-9779-4b349064a9b0","identifier":"a13b3440-ab6e-11e8-9779-4b349064a9b0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["05"],"humanCodingScheme":"MGSE5.MD.3.b","fullStatement":"A solid figure which can be packed without gaps or overlaps using of *n* unit cubes is said to have a volume of *n* cubic units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0650cd30-ab70-11e8-9452-a32a93fd0a96","identifier":"0650cd30-ab70-11e8-9452-a32a93fd0a96","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.4a","fullStatement":"Find the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factors. (GCF) *Example: 36 + 8 = 4(9 + 2)*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1e08200e-ab70-11e8-9f37-a320e6cb7c87","identifier":"1e08200e-ab70-11e8-9f37-a320e6cb7c87","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.NS.4b","fullStatement":"Apply the least common multiple of two whole numbers less than or equal to 12 to solve real-world problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/86223188-ab71-11e8-9beb-3b84775a6550","identifier":"86223188-ab71-11e8-9beb-3b84775a6550","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.9a","fullStatement":"Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a030b298-ab71-11e8-abb1-971966241112","identifier":"a030b298-ab71-11e8-abb1-971966241112","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.EE.9b","fullStatement":"Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. *For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/23186c46-ab72-11e8-ae84-179c91cb218a","identifier":"23186c46-ab72-11e8-ae84-179c91cb218a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.5a","fullStatement":"Reporting the number of observations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/31abe58a-ab72-11e8-80d9-4bbfe82c09d9","identifier":"31abe58a-ab72-11e8-80d9-4bbfe82c09d9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.5b","fullStatement":"Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/41317d44-ab72-11e8-8534-4f29f7e01804","identifier":"41317d44-ab72-11e8-8534-4f29f7e01804","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.5c","fullStatement":"Giving quantitative measures of center (median and/or mean) and variability (interquartile range).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/55ce920a-ab72-11e8-ad80-a1b6c3c079f9","identifier":"55ce920a-ab72-11e8-ad80-a1b6c3c079f9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["06"],"humanCodingScheme":"MGSE6.SP.5d","fullStatement":"Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b4e3b436-ab91-11e8-9ba4-c9e6b9a6b57d","identifier":"b4e3b436-ab91-11e8-9ba4-c9e6b9a6b57d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.4a","fullStatement":"Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c8024bfe-ab91-11e8-b5b9-7df6db827742","identifier":"c8024bfe-ab91-11e8-b5b9-7df6db827742","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.4b","fullStatement":"Use relative frequencies calculated for rows or columns to describe possible association between the two variables. *For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19aa6b6-ac39-11e8-8079-03adcc91c635","identifier":"a19aa6b6-ac39-11e8-8079-03adcc91c635","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP","fullStatement":"Kindergarten - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b0a66-ac39-11e8-a25b-819bc1e83638","identifier":"a19b0a66-ac39-11e8-a25b-819bc1e83638","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In Kindergarten, students begin to build the understanding that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Younger students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, \u201cDoes this make sense?\u201d or they may try another strategy.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b2910-ac39-11e8-8b73-413cf9054ae1","identifier":"a19b2910-ac39-11e8-8b73-413cf9054ae1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Younger students begin to recognize that a number represents a specific quantity. Then, they connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b453a-ac39-11e8-9c56-9310c6500bae","identifier":"a19b453a-ac39-11e8-9c56-9310c6500bae","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Younger students construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They also begin to develop their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d and \u201cWhy is that true?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b60d8-ac39-11e8-acfa-8381a81ef9fe","identifier":"a19b60d8-ac39-11e8-acfa-8381a81ef9fe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.4","fullStatement":"Model with mathematics.","notes":"In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b7d3e-ac39-11e8-a593-b761348cbe61","identifier":"a19b7d3e-ac39-11e8-a593-b761348cbe61","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Younger students begin to consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, kindergarteners may decide that it might be advantageous to use linking cubes to represent two quantities and then compare the two representations side-by-side.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19b9a76-ac39-11e8-9f80-41078bc1ee31","identifier":"a19b9a76-ac39-11e8-9f80-41078bc1ee31","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.6","fullStatement":"Attend to precision.","notes":"As kindergarteners begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19bb6f0-ac39-11e8-9033-d7522f006d04","identifier":"a19bb6f0-ac39-11e8-9033-d7522f006d04","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Younger students begin to discern a pattern or structure. For instance, students recognize the pattern that exists in the teen numbers; every teen number is written with a 1 (representing one ten) and ends with the digit that is first stated. They also recognize that 3 + 2 = 5 and 2 + 3 = 5.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a19bd2b6-ac39-11e8-8623-355ed0884de0","identifier":"a19bd2b6-ac39-11e8-8623-355ed0884de0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["KG"],"humanCodingScheme":"MGSEK.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"In the early grades, students notice repetitive actions in counting and computation, etc. For example, they may notice that the next number in a counting sequence is one more. When counting by tens, the next number in the sequence is \u201cten more\u201d (or one more group of ten). In addition, students continually check their work by asking themselves, \u201cDoes this make sense?\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3c72e69a-ac3e-11e8-bb7b-f10f77a60c2c","identifier":"3c72e69a-ac3e-11e8-bb7b-f10f77a60c2c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1a","fullStatement":"Identify, use, and record appropriate units of measure within context, within data displays, and on graphs;","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/515511be-ac3e-11e8-9d52-a9f11005ae44","identifier":"515511be-ac3e-11e8-9d52-a9f11005ae44","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1b","fullStatement":"Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/632aae30-ac3e-11e8-839c-b51ee4534433","identifier":"632aae30-ac3e-11e8-839c-b51ee4534433","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1c","fullStatement":"Use units within multi-step problems and formulas; interpret units of input and resulting units of output.