{"CFDocument":{"identifier":"e9dd7229-3558-4df2-85c6-57b8938f6180","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180","creator":"Georgia Department of Education","title":"Georgia\u2019s K-12 Mathematics Standards (SY2023-2024) ","lastChangeDateTime":"2024-10-09T13:16:20+00:00","language":"en","adoptionStatus":"Adopted","publisher":"Georgia Department of Education","description":"The new standards are truly Georgia-developed. They were drafted by Georgia mathematics teachers with input from educational leaders, parents, students, business and industry leaders, and community members. They are designed to provide a strong foundation, to be clear, understandable, and present a reasonable amount of content in each year. \n","licenseURI":{"title":"CC BY-NC-SA","identifier":"2f22abe2-eb0a-415f-8b45-a13859b35aca","uri":"https://case.georgiastandards.org/uri/2f22abe2-eb0a-415f-8b45-a13859b35aca"},"notes":"The State Board of Education approved State School Superintendent Richard Woods\u2019 recommendation to adopt the new Georgia\u2019s K-12 Mathematics Standards. The 2021-2022 and 2022-2023 school years will be dedicated to teacher training on the new standards, with implementation to follow in 2023-2024. \u200b","version":"2024"},"CFItems":[{"identifier":"d9dcef93-5266-4a48-9836-c2b77a68bcc2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d9dcef93-5266-4a48-9836-c2b77a68bcc2","fullStatement":"K-5 Mathematics","lastChangeDateTime":"2023-08-02T12:33:53-04:00","language":"eng","CFItemType":"Domain","CFItemTypeURI":{"title":"Domain","identifier":"ccad74b1-3f48-4ef6-b22b-d29e346a9c72","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/ccad74b1-3f48-4ef6-b22b-d29e346a9c72"},"educationLevel":["KG","01","02","03","04","05"]},{"identifier":"96dc9257-62c3-46cf-a462-158ac29faea4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/96dc9257-62c3-46cf-a462-158ac29faea4","fullStatement":"6-8 Mathematics","lastChangeDateTime":"2023-08-02T12:34:03-04:00","language":"eng","CFItemType":"Domain","CFItemTypeURI":{"title":"Domain","identifier":"ccad74b1-3f48-4ef6-b22b-d29e346a9c72","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/ccad74b1-3f48-4ef6-b22b-d29e346a9c72"},"educationLevel":["06","07","08"]},{"identifier":"356ed13e-3b66-42b9-8ca5-804d7ba51549","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/356ed13e-3b66-42b9-8ca5-804d7ba51549","fullStatement":"High School Mathematics","lastChangeDateTime":"2022-03-18T17:34:01+00:00","language":"eng","CFItemType":"Domain","educationLevel":["09","10","11","12"]},{"identifier":"57394421-13ed-4f7a-9d99-f9d40696e0ad","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/57394421-13ed-4f7a-9d99-f9d40696e0ad","fullStatement":"Mathematics/Grade 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6","lastChangeDateTime":"2022-08-03T17:08:32-04:00","humanCodingScheme":"27.02100","language":"eng","educationLevel":["06"],"CFItemType":"Course"},{"identifier":"f67abc96-8733-4af3-bd71-81ba079988cd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f67abc96-8733-4af3-bd71-81ba079988cd","fullStatement":"Mathematics/Grade 7","lastChangeDateTime":"2022-08-03T17:10:48-04:00","humanCodingScheme":"27.02200","language":"eng","educationLevel":["07"],"CFItemType":"Course"},{"identifier":"adbff773-ff86-4951-a063-829204848cc1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/adbff773-ff86-4951-a063-829204848cc1","fullStatement":"Mathematics/Grade 8","lastChangeDateTime":"2023-08-02T12:29:42-04:00","humanCodingScheme":"27.02300","language":"eng","CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"64c17608-fcf5-4578-8bbe-db758391c3cf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/64c17608-fcf5-4578-8bbe-db758391c3cf"},"educationLevel":["08"]},{"identifier":"e1eabba1-58e9-4d80-b659-6cfab09a7422","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1eabba1-58e9-4d80-b659-6cfab09a7422","fullStatement":"Algebra: Concepts and Connections","lastChangeDateTime":"2023-01-11T20:11:50-05:00","humanCodingScheme":"27.08110","notes":"Algebra: Concepts and Connections\tis the first course in a sequence of three high school courses designed to ensure career and college readiness. Students will apply their algebraic and geometric reasoning skills to make sense of problems involving algebra, geometry, bivariate data, and statistics. This course focuses on algebraic, quantitative, geometric, graphical, and statistical reasoning. In this course, students will continue to enhance their algebraic reasoning skills when analyzing and applying a deep understanding of linear functions, sums and products of rational and irrational numbers, systems of linear inequalities, distance, midpoint, slope, area, perimeter, nonlinear equations and functions, quadratic expressions, equations and functions, exponential expressions, equations, and functions, and statistical reasoning.\n\nHigh school course content standards are listed by big ideas including Data and Statistical Reasoning, Probabilistic Reasoning, Functional and Graphical Reasoning, Patterning and Algebraic Reasoning, and Geometric and Spatial Reasoning.","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Course"},{"identifier":"a4956721-d986-4abe-b95f-a863f919a020","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a4956721-d986-4abe-b95f-a863f919a020","fullStatement":"Advanced Algebra: Concepts and Connections","lastChangeDateTime":"2023-01-11T20:12:41-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08310","educationLevel":["09","10","11","12"],"notes":"Advanced Algebra: Concepts & Connections is the third course in a sequence of courses designed to ensure career and college readiness. It is intended to prepare students for fourth mathematics course options relevant to their postsecondary pursuits. High school course content standards are listed by big idea, including Data and Statistical Reasoning, Probabilistic Reasoning, Functional and Graphical Reasoning, Patterning and Algebraic Reasoning, and Geometric and Spatial Reasoning.\n\nIn Advanced Algebra: Concepts & Connections, students will continue to enhance their data and statistical reasoning skills as they learn specific ways to collect, critique, analyze, and interpret data. Students will learn how to use matrices and linear programming to represent data and to solve contextually relevant problems. Students will strengthen their geometric and spatial reasoning skills as they learn how to solve trigonometric equations using the unit circle.\n\nIn previous courses, students studied how to use linear and quadratic functions to model real-life phenomena. In Advanced Algebra: Concepts and Connections, students will further develop their functional and graphical reasoning as they explore and analyze structures and patterns for exponential, logarithmic, radical, polynomial, and rational expressions, equations and functions to further understand the world around them."},{"identifier":"05540335-849a-4c1b-8911-8aca3ae63ccc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/05540335-849a-4c1b-8911-8aca3ae63ccc","fullStatement":"Advanced Financial Algebra","lastChangeDateTime":"2023-01-11T20:13:53-05:00","language":"eng","CFItemType":"Course","educationLevel":["09","10","11","12"],"notes":"Advanced Financial Algebra is a fourth-year mathematics course option designed for students who have successfully completed Advanced Algebra: Concepts and Connections. The course extends and deepens student understanding of algebra, statistics, and research design while introducing students to relevant financial and business applications. Students will create, apply, and interpret a wide variety of algebraic function-models to aid in real-world decision making. Statistical research and analysis will be used to determine the efficacy of model applications and further assist in exploring scenarios with financial implications. Financial contexts for these mathematical concepts will include business operations and optimization, tax considerations, insurance and risk management, banking services, budget creation, loan and credit analysis, investment strategies and retirement plans, stock market performance, real estate fundamentals, and automobile ownership.\n\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.","humanCodingScheme":"27.08430"},{"identifier":"00c7f9e2-7721-4cdf-9426-d077b0e9e970","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/00c7f9e2-7721-4cdf-9426-d077b0e9e970","fullStatement":"Linear Algebra with Computer Science Applications","lastChangeDateTime":"2023-01-11T20:16:58-05:00","language":"eng","CFItemType":"Course","educationLevel":["09","10","11","12"],"humanCodingScheme":"27.08530","notes":"Linear Algebra with Computer Science Applications is designed to meet the needs of students who have completed Precalculus or the Enhanced Advanced Algebra Concepts and Connections and Precalculus course (or the equivalent) and will pursue careers which require linear algebra topics often associated with modern computer science.\n\nThe course will examine the use of vectors and matrices in mathematics and apply these concepts to computer science. There will be a strong focus on the presentation of mathematical ideas through both writing and programming. Mathematical concepts, such as vector spaces and Markov chains, will be presented through an abstract approach that characterizes upper-level mathematics courses. The goal is to give students the skills and techniques they will need as they study advanced mathematics or computer science at the college level. This is an alternative course for those students who do not wish to enroll in an Advanced Placement course, but who still wish to learn higher-level mathematics."},{"identifier":"3fa8818e-36e9-45f7-b090-38615a0c68bb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3fa8818e-36e9-45f7-b090-38615a0c68bb","fullStatement":"Geometry: Concepts and Connections","lastChangeDateTime":"2023-01-11T20:12:23-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08210","educationLevel":["09","10","11","12"],"notes":"Geometry: Concepts and Connections is the second course in a sequence of three high school courses designed to ensure career and college readiness. This course is intended to enhance students\u2019 geometric, algebraic, graphical, and probabilistic reasoning skills. Students will apply their algebraic and geometric reasoning skills to make sense of problems involving geometry, trigonometry, algebra, probability, and statistics. Students will continue to enhance their analytical geometry and reasoning skills when analyzing and applying a deep understanding of polynomial expressions, proofs, constructions, rigid motions and transformations, similarity, congruence, circles, right triangle trigonometry, geometric measurement, and conditional probability.\n\nHigh school course content standards are listed by big ideas including Data and Statistical Reasoning, Probabilistic Reasoning, Functional and Graphical Reasoning, Patterning and Algebraic Reasoning, and Geometric and Spatial Reasoning."},{"identifier":"923062b8-0b2c-45e9-a329-a8c360e3199a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/923062b8-0b2c-45e9-a329-a8c360e3199a","fullStatement":"Advanced Finite Mathematics","lastChangeDateTime":"2023-01-11T20:15:21-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.07910","educationLevel":["09","10","11","12"],"notes":"Advanced Finite Mathematics is a fourth-year mathematics course option designed to meet the needs of advanced students who have completed Precalculus or the Enhanced Advanced Algebra Concepts and Connections and Precalculus course (or the equivalent) and will pursue careers which require the mastery of discrete mathematics topics often associated with modern computer science.\n\nStudents in this course will examine mathematics in four areas through the lens of both pure mathematics and applied mathematics: set theory, number theory, probability/combinatorics, and graph theory. There will be a strong focus on the presentation of mathematical ideas through both written and oral communication, particularly through logic and proofs. Mathematical proofs will be presented through an abstract approach that characterizes upper-level mathematics courses. The goal is for students to develop the skills and techniques they will need as they study advanced mathematics or computer science at the college level. This is an alternative course for those students who do not wish to enroll in an Advanced Placement course, but who still wish to learn higher-level mathematics."},{"identifier":"105de882-18ae-4af8-9a82-29173132bff6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/105de882-18ae-4af8-9a82-29173132bff6","fullStatement":"Advanced Mathematical Decision Making","lastChangeDateTime":"2023-01-11T20:16:33-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08500","educationLevel":["09","10","11","12"],"notes":"Advanced Mathematical Decision Making (AMDM) is a fourth-year mathematics course option designed to follow the completion of Advanced Algebra: Concepts and Connections. Students will enhance their understanding of concepts explored in the context of real-life phenomena. The intent of this course is for students to combine their understanding of multiple mathematical concepts as they explore and solve real-world mathematical problems. Students will investigate applications of mathematics in a variety of contexts, including business and financial decision-making, earning, investing, spending, and borrowing money, using functions to model problem situations in both discrete and continuous relationships, and using ratios, rates, and percentages to solve problems,\n\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 applied, where appropriate, in the context of realistic phenomena."},{"identifier":"3dceac6e-dbe2-40d6-bd88-1a868bd2cb15","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3dceac6e-dbe2-40d6-bd88-1a868bd2cb15","fullStatement":"Precalculus","lastChangeDateTime":"2023-01-11T20:13:30-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08410","educationLevel":["09","10","11","12"],"notes":"Precalculus is a fourth-year mathematics course option for students who have completed Advanced Algebra: Concepts and Connections (or the equivalent). The course is intended to provide students with opportunities to develop a deeper understanding of Algebraic concepts that are critical to the study of Calculus. Students will also deepen their understanding of trigonometry and its applications.\n\nThroughout the Precalculus course there should be a focus on notational fluency and the use of multiple representations. The course includes the study and analysis of piecewise and rational functions; limits and continuity as related to piecewise and rational functions; sequences and series with the incorporation of convergence and divergence; conic sections as implicitly defined curves; the six trigonometric functions and their inverses; applications of trigonometry such as modeling periodic phenomena, modeling with vectors and parametric equations, solving oblique triangles in contextual situations, graphing in the Polar Plane; solutions of trigonometric equations in a variety of contexts; and the manipulation and application of trigonometric identities.\n\nTopics should be analyzed in multiple ways, including verbal and written, numerical, algebraic, and graphical presentations. Instruction and assessment should include the appropriate use of technology. Concepts should be introduced and investigated, where appropriate, in the context of realistic phenomena."},{"identifier":"799d746d-c2a9-44e2-a4ee-2cddf9751ac3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/799d746d-c2a9-44e2-a4ee-2cddf9751ac3","fullStatement":"Calculus","lastChangeDateTime":"2023-01-11T20:14:15-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.07800","educationLevel":["09","10","11","12"],"notes":"Calculus is a fourth-year mathematics course option for students who have completed Precalculus or the Enhanced Advanced Algebra Concepts and Connections and Precalculus course. The course provides students with the opportunity to develop an understanding of the derivative and its applications as well as the integral and its applications. Throughout the course there should be a focus on notational fluency and the use of multiple representations.\n\nThe Calculus course includes the study and analysis of limits and continuity as applied to a variety of functions; the derivative as related to limits and continuity; various derivative rules such as product, quotient, and chain; applications of the derivative including curve analysis, applied max/min situations, related rate problems, and use of Mean Value Theorem; the definite integral as a limit of Riemann sums; properties of definite integrals; the Fundamental Theorem of Calculus as it relates derivatives and integrals; techniques of integration including u-substitution; and applications of the integral including solving separable differential equations, finding a particular solution curve given an initial condition, area between curves on a coordinate plane, and average value situations.\n\nTopics should be analyzed in multiple ways, including verbal and written, numerical, algebraic, and graphical presentations. Instruction and assessment should include the appropriate use of technology. Concepts should be introduced and investigated, where appropriate, in the context of realistic phenomena."},{"identifier":"36f1efdf-86e5-4b96-b0d8-e711f90e6afa","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/36f1efdf-86e5-4b96-b0d8-e711f90e6afa","fullStatement":"Multivariable Calculus","lastChangeDateTime":"2023-01-11T20:14:54-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.07700","educationLevel":["09","10","11","12"],"notes":"Multivariable Calculus is a mathematics course option for students who have completed Advanced Placement (AP) Calculus BC. It includes three-dimensional coordinate geometry; matrices and determinants; eigenvalues and eigenvectors of matrices; limits and continuity of functions with two independent variables; partial differentiation; multiple integration; the gradient; the divergence; the curl; Theorems of Green, Stokes, and Gauss; line integrals; integrals independent of path; and linear first-order differential equations."},{"identifier":"3aa09b4f-d702-42e4-9cf0-aba50651b2c2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3aa09b4f-d702-42e4-9cf0-aba50651b2c2","fullStatement":"Differential Equations","lastChangeDateTime":"2023-01-11T20:14:33-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.07520","educationLevel":["09","10","11","12"],"notes":"Differential Equations is a course option for students who have completed Advanced Placement (AP) Calculus BC. The course introduces 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. The goal is to give students the skills and techniques they will need as they study advanced mathematics at the college level."},{"identifier":"3a701de9-57d8-4921-9280-c8c1e26f7a11","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3a701de9-57d8-4921-9280-c8c1e26f7a11","fullStatement":"Engineering Calculus","lastChangeDateTime":"2023-01-11T20:15:44-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08000","educationLevel":["09","10","11","12"],"notes":"Engineering Calculus is a course option for students who have completed Advanced Placement (AP) Calculus BC. The course provides students with opportunities to develop an understanding of multivariable calculus as it applies to engineering systems, the history of engineering and its contributions to society. The course includes three-dimensional coordinate geometry; matrices and determinants; limits and continuity of functions with two independent variables; partial differentiation; multiple integration; the gradient; the divergence; the curl; Theorems of Green, Stokes, and Gauss; line integrals; integrals independent of path; and linear first-order differential equations.\n\nInstruction and assessment should include the appropriate use of technology. Topics should be presented in multiple ways, such as verbal/written, numeric/data-based, algebraic, and graphical. Concepts should be introduced and applied, where appropriate, in the context of realistic phenomena."},{"identifier":"41a6e2ac-c8a1-4824-abb8-a6fed2c3d233","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/41a6e2ac-c8a1-4824-abb8-a6fed2c3d233","fullStatement":"College Readiness Mathematics (Mathematics Capstone Course)","lastChangeDateTime":"2023-01-11T20:19:08-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08900","educationLevel":["09","10","11","12"],"notes":"College Readiness Mathematics Capstone Course (CRM) is a fourth mathematics course option for students who have completed Advanced Algebra: Concepts and Connections\t (or the equivalent). The course is designed to serve as a bridge for high school students who will enroll in a non-STEM postsecondary program of study. The course has been approved by the University System of Georgia as a fourth mathematics course beyond Advanced Algebra: Concepts and Connections for non-STEM majors; this course will NOT meet the needs of collegebound seniors who will pursue STEM fields.\n\nThe focus of this course is on key content and practice standards to ensure that students will be ready for postsecondary 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. Instruction 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. The Standards for Mathematical Practice will provide the foundation for instruction and assessment. The content standards selected are essential for postsecondary preparation in non-STEM study.\n\nStudents will be expected to complete a capstone project where they select one of the areas listed in the standard to identify a problem and use mathematical modeling to address it."},{"identifier":"ff37cc18-c70e-4050-bc04-a91602cacb47","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff37cc18-c70e-4050-bc04-a91602cacb47","fullStatement":"Mathematics of Industry and Government","lastChangeDateTime":"2023-01-11T20:17:28-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08600","educationLevel":["09","10","11","12"],"notes":"Mathematics of Industry and Government is a fourth-year mathematics course designed for students who have successfully completed Advanced Algebra: Concepts and Connections. Modeled after operations research courses, this course allows students to explore decision making in a variety of industries, such as: Airline - scheduling planes and crews, pricing tickets, taking reservations, and planning the size of the fleet; Pharmaceutical - R& D management; Logistics companies - routing and planning; Lumber and wood products - managing forests and cutting timber; Local government - deployment of emergency services, and Policy studies and regulation - environmental pollution, air traffic safety, AIDS, and criminal justice policy.\n\nThe focus of this course is on the development of mathematical models that can be used to model, improve, predict, and optimize real-world systems. These mathematical models include both deterministic models such as mathematical programming, routing or network flows and probabilistic models such as queuing, and simulation."},{"identifier":"1cc5579a-dc39-4a20-86c9-73396c6593af","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1cc5579a-dc39-4a20-86c9-73396c6593af","fullStatement":"Statistical Reasoning","lastChangeDateTime":"2023-01-11T20:18:38-05:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08800","educationLevel":["09","10","11","12"],"notes":"The Statistical Reasoning course offers students opportunities to strengthen their understanding of the statistical method of inquiry and statistical simulations. Students will formulate statistical investigative 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. The Mathematical Modeling and Statistical Reasoning Frameworks will provide the foundation for instruction and assessment. Topics should be introduced and assessed using simulations and appropriate supporting technology."},{"identifier":"957f22bd-adb8-4b23-8409-235cbf23298d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/957f22bd-adb8-4b23-8409-235cbf23298d","fullStatement":"History of Mathematics (full year)","lastChangeDateTime":"2023-07-24T15:22:23-04:00","language":"eng","CFItemType":"Course","humanCodingScheme":"27.08630","educationLevel":["09","10","11","12"],"notes":"History of Mathematics is a two-semester elective course option for students who have completed Advanced Placement (AP) Calculus or are taking AP Calculus concurrently. The courses traces the development of major branches of mathematics throughout history, specifically algebra, geometry, number theory, and methods of proofs, how that development was influenced by the needs of various world cultures, and how the mathematics in turn influenced world culture.\n\nInstruction and assessment should include appropriate use of technology and manipulatives. Concepts should be introduced and used in an appropriate historical context.","CFItemTypeURI":{"title":"Course","identifier":"64c17608-fcf5-4578-8bbe-db758391c3cf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/64c17608-fcf5-4578-8bbe-db758391c3cf"}},{"identifier":"bf787dfd-0fab-4c8f-9eb1-fe9da88b4cc6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bf787dfd-0fab-4c8f-9eb1-fe9da88b4cc6","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:29:07+00:00","humanCodingScheme":"K.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["KG"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"d34b590b-a571-4107-aacf-b3b9000421be","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d34b590b-a571-4107-aacf-b3b9000421be","fullStatement":"Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set).","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.NR.1","notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, money, place value, numbers to 20, addition, subtraction and fluency","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"444b0b9c-4f77-4eb1-9e72-e4625a1d217e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/444b0b9c-4f77-4eb1-9e72-e4625a1d217e","fullStatement":"Use count sequences within 100 to count forward and backward in sequence.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.NR.2","notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, money, place value, numbers to 20, addition, subtraction and fluency","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"71443b95-2f69-4aba-966d-1ee4f81f48a2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/71443b95-2f69-4aba-966d-1ee4f81f48a2","fullStatement":"Use place value understanding to compose and decompose numbers from 11\u201319.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.NR.3","notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, money, place value, numbers to 20, addition, subtraction and fluency","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"daefc429-2264-4233-8066-e37a624c2a78","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/daefc429-2264-4233-8066-e37a624c2a78","fullStatement":"Identify, write, represent, and compare numbers up to 20.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.NR.4","notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, money, place value, numbers to 20, addition, subtraction and fluency","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"33a43a74-a446-42c9-800b-c71d4e80aaf3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/33a43a74-a446-42c9-800b-c71d4e80aaf3","fullStatement":"Explain the concepts of addition, subtraction, and equality and use these concepts to solve real-life problems within 10.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.NR.5","notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, money, place value, numbers to 20, addition, subtraction and fluency","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"0a0bc670-3029-45ca-8262-9cdb23c98e80","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0a0bc670-3029-45ca-8262-9cdb23c98e80","fullStatement":"Explain, extend, and create repeating patterns with a repetition, not exceeding 4 and describe patterns involving the passage of time.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.PAR.6","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 repeating patterns and time","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"90c7aeac-3cb8-44ff-b0d4-616b2b501d82","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90c7aeac-3cb8-44ff-b0d4-616b2b501d82","fullStatement":"Observe, describe, and compare the physical and measurable attributes of objects and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.MDR.7","notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 attributes of objects, classifying objects","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"d5472dd7-e720-45fd-943f-9dc00d184f3a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d5472dd7-e720-45fd-943f-9dc00d184f3a","fullStatement":"Identify, describe, and compare basic shapes encountered in the environment, and form two-dimensional shapes and three-dimensional figures.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"K.GSR.8","notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 2D and 3D shapes, relative locations, attributes","language":"eng","educationLevel":["KG"],"CFItemType":"Content Standard"},{"identifier":"7816b664-6620-4f20-bcc0-817ad9c28236","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7816b664-6620-4f20-bcc0-817ad9c28236","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:45:18+00:00","humanCodingScheme":"1.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"33586537-10a6-42ba-a235-e27c2a48a4d3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/33586537-10a6-42ba-a235-e27c2a48a4d3","fullStatement":"Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, numbers, equality, place value, addition, subtraction"},{"identifier":"ab1cf735-27cc-437b-979b-cdc22ecde12e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab1cf735-27cc-437b-979b-cdc22ecde12e","fullStatement":"Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addition and subtraction problems within 20.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.NR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting, numbers, equality, place value, addition, subtraction"},{"identifier":"b0617ddb-86ea-47bb-81fe-0961b4413a00","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b0617ddb-86ea-47bb-81fe-0961b4413a00","fullStatement":"Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns found in real-life situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.PAR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 repeating patterns, growing, patterns, and shrinking patterns"},{"identifier":"90436b36-6b76-40c4-9afe-1dd95340141f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90436b36-6b76-40c4-9afe-1dd95340141f","fullStatement":"Compose shapes, analyze the attributes of shapes, and relate their parts to the whole.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.GSR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 shapes, attributes, partitions of circles and rectangles"},{"identifier":"cfab637e-7dbc-49a6-84b5-a87a1803bb50","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cfab637e-7dbc-49a6-84b5-a87a1803bb50","fullStatement":"Use concrete models, the base ten structure, and properties of operations to add and subtract within 100.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.NR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 base ten structure, addition and subtraction within 100"},{"identifier":"03d2622a-8bcb-46cb-baf7-cd5c882a43d3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/03d2622a-8bcb-46cb-baf7-cd5c882a43d3","fullStatement":"Use appropriate tools to measure, order, and compare intervals of length and time, as well as denominations of money to solve real-life, mathematical problems and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"1.MDR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["01"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 length, time, money"},{"identifier":"e94460f3-ed0b-45ea-aea0-e02ed76e4ca8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e94460f3-ed0b-45ea-aea0-e02ed76e4ca8","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:45:27+00:00","humanCodingScheme":"2.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"5b0d6a29-2e3e-4b6a-ada6-c0352e991bc8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5b0d6a29-2e3e-4b6a-ada6-c0352e991bc8","fullStatement":"Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to 1000 and describe basic place-value relationships and structures.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting within 1000, place value, addition and subtraction, fluency to 20, developing multiplication through arrays"},{"identifier":"c5411151-6ed7-4194-900e-fdad4a31e29c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c5411151-6ed7-4194-900e-fdad4a31e29c","fullStatement":"Apply multiple part-whole strategies, properties of operations and place value understanding to solve real-life, mathematical problems involving addition and subtraction within 1,000.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.NR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting within 1000, place value, addition and subtraction, fluency to 20, developing multiplication through arrays"},{"identifier":"df142e86-b3f5-4021-9e23-1b6852ffeae0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/df142e86-b3f5-4021-9e23-1b6852ffeae0","fullStatement":"Work with equal groups to gain foundations for multiplication through real-life, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.NR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 counting within 1000, place value, addition and subtraction, fluency to 20, developing multiplication through arrays"},{"identifier":"735997d6-096a-4f0d-bf9e-bcbb8a2e77f3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/735997d6-096a-4f0d-bf9e-bcbb8a2e77f3","fullStatement":"Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.PAR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 patterns up to 20 and addition and subtraction within 1,000"},{"identifier":"d90112c6-ccf0-4232-84d1-c856a1506b35","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d90112c6-ccf0-4232-84d1-c856a1506b35","fullStatement":"Estimate and measure the lengths of objects and distance to solve problems found in real-life using standard units of measurement, including inches, feet, and yards and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.MDR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 length, distance, time, and money"},{"identifier":"fbfa3b03-aae5-4987-a29b-fd185844a539","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fbfa3b03-aae5-4987-a29b-fd185844a539","fullStatement":"Solve real-life problems involving time and money.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.MDR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 length, distance, time, and money"},{"identifier":"05c0f8ae-0274-485d-9fa6-a0e38f08d4f6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/05c0f8ae-0274-485d-9fa6-a0e38f08d4f6","fullStatement":"Draw and partition shapes and other objects with specific attributes, and conduct observations of everyday items and structures to identify how shapes exist in the world.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"2.GSR.7","language":"eng","CFItemType":"Content Standard","educationLevel":["02"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 sorting shapes, lines of symmetry, partitioning circles and rectangles"},{"identifier":"5f252f2d-c889-493f-b0a6-552aec575be3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5f252f2d-c889-493f-b0a6-552aec575be3","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:45:34+00:00","humanCodingScheme":"3.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"81f4f9e6-8fa2-45f5-ba56-cd2eba8c0286","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/81f4f9e6-8fa2-45f5-ba56-cd2eba8c0286","fullStatement":"Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 base ten numerals and place value up to 10,000, and rounding up to 1,000"},{"identifier":"5be59005-4776-47ee-96b9-7d404afcf78b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5be59005-4776-47ee-96b9-7d404afcf78b","fullStatement":"Use part-whole strategies to represent and solve real-life problems involving addition and subtraction with whole numbers up to 10,000.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.PAR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 fluency, addition and subtraction within 10,000, multiplication and division within 100, equality, properties of operations"},{"identifier":"fd5543a9-d2fa-471f-b5b6-8caca7dca6e7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd5543a9-d2fa-471f-b5b6-8caca7dca6e7","fullStatement":"Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.PAR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 fluency, addition and subtraction within 10,000, multiplication and division within 100, equality, properties of operations"},{"identifier":"e075051e-8e78-4118-94fa-e56c137dc7fe","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e075051e-8e78-4118-94fa-e56c137dc7fe","fullStatement":"Represent fractions with denominators of 2, 3, 4, 6 and 8 in multiple ways within a framework using visual models.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.NR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 unit fractions, equivalent fractions, fractions greater than 1"},{"identifier":"fdbaf91d-191e-4f58-8264-432e066b7515","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fdbaf91d-191e-4f58-8264-432e066b7515","fullStatement":"Solve real-life, mathematical problems involving length, liquid volume, mass, and time and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.MDR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 elapsed time, liquid volume, mass, lengths in half and fourth of an inch, data"},{"identifier":"4a7aa3f3-aa89-46f6-a020-b835e29c01b2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4a7aa3f3-aa89-46f6-a020-b835e29c01b2","fullStatement":"Identify the attributes of polygons, including parallel segments, perpendicular segments, right angles, and symmetry.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.GSR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 polygons, parallel line segments, perpendicular line segments, right angles, lines of symmetry, area, perimeter"},{"identifier":"f00eac5c-0b0f-4c7f-9266-2b6ae16a2764","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f00eac5c-0b0f-4c7f-9266-2b6ae16a2764","fullStatement":"Identify area as a measurable attribute of rectangles and determine the area of a rectangle presented in real-life, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.GSR.7","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 polygons, parallel line segments, perpendicular line segments, right angles, lines of symmetry, area, perimeter"},{"identifier":"03463b5a-bb5c-434f-a954-3621d881f282","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/03463b5a-bb5c-434f-a954-3621d881f282","fullStatement":"Determine the perimeter of a polygon presented in real-life, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"3.GSR.8","language":"eng","CFItemType":"Content Standard","educationLevel":["03"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 polygons, parallel line segments, perpendicular line segments, right angles, lines of symmetry, area, perimeter"},{"identifier":"f84220e9-01be-4824-ab48-0dbbc0ac8cff","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f84220e9-01be-4824-ab48-0dbbc0ac8cff","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:45:40+00:00","humanCodingScheme":"4.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"736a8b3c-1de4-4544-9e3b-e6973b9c0bce","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/736a8b3c-1de4-4544-9e3b-e6973b9c0bce","fullStatement":"Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare and round multi-digit whole numbers through the hundred-thousands place and compare decimal numbers to the hundredths place.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, rounding, comparisons with multi-digit numbers, addition and subtraction, multiplicative comparisons, multiplication, and division involving whole numbers"},{"identifier":"11022c4c-c313-4792-85e2-779dc7e4d16c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/11022c4c-c313-4792-85e2-779dc7e4d16c","fullStatement":"Using part-whole strategies, solve problems involving addition and subtraction through the hundred-thousands place, as well as multiplication and division of multi-digit whole numbers presented in real-life, mathematical situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.NR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, rounding, comparisons with multi-digit numbers, addition and subtraction, multiplicative comparisons, multiplication, and division involving whole numbers"},{"identifier":"21af665e-78ca-472c-bf3c-552d3e33ef9e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/21af665e-78ca-472c-bf3c-552d3e33ef9e","fullStatement":"Generate and analyze patterns, including those involving shapes, input/output diagrams, factors, multiples, prime numbers, and composite numbers.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.PAR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 patterns, input-output tables, factors, multiples, composite numbers, prime numbers"},{"identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","fullStatement":"Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.NR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 fraction equivalence, comparison of fractions, and addition and subtraction of fractions with like denominators"},{"identifier":"a744a60a-08ff-4619-a820-e36799b22233","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a744a60a-08ff-4619-a820-e36799b22233","fullStatement":"Solve real-life problems involving addition, equivalence, comparison of fractions with denominators of 10 and 100, and comparison of decimal numbers as tenths and hundredths using part-whole strategies and visual models.","lastChangeDateTime":"2022-08-25T16:15:22-04:00","humanCodingScheme":"4.NR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 fraction equivalence, comparison of fractions, and addition and subtraction of fractions with like denominators"},{"identifier":"60acf258-3e61-47d5-a72e-adb994a25926","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/60acf258-3e61-47d5-a72e-adb994a25926","fullStatement":"Measure time and objects that exist in the world to solve real-life, mathematical problems and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.MDR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 time, metric measurements, distance, elapsed time, liquid volume, mass, and length"},{"identifier":"91bcdd44-8864-4cd3-8a79-d67246000c82","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/91bcdd44-8864-4cd3-8a79-d67246000c82","fullStatement":"Investigate the concepts of angles and angle measurement to estimate and measure angles.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.GSR.7","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 polygons, points, lines, line segments, rays, angles, perpendicular lines, area, perimeter"},{"identifier":"abb88c79-7fee-41b5-936f-23452094f6e0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/abb88c79-7fee-41b5-936f-23452094f6e0","fullStatement":"Identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"4.GSR.8","language":"eng","CFItemType":"Content Standard","educationLevel":["04"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 polygons, points, lines, line segments, rays, angles, perpendicular lines, area, perimeter"},{"identifier":"84d0c6a9-cc63-4397-9563-40f5a26755b3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/84d0c6a9-cc63-4397-9563-40f5a26755b3","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:45:47+00:00","humanCodingScheme":"5.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"2aaa92c7-10ef-488c-8d59-e9cceb4982b6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2aaa92c7-10ef-488c-8d59-e9cceb4982b6","fullStatement":"Use place value understanding to solve real-life, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions"},{"identifier":"7a71fb2d-cc21-4cf4-9ef5-14162c550a74","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7a71fb2d-cc21-4cf4-9ef5-14162c550a74","fullStatement":"Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.NR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions"},{"identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965","fullStatement":"Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.NR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions"},{"identifier":"c7bb3bdc-c14a-47c0-b4a2-8e06e1095236","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c7bb3bdc-c14a-47c0-b4a2-8e06e1095236","fullStatement":"Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.NR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions"},{"identifier":"9cd27b32-e841-4dcf-8e8a-95fa40fb5695","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9cd27b32-e841-4dcf-8e8a-95fa40fb5695","fullStatement":"Write, interpret, and evaluate numerical expressions within authentic problems.