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e6bb4156-ac61-11e8-bb78-c1a193c16cfd","identifier":"e6bb4156-ac61-11e8-bb78-c1a193c16cfd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1a","fullStatement":"Identify, use, and record appropriate units of measure within context, within data displays, and on graphs;","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/01ecf352-ac62-11e8-8ccc-635ce4b6996a","identifier":"01ecf352-ac62-11e8-8ccc-635ce4b6996a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1b","fullStatement":"Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2fff939e-ac62-11e8-b268-3f4b1e511e82","identifier":"2fff939e-ac62-11e8-b268-3f4b1e511e82","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1c","fullStatement":"Use units within multi-step problems and formulas; interpret units of input and resulting units of output.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7bbb7fa8-ac64-11e8-8e1e-7355cc95f794","identifier":"7bbb7fa8-ac64-11e8-8e1e-7355cc95f794","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1a","fullStatement":"The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8e80132e-ac64-11e8-a816-5f959c94139d","identifier":"8e80132e-ac64-11e8-a816-5f959c94139d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1b","fullStatement":"The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55f1f9c-ac66-11e8-b9dd-595782c5038f","identifier":"b55f1f9c-ac66-11e8-b9dd-595782c5038f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP","fullStatement":"Grade 1 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction.* \r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55f77e4-ac66-11e8-9531-d1495d434b1d","identifier":"b55f77e4-ac66-11e8-9531-d1495d434b1d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In first grade, students realize that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Younger students may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, \u201cDoes this make sense?\u201d They are willing to try other approaches.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55f9404-ac66-11e8-987c-a9538ba323aa","identifier":"b55f9404-ac66-11e8-987c-a9538ba323aa","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55fadc2-ac66-11e8-89b0-09298ed96fc1","identifier":"b55fadc2-ac66-11e8-89b0-09298ed96fc1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"First graders construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They also practice their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d \u201cExplain your thinking,\u201d and \u201cWhy is that true?\u201d They not only explain their own thinking, but listen to others\u2019 explanations. They decide if the explanations make sense and ask questions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55fc7c6-ac66-11e8-bf20-4b004af097f3","identifier":"b55fc7c6-ac66-11e8-bf20-4b004af097f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.4","fullStatement":"Model with mathematics.","notes":"In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55fe1f2-ac66-11e8-a74f-bd0f7bee22d3","identifier":"b55fe1f2-ac66-11e8-a74f-bd0f7bee22d3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"In first grade, students begin to consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, first graders decide it might be best to use colored chips to model an addition problem.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b55ffb1a-ac66-11e8-bd0e-ff275b4ce35f","identifier":"b55ffb1a-ac66-11e8-bd0e-ff275b4ce35f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.6","fullStatement":"Attend to precision.","notes":"As young children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and when they explain their own reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b5601848-ac66-11e8-8365-1d4d2198bf6d","identifier":"b5601848-ac66-11e8-8365-1d4d2198bf6d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.7","fullStatement":"Look for and make use of structure.","notes":"First graders begin to discern a pattern or structure. For instance, if students recognize 12 + 3 = 15, then they also know *3 + 12 = 15*. (*Commutative property of addition.*) To add *4 + 6 + 4, the first two numbers can be added to make a ten, so 4 + 6 + 4 = 10 + 4 = 14*.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b56033be-ac66-11e8-be08-b5e3927df321","identifier":"b56033be-ac66-11e8-be08-b5e3927df321","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["01"],"humanCodingScheme":"MGSE1.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"In the early grades, students notice repetitive actions in counting and computation, etc. When children have multiple opportunities to add and subtract \u201cten\u201d and multiples of \u201cten\u201d they notice the pattern and gain a better understanding of place value. Students continually check their work by asking themselves, \u201cDoes this make sense?\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/305f51e8-ac6d-11e8-9d86-614b42eaf0e9","identifier":"305f51e8-ac6d-11e8-9d86-614b42eaf0e9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Domain","educationLevel":["09","10","11","12"],"fullStatement":"Quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/305ff166-ac6d-11e8-bc98-034e64da3766","identifier":"305ff166-ac6d-11e8-bc98-034e64da3766","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1a","fullStatement":"Identify, use, and record appropriate units of measure within context, within data displays, and on graphs;","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/305fb80e-ac6d-11e8-aec7-59f26c989ff9","identifier":"305fb80e-ac6d-11e8-aec7-59f26c989ff9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1","fullStatement":"Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/305f82a8-ac6d-11e8-8122-01ab5bb8afa1","identifier":"305f82a8-ac6d-11e8-8122-01ab5bb8afa1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Reason quantitatively and use units to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/30604e54-ac6d-11e8-8590-c5f7b23dfc4d","identifier":"30604e54-ac6d-11e8-8590-c5f7b23dfc4d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.2","fullStatement":"Define appropriate quantities for the purpose of descriptive modeling. Given a situation, context, or problem, students will determine, identify, and use appropriate quantities for representing the situation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/30606b3c-ac6d-11e8-9baf-9f06e7cb3580","identifier":"30606b3c-ac6d-11e8-9baf-9f06e7cb3580","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.3","fullStatement":"Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. *For example, money situations are generally reported to the nearest cent (hundredth). Also, an answers' precision is limited to the precision of the data given.*","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3060118c-ac6d-11e8-b8de-b198ce24b52f","identifier":"3060118c-ac6d-11e8-b8de-b198ce24b52f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1b","fullStatement":"Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/30602fd2-ac6d-11e8-86da-2f6b04eb1134","identifier":"30602fd2-ac6d-11e8-86da-2f6b04eb1134","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1c","fullStatement":"Use units within multi-step problems and formulas; interpret units of input and resulting units of output.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ebf634-ac6e-11e8-9e2d-a337bf06903c","identifier":"b6ebf634-ac6e-11e8-9e2d-a337bf06903c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand similarity in terms of similarity transformations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ec6222-ac6e-11e8-ab8a-8fbd00e5e3b8","identifier":"b6ec6222-ac6e-11e8-ab8a-8fbd00e5e3b8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1a","fullStatement":"The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ec33ce-ac6e-11e8-94b8-15c0df8d3cf5","identifier":"b6ec33ce-ac6e-11e8-94b8-15c0df8d3cf5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1","fullStatement":"Verify experimentally the properties of dilations given by a center and a scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ec7d84-ac6e-11e8-a7fb-8f4811ff43c2","identifier":"b6ec7d84-ac6e-11e8-a7fb-8f4811ff43c2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1b","fullStatement":"The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ec974c-ac6e-11e8-9113-e57e6ba962f0","identifier":"b6ec974c-ac6e-11e8-9113-e57e6ba962f0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.3","fullStatement":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6ecb0c4-ac6e-11e8-b07b-177fede8da64","identifier":"b6ecb0c4-ac6e-11e8-b07b-177fede8da64","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.2","fullStatement":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/594c7840-ac6f-11e8-a6b6-81fcf225eb3c","identifier":"594c7840-ac6f-11e8-a6b6-81fcf225eb3c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1a","fullStatement":"Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6cfe3036-ac6f-11e8-bfb8-4be0bf54f9c8","identifier":"6cfe3036-ac6f-11e8-bfb8-4be0bf54f9c8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1b","fullStatement":"Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri\u2019s principle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a839fa4c-ac72-11e8-b7e9-e9c69df99fba","identifier":"a839fa4c-ac72-11e8-b7e9-e9c69df99fba","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand similarity in terms of similarity transformations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a83a6608-ac72-11e8-b43c-e5fa5d306d32","identifier":"a83a6608-ac72-11e8-b43c-e5fa5d306d32","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1a","fullStatement":"The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a83a366a-ac72-11e8-9f09-45e443b19e46","identifier":"a83a366a-ac72-11e8-9f09-45e443b19e46","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1","fullStatement":"Verify experimentally the properties of dilations given by a center and a scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a83a8322-ac72-11e8-a4fb-5de8fbc9f24f","identifier":"a83a8322-ac72-11e8-a4fb-5de8fbc9f24f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1b","fullStatement":"The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a83aa0be-ac72-11e8-a6c6-73ba49b53ae2","identifier":"a83aa0be-ac72-11e8-a6c6-73ba49b53ae2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.3","fullStatement":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a83abcd4-ac72-11e8-8af3-cbbbe15ac9e6","identifier":"a83abcd4-ac72-11e8-8af3-cbbbe15ac9e6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.2","fullStatement":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4003ea36-ac73-11e8-bc7a-35fa0fddeee7","identifier":"4003ea36-ac73-11e8-bc7a-35fa0fddeee7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Explain volume formulas and use them to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/40046100-ac73-11e8-adb3-5ff5d05fa06a","identifier":"40046100-ac73-11e8-adb3-5ff5d05fa06a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1a","fullStatement":"Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/40042de8-ac73-11e8-92c2-75d4a4a2d9d8","identifier":"40042de8-ac73-11e8-92c2-75d4a4a2d9d8","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1","fullStatement":"Give informal arguments for geometric formulas.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4004800e-ac73-11e8-a0da-f7c6370b73bc","identifier":"4004800e-ac73-11e8-a0da-f7c6370b73bc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1b","fullStatement":"Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri\u2019s principle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/40049e04-ac73-11e8-b216-29fd266e78f3","identifier":"40049e04-ac73-11e8-b216-29fd266e78f3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.2","fullStatement":"Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4004ba4c-ac73-11e8-82a1-0526f4da64f4","identifier":"4004ba4c-ac73-11e8-82a1-0526f4da64f4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.3","fullStatement":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c90aab8-ac74-11e8-acfd-57b4590159f1","identifier":"9c90aab8-ac74-11e8-acfd-57b4590159f1","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP","fullStatement":"Grade 2 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c91035a-ac74-11e8-b418-0763bbcae0b2","identifier":"9c91035a-ac74-11e8-b418-0763bbcae0b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In second grade, students realize that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. They may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, \u201cDoes this make sense?\u201d They make conjectures about the solution and plan out a problem-solving approach.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c911f48-ac74-11e8-b4e6-534bbcc7faa9","identifier":"9c911f48-ac74-11e8-b4e6-534bbcc7faa9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities. Second graders begin to know and use different properties of operations and objects","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c9138b6-ac74-11e8-bf22-a5c2ed9c2fff","identifier":"9c9138b6-ac74-11e8-bf22-a5c2ed9c2fff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Second graders may construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They practice their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d, \u201cExplain your thinking,\u201d and \u201cWhy is that true?