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.NR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions"},{"identifier":"a3ca23cc-18bf-4f1d-9241-69586f5f72fd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a3ca23cc-18bf-4f1d-9241-69586f5f72fd","fullStatement":"Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.PAR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 generating patterns, plotting ordered pairs in the first quadrant"},{"identifier":"d87b24e1-f313-4b2e-9722-fbc40c8612ec","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d87b24e1-f313-4b2e-9722-fbc40c8612ec","fullStatement":"Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.MDR.7","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** MEASUREMENT & DATA REASONING \u2013 measurements within the metric system, measurement conversions and time as a unit of measurement"},{"identifier":"d4aa33cb-bd48-485b-bd04-46efdd9069db","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d4aa33cb-bd48-485b-bd04-46efdd9069db","fullStatement":"Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"5.GSR.8","language":"eng","CFItemType":"Content Standard","educationLevel":["05"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 Properties of polygons and rectangular prisms, classify polygons"},{"identifier":"9c3db874-5cde-45cf-8dd9-065d0b0e4394","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c3db874-5cde-45cf-8dd9-065d0b0e4394","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:46:00+00:00","humanCodingScheme":"6.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"94b4572d-40ea-4935-a52c-754a32fe1166","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/94b4572d-40ea-4935-a52c-754a32fe1166","fullStatement":"Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 multiplication and division of whole numbers and fractions, and all four operations with decimal numbers"},{"identifier":"795830c1-c973-4ca6-9813-158b660d349e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/795830c1-c973-4ca6-9813-158b660d349e","fullStatement":"Apply operations with whole numbers, fractions and decimals within relevant applications.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.NR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 multiplication and division of whole numbers and fractions, and all four operations with decimal numbers"},{"identifier":"6377248e-f9af-425a-8660-46b73afded70","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6377248e-f9af-425a-8660-46b73afded70","fullStatement":"Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.NR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 multiplication and division of whole numbers and fractions, and all four operations with decimal numbers"},{"identifier":"12e6d05b-bdac-4ee3-bb29-30456a6b2413","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/12e6d05b-bdac-4ee3-bb29-30456a6b2413","fullStatement":"Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.NR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 multiplication and division of whole numbers and fractions, and all four operations with decimal numbers"},{"identifier":"ba49c35d-ad1e-45f1-96c5-0727c33246b7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ba49c35d-ad1e-45f1-96c5-0727c33246b7","fullStatement":"Solve relevant problems involving area, surface area, and volume.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.GSR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 area of polygons, volume of right rectangular prisms, surface area of 3-D figures"},{"identifier":"7d601a8c-72f3-49b2-89c5-d3fb365587d2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7d601a8c-72f3-49b2-89c5-d3fb365587d2","fullStatement":"Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.PAR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 numerical and algebraic expressions, factors, multiples, algebraic expressions, plotting points in all four quadrants, rational numbers on a number line, polygons in the coordinate plane"},{"identifier":"4df8c862-2b9c-44bf-830b-6c5cf92b101e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4df8c862-2b9c-44bf-830b-6c5cf92b101e","fullStatement":"Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.PAR.7","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 numerical and algebraic expressions, factors, multiples, algebraic expressions, plotting points in all four quadrants, rational numbers on a number line, polygons in the coordinate plane"},{"identifier":"2fd8c8c3-47d8-4aa6-8935-a4e0c8e9c0a2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2fd8c8c3-47d8-4aa6-8935-a4e0c8e9c0a2","fullStatement":"Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"6.PAR.8","language":"eng","CFItemType":"Content Standard","educationLevel":["06"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 numerical and algebraic expressions, factors, multiples, algebraic expressions, plotting points in all four quadrants, rational numbers on a number line, polygons in the coordinate plane"},{"identifier":"ddf4057d-458c-409e-979d-5a48385864ca","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddf4057d-458c-409e-979d-5a48385864ca","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:46:04+00:00","humanCodingScheme":"7.MP","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"c619ebd3-9768-4fe2-8499-a5f3cd84ff77","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c619ebd3-9768-4fe2-8499-a5f3cd84ff77","fullStatement":"Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.NR.1","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** NUMERICAL REASONING \u2013 integers, percentages, fractions, decimal numbers"},{"identifier":"9f339168-c988-4194-a6d7-7f6fbbf7bc26","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9f339168-c988-4194-a6d7-7f6fbbf7bc26","fullStatement":"Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant contextual situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.PAR.2","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 linear expressions with rational coefficients, complex unit rates, proportional relationships"},{"identifier":"704fea5f-d5eb-4277-b64c-ce5317295ba8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/704fea5f-d5eb-4277-b64c-ce5317295ba8","fullStatement":"Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.PAR.3","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 linear expressions with rational coefficients, complex unit rates, proportional relationships"},{"identifier":"c98c1d12-470d-44bc-9b42-1380c1f365dd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c98c1d12-470d-44bc-9b42-1380c1f365dd","fullStatement":"Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.PAR.4","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 linear expressions with rational coefficients, complex unit rates, proportional relationships"},{"identifier":"c18ae7de-2349-4d1c-92d1-896bd8b4561b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c18ae7de-2349-4d1c-92d1-896bd8b4561b","fullStatement":"Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.GSR.5","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 vertical, adjacent, complementary, and supplementary angles, circumference and area of circles, area and surface area, volume of cubes, right prisms, and cylinders"},{"identifier":"8d411856-f397-4bc1-b6e6-3e8c6accd878","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8d411856-f397-4bc1-b6e6-3e8c6accd878","fullStatement":"Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"7.PR.6","language":"eng","CFItemType":"Content Standard","educationLevel":["07"],"notes":"**Big Idea:** PROBABILITY REASONING \u2013 likelihood, theoretical and experimental probability"},{"identifier":"f25147bb-2e7d-41f5-961e-62050c7fca76","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f25147bb-2e7d-41f5-961e-62050c7fca76","fullStatement":"Read and write multi-digit whole numbers up to 10,000 to the thousands using base-ten numerals and expanded form.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.NR.1.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"75222b39-2bc1-4e8a-b934-7ece6af3f9f1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/75222b39-2bc1-4e8a-b934-7ece6af3f9f1","fullStatement":"Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results of comparisons.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.NR.1.2","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"a6e06ca1-8437-4d42-a2b6-b8d2463c98b3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a6e06ca1-8437-4d42-a2b6-b8d2463c98b3","fullStatement":"Use place value understanding to round whole numbers within up to 1000 to the nearest 10 or 100.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.NR.1.3","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"9e146e71-7602-414e-ba06-7022c762870f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9e146e71-7602-414e-ba06-7022c762870f","fullStatement":"Fluently add and subtract within 1000 to solve problems.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.PAR.2.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"4a773e72-9cfb-4725-b0f9-beaf0580a589","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4a773e72-9cfb-4725-b0f9-beaf0580a589","fullStatement":"Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving addition and subtraction within 10,000. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.PAR.2.2","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"6946a13f-a0b4-45e9-96d8-f2bd611369e5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6946a13f-a0b4-45e9-96d8-f2bd611369e5","fullStatement":"Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.PAR.3.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"f38af5c5-df62-4779-b9ba-a6c12136caa9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f38af5c5-df62-4779-b9ba-a6c12136caa9","fullStatement":"Represent single digit multiplication and division facts using a variety of strategies. 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Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.PAR.3.7","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"2a77fce5-a9d8-4268-8d87-f34a3e666f3d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2a77fce5-a9d8-4268-8d87-f34a3e666f3d","fullStatement":"Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. 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Solve problems involving mass, length, and volume given in the same unit, and reason about the relative sizes of measurement units within the customary system.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.MDR.5.5","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"2f371807-90e3-4978-b092-36278e347b18","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2f371807-90e3-4978-b092-36278e347b18","fullStatement":"Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve problems involving parallel line segments, perpendicular line segments, and right angles.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.6.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"828473f6-3e66-45da-867a-0a6fdde9de5b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/828473f6-3e66-45da-867a-0a6fdde9de5b","fullStatement":"Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3-dimensional figures to identify and describe quadrilaterals as faces of these figures.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.6.2","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"a71f5f7e-3c70-401f-8d78-f2472cb6ff4e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a71f5f7e-3c70-401f-8d78-f2472cb6ff4e","fullStatement":"Identify lines of symmetry in polygons.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.6.3","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"b91f2e81-0225-4bee-bdd8-6c31d4d9e735","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b91f2e81-0225-4bee-bdd8-6c31d4d9e735","fullStatement":"Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space).","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.7.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"c843d8d1-553c-467c-b37a-90d7976ec8e7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c843d8d1-553c-467c-b37a-90d7976ec8e7","fullStatement":"Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and counting.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.7.2","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"14f0fe15-01a3-4084-ad94-6fa6371a7139","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/14f0fe15-01a3-4084-ad94-6fa6371a7139","fullStatement":"Discover and explain how area can be found by multiplying the dimensions of a rectangle.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.7.3","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"b6c71889-bdb7-4817-a955-324a576c8f71","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6c71889-bdb7-4817-a955-324a576c8f71","fullStatement":"Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.8.1","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"4b150315-1d1c-4637-b83b-bd9e39e92835","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4b150315-1d1c-4637-b83b-bd9e39e92835","fullStatement":"Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.","lastChangeDateTime":"2022-03-18T05:25:20+00:00","humanCodingScheme":"3.GSR.8.2","language":"eng","CFItemType":"Element","educationLevel":["03"]},{"identifier":"e73c5a72-cd4e-4788-8390-c59b964e0358","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e73c5a72-cd4e-4788-8390-c59b964e0358","fullStatement":"Count up to 20 objects in a variety of structured arrangements and up to 10 objects in a scattered arrangement.","lastChangeDateTime":"2022-04-12T15:20:11+00:00","humanCodingScheme":"K.NR.1.1","language":"eng","CFItemType":"Element","educationLevel":["KG"]},{"identifier":"16d84b17-7171-4257-b683-9a9b07ae8ac8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/16d84b17-7171-4257-b683-9a9b07ae8ac8","fullStatement":"When counting objects, explain that the last number counted represents the total quantity in a set (cardinality), regardless of the arrangement and order.","lastChangeDateTime":"2022-04-12T15:20:11+00:00","humanCodingScheme":"K.NR.1.2","language":"eng","CFItemType":"Element","educationLevel":["KG"]},{"identifier":"90d5d642-5f01-4562-ada6-0356e4940646","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90d5d642-5f01-4562-ada6-0356e4940646","fullStatement":"Given a number from 1-20, identify the number that is one more or one 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ones.","lastChangeDateTime":"2022-04-12T15:20:11+00:00","humanCodingScheme":"K.NR.2.1","language":"eng","CFItemType":"Element","educationLevel":["KG"]},{"identifier":"b3ba8262-9c5a-4590-967b-39394802618d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b3ba8262-9c5a-4590-967b-39394802618d","fullStatement":"Count forward beginning from any number within 100 and count backward from any number within 20.","lastChangeDateTime":"2022-04-12T15:20:11+00:00","humanCodingScheme":"K.NR.2.2","language":"eng","CFItemType":"Element","educationLevel":["KG"]},{"identifier":"bc3067ef-52f3-48a5-a857-01fe17558cd7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bc3067ef-52f3-48a5-a857-01fe17558cd7","fullStatement":"Describe numbers from 11 to 19 by composing (putting together) and decomposing (breaking apart) the numbers into ten ones and some more 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Compare unit models to rulers.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.5.1","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"095e9e7b-e73d-4f55-9e48-96414d021132","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/095e9e7b-e73d-4f55-9e48-96414d021132","fullStatement":"Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.5.2","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"5826c12e-79b6-4c52-8fdf-c2f4b08a6efe","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5826c12e-79b6-4c52-8fdf-c2f4b08a6efe","fullStatement":"Measure to determine how much longer one object is than another and express the length difference in terms of a standard-length unit.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.5.3","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"1a34be21-3938-4341-a56f-6e93dffb423d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a34be21-3938-4341-a56f-6e93dffb423d","fullStatement":"Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.5.4","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"298f41d8-de00-4ca6-927a-ec3712fc3c98","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/298f41d8-de00-4ca6-927a-ec3712fc3c98","fullStatement":"Represent whole-number sums and differences within a standard unit of measurement on a number line diagram.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.5.5","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"3779c839-d0dd-45ef-9cb9-a058c5486bd5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3779c839-d0dd-45ef-9cb9-a058c5486bd5","fullStatement":"Tell and write time from analog and digital clocks to the nearest five minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.6.1","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"27db922d-0bae-400c-997f-b1eca13495b1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27db922d-0bae-400c-997f-b1eca13495b1","fullStatement":"Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one hundred cents, and solve problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and \u00a2 symbols appropriately.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.MDR.6.2","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"9bdd7a29-2622-45f7-b4a9-2b04f3142e89","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9bdd7a29-2622-45f7-b4a9-2b04f3142e89","fullStatement":"Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.GSR.7.1","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"e3ef1ccb-daa9-41ac-916c-a50fc3a2a7c1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e3ef1ccb-daa9-41ac-916c-a50fc3a2a7c1","fullStatement":"Identify at least one line of symmetry in everyday objects to describe each object as a whole.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.GSR.7.2","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"27aed36f-e8a1-4d0e-a3c2-3e7348812ad9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27aed36f-e8a1-4d0e-a3c2-3e7348812ad9","fullStatement":"Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (\u201chalves,\u201d \u201cthirds,\u201d \u201cfourths\u201d, \u201chalf of,\u201d \u201cthird of,\u201d \u201cquarter of,\u201d etc.).","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.GSR.7.3","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"53b8e144-09fc-4e0c-95c3-a5a29c558260","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/53b8e144-09fc-4e0c-95c3-a5a29c558260","fullStatement":"Recognize that equal shares of identical wholes may be different shapes within the same whole.","lastChangeDateTime":"2022-03-18T05:25:33+00:00","humanCodingScheme":"2.GSR.7.4","language":"eng","CFItemType":"Element","educationLevel":["02"]},{"identifier":"1d2f3204-950d-4579-a5af-208fe2b1ce07","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1d2f3204-950d-4579-a5af-208fe2b1ce07","fullStatement":"Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.1.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"c3226417-bf6f-4849-bcb6-2360eaa4975c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c3226417-bf6f-4849-bcb6-2360eaa4975c","fullStatement":"Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.1.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"8b906083-b728-4933-837d-5651d5682808","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8b906083-b728-4933-837d-5651d5682808","fullStatement":"Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the results of comparisons.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.1.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"49ec11b2-0bf2-4e0d-97e1-89531da1e9d0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/49ec11b2-0bf2-4e0d-97e1-89531da1e9d0","fullStatement":"Use place value understanding to round multi-digit whole numbers.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.1.4","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"50cd8acc-2694-4272-9f0e-88b19a5ef18e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/50cd8acc-2694-4272-9f0e-88b19a5ef18e","fullStatement":"Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.2.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"272130ac-b665-4951-9920-98f066748592","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/272130ac-b665-4951-9920-98f066748592","fullStatement":"Interpret, model, and solve problems involving multiplicative comparison.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.2.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"e48561be-af32-49e3-a9e4-5249053481a9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e48561be-af32-49e3-a9e4-5249053481a9","fullStatement":"Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of 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.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.2.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"ac622561-0579-46ce-ba33-d35233a98305","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ac622561-0579-46ce-ba33-d35233a98305","fullStatement":"Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.2.4","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"e24a9810-0db8-4bde-8262-94eff73d57cd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e24a9810-0db8-4bde-8262-94eff73d57cd","fullStatement":"Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.2.5","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"26b198d1-3b49-4721-82fe-d491e063fa40","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/26b198d1-3b49-4721-82fe-d491e063fa40","fullStatement":"Generate both number and shape patterns that follow a provided rule.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.PAR.3.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"94fc009d-d346-49cc-ae26-8a66ad5b597d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/94fc009d-d346-49cc-ae26-8a66ad5b597d","fullStatement":"Use input-output rules, tables, and charts to represent and describe patterns, find relationships, and solve problems.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.PAR.3.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"af9324d6-424a-4dd0-a534-28148e248a83","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/af9324d6-424a-4dd0-a534-28148e248a83","fullStatement":"Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships.","lastChangeDateTime":"2022-08-25T16:08:53-04:00","humanCodingScheme":"4.NR.4.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"7e19cf99-0aec-4cbc-8fc9-92ed8f65d999","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7e19cf99-0aec-4cbc-8fc9-92ed8f65d999","fullStatement":"Find factor pairs in the range 1\u2013100 and find multiples of single-digit numbers up to 100.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.PAR.3.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"538fe169-24d0-4228-b1e7-eff8d2a5cf39","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/538fe169-24d0-4228-b1e7-eff8d2a5cf39","fullStatement":"Identify composite numbers and prime numbers and explain the relationship with the factor pairs.