\u201d They not only explain their own thinking, but listen to others\u2019 explanations. They decide if the explanations make sense and ask appropriate questions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c91524c-ac74-11e8-82fa-41362b86451c","identifier":"9c91524c-ac74-11e8-82fa-41362b86451c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.4","fullStatement":"Model with mathematics.","notes":"In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c916bb0-ac74-11e8-866b-0543568c5ac2","identifier":"9c916bb0-ac74-11e8-866b-0543568c5ac2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"In second grade, students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be better suited. For instance, second graders may decide to solve a problem by drawing a picture rather than writing an equation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c9184a6-ac74-11e8-a6c9-7f4e46f6b91b","identifier":"9c9184a6-ac74-11e8-a6c9-7f4e46f6b91b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.6","fullStatement":"Attend to precision.","notes":"As children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and when they explain their own reasoning.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c919e1e-ac74-11e8-8dac-134e54f51fe9","identifier":"9c919e1e-ac74-11e8-8dac-134e54f51fe9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Second graders look for patterns. For instance, they adopt mental math strategies based on patterns (making ten, fact families, doubles).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c91b688-ac74-11e8-82ea-fd9a8734b907","identifier":"9c91b688-ac74-11e8-82ea-fd9a8734b907","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["02"],"humanCodingScheme":"MGSE2.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Students notice repetitive actions in counting and computation, etc. When children have multiple opportunities to add and subtract, they look for shortcuts, such as rounding up and then adjusting the answer to compensate for the rounding. Students continually check their work by asking themselves, does this make sense?","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/df63854c-ac77-11e8-a42d-1b4c1d740c93","identifier":"df63854c-ac77-11e8-a42d-1b4c1d740c93","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Construct and compare linear, quadratic, and exponential models and solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/40806b38-ac78-11e8-978c-4d3a03f6c8c9","identifier":"40806b38-ac78-11e8-978c-4d3a03f6c8c9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Explain volume formulas and use them to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4080d94c-ac78-11e8-b136-ad774d9ebee3","identifier":"4080d94c-ac78-11e8-b136-ad774d9ebee3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1a","fullStatement":"Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4080a788-ac78-11e8-ba50-ab7ee32ca914","identifier":"4080a788-ac78-11e8-ba50-ab7ee32ca914","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1","fullStatement":"Give informal arguments for geometric formulas.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4080f67a-ac78-11e8-9c43-ab1ee2335ffd","identifier":"4080f67a-ac78-11e8-9c43-ab1ee2335ffd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1b","fullStatement":"Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri\u2019s principle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/408113b2-ac78-11e8-bdaa-f7c0fa50ff71","identifier":"408113b2-ac78-11e8-bdaa-f7c0fa50ff71","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.2","fullStatement":"Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/40812fd2-ac78-11e8-8ef4-7b0fdb416285","identifier":"40812fd2-ac78-11e8-8ef4-7b0fdb416285","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.3","fullStatement":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/748942fe-ac7a-11e8-b336-b1d75d3a1e5d","identifier":"748942fe-ac7a-11e8-b336-b1d75d3a1e5d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Understand similarity in terms of similarity transformations","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7489acee-ac7a-11e8-b676-c16602be0dc7","identifier":"7489acee-ac7a-11e8-b676-c16602be0dc7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1a","fullStatement":"The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/74897ec2-ac7a-11e8-8171-f503441772ad","identifier":"74897ec2-ac7a-11e8-8171-f503441772ad","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1","fullStatement":"Verify experimentally the properties of dilations given by a center and a scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7489c828-ac7a-11e8-89bf-e1798f4df2c3","identifier":"7489c828-ac7a-11e8-89bf-e1798f4df2c3","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.1b","fullStatement":"The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7489e254-ac7a-11e8-9a98-dbf73692091e","identifier":"7489e254-ac7a-11e8-9a98-dbf73692091e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.3","fullStatement":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7489fb0e-ac7a-11e8-8622-4f9586e9eea7","identifier":"7489fb0e-ac7a-11e8-8622-4f9586e9eea7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.SRT.2","fullStatement":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196b3e26-ac7b-11e8-a7e5-09921c7e0400","identifier":"196b3e26-ac7b-11e8-a7e5-09921c7e0400","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Cluster","educationLevel":["09","10","11","12"],"fullStatement":"Explain volume formulas and use them to solve problems","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196badf2-ac7b-11e8-9a7a-9b319e6aeae7","identifier":"196badf2-ac7b-11e8-9a7a-9b319e6aeae7","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1a","fullStatement":"Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196b7eae-ac7b-11e8-b1bc-4fcfddc6bb6d","identifier":"196b7eae-ac7b-11e8-b1bc-4fcfddc6bb6d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1","fullStatement":"Give informal arguments for geometric formulas.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196bc86e-ac7b-11e8-bbf5-c974295ec43d","identifier":"196bc86e-ac7b-11e8-bbf5-c974295ec43d","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1b","fullStatement":"Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri\u2019s principle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196be358-ac7b-11e8-b6b5-ef2155070d49","identifier":"196be358-ac7b-11e8-b6b5-ef2155070d49","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.2","fullStatement":"Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/196bfd2a-ac7b-11e8-9019-bd40e5d747a5","identifier":"196bfd2a-ac7b-11e8-9019-bd40e5d747a5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.3","fullStatement":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb06fcce-ac85-11e8-b9d6-91ca84a09600","identifier":"cb06fcce-ac85-11e8-b9d6-91ca84a09600","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP","fullStatement":"Grade 3 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction.* \r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb07594e-ac85-11e8-8f32-57f08ef38808","identifier":"cb07594e-ac85-11e8-8f32-57f08ef38808","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In third grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, \u201cDoes this make sense?\u201d They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb0777e4-ac85-11e8-94b7-dfe517c0b620","identifier":"cb0777e4-ac85-11e8-94b7-dfe517c0b620","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Third graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb07958a-ac85-11e8-b46d-c93bd633041b","identifier":"cb07958a-ac85-11e8-b46d-c93bd633041b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In third grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d and \u201cWhy is that true?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb07b1fa-ac85-11e8-a68c-0923225ab135","identifier":"cb07b1fa-ac85-11e8-a68c-0923225ab135","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.4","fullStatement":"Model with mathematics.","notes":"Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Third graders should evaluate their results in the context of the situation and reflect on whether the results make sense.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb07cf82-ac85-11e8-b83f-3924b5136381","identifier":"cb07cf82-ac85-11e8-b83f-3924b5136381","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Third graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb07ecf6-ac85-11e8-ae5b-a15b472018dd","identifier":"cb07ecf6-ac85-11e8-ae5b-a15b472018dd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.6","fullStatement":"Attend to precision.","notes":"As third graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb080952-ac85-11e8-b1ad-3368c8d6b29a","identifier":"cb080952-ac85-11e8-b1ad-3368c8d6b29a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.7","fullStatement":"Look for and make use of structure.","notes":"In third grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb082716-ac85-11e8-8c38-7d11916542b2","identifier":"cb082716-ac85-11e8-8c38-7d11916542b2","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["03"],"humanCodingScheme":"MGSE3.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don\u2019t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, \u201cDoes this make sense?","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27efae8e-ad19-11e8-b68b-2b855c461b90","identifier":"27efae8e-ad19-11e8-b68b-2b855c461b90","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP","fullStatement":"Grade 4 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately),","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f00d70-ad19-11e8-8474-a39a4eec6398","identifier":"27f00d70-ad19-11e8-8474-a39a4eec6398","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In fourth grade, students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, \u201cDoes this make sense?\u201d They listen to the strategies of others and will try different approaches. They often will use another method to check their answers","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f0292c-ad19-11e8-b3da-f1fa76c1daa0","identifier":"27f0292c-ad19-11e8-b3da-f1fa76c1daa0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f04358-ad19-11e8-98dc-dd3dd717f42b","identifier":"27f04358-ad19-11e8-98dc-dd3dd717f42b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In fourth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between models and equations. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d and \u201cWhy is that true?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f05dca-ad19-11e8-b1ff-133eb6d04188","identifier":"27f05dca-ad19-11e8-b1ff-133eb6d04188","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.4","fullStatement":"Model with mathematics.","notes":"Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f0767a-ad19-11e8-8798-bf79b922e54e","identifier":"27f0767a-ad19-11e8-8798-bf79b922e54e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f09010-ad19-11e8-8d9a-c753831535a6","identifier":"27f09010-ad19-11e8-8d9a-c753831535a6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.6","fullStatement":"Attend to precision.","notes":"As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f0a992-ad19-11e8-99e7-3fb42884f10a","identifier":"27f0a992-ad19-11e8-99e7-3fb42884f10a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.7","fullStatement":"Look for and make use of structure.","notes":"In fourth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations to explain calculations (partial products model). They relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns that follow a given rule.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27f0c21a-ad19-11e8-a345-87ac23e16ef6","identifier":"27f0c21a-ad19-11e8-a345-87ac23e16ef6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["04"],"humanCodingScheme":"MGSE4.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent fractions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248ea020-ad1d-11e8-ad2c-713c44beabec","identifier":"248ea020-ad1d-11e8-ad2c-713c44beabec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP","fullStatement":"Grade 5 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248ef8e0-ad1d-11e8-8387-09d1709efd10","identifier":"248ef8e0-ad1d-11e8-8387-09d1709efd10","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, \u201cWhat is the most efficient way to solve the problem?\u201d, \u201cDoes this make sense?\u201d, and \u201cCan I solve the problem in a different way?\u201d.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f1500-ad1d-11e8-aeaa-6d221e286f10","identifier":"248f1500-ad1d-11e8-aeaa-6d221e286f10","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Fifth graders should recognize that a number represents a specific quantity. They connect quantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions that record calculations with numbers and represent or round numbers using place value concepts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f2fea-ad1d-11e8-a881-2fe5c11eca70","identifier":"248f2fea-ad1d-11e8-a881-2fe5c11eca70","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In fifth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain calculations based upon models and properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like \u201cHow did you get that?\u201d and \u201cWhy is that true?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f4944-ad1d-11e8-96ca-5924dd71b469","identifier":"248f4944-ad1d-11e8-96ca-5924dd71b469","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.4","fullStatement":"Model with mathematics.","notes":"Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f632a-ad1d-11e8-a27f-a9e08034349f","identifier":"248f632a-ad1d-11e8-a27f-a9e08034349f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f7ce8-ad1d-11e8-9a44-e386342fac8a","identifier":"248f7ce8-ad1d-11e8-9a44-e386342fac8a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.6","fullStatement":"Attend to precision.","notes":"Students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248f95d4-ad1d-11e8-a450-2365f2540721","identifier":"248f95d4-ad1d-11e8-a450-2365f2540721","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.7","fullStatement":"Look for and make use of structure.","notes":"In fifth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/248fafa6-ad1d-11e8-98e7-67b0d3db6498","identifier":"248fafa6-ad1d-11e8-98e7-67b0d3db6498","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["05"],"humanCodingScheme":"MGSE5.