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.PAR.3.4","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"04046bca-94a6-4345-bcd2-a4f1867478f7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/04046bca-94a6-4345-bcd2-a4f1867478f7","fullStatement":"Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole.","lastChangeDateTime":"2022-08-25T16:14:03-04:00","humanCodingScheme":"4.NR.4.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"6de37972-157c-4518-a66b-57992d163796","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6de37972-157c-4518-a66b-57992d163796","fullStatement":"Compare two fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.4.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"ab828bff-043f-4ebd-9f35-488d9bb46e7e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab828bff-043f-4ebd-9f35-488d9bb46e7e","fullStatement":"Represent whole numbers and fractions as the sum of unit fractions.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.4.4","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"a4fa6787-2ff8-4d8a-8de6-e54bd756dcad","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a4fa6787-2ff8-4d8a-8de6-e54bd756dcad","fullStatement":"Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.4.5","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"df825620-e2b6-4ba9-9921-7d4572a57b55","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/df825620-e2b6-4ba9-9921-7d4572a57b55","fullStatement":"Add and subtract fractions and mixed numbers with like denominators using a variety of tools.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.4.6","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"d0aee976-3eea-4610-a12d-76f7d6f9950c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d0aee976-3eea-4610-a12d-76f7d6f9950c","fullStatement":"Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.5.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"ed5b1e25-f595-4119-a940-47480e8a6156","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ed5b1e25-f595-4119-a940-47480e8a6156","fullStatement":"Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the hundredths place as fractions, using concrete materials and drawings.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.5.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"b975802a-a952-4052-af3e-f64fcca12bfb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b975802a-a952-4052-af3e-f64fcca12bfb","fullStatement":"Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.NR.5.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"e084a030-3854-4820-906e-9c187a12f705","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e084a030-3854-4820-906e-9c187a12f705","fullStatement":"Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.MDR.6.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"04f03371-b87b-4d5d-8da0-a12a4932e052","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/04f03371-b87b-4d5d-8da0-a12a4932e052","fullStatement":"Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.MDR.6.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"79f76d02-ec1b-4387-afe3-ee529c86549b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/79f76d02-ec1b-4387-afe3-ee529c86549b","fullStatement":"Create dot plots to display a distribution of numerical (quantitative) measurement data.","lastChangeDateTime":"2022-08-25T16:15:52-04:00","humanCodingScheme":"4.MDR.6.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"16a662ab-2f37-4ea4-88fa-fe4bf6528c94","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/16a662ab-2f37-4ea4-88fa-fe4bf6528c94","fullStatement":"Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.GSR.7.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"a347ddc3-68e8-46e6-8202-f92446734d61","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a347ddc3-68e8-46e6-8202-f92446734d61","fullStatement":"Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle\u2019s measure in relation to the 360 degrees in a circle through division or as a missing factor problem.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.GSR.7.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"77b635ca-5540-468d-aa3c-e432821b427e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/77b635ca-5540-468d-aa3c-e432821b427e","fullStatement":"Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, parallel lines, and lines of symmetry. Identify these in two-dimensional figures.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.GSR.8.1","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"985c0d9f-eb92-4b34-a582-12d818951e60","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/985c0d9f-eb92-4b34-a582-12d818951e60","fullStatement":"Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a specified size and based on side lengths.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.GSR.8.2","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"4165a6e6-50e0-437b-b8c9-3f011140dd73","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4165a6e6-50e0-437b-b8c9-3f011140dd73","fullStatement":"Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.","lastChangeDateTime":"2022-03-18T05:25:10+00:00","humanCodingScheme":"4.GSR.8.3","language":"eng","CFItemType":"Element","educationLevel":["04"]},{"identifier":"53efdf79-df91-4a8d-9c24-3dbaac4bf7e1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/53efdf79-df91-4a8d-9c24-3dbaac4bf7e1","fullStatement":"Explain 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 $\\frac{1}{10}$ of what it represents in the place to its left.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.1.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"be60534e-9ec0-42bb-a603-ef66a540e58e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/be60534e-9ec0-42bb-a603-ef66a540e58e","fullStatement":"Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to $10^3$.","lastChangeDateTime":"2022-03-18T18:21:26+00:00","humanCodingScheme":"5.NR.1.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"86a897e4-f45c-4a76-b67d-9709bc729c21","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/86a897e4-f45c-4a76-b67d-9709bc729c21","fullStatement":"Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems.","lastChangeDateTime":"2022-08-25T16:16:18-04:00","humanCodingScheme":"5.NR.2.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"b45d0350-b14f-4f42-a42e-7720843e6320","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b45d0350-b14f-4f42-a42e-7720843e6320","fullStatement":"Fluently divide multi-digit whole numbers (up to 4-digit dividends and\n2-digit divisors no greater than 25) to solve practical problems.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.2.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"a090d07e-3056-4b1e-b2a5-769931fc959f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a090d07e-3056-4b1e-b2a5-769931fc959f","fullStatement":"Explain the meaning of a fraction as division of the numerator by the denominator ($\\frac{a}{b}$ = a \u00f7 b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"b6b32abc-0051-4ba0-9928-8e101ef69cbf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b6b32abc-0051-4ba0-9928-8e101ef69cbf","fullStatement":"Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"e3ecf135-afc8-453b-8245-fcaf401aa5b4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e3ecf135-afc8-453b-8245-fcaf401aa5b4","fullStatement":"Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.3","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"d38a07a4-052c-44cd-b5e4-c3336c4663c8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d38a07a4-052c-44cd-b5e4-c3336c4663c8","fullStatement":"Model and solve problems involving multiplication of a fraction and a whole number.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.4","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"9885f949-f81d-4236-9c69-d0b19d5bb249","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9885f949-f81d-4236-9c69-d0b19d5bb249","fullStatement":"Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.5","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"bc4f9e36-dd44-4e3d-9073-55832069a22e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bc4f9e36-dd44-4e3d-9073-55832069a22e","fullStatement":"Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.3.6","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"d31a86aa-6a0e-44c4-a528-c07c2ca23fae","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d31a86aa-6a0e-44c4-a528-c07c2ca23fae","fullStatement":"Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded form.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.4.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"301571a4-09b5-4e69-8df7-830bedb65814","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/301571a4-09b5-4e69-8df7-830bedb65814","fullStatement":"Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.4.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"910dc8f1-591d-44eb-81d8-945a6ca74407","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/910dc8f1-591d-44eb-81d8-945a6ca74407","fullStatement":"Use place value understanding to round decimal numbers to the hundredths place.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.4.3","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"21558e50-67e8-4eeb-89d7-1f7eeee3c062","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/21558e50-67e8-4eeb-89d7-1f7eeee3c062","fullStatement":"Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.4.4","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"6d103bd0-2dd4-4fd1-94bb-d18bdd4d6db5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6d103bd0-2dd4-4fd1-94bb-d18bdd4d6db5","fullStatement":"Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.NR.5.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"65a77809-6acc-4cb2-ba77-8e260f41b913","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/65a77809-6acc-4cb2-ba77-8e260f41b913","fullStatement":"Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.PAR.6.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"d7bf2a0e-690d-408c-9717-972944c5ae07","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d7bf2a0e-690d-408c-9717-972944c5ae07","fullStatement":"Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.PAR.6.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"22f2d051-460c-4aed-b6be-b9c7b0c50eaf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/22f2d051-460c-4aed-b6be-b9c7b0c50eaf","fullStatement":"Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.MDR.7.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"d266dc47-8f46-4e64-a4db-619175e678ce","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d266dc47-8f46-4e64-a4db-619175e678ce","fullStatement":"Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.MDR.7.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"623f13cc-32d5-48ff-8a23-eef61ee4d606","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/623f13cc-32d5-48ff-8a23-eef61ee4d606","fullStatement":"Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.MDR.7.3","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"3d6368a4-2a54-40aa-89be-e12a91814448","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3d6368a4-2a54-40aa-89be-e12a91814448","fullStatement":"Convert among units within relative sizes of measurement units within the customary measurement system.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.MDR.7.4","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"9140f67e-41b0-409b-91d3-874d08bb4a52","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9140f67e-41b0-409b-91d3-874d08bb4a52","fullStatement":"Classify, compare, and contrast polygons based on properties.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.GSR.8.1","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"64c0bd73-4d62-4d3e-96b6-b5669df64b16","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/64c0bd73-4d62-4d3e-96b6-b5669df64b16","fullStatement":"Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.","lastChangeDateTime":"2023-02-06T15:08:57-05:00","humanCodingScheme":"5.GSR.8.2","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"6de9c6dc-781a-48ca-a1f7-65e7b8ec5571","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6de9c6dc-781a-48ca-a1f7-65e7b8ec5571","fullStatement":"Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.GSR.8.3","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"371c0ae7-7877-4e51-8063-c23665668755","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/371c0ae7-7877-4e51-8063-c23665668755","fullStatement":"Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.","lastChangeDateTime":"2022-03-18T05:24:56+00:00","humanCodingScheme":"5.GSR.8.4","language":"eng","CFItemType":"Element","educationLevel":["05"]},{"identifier":"116fe9b5-1494-4048-871a-78d9e325f963","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/116fe9b5-1494-4048-871a-78d9e325f963","fullStatement":"Fluently add and subtract any combination of fractions to solve problems.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.1.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"576676f5-a837-42f5-ab8e-6b154f66a7c8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/576676f5-a837-42f5-ab8e-6b154f66a7c8","fullStatement":"Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.1.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"694625f3-6c89-4484-86a7-4994732f49a9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/694625f3-6c89-4484-86a7-4994732f49a9","fullStatement":"Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.1.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"06415bf2-e7a9-4ef8-9a26-4d67a45ad1cd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/06415bf2-e7a9-4ef8-9a26-4d67a45ad1cd","fullStatement":"Describe and interpret the center of the distribution by the equal share value (mean).","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.2.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"5187c1ee-ad72-46d2-a003-2aac28e0246a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5187c1ee-ad72-46d2-a003-2aac28e0246a","fullStatement":"Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.2.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"3fa81fbf-fe59-41d5-8df3-c68cc13be7b8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3fa81fbf-fe59-41d5-8df3-c68cc13be7b8","fullStatement":"Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape.","lastChangeDateTime":"2022-08-25T15:40:41-04:00","humanCodingScheme":"6.NR.2.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"e56e0a02-b24b-4d76-89b2-d950e46d2dd4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e56e0a02-b24b-4d76-89b2-d950e46d2dd4","fullStatement":"Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.2.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"0a60e887-ad4d-436d-9714-4586e8d0899f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0a60e887-ad4d-436d-9714-4586e8d0899f","fullStatement":"Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.2.5","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"e5af3361-5750-4ed0-81d2-7ef0d74e25c9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e5af3361-5750-4ed0-81d2-7ef0d74e25c9","fullStatement":"Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.2.6","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"b810b577-9953-4fd8-af2f-e7773ad0d3b2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b810b577-9953-4fd8-af2f-e7773ad0d3b2","fullStatement":"Identify and compare integers and explain the meaning of zero based on multiple authentic situations.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"3e451234-27c1-4eea-a917-772aa2923a91","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3e451234-27c1-4eea-a917-772aa2923a91","fullStatement":"Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"563820a0-3bb7-4e7d-ac9b-706b5e346ea7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/563820a0-3bb7-4e7d-ac9b-706b5e346ea7","fullStatement":"Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"8af2eee7-5701-4877-b36e-95a9b8624782","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8af2eee7-5701-4877-b36e-95a9b8624782","fullStatement":"Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"99934a29-f082-463c-8e4f-2892f799d755","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/99934a29-f082-463c-8e4f-2892f799d755","fullStatement":"Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.5","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"c554e785-7e3b-42a9-b9f0-5f506f26a7ce","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c554e785-7e3b-42a9-b9f0-5f506f26a7ce","fullStatement":"Distinguish comparisons of absolute value from statements about order.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.3.6","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"5803b65f-afeb-49e5-85e1-0a183674e3e6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5803b65f-afeb-49e5-85e1-0a183674e3e6","fullStatement":"Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"7f87e7bb-8fff-4873-b874-b2f4c3675965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7f87e7bb-8fff-4873-b874-b2f4c3675965","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.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"36642833-487c-4383-9b05-af7e36c18266","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/36642833-487c-4383-9b05-af7e36c18266","fullStatement":"Solve problems involving proportions using a variety of student-selected strategies.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"375d2390-a59b-494e-8e8b-8f19b5139d8d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/375d2390-a59b-494e-8e8b-8f19b5139d8d","fullStatement":"Describe the concept of rates and unit rate in the context of a ratio relationship.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"6a81c2b4-7c5c-4ef5-a243-4890a8fe6231","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6a81c2b4-7c5c-4ef5-a243-4890a8fe6231","fullStatement":"Solve unit rate problems including those involving unit pricing and constant speed.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.5","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"7e8a8208-a2f5-4f50-b40c-7b625a099e9f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7e8a8208-a2f5-4f50-b40c-7b625a099e9f","fullStatement":"Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.6","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"fecf406f-92d0-434c-8df2-7145778de3b5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fecf406f-92d0-434c-8df2-7145778de3b5","fullStatement":"Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.NR.4.7","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"148edfca-d51c-45c2-b7c3-ccd3baa599cc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/148edfca-d51c-45c2-b7c3-ccd3baa599cc","fullStatement":"Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.GSR.5.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"15991e40-610b-4b32-839c-0013d19306c9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/15991e40-610b-4b32-839c-0013d19306c9","fullStatement":"Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.GSR.5.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"e8cca2ac-14f1-41a7-ae42-0a5c2aaa2dee","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e8cca2ac-14f1-41a7-ae42-0a5c2aaa2dee","fullStatement":"Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height).","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.GSR.5.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"8b9e2989-8b9d-462c-99ab-442909f60701","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8b9e2989-8b9d-462c-99ab-442909f60701","fullStatement":"Write and evaluate numerical expressions involving rational bases and whole-number exponents.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.6.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"0df3e728-aab4-4e85-8908-82a841279f8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0df3e728-aab4-4e85-8908-82a841279f8c","fullStatement":"Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.6.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"d0a0f47b-6f93-4ba8-88dc-32f71a0c2152","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d0a0f47b-6f93-4ba8-88dc-32f71a0c2152","fullStatement":"Write and read expressions that represent operations with numbers and variables in realistic situations.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.6.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"6949e1c3-e7dd-46de-8c25-e0fb3bbe8f38","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6949e1c3-e7dd-46de-8c25-e0fb3bbe8f38","fullStatement":"Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.6.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"ce42914a-427c-4ad0-b69d-a721e57d7603","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ce42914a-427c-4ad0-b69d-a721e57d7603","fullStatement":"Apply the properties of operations to identify and generate equivalent expressions.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.6.5","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"651aa517-2287-4724-b596-c5292145d89d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/651aa517-2287-4724-b596-c5292145d89d","fullStatement":"Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.7.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"465b09ed-b1a1-422b-85d3-6424f4d91bf5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/465b09ed-b1a1-422b-85d3-6424f4d91bf5","fullStatement":"Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.7.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"62d52cb3-e857-46d3-b772-885bed3b7f7e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/62d52cb3-e857-46d3-b772-885bed3b7f7e","fullStatement":"Solve problems by writing and solving equations of the form x + p = q, px = q and $\\frac{x}{p}$ = q for cases in which p, q and x are all nonnegative rational numbers.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.7.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"67fcfa95-28d9-4ec0-97a2-f579be6271e6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/67fcfa95-28d9-4ec0-97a2-f579be6271e6","fullStatement":"Recognize and generate inequalities of the form x > c, x \u2265 c, x \u2264 c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line.","lastChangeDateTime":"2023-02-06T14:52:36-05:00","humanCodingScheme":"6.PAR.7.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"1957d2bc-21d9-4129-836f-b274094314d8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1957d2bc-21d9-4129-836f-b274094314d8","fullStatement":"Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.8.1","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"17698d41-02df-4b44-a56b-02b60f4b6e75","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/17698d41-02df-4b44-a56b-02b60f4b6e75","fullStatement":"Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.8.2","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"d0ba77f6-acc0-44bb-93b5-ddc465c22d4d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d0ba77f6-acc0-44bb-93b5-ddc465c22d4d","fullStatement":"Solve 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 x-coordinate or the same y-coordinate.