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Fifth graders use repeated reasoning to understand algorithms and make generalizations about patterns. Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate generalizations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4846c14e-ad1f-11e8-8260-fb31e562289c","identifier":"4846c14e-ad1f-11e8-8260-fb31e562289c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1","fullStatement":"Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems:","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/48470064-ad1f-11e8-8c27-8faba6d2fa62","identifier":"48470064-ad1f-11e8-8c27-8faba6d2fa62","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1a","fullStatement":"Identify, use, and record appropriate units of measure within context, within data displays, and on graphs;","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/48471c2a-ad1f-11e8-bda0-f5f163c3e14f","identifier":"48471c2a-ad1f-11e8-bda0-f5f163c3e14f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1b","fullStatement":"Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/48473552-ad1f-11e8-8672-b9335fad6ce6","identifier":"48473552-ad1f-11e8-8672-b9335fad6ce6","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.N.Q.1c","fullStatement":"Use units within multi-step problems and formulas; interpret units of input and resulting units of output.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bce62f52-ad20-11e8-ad08-5b9c661ad222","identifier":"bce62f52-ad20-11e8-ad08-5b9c661ad222","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Content Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1","fullStatement":"Give informal arguments for geometric formulas.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bce664ae-ad20-11e8-a7e6-eb1edf96e579","identifier":"bce664ae-ad20-11e8-a7e6-eb1edf96e579","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1a","fullStatement":"Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bce68056-ad20-11e8-9a3c-633aae8a73df","identifier":"bce68056-ad20-11e8-9a3c-633aae8a73df","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Element","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.G.GMD.1b","fullStatement":"Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri\u2019s principle.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5db5d14-ad27-11e8-bbbc-351e12a9d791","identifier":"d5db5d14-ad27-11e8-bbbc-351e12a9d791","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP","fullStatement":"Grade 6 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction.* \r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dbb7d2-ad27-11e8-8a3f-1d7408920a69","identifier":"d5dbb7d2-ad27-11e8-8a3f-1d7408920a69","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In grade 6, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, \u201cWhat is the most efficient way to solve the problem?\u201d, \u201cDoes this make sense?\u201d, and \u201cCan I solve the problem in a different way?\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dbd49c-ad27-11e8-8ee2-414fc2a497e0","identifier":"d5dbd49c-ad27-11e8-8ee2-414fc2a497e0","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"In grade 6, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dbef0e-ad27-11e8-bd0c-97e3b1d06ca4","identifier":"d5dbef0e-ad27-11e8-bd0c-97e3b1d06ca4","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In grade 6, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like \u201cHow did you get that?\u201d, \u201cWhy is that true?\u201d \u201cDoes that always work?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dc07dc-ad27-11e8-ae56-238c6a87bf48","identifier":"d5dc07dc-ad27-11e8-ae56-238c6a87bf48","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.4","fullStatement":"Model with mathematics.","notes":"In grade 6, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students begin to explore covariance and represent two quantities simultaneously. Students use number lines to compare numbers and represent inequalities. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences about and make comparisons between data sets. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dc2172-ad27-11e8-ae37-b10db51cc582","identifier":"d5dc2172-ad27-11e8-ae37-b10db51cc582","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 6 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Additionally, students might use physical objects or applets to construct nets and calculate the surface area of three-dimensional figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dc3b1c-ad27-11e8-a551-d17d770e723b","identifier":"d5dc3b1c-ad27-11e8-a551-d17d770e723b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.6","fullStatement":"Attend to precision.","notes":"In grade 6, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to rates, ratios, geometric figures, data displays, and components of expressions, equations or inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dc53b8-ad27-11e8-8a1e-3fa55b247414","identifier":"d5dc53b8-ad27-11e8-8a1e-3fa55b247414","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students apply properties to generate equivalent expressions (i.e. 6 + 3*x* = 3 (2 + *x*) by distributive property) and solve equations (i.e. 2*c* + 3 = 15, 2*c* = 12 by subtraction property of equality), *c*=6 by division property of equality). Students compose and decompose two- and three-dimensional figures to solve real world problems involving area and volume","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5dc6d3a-ad27-11e8-a4bb-0703604858a5","identifier":"d5dc6d3a-ad27-11e8-a4bb-0703604858a5","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["06"],"humanCodingScheme":"MGSE6.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"In grade 6, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that *a/b* \u00f7 *c/d* = *ad/bc* and construct other examples and models that confirm their generalization. Students connect place value and their prior work with operations to understand algorithms to fluently divide multi-digit numbers and perform all operations with multi-digit decimals. Students informally begin to make connections between covariance, rates, and representations showing the relationships between quantities","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1ce94c-ad28-11e8-a503-c96930986a84","identifier":"fc1ce94c-ad28-11e8-a503-c96930986a84","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP","fullStatement":"Grade 7 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1d4a40-ad28-11e8-b337-2b0d3ca4df45","identifier":"fc1d4a40-ad28-11e8-b337-2b0d3ca4df45","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In grade 7, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, \u201cWhat is the most efficient way to solve the problem?\u201d, \u201cDoes this make sense?\u201d, and \u201cCan I solve the problem in a different way?\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1d69a8-ad28-11e8-9de6-030e9ea78dcf","identifier":"fc1d69a8-ad28-11e8-9de6-030e9ea78dcf","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"In grade 7, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1d86d6-ad28-11e8-9382-79028cab3ada","identifier":"fc1d86d6-ad28-11e8-9382-79028cab3ada","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In grade 7, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like \u201cHow did you get that?\u201d, \u201cWhy is that true?\u201d \u201cDoes that always work?\u201d. They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1da332-ad28-11e8-86d3-ffb96f416b52","identifier":"fc1da332-ad28-11e8-86d3-ffb96f416b52","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.4","fullStatement":"Model with mathematics.","notes":"In grade 7, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students explore covariance and represent two quantities simultaneously. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences, make comparisons and formulate predictions. Students use experiments or simulations to generate data sets and create probability models. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1dc132-ad28-11e8-ad3d-2f109bea60df","identifier":"fc1dc132-ad28-11e8-ad3d-2f109bea60df","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Students might use physical objects or applets to generate probability data and use graphing calculators or spreadsheets to manage and represent data in different forms.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1ddeba-ad28-11e8-a07c-53575bb80c10","identifier":"fc1ddeba-ad28-11e8-a07c-53575bb80c10","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.6","fullStatement":"Attend to precision.","notes":"In grade 7, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students define variables, specify units of measure, and label axes accurately. Students use appropriate terminology when referring to rates, ratios, probability models, geometric figures, data displays, and components of expressions, equations or inequalities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1dfc10-ad28-11e8-8da1-2f3eda66568c","identifier":"fc1dfc10-ad28-11e8-8da1-2f3eda66568c","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables making connections between the constant of proportionality in a table with the slope of a graph. Students apply properties to generate equivalent expressions (i.e. 6 + 3x = 3 (2 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality), c=6 by division property of equality). Students compose and decompose two- and three-dimensional figures to solve real world problems involving scale drawings, surface area, and volume. Students examine tree diagrams or systematic lists to determine the sample space for compound events and verify that they have listed all possibilities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fc1e1858-ad28-11e8-ae49-676d2dd0688f","identifier":"fc1e1858-ad28-11e8-ae49-676d2dd0688f","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["07"],"humanCodingScheme":"MGSE7.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"In grade 7, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a*/b \u00f7 c/d = ad/bc* and construct other examples and models that confirm their generalization. They extend their thinking to include complex fractions and rational numbers. Students formally begin to make connections between covariance, rates, and representations showing the relationships between quantities. They create, explain, evaluate, and modify probability models to describe simple and compound events.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf80c62-ad29-11e8-ab88-5d017509e9ec","identifier":"faf80c62-ad29-11e8-ab88-5d017509e9ec","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP","fullStatement":"Grade 8 - Standards for Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction. *\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf86c16-ad29-11e8-9538-3b4023566642","identifier":"faf86c16-ad29-11e8-9538-3b4023566642","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"In grade 8, students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, \u201cWhat is the most efficient way to solve the problem?\u201d, \u201cDoes this make sense?\u201d, and \u201cCan I solve the problem in a different way?\u201d","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf889f8-ad29-11e8-884f-a3e9ea8702a9","identifier":"faf889f8-ad29-11e8-884f-a3e9ea8702a9","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"In grade 8, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. They examine patterns in data and assess the degree of linearity of functions. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf8a6ae-ad29-11e8-ae27-4305a92d8d55","identifier":"faf8a6ae-ad29-11e8-ae27-4305a92d8d55","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"In grade 8, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like \u201cHow did you get that?\u201d, \u201cWhy is that true?\u201d \u201cDoes that always work?\u201d They explain their thinking to others and respond to others\u2019 thinking.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf8c2ba-ad29-11e8-b179-f1a8641afbff","identifier":"faf8c2ba-ad29-11e8-b179-f1a8641afbff","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.4","fullStatement":"Model with mathematics.","notes":"In grade 8, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students solve systems of linear equations and compare properties of functions provided in different forms. Students use scatterplots to represent data and describe associations between variables. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf8ddcc-ad29-11e8-bcbe-bbc8bf8a24bc","identifier":"faf8ddcc-ad29-11e8-bcbe-bbc8bf8a24bc","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 8 may translate a set of data given in tabular form to a graphical representation to compare it to another data set. Students might draw pictures, use applets, or write equations to show the relationships between the angles created by a transversal.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf8fa3c-ad29-11e8-919f-5beb5a10549e","identifier":"faf8fa3c-ad29-11e8-919f-5beb5a10549e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.6","fullStatement":"Attend to precision.","notes":"In grade 8, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to the number system, functions, geometric figures, and data displays.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf916e8-ad29-11e8-b872-9708140c840a","identifier":"faf916e8-ad29-11e8-b872-9708140c840a","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.7","fullStatement":"Look for and make use of structure.","notes":"Students routinely seek patterns or structures to model and solve problems. In grade 8, students apply properties to generate equivalent expressions and solve equations. Students examine patterns in tables and graphs to generate equations and describe relationships. Additionally, students experimentally verify the effects of transformations and describe them in terms of congruence and similarity","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/faf932fe-ad29-11e8-ac27-635c23bf3682","identifier":"faf932fe-ad29-11e8-ac27-635c23bf3682","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["08"],"humanCodingScheme":"MGSE8.