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.8.3","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"6273ff4e-41bf-4e54-9a48-2f7786520c60","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6273ff4e-41bf-4e54-9a48-2f7786520c60","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 x-coordinate or the same y-coordinate.","lastChangeDateTime":"2022-03-18T05:24:28+00:00","humanCodingScheme":"6.PAR.8.4","language":"eng","CFItemType":"Element","educationLevel":["06"]},{"identifier":"2bbc6a04-9d59-4a82-8ff0-61aeb58f77f7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2bbc6a04-9d59-4a82-8ff0-61aeb58f77f7","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-04-12T15:46:09+00:00","humanCodingScheme":"8.MP","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. In well-designed lessons, there are often two or more Standards for Mathematical Practice present."},{"identifier":"4a08c2a7-2579-4fb3-afcc-7203c391cd51","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4a08c2a7-2579-4fb3-afcc-7203c391cd51","fullStatement":"Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.NR.1","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** NUMERICAL REASONING \u2013 rational and irrational numbers, decimal expansion, integer exponents, square and cube roots, scientific notation"},{"identifier":"3bd80e19-1614-455d-964d-daaf9893b13e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3bd80e19-1614-455d-964d-daaf9893b13e","fullStatement":"Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.NR.1.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"5ac5239b-3712-4cc6-bb94-1f63ccf54643","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5ac5239b-3712-4cc6-bb94-1f63ccf54643","fullStatement":"Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.NR.1.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"1b8fe278-1208-4440-aae9-698d2f9c79d5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1b8fe278-1208-4440-aae9-698d2f9c79d5","fullStatement":"Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.NR.2","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** NUMERICAL REASONING \u2013 rational and irrational numbers, decimal expansion, integer exponents, square and cube roots, scientific notation"},{"identifier":"d6ae3ce2-49ac-43bd-8ad0-dc1a4125c507","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d6ae3ce2-49ac-43bd-8ad0-dc1a4125c507","fullStatement":"Apply the properties of integer exponents to generate equivalent numerical expressions.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.NR.2.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"42bc6294-1427-4bd7-a217-6ad247a63a26","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/42bc6294-1427-4bd7-a217-6ad247a63a26","fullStatement":"Use square root and cube root symbols to represent solutions to equations. Recognize that $x^2 = p$ (where p is a positive rational number and |x| &le; 25) has two solutions and $x^3 = p$ (where p is a negative or positive rational number and |x| &le; 10) has one solution. Evaluate square roots of perfect squares &le; 625 and cube roots of perfect cubes &ge; -1000 and &le; 1000.","lastChangeDateTime":"2022-08-25T15:50:05-04:00","humanCodingScheme":"8.NR.2.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"c2266a49-39b9-48ba-a428-0ee113dbb1d1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c2266a49-39b9-48ba-a428-0ee113dbb1d1","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.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.NR.2.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"44873202-d5e6-4311-ba0b-a8aefe840dc0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/44873202-d5e6-4311-ba0b-a8aefe840dc0","fullStatement":"Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.NR.2.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"2f51c4f3-51ce-43db-9406-9a625cfb9a17","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2f51c4f3-51ce-43db-9406-9a625cfb9a17","fullStatement":"Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.PAR.3","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 expressions, linear equations, and inequalities"},{"identifier":"b1767200-4d96-4d32-94a4-8e18c643310f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1767200-4d96-4d32-94a4-8e18c643310f","fullStatement":"Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"3272e97e-1cf1-4417-9ca9-c2e7f9818e0c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3272e97e-1cf1-4417-9ca9-c2e7f9818e0c","fullStatement":"Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). 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).","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"8b8e152a-e92f-429c-abe1-8f63c1920f9f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8b8e152a-e92f-429c-abe1-8f63c1920f9f","fullStatement":"Create and solve linear equations and inequalities in one variable within a relevant application.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"4bd7b2a8-5044-4d23-964a-c1c0fdff601c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4bd7b2a8-5044-4d23-964a-c1c0fdff601c","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"0624cf4d-c899-45fa-b6a3-ec4cfed9d749","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0624cf4d-c899-45fa-b6a3-ec4cfed9d749","fullStatement":"Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.5","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"49f99063-7f0f-4c76-860c-90362d51efd7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/49f99063-7f0f-4c76-860c-90362d51efd7","fullStatement":"Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.3.6","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"05b03b5c-b5c6-47e9-a9de-e4e065aab93b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/05b03b5c-b5c6-47e9-a9de-e4e065aab93b","fullStatement":"Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.PAR.4","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 expressions, linear equations, and inequalities"},{"identifier":"908b0c11-b6c4-4d85-a2a9-af6549f452c5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/908b0c11-b6c4-4d85-a2a9-af6549f452c5","fullStatement":"Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.4.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"98a9a394-ad53-40a9-a541-8baf4a6b25a3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/98a9a394-ad53-40a9-a541-8baf4a6b25a3","fullStatement":"Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.PAR.4.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"33a7274b-3776-4d52-955a-2d13de2551ae","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/33a7274b-3776-4d52-955a-2d13de2551ae","fullStatement":"Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.FGR.5","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines"},{"identifier":"f23f34e7-4457-4ea6-928b-c7e86194337e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f23f34e7-4457-4ea6-928b-c7e86194337e","fullStatement":"Show and explain that a function is a rule that assigns to each input exactly one output.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"f66dc304-fe41-4dd6-bddd-2b4c37063086","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f66dc304-fe41-4dd6-bddd-2b4c37063086","fullStatement":"Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"4924497f-81f5-4e15-98d5-ae865b54fbbd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4924497f-81f5-4e15-98d5-ae865b54fbbd","fullStatement":"Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"c1b62146-428c-4978-a610-2a2d3152844d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c1b62146-428c-4978-a610-2a2d3152844d","fullStatement":"Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"da2a3416-0d04-456c-8854-af3e6f0f0aea","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da2a3416-0d04-456c-8854-af3e6f0f0aea","fullStatement":"Write and explain the equations $y = mx + b$ (slope-intercept form), $Ax + By = C$ (standard form), and $(y - y_1) = m(x - x_1)$ (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.5","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"2e803b80-a098-4795-a37a-a444a1534001","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2e803b80-a098-4795-a37a-a444a1534001","fullStatement":"Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.6","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"a8040a42-0745-4be6-ac0a-2ab2eaff87f1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a8040a42-0745-4be6-ac0a-2ab2eaff87f1","fullStatement":"Construct a function to model a linear relationship between two quantities. 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.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.7","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"8c719f3a-8f75-4206-a652-8b4f493375ec","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8c719f3a-8f75-4206-a652-8b4f493375ec","fullStatement":"Explain the meaning of 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.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.8","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"ce264f18-1dec-46b2-96e9-134182e4dcb2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ce264f18-1dec-46b2-96e9-134182e4dcb2","fullStatement":"Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.5.9","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"cf0c02f3-b2fd-4ed3-a5fa-587341c62181","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cf0c02f3-b2fd-4ed3-a5fa-587341c62181","fullStatement":"Solve practical, linear problems involving situations using bivariate quantitative data.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.FGR.6","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines"},{"identifier":"2ced64e4-4aa7-4569-96a1-39664e0c6628","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2ced64e4-4aa7-4569-96a1-39664e0c6628","fullStatement":"Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.6.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"efe35755-0f8f-4a33-9086-d76edb763030","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/efe35755-0f8f-4a33-9086-d76edb763030","fullStatement":"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.6.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"dfbf53f8-707c-441e-9e07-a22953ac3a1e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/dfbf53f8-707c-441e-9e07-a22953ac3a1e","fullStatement":"Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.6.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"54b82807-b9cd-49ab-a6ad-477f1ffae7c4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/54b82807-b9cd-49ab-a6ad-477f1ffae7c4","fullStatement":"Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and answer the statistical investigative question posed in an unbiased statistical study.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.FGR.6.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"27867f4f-7d3e-489b-8f13-667c93de47ad","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27867f4f-7d3e-489b-8f13-667c93de47ad","fullStatement":"Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.","lastChangeDateTime":"2022-04-12T19:47:30-04:00","humanCodingScheme":"8.FGR.7","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines"},{"identifier":"52478656-a936-471c-9259-8283ed0be768","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/52478656-a936-471c-9259-8283ed0be768","fullStatement":"Interpret and solve relevant mathematical problems leading to two linear equations in two 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problems.","lastChangeDateTime":"2022-03-17T20:45:00+00:00","humanCodingScheme":"8.GSR.8.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"59409689-169d-4554-982e-f6d1be0f175a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/59409689-169d-4554-982e-f6d1be0f175a","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.","lastChangeDateTime":"2022-08-25T15:41:06-04:00","humanCodingScheme":"7.NR.1.1","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"8dd755d5-dd99-441e-92ab-bb224f0db79b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8dd755d5-dd99-441e-92ab-bb224f0db79b","fullStatement":"Show and explain $p + q$ 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 applicable situations.","lastChangeDateTime":"2022-03-18T05:46:49+00:00","humanCodingScheme":"7.NR.1.2","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"295fc2fd-03a3-46d3-b623-e2d55eea9329","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/295fc2fd-03a3-46d3-b623-e2d55eea9329","fullStatement":"Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.","lastChangeDateTime":"2022-03-18T05:46:19+00:00","humanCodingScheme":"7.NR.1.3","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"76f96509-32d1-4fdb-b187-e86a9dfd5d7f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/76f96509-32d1-4fdb-b187-e86a9dfd5d7f","fullStatement":"Show and explain 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 contextual situations.","lastChangeDateTime":"2022-03-18T05:46:19+00:00","humanCodingScheme":"7.NR.1.4","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"4516cd2c-6d7f-4bb0-a215-960de6d5284e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4516cd2c-6d7f-4bb0-a215-960de6d5284e","fullStatement":"Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.","lastChangeDateTime":"2022-03-18T05:46:19+00:00","humanCodingScheme":"7.NR.1.5","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"12984cf0-7e08-4846-a90d-2742abd181d2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/12984cf0-7e08-4846-a90d-2742abd181d2","fullStatement":"Make sense of multiplication of rational numbers using realistic applications.","lastChangeDateTime":"2022-03-18T05:50:09+00:00","humanCodingScheme":"7.NR.1.6","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"9192ccf3-f92c-4d29-99ec-26b74121dc3f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9192ccf3-f92c-4d29-99ec-26b74121dc3f","fullStatement":"Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.","lastChangeDateTime":"2022-03-18T05:50:54+00:00","humanCodingScheme":"7.NR.1.7","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"5782e981-770c-4136-a7c3-3f04f5c4b648","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5782e981-770c-4136-a7c3-3f04f5c4b648","fullStatement":"Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.","lastChangeDateTime":"2022-08-25T15:41:38-04:00","humanCodingScheme":"7.NR.1.8","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"f0d4a943-44a3-4f00-9418-9409a13ed558","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f0d4a943-44a3-4f00-9418-9409a13ed558","fullStatement":"Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.","lastChangeDateTime":"2022-03-18T05:56:31+00:00","humanCodingScheme":"7.NR.1.9","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"fe36389d-9f6e-444e-8a20-4096aa3eff8d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fe36389d-9f6e-444e-8a20-4096aa3eff8d","fullStatement":"Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.","lastChangeDateTime":"2022-03-18T06:01:12+00:00","humanCodingScheme":"7.NR.1.10","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"406efe31-7310-447c-9153-4ca48cb3c816","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/406efe31-7310-447c-9153-4ca48cb3c816","fullStatement":"Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.","lastChangeDateTime":"2022-03-18T05:46:19+00:00","humanCodingScheme":"7.NR.1.11","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"93c91294-a017-47c7-a6b0-e220aae72f32","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/93c91294-a017-47c7-a6b0-e220aae72f32","fullStatement":"Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.","lastChangeDateTime":"2022-03-18T06:00:31+00:00","humanCodingScheme":"7.PAR.2.1","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"1b4230ec-3c34-42c6-9ae6-0d2794dfde2b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1b4230ec-3c34-42c6-9ae6-0d2794dfde2b","fullStatement":"Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.","lastChangeDateTime":"2022-03-18T05:59:42+00:00","humanCodingScheme":"7.PAR.2.2","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"f8e81e09-f933-4420-b751-9fb538233409","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f8e81e09-f933-4420-b751-9fb538233409","fullStatement":"Construct algebraic equations to solve practical problems leading to equations of the form $px + q = r$ and $p(x + q) = r$, where $p$, $q$, and $r$ are specific rational numbers. Interpret the solution based on the situation.","lastChangeDateTime":"2022-03-18T06:09:23+00:00","humanCodingScheme":"7.PAR.3.1","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"72da8222-dcd1-407d-84fb-5e9d4f75f947","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/72da8222-dcd1-407d-84fb-5e9d4f75f947","fullStatement":"Construct algebraic inequalities to solve problems, leading to inequalities of the form $px \u00b1 q \\gt r$, $px \u00b1 q \\lt r$, $px \u00b1 q \\le r$, or $px \u00b1 q \\ge r$, where $p$, $q$, and $r$ are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.","lastChangeDateTime":"2022-08-25T15:48:25-04:00","humanCodingScheme":"7.PAR.3.2","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"bb837b33-28a1-4ab1-bcbe-08fc5f2debfd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bb837b33-28a1-4ab1-bcbe-08fc5f2debfd","fullStatement":"Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems.","lastChangeDateTime":"2022-03-18T15:01:02+00:00","humanCodingScheme":"7.PAR.4.1","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"8f3c781f-7b96-4852-ab3f-56fb0d60c70f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8f3c781f-7b96-4852-ab3f-56fb0d60c70f","fullStatement":"Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.","lastChangeDateTime":"2022-03-18T15:02:08+00:00","humanCodingScheme":"7.PAR.4.2","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"0227662a-cb0e-4a03-8e10-0e4e41d198ec","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0227662a-cb0e-4a03-8e10-0e4e41d198ec","fullStatement":"Determine whether two quantities presented in authentic problems are in a proportional relationship.","lastChangeDateTime":"2022-03-18T15:02:58+00:00","humanCodingScheme":"7.PAR.4.3","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"f12dd39a-674e-4015-8a4b-cf2a093960bb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f12dd39a-674e-4015-8a4b-cf2a093960bb","fullStatement":"Identify, represent, and use proportional relationships.","lastChangeDateTime":"2022-03-18T15:03:55+00:00","humanCodingScheme":"7.PAR.4.4","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"c3357d08-b33e-4c2b-89ce-1907c29cc74d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c3357d08-b33e-4c2b-89ce-1907c29cc74d","fullStatement":"Use context to 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.","lastChangeDateTime":"2022-03-18T15:04:28+00:00","humanCodingScheme":"7.PAR.4.5","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"1454ed69-fd8e-408e-a891-9973dfc55e12","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1454ed69-fd8e-408e-a891-9973dfc55e12","fullStatement":"Solve everyday 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.","lastChangeDateTime":"2022-03-18T15:05:51+00:00","humanCodingScheme":"7.PAR.4.6","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"bef72e49-b566-4442-80dc-e24b381b3e95","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bef72e49-b566-4442-80dc-e24b381b3e95","fullStatement":"Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane.","lastChangeDateTime":"2022-03-18T15:06:32+00:00","humanCodingScheme":"7.PAR.4.7","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"a92c0d03-d416-4eb5-8989-19324f3b1d20","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a92c0d03-d416-4eb5-8989-19324f3b1d20","fullStatement":"Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.","lastChangeDateTime":"2022-03-18T15:08:43+00:00","humanCodingScheme":"7.PAR.4.8","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"41fbb4ba-351a-4f38-b6bc-02b976eea1ba","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/41fbb4ba-351a-4f38-b6bc-02b976eea1ba","fullStatement":"Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.","lastChangeDateTime":"2022-03-18T15:09:54+00:00","humanCodingScheme":"7.PAR.4.9","language":"eng","educationLevel":["07"],"CFItemType":"Element"},{"identifier":"f9b1d0bb-67e7-4aa7-90c1-c3d497fa6f3f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f9b1d0bb-67e7-4aa7-90c1-c3d497fa6f3f","fullStatement":"Predict characteristics of a population by examining the characteristics of a representative sample. 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Compare experimental and theoretical probabilities of events. 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graph inequalities on coordinate axes with labels and scales.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.4.1","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"9050e635-aea8-49b0-8f7a-41cd33e9d2e7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9050e635-aea8-49b0-8f7a-41cd33e9d2e7","fullStatement":"Represent constraints of linear inequalities and interpret data points as possible or not possible.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.4.2","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"07b7a628-adca-4b8d-98c7-eb29cc76b7c2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/07b7a628-adca-4b8d-98c7-eb29cc76b7c2","fullStatement":"Solve systems of linear inequalities by graphing, including systems representing a mathematically applicable situation.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.4.3","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"6cd2f209-e8c2-403e-b27d-6caee18222e1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6cd2f209-e8c2-403e-b27d-6caee18222e1","fullStatement":"Rewrite algebraic and numeric expressions involving radicals.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.NR.5.1","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"8935c171-94c6-493e-ac5c-517941014be6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8935c171-94c6-493e-ac5c-517941014be6","fullStatement":"Using numerical reasoning, show and explain that the sum or product of rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.NR.5.2","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"3897825c-73ac-4964-b4a4-48627f0c2639","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3897825c-73ac-4964-b4a4-48627f0c2639","fullStatement":"Interpret quadratic expressions and parts of a quadratic expression that represent a quantity in terms of its context.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.6.1","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"ff2e3c70-2998-4b88-aaa4-828d9616eb4e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff2e3c70-2998-4b88-aaa4-828d9616eb4e","fullStatement":"Fluently choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the expression.