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"In grade 8, students use repeated reasoning to understand algorithms and make generalizations about patterns. Students use iterative processes to determine more precise rational approximations for irrational numbers. During multiple opportunities to solve and model problems, they notice that the slope of a line and rate of change are the same value. Students flexibly make connections between covariance, rates, and representations showing the relationships between quantities.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6251e9e0-ad2b-11e8-8c92-213ebf89a47e","identifier":"6251e9e0-ad2b-11e8-8c92-213ebf89a47e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Core Disciplinary Idea","educationLevel":["09","10","11","12"],"fullStatement":"High School - Mathematical Practice","notes":"*Mathematical Practices are listed with each grade\u2019s mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction.*\r\n\r\nThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important \u201cprocesses and proficiencies\u201d with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council\u2019s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one\u2019s own efficacy).","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6252455c-ad2b-11e8-aa95-c9d619f6cb89","identifier":"6252455c-ad2b-11e8-aa95-c9d619f6cb89","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"High school students start to examine problems by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. By high school, students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. They check their answers to problems using different methods and continually ask themselves, \u201cDoes this make sense?\u201d They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/625263a2-ad2b-11e8-9a0f-732e676ccb45","identifier":"625263a2-ad2b-11e8-9a0f-732e676ccb45","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"High school students seek to make sense of quantities and their relationships in problem situations. They abstract a given situation and represent it symbolically, manipulate the representing symbols, and pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Students use quantitative reasoning to create coherent representations of the problem at hand; consider the units involved; attend to the meaning of quantities, not just how to compute them; and know and flexibly use different properties of operations and objects.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/625280d0-ad2b-11e8-8fb2-5b0981dcf337","identifier":"625280d0-ad2b-11e8-8fb2-5b0981dcf337","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"High school students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. High school students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and\u2014if there is a flaw in an argument\u2014explain what it is. High school students learn to determine domains to which an argument applies, listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/62529d36-ad2b-11e8-96b7-ed83ef50f13e","identifier":"62529d36-ad2b-11e8-96b7-ed83ef50f13e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.4","fullStatement":"Model with mathematics.","notes":"High school students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. High school students making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6252b910-ad2b-11e8-8330-f521f412adfe","identifier":"6252b910-ad2b-11e8-8330-f521f412adfe","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.5","fullStatement":"Use appropriate tools strategically.","notes":"High school students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. High school students should be sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. They are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6252d652-ad2b-11e8-b66a-57fcff89782e","identifier":"6252d652-ad2b-11e8-b66a-57fcff89782e","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.6","fullStatement":"Attend to precision.","notes":"High school students try to communicate precisely to others by using clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. By the time they reach high school they have learned to examine claims and make explicit use of definitions.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6252f358-ad2b-11e8-9647-0126c455d102","identifier":"6252f358-ad2b-11e8-9647-0126c455d102","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.7","fullStatement":"Look for and make use of structure.","notes":"By high school, students look closely to discern a pattern or structure. In the expression x 2 + 9x + 14, older students can see the 14 as 2 \u00d7 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 \u2013 3(*x* \u2013 *y*)\u00b2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers *x* and *y*. High school students use these patterns to create equivalent expressions, factor and solve equations, and compose functions, and transform figures.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/62530fd2-ad2b-11e8-8c9b-6134460134bd","identifier":"62530fd2-ad2b-11e8-8c9b-6134460134bd","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Standard","educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.SMP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"High school students notice if calculations are repeated, and look both for general methods and for shortcuts. Noticing the regularity in the way terms cancel when expanding (*x* \u2013 1)(*x* + 1), (*x* \u2013 1)(*x*\u00b2 + x + 1), and (*x* \u2013 1)(*x*\u00b3 + *x*\u00b2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, derive formulas or make generalizations, high school students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.","language":"en","statusEndDate":"2023-07-31"},{"uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/51aca610-baab-11e8-9b3e-efae8292141b","identifier":"51aca610-baab-11e8-9b3e-efae8292141b","lastChangeDateTime":"2026-07-22T13:39:31+00:00","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.07520","fullStatement":"Differential Equations","notes":"Differential Equations is an option for students who wish to enroll in a mathematics course beyond Multivariable Calculus. The course provides an introduction to ordinary differential equations. Topics include the solution of first, second, and higher order differential equations, systems of differential equations, series solutions and Laplace transforms. There will be a strong focus on the presentation of mathematical ideas through both written and oral communication. 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