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.6.2","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"06ec1d70-47b1-4b42-809e-5a52a01eba40","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/06ec1d70-47b1-4b42-809e-5a52a01eba40","fullStatement":"Create and solve quadratic equations in one variable and explain the solution in the framework of applicable phenomena.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.6.3","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"92b5e62b-b0d2-4276-9653-11d6cc3c95c6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/92b5e62b-b0d2-4276-9653-11d6cc3c95c6","fullStatement":"Represent constraints by quadratic equations and interpret data points as possible or not possible in a modeling framework.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.PAR.6.4","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"21b63cc1-b521-4bae-aabc-287ae60ee3a7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/21b63cc1-b521-4bae-aabc-287ae60ee3a7","fullStatement":"Use function notation to build and evaluate quadratic functions for inputs in their domains and interpret statements that use function notation in terms of a given framework.","lastChangeDateTime":"2022-04-12T15:51:02+00:00","humanCodingScheme":"A.FGR.7.1","language":"eng","CFItemType":"Element","educationLevel":["09","10","11","12"]},{"identifier":"f498e2e3-84cf-4252-8b9c-e0d7a724ded1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f498e2e3-84cf-4252-8b9c-e0d7a724ded1","fullStatement":"Identify the effect on the graph generated by a quadratic function when replacing $f(x)$ with $f(x) + k$, $kf(x)$, $f(kx)$, and $f(x + k)$ for specific values of $k$ (both positive and negative); 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Students will continue to enhance their algebraic reasoning skills when analyzing and applying a deep understanding of systems of linear inequalities and sums and products of rational and irrational numbers. 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Convert a decimal expansion which repeats eventually into a rational number.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.1.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"dec666e4-7dda-4e29-84f5-2e2fbe8abe59","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/dec666e4-7dda-4e29-84f5-2e2fbe8abe59","fullStatement":"Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.1.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"424add3a-41f3-43d9-a5e2-4790ae5af41e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/424add3a-41f3-43d9-a5e2-4790ae5af41e","fullStatement":"Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.2","notes":"**Big Idea:** NUMERICAL REASONING \u2013 rational and irrational numbers, decimal expansion, integer exponents, square and cube roots, scientific notation","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"48b30fa7-1757-40ef-9e71-70e781fc5b48","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/48b30fa7-1757-40ef-9e71-70e781fc5b48","fullStatement":"Apply the properties of integer exponents to generate equivalent numerical expressions.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.2.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"d7f02e87-3460-4dba-9b51-9ad3170142e5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d7f02e87-3460-4dba-9b51-9ad3170142e5","fullStatement":"Use square root and cube root symbols to represent solutions to equations. Recognize that $x^2 = p$ (where p is a positive rational number and |x| &le; 25) has two solutions and $x^3 = p$ (where p is a negative or positive rational number and |x| &le; 10) has one solution. Evaluate square roots of perfect squares &le; 625 and cube roots of perfect cubes &ge; -1000 and &le; 1000.","lastChangeDateTime":"2022-08-25T15:54:01-04:00","humanCodingScheme":"8.NR.2.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"4ab786ca-991c-462f-aefd-e63297903b56","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4ab786ca-991c-462f-aefd-e63297903b56","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.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.2.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"e1e60d92-07df-4f5f-b3a9-5414289944df","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e1e60d92-07df-4f5f-b3a9-5414289944df","fullStatement":"Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.NR.2.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"5c3f99ed-ed96-4ea0-b1a1-81f43312da4e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5c3f99ed-ed96-4ea0-b1a1-81f43312da4e","fullStatement":"Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.4","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 expressions, linear equations, and inequalities","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"edbd48e7-623a-4dc5-9f80-7012a0190507","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/edbd48e7-623a-4dc5-9f80-7012a0190507","fullStatement":"Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.4.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"46a403cb-6c25-4ce3-9383-01a18ba91787","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/46a403cb-6c25-4ce3-9383-01a18ba91787","fullStatement":"Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.4.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"54ffc0dd-1e5d-4fef-93ad-0fd8a5b1d7e4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/54ffc0dd-1e5d-4fef-93ad-0fd8a5b1d7e4","fullStatement":"Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"c7655734-8aa3-47fe-b0eb-1f520d71c62a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c7655734-8aa3-47fe-b0eb-1f520d71c62a","fullStatement":"Show and explain that a function is a rule that assigns to each input exactly one output.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"2ccbc6e7-2887-434b-951d-7e46c0c5b8ed","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2ccbc6e7-2887-434b-951d-7e46c0c5b8ed","fullStatement":"Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"1c302e8e-5d08-40ea-96db-158f74bf45df","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1c302e8e-5d08-40ea-96db-158f74bf45df","fullStatement":"Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"b2a97997-939d-43ac-b022-5e43c12d080f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b2a97997-939d-43ac-b022-5e43c12d080f","fullStatement":"Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"6b4fe1a0-cc7f-4a69-ab42-a5bffb258933","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6b4fe1a0-cc7f-4a69-ab42-a5bffb258933","fullStatement":"Write and explain the equations $y = mx + b$ (slope-intercept form), $Ax + By = C$ (standard form), and $(y - y_1) = m(x - x_1)$ (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.5","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"e2abdfab-1a95-4429-9137-6f6bb5f7e499","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e2abdfab-1a95-4429-9137-6f6bb5f7e499","fullStatement":"Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.6","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"1c7308f3-67a1-4013-9ea3-622fc268155d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1c7308f3-67a1-4013-9ea3-622fc268155d","fullStatement":"Construct a function to model a linear relationship between two quantities. 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.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.7","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"c9911a50-156b-4f7e-9942-bd02e374380d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c9911a50-156b-4f7e-9942-bd02e374380d","fullStatement":"Explain the meaning of 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.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.8","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"bfe30491-d271-4436-9885-364b4c3bdddb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bfe30491-d271-4436-9885-364b4c3bdddb","fullStatement":"Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.5.9","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"fe623da4-4265-40d9-bdd2-8a238a4be23f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fe623da4-4265-40d9-bdd2-8a238a4be23f","fullStatement":"Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 expressions, linear equations, and inequalities","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"73a3d30d-27ad-41ed-abe4-0c96778c6d40","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/73a3d30d-27ad-41ed-abe4-0c96778c6d40","fullStatement":"Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"ff8c2b31-9c78-4bd9-9801-7a04f61d9826","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff8c2b31-9c78-4bd9-9801-7a04f61d9826","fullStatement":"Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). 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).","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"71d3a5f4-64c2-4bcb-b166-8e46e6f3ec7e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/71d3a5f4-64c2-4bcb-b166-8e46e6f3ec7e","fullStatement":"Create and solve linear equations and inequalities in one variable within a relevant application.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"4a6ccb3e-5085-4e1f-9f97-ecf1501040c6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4a6ccb3e-5085-4e1f-9f97-ecf1501040c6","fullStatement":"Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"784082d1-14c8-4e5f-bc6f-f73012954be6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/784082d1-14c8-4e5f-bc6f-f73012954be6","fullStatement":"Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.5","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"2109609b-b31c-4c75-b55b-1934c4493aa3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2109609b-b31c-4c75-b55b-1934c4493aa3","fullStatement":"Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.PAR.3.6","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"8d8fe7ad-3ce1-4552-81ac-9c9f6bda79fb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8d8fe7ad-3ce1-4552-81ac-9c9f6bda79fb","fullStatement":"Solve practical, linear problems involving situations using bivariate quantitative data.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.6","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"6548ad07-2fcc-4ac4-9991-2d0fcde9f02d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6548ad07-2fcc-4ac4-9991-2d0fcde9f02d","fullStatement":"Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.6.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"086aa1cc-f85a-4b21-86ee-94eedc39c121","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/086aa1cc-f85a-4b21-86ee-94eedc39c121","fullStatement":"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.6.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"83677944-843b-4dcf-b0e6-44d347e5e8b8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/83677944-843b-4dcf-b0e6-44d347e5e8b8","fullStatement":"Explain the meaning of the predicted 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systems of linear equations to model and explain realistic phenomena.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.7","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"cf0184ff-99be-4370-b8b4-fe9329554476","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cf0184ff-99be-4370-b8b4-fe9329554476","fullStatement":"Interpret and solve relevant mathematical problems leading to two linear equations in two variables.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.7.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"cf5c2e60-83ba-40f6-a858-a6e2c02f52f4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cf5c2e60-83ba-40f6-a858-a6e2c02f52f4","fullStatement":"Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.7.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"ec73b874-dd77-4e35-9c73-55af45da1db9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ec73b874-dd77-4e35-9c73-55af45da1db9","fullStatement":"Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.7.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"0d9686ff-b023-4b6f-8a4d-e715aaa4942f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0d9686ff-b023-4b6f-8a4d-e715aaa4942f","fullStatement":"Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.FGR.7.5","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"be9e9c3a-e405-4c7c-8d2f-7a806299224d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/be9e9c3a-e405-4c7c-8d2f-7a806299224d","fullStatement":"Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.GSR.8","notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 Pythagorean theorem and volume of triangles, rectangles, cones, cylinders, and spheres","language":"eng","educationLevel":["08"],"CFItemType":"Content Standard"},{"identifier":"f9aa598a-7b98-41d1-b741-2ea70a779ef3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f9aa598a-7b98-41d1-b741-2ea70a779ef3","fullStatement":"Explain a proof of the Pythagorean Theorem and its converse using visual models.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.GSR.8.1","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"e32ecc93-af9e-40a0-a5ef-8be06d19e0f7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e32ecc93-af9e-40a0-a5ef-8be06d19e0f7","fullStatement":"Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.GSR.8.2","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"59c68034-ee98-4edf-b833-b03749900acc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/59c68034-ee98-4edf-b833-b03749900acc","fullStatement":"Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.GSR.8.3","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"a9e04009-6f8c-45eb-b4b0-f0b883c60e12","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a9e04009-6f8c-45eb-b4b0-f0b883c60e12","fullStatement":"Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.","lastChangeDateTime":"2022-08-03T17:19:17-04:00","humanCodingScheme":"8.GSR.8.4","language":"eng","educationLevel":["08"],"CFItemType":"Element"},{"identifier":"4d5332aa-9f7d-435b-b322-f8a8980071bf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4d5332aa-9f7d-435b-b322-f8a8980071bf","fullStatement":"Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.MP","notes":"The Mathematical Practices describe the reasoning behaviors students should develop as they build an understanding of mathematics \u2013 the \u201chabits of mind\u201d that help students become mathematical thinkers. There are eight standards, which apply to all grade levels and conceptual categories.\n\nThese mathematical practices describe how students should engage with the mathematics content for their grade level. Developing these habits of mind builds students\u2019 capacity to become mathematical thinkers. These practices can be applied individually or together in mathematics lessons, and no particular order is required. 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identify, use, and record appropriate units of measure within the given framework, within data displays, and on graphs; convert units and rates using proportional reasoning given a conversion factor; use units within multi-step problems and formulas; interpret units of input and resulting units of output.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.MM.1.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"0a2fa96f-8ab6-4420-821d-348e3906f8b3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0a2fa96f-8ab6-4420-821d-348e3906f8b3","fullStatement":"Use various mathematical representations and structures with this information to represent and solve real-life problems.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.MM.1.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"a54ea679-3aa4-4e1f-85b2-cd640636e078","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a54ea679-3aa4-4e1f-85b2-cd640636e078","fullStatement":"Define appropriate quantities for the purpose of descriptive modeling.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.MM.1.5","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"0b37f05b-2b69-4dd7-9beb-f2229b653a18","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0b37f05b-2b69-4dd7-9beb-f2229b653a18","fullStatement":"Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013 function notation, modeling linear functions, linear vs. nonlinear comparisons","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"575c32d2-3b95-46a4-88c6-8f324e6c42b1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/575c32d2-3b95-46a4-88c6-8f324e6c42b1","fullStatement":"Use mathematically applicable situations algebraically and graphically to build and interpret arithmetic sequences as functions whose domain is a subset of the integers.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"ab5b5c6e-768c-447d-bddd-bbecea533a64","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab5b5c6e-768c-447d-bddd-bbecea533a64","fullStatement":"Construct and interpret the graph of a linear function that models real-life phenomena and represent key characteristics of the graph using formal notation.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"878722ed-948f-4068-92b2-69ac95f6198e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/878722ed-948f-4068-92b2-69ac95f6198e","fullStatement":"Relate the domain and range of a linear function to its graph and, where applicable, to the quantitative relationship it describes. Use formal interval and set notation to describe the domain and range of linear functions.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"94095858-f997-4a73-a153-7efa7088b8b1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/94095858-f997-4a73-a153-7efa7088b8b1","fullStatement":"Use function notation to build and evaluate linear functions for inputs in their domains and interpret statements that use function notation in terms of a mathematical framework.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"113e80ff-2ba1-4275-8272-3ccb1b075230","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/113e80ff-2ba1-4275-8272-3ccb1b075230","fullStatement":"Analyze the difference between linear functions and nonlinear functions by informally analyzing the graphs of various parent functions (linear, quadratic, exponential, absolute value, square root, and cube root parent curves).","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.2.5","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"d1d41e30-12b9-4a8c-a51d-5c6f95e5f529","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d1d41e30-12b9-4a8c-a51d-5c6f95e5f529","fullStatement":"Solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.GSR.3","notes":"**Big Idea:** GEOMETRIC & SPATIAL REASONING \u2013 distance, midpoint, slope, area, and perimeter","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"9747b13a-869e-478c-a3cd-9867d140b583","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9747b13a-869e-478c-a3cd-9867d140b583","fullStatement":"Solve real-life problems involving slope, parallel lines, perpendicular lines, area, and perimeter.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.GSR.3.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"ff8c198d-4099-43c1-b916-653061ab2241","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ff8c198d-4099-43c1-b916-653061ab2241","fullStatement":"Apply the distance formula, midpoint formula, and slope of line segments to solve real-world problems.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.GSR.3.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"13600897-09db-4ad9-bcb2-f87069d4479c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/13600897-09db-4ad9-bcb2-f87069d4479c","fullStatement":"Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.4","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 linear inequalities and systems of linear inequalities","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"bfdaf005-8f51-4673-adab-d2e15a19a63f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bfdaf005-8f51-4673-adab-d2e15a19a63f","fullStatement":"Create and solve linear inequalities in two variables to represent relationships between quantities including mathematically applicable situations; graph inequalities on coordinate axes with labels and scales.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.4.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"000bf480-bafa-4bb6-8867-05928d1ab763","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/000bf480-bafa-4bb6-8867-05928d1ab763","fullStatement":"Represent constraints of linear inequalities and interpret data points as possible or not possible.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.4.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"ed755960-6b30-4b5f-9186-2f5773adf6b2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ed755960-6b30-4b5f-9186-2f5773adf6b2","fullStatement":"Solve systems of linear inequalities by graphing, including systems representing a mathematically applicable situation.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.4.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"ab188cc1-8e8f-49fa-bb87-b3c5405faf9f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab188cc1-8e8f-49fa-bb87-b3c5405faf9f","fullStatement":"Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.NR.5","notes":"**Big Idea:** NUMERICAL REASONING - rational and irrational numbers, square roots and cube roots","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"bcc5abd6-2b54-4f3c-9a0d-3967d9a7f8b6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bcc5abd6-2b54-4f3c-9a0d-3967d9a7f8b6","fullStatement":"Rewrite algebraic and numeric expressions involving radicals.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.NR.5.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"56e4cf06-db6e-4ee4-ae18-57b5b946cd0d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/56e4cf06-db6e-4ee4-ae18-57b5b946cd0d","fullStatement":"Using numerical reasoning, show and explain that the sum or product of rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.NR.5.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"b0a6369c-0a4c-4635-80dc-8cc9906e94eb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b0a6369c-0a4c-4635-80dc-8cc9906e94eb","fullStatement":"Build quadratic expressions and equations to represent and model real-life phenomena; 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find the value of $k$ given the graphs.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"72050d0f-ea11-45f5-af4d-c00d302074e0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/72050d0f-ea11-45f5-af4d-c00d302074e0","fullStatement":"Graph and analyze the key characteristics of quadratic functions.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"6d99799b-ba45-423f-b1d0-0bfd5df7996c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6d99799b-ba45-423f-b1d0-0bfd5df7996c","fullStatement":"Relate the domain and range of a quadratic function to its graph and, where applicable, to the quantitative relationship it describes.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"93289c21-a6d5-4872-9bfa-be1e51f78fc4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/93289c21-a6d5-4872-9bfa-be1e51f78fc4","fullStatement":"Rewrite a quadratic function representing a mathematically applicable situation to reveal the maximum or minimum value of the function it defines. Explain what the value describes in context.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.5","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"5981fe53-6033-43fd-a1bb-e33e53ff2d69","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5981fe53-6033-43fd-a1bb-e33e53ff2d69","fullStatement":"Create quadratic functions in two variables to represent relationships between quantities; graph quadratic functions on the coordinate axes with labels and scales.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.6","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"a58cdfc1-0958-4558-8aa4-98fc17d669a8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a58cdfc1-0958-4558-8aa4-98fc17d669a8","fullStatement":"Estimate, calculate, and interpret the average rate of change of a quadratic function and make comparisons to the average rate of change of linear functions.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.7","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"d1534e17-87fc-4599-83b3-2d6f5a93e65b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d1534e17-87fc-4599-83b3-2d6f5a93e65b","fullStatement":"Write a function defined by a quadratic expression in different but equivalent forms to reveal and explain different properties of the function.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.8","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"eea149da-9f38-44ac-9611-a7dd67505042","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eea149da-9f38-44ac-9611-a7dd67505042","fullStatement":"Compare characteristics of two functions each represented in a different way.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.7.9","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"4e8be323-371d-45c5-a18d-1e76a0aaade3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4e8be323-371d-45c5-a18d-1e76a0aaade3","fullStatement":"Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.8","notes":"**Big Idea:** PATTERNING & ALGEBRAIC REASONING \u2013 exponential expressions and equations","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"fb7d61be-3d83-4ff0-ba1a-40739a02b9cc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fb7d61be-3d83-4ff0-ba1a-40739a02b9cc","fullStatement":"Interpret exponential expressions and parts of an exponential expression that represent a quantity in terms of its framework.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.8.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"06d80a67-8f84-412a-abd6-74782f9a5f45","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/06d80a67-8f84-412a-abd6-74782f9a5f45","fullStatement":"Create exponential equations in one variable and use them to solve problems, including mathematically applicable situations.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.8.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"3f1fe19c-5f33-4080-84b7-49bead8b72e9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3f1fe19c-5f33-4080-84b7-49bead8b72e9","fullStatement":"Create exponential equations in two variables to represent relationships between quantities, including in mathematically applicable situations; graph equations on coordinate axes with labels and scales.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.PAR.8.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"760434bd-e6ee-474c-b64b-924a822b78c7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/760434bd-e6ee-474c-b64b-924a822b78c7","fullStatement":"Represent constraints by exponential equations and interpret data points as possible or not possible in a modeling environment.","lastChangeDateTime":"2023-08-02T12:31:03-04:00","humanCodingScheme":"A.PAR.8.4","language":"eng","CFItemType":"Element","CFItemTypeURI":{"title":"Element","identifier":"80a1c4b7-1296-45c0-8f73-5f9f511bc5f6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/80a1c4b7-1296-45c0-8f73-5f9f511bc5f6"},"educationLevel":["09","10","11","12"]},{"identifier":"01586cab-7112-4984-979e-c6641fa5326f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/01586cab-7112-4984-979e-c6641fa5326f","fullStatement":"Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013 exponential functions","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"0dab7172-b94a-4bd6-b3ce-f5be5cd7f9c6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0dab7172-b94a-4bd6-b3ce-f5be5cd7f9c6","fullStatement":"Use function notation to build and evaluate exponential functions for inputs in their domains and interpret statements that use function notation in terms of a context.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"6c4609f9-baef-4c6f-970d-311d07ffabf6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6c4609f9-baef-4c6f-970d-311d07ffabf6","fullStatement":"Graph and analyze the key characteristics of simple exponential functions based on mathematically applicable situations.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"aefb8fc1-cb7f-4712-a992-1dc7dbd3643b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/aefb8fc1-cb7f-4712-a992-1dc7dbd3643b","fullStatement":"Identify the effect on the graph generated by an exponential function when replacing $f(x)$ with $f(x)$ + $k$, and $k f(x)$, for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"55362048-de20-4fa9-a2ef-19504bdf7d5c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/55362048-de20-4fa9-a2ef-19504bdf7d5c","fullStatement":"Use mathematically applicable situations algebraically and graphically to build and interpret geometric sequences as functions whose domain is a subset of the integers.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"1a0d4bd1-1b37-4929-9bdd-f15568cee648","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a0d4bd1-1b37-4929-9bdd-f15568cee648","fullStatement":"Compare characteristics of two functions each represented in a different way.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.FGR.9.5","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"1f0d5529-f70d-4e05-9b63-2ee257bb8a4c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1f0d5529-f70d-4e05-9b63-2ee257bb8a4c","fullStatement":"Collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems; Represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve real-life problems.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10","notes":"**Big Idea:** DATA & STATISTICAL REASONING \u2013 univariate data and single quantitative variables; bivariate data","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"5722bfcc-c159-4cf5-9e33-7c9666e6e950","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5722bfcc-c159-4cf5-9e33-7c9666e6e950","fullStatement":"Use statistics appropriate to the shape of the data distribution to compare and represent center (median and mean) and variability (interquartile range, standard deviation) of two or more distributions by hand and using technology.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.1","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"7a03506b-17fd-4f13-bbda-8605b54ca64d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7a03506b-17fd-4f13-bbda-8605b54ca64d","fullStatement":"Interpret differences in shape, center, and variability of the distributions based on the investigation, accounting for possible effects of extreme data points (outliers).","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.2","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"6fa92495-4f09-4ca9-a1ef-dced77ecc17f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6fa92495-4f09-4ca9-a1ef-dced77ecc17f","fullStatement":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"8fe9d976-3a88-44aa-8d77-f75a6dec04c7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8fe9d976-3a88-44aa-8d77-f75a6dec04c7","fullStatement":"Interpret the slope (predicted rate of change) and the intercept (constant term) of a linear model based on the investigation of the data.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"8ad69e97-6d0f-47c9-b195-56a77acb3bd3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8ad69e97-6d0f-47c9-b195-56a77acb3bd3","fullStatement":"Calculate the line of best fit and interpret the correlation coefficient, $r$, of a linear fit using technology. Use $r$ to describe the strength of the goodness of fit of the regression. Use the linear function to make predictions and assess how reasonable the prediction is in context.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.5","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"c090a985-119b-4295-8387-6c9258854dc4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c090a985-119b-4295-8387-6c9258854dc4","fullStatement":"Decide which type of function is most appropriate by observing graphed data.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.6","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"5a3113e9-9ed7-4bbd-9633-9dff3e25a2dd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5a3113e9-9ed7-4bbd-9633-9dff3e25a2dd","fullStatement":"Distinguish between correlation and causation.","lastChangeDateTime":"2022-08-03T17:22:25-04:00","humanCodingScheme":"A.DSR.10.7","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"6c1f041e-b0d4-41ef-a1c5-3401ccb7d908","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6c1f041e-b0d4-41ef-a1c5-3401ccb7d908","fullStatement":"Enhanced Advanced Algebra and AP Precalculus: Concepts and Connections","lastChangeDateTime":"2024-08-02T23:34:04+00:00","humanCodingScheme":"27.09310","notes":"May substitute for 27.08410\n\nEquivalent to 27.08310\n\nThe Enhanced Advanced Algebra and Precalculus: Concepts and Connections course is a thoughtful blend of the topics from Advanced Algebra: Concepts & Connections and Precalculus. This is a single credit course, intended to provide students the opportunity to develop a deeper understanding of mathematical concepts that are critical to the study of advanced fourth mathematics course options, including Calculus. In Enhanced Advanced Algebra and Precalculus: Concepts and Connections, students will continue to enhance their understanding of data and statistical reasoning, functional and graphical reasoning, patterning and algebraic reasoning, and geometric and spatial reasoning. There should be an emphasis on notational fluency and the use of multiple representations as students engage with all topics. Some of those topics include, sequences and series with the incorporation of convergence and divergence; conic sections as implicitly defined curves; the six trigonometric functions and their inverses; applications of trigonometry such as modeling periodic phenomena, modeling with vectors and parametric equations, solving oblique triangles in contextual situations, graphing in the Polar Plane; solutions of trigonometric equations in a variety of contexts; and the manipulation and application of trigonometric identities. In previous courses, students studied how to use linear and quadratic functions to model real-life phenomena. In the Enhanced Advanced Algebra and Precalculus: Concepts and Connections course, students will further develop their algebraic, functional, and graphical reasoning as they explore and analyze structures and patterns for exponential, logarithmic, radical, polynomial, piecewise and rational expressions, equations, and functions to further understand the world around them. Topics should be analyzed in multiple ways, including verbal and written, numerical, algebraic, and graphical presentations. Instruction and assessment should include the appropriate use of technology. Concepts should be investigated and applied, where appropriate, within the context of realistic phenomena.\n\nThe identified prerequisite for this course is Geometry: Concepts & Connections.","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"64c17608-fcf5-4578-8bbe-db758391c3cf","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItemTypes/64c17608-fcf5-4578-8bbe-db758391c3cf"}},{"identifier":"ab995df7-d8d5-4d02-acb0-a1a33c291e3f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab995df7-d8d5-4d02-acb0-a1a33c291e3f","fullStatement":"Communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting real-world data.","lastChangeDateTime":"2022-08-03T17:40:21-04:00","humanCodingScheme":"AA.DSR.2","notes":"**Big Idea:** DATA & STATISTICAL REASONING \u2013 descriptive and inferential statistics","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"ccb3d7d6-3b25-406b-9c9b-d873160ce313","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ccb3d7d6-3b25-406b-9c9b-d873160ce313","fullStatement":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 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Use sample statistics to make inferences about population parameters based on a random sample from that population and to communicate conclusions using appropriate statistical language.","lastChangeDateTime":"2022-08-03T17:40:21-04:00","humanCodingScheme":"AA.DSR.2.3","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"13851265-3efc-4add-9f2e-8a88eab67920","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/13851265-3efc-4add-9f2e-8a88eab67920","fullStatement":"Calculate and interpret z-scores as a measure of relative standing and as a method of standardizing units.","lastChangeDateTime":"2022-08-03T17:40:21-04:00","humanCodingScheme":"AA.DSR.2.4","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Element"},{"identifier":"70bd2a7b-5595-4c3f-8062-676473d993e1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/70bd2a7b-5595-4c3f-8062-676473d993e1","fullStatement":"Given a normally distributed 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phenomena.","lastChangeDateTime":"2022-08-03T17:40:21-04:00","humanCodingScheme":"AA.FGR.3","notes":"**Big Idea:** FUNCTIONAL & GRAPHICAL REASONING \u2013 exponential and logarithmic functions","language":"eng","educationLevel":["09","10","11","12"],"CFItemType":"Content Standard"},{"identifier":"c845b3a6-8f86-44fd-b877-85e7d9886d77","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c845b3a6-8f86-44fd-b877-85e7d9886d77","fullStatement":"Find the inverse of exponential and logarithmic functions using equations, tables, and graphs, limiting the domain of inverses where necessary to maintain functionality, and prove by composition or verify by inspection that one function is the inverse of 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(:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"777ce7b6-9d73-11e7-a8c6-896c75dec0b9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/777ce7b6-9d73-11e7-a8c6-896c75dec0b9"},"destinationNodeURI":{"title":"1.NR.2 Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addition and subtraction problems within 20. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"ab1cf735-27cc-437b-979b-cdc22ecde12e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab1cf735-27cc-437b-979b-cdc22ecde12e"},"lastChangeDateTime":"2022-04-12T21:44:21-04:00"},{"identifier":"e1082634-7ddd-481a-aba3-6ebb20274231","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/e1082634-7ddd-481a-aba3-6ebb20274231","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE1.OA.3 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.) (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"9e78a3c8-9d73-11e7-831b-b1f891bbe83a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9e78a3c8-9d73-11e7-831b-b1f891bbe83a"},"destinationNodeURI":{"title":"1.NR.2 Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addition and subtraction problems within 20. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"ab1cf735-27cc-437b-979b-cdc22ecde12e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ab1cf735-27cc-437b-979b-cdc22ecde12e"},"lastChangeDateTime":"2022-04-12T21:44:26-04:00"},{"identifier":"ec4f12b4-fadc-4b0d-abcf-f74cecef5db7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/ec4f12b4-fadc-4b0d-abcf-f74cecef5db7","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE1.OA.6a 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). 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(*See Mathematics Glossary, Table 2: Multiplication and Division Within 100.*) (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"da8ba008-9d60-11e7-b5ff-7078faefe334","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/da8ba008-9d60-11e7-b5ff-7078faefe334"},"destinationNodeURI":{"title":"3.PAR.3 Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"fd5543a9-d2fa-471f-b5b6-8caca7dca6e7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fd5543a9-d2fa-471f-b5b6-8caca7dca6e7"},"lastChangeDateTime":"2022-04-15T23:05:58-04:00"},{"identifier":"e1e0786b-057c-45fa-b103-7468406f0b32","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/e1e0786b-057c-45fa-b103-7468406f0b32","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE3.OA.4 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 = ?*. 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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.)* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"29a11328-9d78-11e7-885a-871584fb9874","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/29a11328-9d78-11e7-885a-871584fb9874"},"destinationNodeURI":{"title":"3.PAR.3 Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"6ba6ae7c-9d78-11e7-9141-abc139a1d475","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ba6ae7c-9d78-11e7-9141-abc139a1d475"},"destinationNodeURI":{"title":"3.PAR.3 Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100. 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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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"e6f0fa52-9e2b-11e7-b162-704f8259080a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e6f0fa52-9e2b-11e7-b162-704f8259080a"},"destinationNodeURI":{"title":"3.NR.4 Represent fractions with denominators of 2, 3, 4, 6 and 8 in multiple ways within a framework using visual models. 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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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"3fc9289c-9d79-11e7-8b6e-e579a8459bd4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/3fc9289c-9d79-11e7-8b6e-e579a8459bd4"},"destinationNodeURI":{"title":"3.MDR.5 Solve real-life, mathematical problems involving length, liquid volume, mass, and time and analyze graphical displays of data to answer relevant questions. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"fdbaf91d-191e-4f58-8264-432e066b7515","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/fdbaf91d-191e-4f58-8264-432e066b7515"},"lastChangeDateTime":"2022-04-15T23:15:57-04:00"},{"identifier":"302e72fd-ed47-46c7-acdc-3c6cc7c34348","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/302e72fd-ed47-46c7-acdc-3c6cc7c34348","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE3.MD.2 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).* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"803dc0a4-9d79-11e7-b7af-79e2d55b9808","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/803dc0a4-9d79-11e7-b7af-79e2d55b9808"},"destinationNodeURI":{"title":"3.MDR.5 Solve real-life, mathematical problems involving length, liquid volume, mass, and time and analyze graphical displays of data to answer relevant questions. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"8cae6eb0-9d79-11e7-b7d2-0fdc2d9699c5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8cae6eb0-9d79-11e7-b7d2-0fdc2d9699c5"},"destinationNodeURI":{"title":"3.MDR.5 Solve real-life, mathematical problems involving length, liquid volume, mass, and time and analyze graphical displays of data to answer relevant questions. 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Set and monitor goals. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e94460f3-ed0b-45ea-aea0-e02ed76e4ca8","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e94460f3-ed0b-45ea-aea0-e02ed76e4ca8"},"lastChangeDateTime":"2022-04-16T19:57:23-04:00"},{"identifier":"87877567-d102-47a1-ad02-2eb1eb0c4866","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/87877567-d102-47a1-ad02-2eb1eb0c4866","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE3.SMP Grade 3 - Standards for Mathematical Practice (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"cb06fcce-ac85-11e8-b9d6-91ca84a09600","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cb06fcce-ac85-11e8-b9d6-91ca84a09600"},"destinationNodeURI":{"title":"3.MP Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5f252f2d-c889-493f-b0a6-552aec575be3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5f252f2d-c889-493f-b0a6-552aec575be3"},"lastChangeDateTime":"2022-04-16T19:57:32-04:00"},{"identifier":"4dee73f0-8cbb-4250-80f2-b7c08b511255","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/4dee73f0-8cbb-4250-80f2-b7c08b511255","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.SMP Grade 4 - Standards for Mathematical Practice (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"27efae8e-ad19-11e8-b68b-2b855c461b90","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/27efae8e-ad19-11e8-b68b-2b855c461b90"},"destinationNodeURI":{"title":"4.MP Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. 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Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. 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Set and monitor goals. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"9c3db874-5cde-45cf-8dd9-065d0b0e4394","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c3db874-5cde-45cf-8dd9-065d0b0e4394"},"lastChangeDateTime":"2022-04-16T19:58:24-04:00"},{"identifier":"740bc91c-43fd-4cc0-9984-b9f1ce630ed6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/740bc91c-43fd-4cc0-9984-b9f1ce630ed6","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE2.OA.1 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.)* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"4b1ee56e-9d75-11e7-bf09-7dc7cbab37ca","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4b1ee56e-9d75-11e7-bf09-7dc7cbab37ca"},"destinationNodeURI":{"title":"2.PAR.4 Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"11022c4c-c313-4792-85e2-779dc7e4d16c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/11022c4c-c313-4792-85e2-779dc7e4d16c"},"lastChangeDateTime":"2022-04-17T22:08:18-04:00"},{"identifier":"3ba1f71d-0cfd-4799-924f-116d67be63c7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/3ba1f71d-0cfd-4799-924f-116d67be63c7","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NBT.6 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"11022c4c-c313-4792-85e2-779dc7e4d16c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/11022c4c-c313-4792-85e2-779dc7e4d16c"},"lastChangeDateTime":"2022-04-17T22:08:19-04:00"},{"identifier":"0b9b902f-b7cc-4db4-b5cb-b1410ae6fcf0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/0b9b902f-b7cc-4db4-b5cb-b1410ae6fcf0","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.OA.4 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. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"4af2f03e-9d7b-11e7-8d7f-9548bbf49422","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/4af2f03e-9d7b-11e7-8d7f-9548bbf49422"},"destinationNodeURI":{"title":"4.PAR.3 Generate and analyze patterns, including those involving shapes, input/output diagrams, factors, multiples, prime numbers, and composite numbers. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"21af665e-78ca-472c-bf3c-552d3e33ef9e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/21af665e-78ca-472c-bf3c-552d3e33ef9e"},"lastChangeDateTime":"2022-04-17T22:10:21-04:00"},{"identifier":"e056de91-0b2e-41e8-8bd1-e5ff6eb514a0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/e056de91-0b2e-41e8-8bd1-e5ff6eb514a0","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.1 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:11:57-04:00"},{"identifier":"44e53efd-7eed-4de2-8031-17dfb8401361","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/44e53efd-7eed-4de2-8031-17dfb8401361","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.2 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:11:58-04:00"},{"identifier":"4f7a0096-8e09-4430-964f-2c0d2d2356aa","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/4f7a0096-8e09-4430-964f-2c0d2d2356aa","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.3 Understand a fraction $\\frac{a}{b}$ with a numerator > 1 as a sum of unit fractions $\\frac{1}{b}$. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"ddc8a8ba-9d60-11e7-86f2-2e138d5b4aa5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8a8ba-9d60-11e7-86f2-2e138d5b4aa5"},"destinationNodeURI":{"title":"4.NR.4 Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:12:16-04:00"},{"identifier":"a3143df5-0f6a-4157-80b8-e482a7e67586","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/a3143df5-0f6a-4157-80b8-e482a7e67586","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"ddc8d5ce-9d60-11e7-8870-795b5404e3ab","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8d5ce-9d60-11e7-8870-795b5404e3ab"},"destinationNodeURI":{"title":"4.NR.4 Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:12:18-04:00"},{"identifier":"698a0930-7171-430e-9e09-d2f1eb37a70a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/698a0930-7171-430e-9e09-d2f1eb37a70a","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.3c 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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"ddc8f004-9d60-11e7-84c3-23a46d78972f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc8f004-9d60-11e7-84c3-23a46d78972f"},"destinationNodeURI":{"title":"4.NR.4 Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:12:19-04:00"},{"identifier":"354b8f61-cb0c-430e-888a-de4b68cd9df1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/354b8f61-cb0c-430e-888a-de4b68cd9df1","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.3b 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 + $\\frac{1}{8}$ = $\\frac{8}{8}$ + $\\frac{8}{8}$ + $\\frac{1}{8}$.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"e924c8fe-9d7b-11e7-b1d4-61c1b18ff56a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e924c8fe-9d7b-11e7-b1d4-61c1b18ff56a"},"destinationNodeURI":{"title":"4.NR.4 Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:12:20-04:00"},{"identifier":"853f7179-623c-47b9-94d9-3b4a39e75b6e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/853f7179-623c-47b9-94d9-3b4a39e75b6e","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.3d 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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"08d1cca6-9d7c-11e7-92a7-392595d24d8f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/08d1cca6-9d7c-11e7-92a7-392595d24d8f"},"destinationNodeURI":{"title":"4.NR.4 Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"5dfed155-81d7-489c-ae2c-b7de6b8b3ef4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/5dfed155-81d7-489c-ae2c-b7de6b8b3ef4"},"lastChangeDateTime":"2022-04-17T22:12:22-04:00"},{"identifier":"587f3f7f-e344-46f8-9668-13cc7afb2189","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/587f3f7f-e344-46f8-9668-13cc7afb2189","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.5 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.)* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"ddc93af0-9d60-11e7-bf6b-ea74ee44ec17","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc93af0-9d60-11e7-bf6b-ea74ee44ec17"},"destinationNodeURI":{"title":"4.NR.5 Solve real-life problems involving addition, equivalence, comparison of fractions with denominators of 10 and 100, and comparison of decimal numbers as tenths and hundredths using partwhole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"a744a60a-08ff-4619-a820-e36799b22233","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a744a60a-08ff-4619-a820-e36799b22233"},"lastChangeDateTime":"2022-04-17T22:15:50-04:00"},{"identifier":"4a060360-0d3d-446e-9bed-e9a39044d171","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/4a060360-0d3d-446e-9bed-e9a39044d171","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE4.NF.6 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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"ddc95436-9d60-11e7-8202-14b6b60467bd","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ddc95436-9d60-11e7-8202-14b6b60467bd"},"destinationNodeURI":{"title":"4.NR.5 Solve real-life problems involving addition, equivalence, comparison of fractions with denominators of 10 and 100, and comparison of decimal numbers as tenths and hundredths using partwhole strategies and visual models. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"08bff524-9d7e-11e7-a11a-4990e2106051","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/08bff524-9d7e-11e7-a11a-4990e2106051"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:07:09-04:00"},{"identifier":"78420e85-66c9-4d3e-a299-7e0aec63d1c2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/78420e85-66c9-4d3e-a299-7e0aec63d1c2","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NF.5.b 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> (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"cdd380c6-ab6d-11e8-a658-91603fd6d1e4","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/cdd380c6-ab6d-11e8-a658-91603fd6d1e4"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. 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But division of a fraction by a fraction is not a requirement at this grade.)* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"929f5d2a-9d7e-11e7-8198-41afacd10c4c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/929f5d2a-9d7e-11e7-8198-41afacd10c4c"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:07:35-04:00"},{"identifier":"2c14dea4-d6bd-4116-8425-1e70b8b8813a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/2c14dea4-d6bd-4116-8425-1e70b8b8813a","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NF.7a 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/> (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"a0b6592c-9d7e-11e7-9001-98018d2b9ac1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a0b6592c-9d7e-11e7-9001-98018d2b9ac1"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:07:42-04:00"},{"identifier":"f6160f31-6ad5-47be-8669-470c0ac28cb7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/f6160f31-6ad5-47be-8669-470c0ac28cb7","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NF.7b 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> (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"adb72700-9d7e-11e7-a430-f46fc442494d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/adb72700-9d7e-11e7-a430-f46fc442494d"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:07:43-04:00"},{"identifier":"b6955960-42d9-4276-b0bb-3aceedd7584e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/b6955960-42d9-4276-b0bb-3aceedd7584e","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NF.7c 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> (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"b69b7a06-9d7e-11e7-b96d-224d5fd6623d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b69b7a06-9d7e-11e7-b96d-224d5fd6623d"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:07:47-04:00"},{"identifier":"66fc00b3-15b1-4777-87e2-f2e0131e439d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/66fc00b3-15b1-4777-87e2-f2e0131e439d","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"e00ddf92-9d7d-11e7-ae31-9fdcc8db2303","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e00ddf92-9d7d-11e7-ae31-9fdcc8db2303"},"destinationNodeURI":{"title":"5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"90dbfc00-0236-4244-be61-67dbf3090965","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/90dbfc00-0236-4244-be61-67dbf3090965"},"lastChangeDateTime":"2022-04-18T10:12:34-04:00"},{"identifier":"0182bb7c-9767-4e2a-927a-ef1f1d6903bb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/0182bb7c-9767-4e2a-927a-ef1f1d6903bb","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NBT.3 Read, write, and compare decimals to thousandths. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"e193f512-9d60-11e7-99b3-215eb97f167f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e193f512-9d60-11e7-99b3-215eb97f167f"},"destinationNodeURI":{"title":"5.NR.4 Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"c7bb3bdc-c14a-47c0-b4a2-8e06e1095236","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c7bb3bdc-c14a-47c0-b4a2-8e06e1095236"},"lastChangeDateTime":"2022-04-18T10:19:08-04:00"},{"identifier":"a803be70-5ffe-47fb-b5e8-38b0b7f46879","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/a803be70-5ffe-47fb-b5e8-38b0b7f46879","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.NBT.3a 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 ($\\frac{1}{1000}$). 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"c7bb3bdc-c14a-47c0-b4a2-8e06e1095236","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/c7bb3bdc-c14a-47c0-b4a2-8e06e1095236"},"lastChangeDateTime":"2022-04-18T10:19:39-04:00"},{"identifier":"079af694-c230-439c-90a3-a4e0603e464c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/079af694-c230-439c-90a3-a4e0603e464c","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"7156395a-9d7d-11e7-8ad1-54f098aa83e9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7156395a-9d7d-11e7-8ad1-54f098aa83e9"},"destinationNodeURI":{"title":"5.NR.5 Write, interpret, and evaluate numerical expressions within authentic problems. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"9cd27b32-e841-4dcf-8e8a-95fa40fb5695","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9cd27b32-e841-4dcf-8e8a-95fa40fb5695"},"lastChangeDateTime":"2022-04-18T10:21:36-04:00"},{"identifier":"83a681ee-72ac-489b-89fc-c45108c51d4e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/83a681ee-72ac-489b-89fc-c45108c51d4e","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE5.OA.2 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. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"85857bf0-a9dc-11e7-ba79-66bac388e548","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/85857bf0-a9dc-11e7-ba79-66bac388e548"},"destinationNodeURI":{"title":"7.PAR.4 Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"8d411856-f397-4bc1-b6e6-3e8c6accd878","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/8d411856-f397-4bc1-b6e6-3e8c6accd878"},"lastChangeDateTime":"2022-04-18T18:03:36-04:00"},{"identifier":"afac0fc3-3324-4d0b-9731-2223789ab814","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/afac0fc3-3324-4d0b-9731-2223789ab814","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE7.SP.5 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. 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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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"b3c5f9fe-a9dc-11e7-94d0-93af3863a10c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b3c5f9fe-a9dc-11e7-94d0-93af3863a10c"},"destinationNodeURI":{"title":"7.PR.6 Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1b8fe278-1208-4440-aae9-698d2f9c79d5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1b8fe278-1208-4440-aae9-698d2f9c79d5"},"lastChangeDateTime":"2022-04-18T18:08:46-04:00"},{"identifier":"030625c3-4b7a-403c-aec5-9b285c172dba","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/030625c3-4b7a-403c-aec5-9b285c172dba","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE8.EE.2 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. 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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.~~) (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"d11a9a74-d61d-11e7-b70d-6da7a9c1abfc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d11a9a74-d61d-11e7-b70d-6da7a9c1abfc"},"destinationNodeURI":{"title":"A.GSR.3 Solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"946b9f9a-b82b-4356-b11f-46144cf47164","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/946b9f9a-b82b-4356-b11f-46144cf47164"},"lastChangeDateTime":"2022-04-21T18:05:07-04:00"},{"identifier":"66b4bcd7-b992-4385-87df-d7b1ba121369","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/66b4bcd7-b992-4385-87df-d7b1ba121369","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 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(:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"b69bc832-a1ff-11e7-b325-c156d79cf3b9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b69bc832-a1ff-11e7-b325-c156d79cf3b9"},"destinationNodeURI":{"title":"A.PAR.4 Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena. 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(:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"376ad796-a1fb-11e7-9bf7-22ce43ef0c95","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/376ad796-a1fb-11e7-9bf7-22ce43ef0c95"},"destinationNodeURI":{"title":"A.PAR.4 Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"7e196638-7acd-4970-8835-ec8ce588eb8e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/7e196638-7acd-4970-8835-ec8ce588eb8e"},"lastChangeDateTime":"2022-04-21T18:09:47-04:00"},{"identifier":"78b7abbe-b464-40d5-9eb9-a384acced907","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/78b7abbe-b464-40d5-9eb9-a384acced907","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.LE.5 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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"053803e8-a20f-11e7-8604-5f8f06131ec0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/053803e8-a20f-11e7-8604-5f8f06131ec0"},"destinationNodeURI":{"title":"A.PAR.4 Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"900cb84e-50fe-4adb-a850-bf81607b49ea","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/900cb84e-50fe-4adb-a850-bf81607b49ea"},"lastChangeDateTime":"2022-04-21T18:13:43-04:00"},{"identifier":"54b03b5a-b02a-4ec5-b6e1-d36494e1c86b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/54b03b5a-b02a-4ec5-b6e1-d36494e1c86b","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.N.RN.3 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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"eb372344-9fe7-11e7-91dd-3acb407267ad","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/eb372344-9fe7-11e7-91dd-3acb407267ad"},"destinationNodeURI":{"title":"A.NR.5 Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"900cb84e-50fe-4adb-a850-bf81607b49ea","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/900cb84e-50fe-4adb-a850-bf81607b49ea"},"lastChangeDateTime":"2022-04-21T18:13:47-04:00"},{"identifier":"7fe8e830-2e31-45cc-b2a0-b885556564e2","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/7fe8e830-2e31-45cc-b2a0-b885556564e2","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"bb761582-9fe9-11e7-834e-e60853ae2fb9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bb761582-9fe9-11e7-834e-e60853ae2fb9"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:15:32-04:00"},{"identifier":"b3f1c2bd-71f5-47e6-8c87-acdd53e6be12","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/b3f1c2bd-71f5-47e6-8c87-acdd53e6be12","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"d4ac143e-9fe9-11e7-95dd-a1063590f785","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d4ac143e-9fe9-11e7-95dd-a1063590f785"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:15:41-04:00"},{"identifier":"11491646-4fcb-44fc-8ac4-3edf320165ba","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/11491646-4fcb-44fc-8ac4-3edf320165ba","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"f21aeda6-9fe9-11e7-85b7-a864a95e8e5c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f21aeda6-9fe9-11e7-85b7-a864a95e8e5c"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:15:55-04:00"},{"identifier":"008dd0e5-0963-44da-bbac-cd62a65696eb","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/008dd0e5-0963-44da-bbac-cd62a65696eb","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.2 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 $(x^2 - y^2) (x^2 + y^2)$.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"0eb29a40-9fea-11e7-8a00-347de45fd4e0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0eb29a40-9fea-11e7-8a00-347de45fd4e0"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:16:09-04:00"},{"identifier":"b38e72d3-c1f5-4cd9-9da4-69644dc8cc97","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/b38e72d3-c1f5-4cd9-9da4-69644dc8cc97","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"2b9a24e8-9fea-11e7-8dfc-0ae1f8979f3b","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/2b9a24e8-9fea-11e7-8dfc-0ae1f8979f3b"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:16:21-04:00"},{"identifier":"186eefa1-daf6-4f5b-8912-06de0212be84","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/186eefa1-daf6-4f5b-8912-06de0212be84","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by the expression. 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(:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"9c1f9752-9fea-11e7-96c3-230f8af849e6","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9c1f9752-9fea-11e7-96c3-230f8af849e6"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:16:58-04:00"},{"identifier":"3dc0600c-2a18-4a52-8eb3-e2d9cdc8d4ec","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/3dc0600c-2a18-4a52-8eb3-e2d9cdc8d4ec","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.CED.1 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). (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"03a48c22-a1fb-11e7-801b-bea2cddcf849","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/03a48c22-a1fb-11e7-801b-bea2cddcf849"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:17:50-04:00"},{"identifier":"33c2af2c-02a5-4541-a7f6-041ec350b93e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/33c2af2c-02a5-4541-a7f6-041ec350b93e","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.CED.3 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:18:29-04:00"},{"identifier":"33445302-065d-4ccf-ba95-6a3051cb8a57","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/33445302-065d-4ccf-ba95-6a3051cb8a57","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.REI.4b 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). 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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.) In context, students should describe what these parameters mean in terms of change and starting value. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"053803e8-a20f-11e7-8604-5f8f06131ec0","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/053803e8-a20f-11e7-8604-5f8f06131ec0"},"destinationNodeURI":{"title":"A.PAR.6 Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"e71b821c-e803-4dbd-8bde-77e48c7c001f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/e71b821c-e803-4dbd-8bde-77e48c7c001f"},"lastChangeDateTime":"2022-04-21T18:19:39-04:00"},{"identifier":"33786616-3a5e-4189-9ee6-f7f0ff29a779","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/33786616-3a5e-4189-9ee6-f7f0ff29a779","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.1 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). 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:02:52-04:00"},{"identifier":"2716ba9a-f81c-459f-ac25-4db34998f608","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/2716ba9a-f81c-459f-ac25-4db34998f608","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"048023ea-a200-11e7-8a66-3b669ef08fa1","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/048023ea-a200-11e7-8a66-3b669ef08fa1"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:02:59-04:00"},{"identifier":"b9574f67-391f-4bf2-b92a-8ec81e423735","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/b9574f67-391f-4bf2-b92a-8ec81e423735","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.4 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.~~ (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"851fe5f8-a20a-11e7-b75a-26e1c2510104","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/851fe5f8-a20a-11e7-b75a-26e1c2510104"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:09-04:00"},{"identifier":"3161a564-2e45-4cc6-85da-be813da24959","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/3161a564-2e45-4cc6-85da-be813da24959","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.5 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*. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"9f18667e-a20a-11e7-aea7-f19ca308d294","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9f18667e-a20a-11e7-aea7-f19ca308d294"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:15-04:00"},{"identifier":"4194ebf9-408e-4e80-ad77-1fce6610527d","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/4194ebf9-408e-4e80-ad77-1fce6610527d","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.6 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. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"b1e4054c-a20a-11e7-b6ed-fdef7c590b21","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b1e4054c-a20a-11e7-b6ed-fdef7c590b21"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:23-04:00"},{"identifier":"5e0f261c-a030-4f31-80b2-602d9f337acc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/5e0f261c-a030-4f31-80b2-602d9f337acc","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"00ade2c4-a20b-11e7-87ec-0b48a00aa91c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/00ade2c4-a20b-11e7-87ec-0b48a00aa91c"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:32-04:00"},{"identifier":"8614b4a2-6952-4b5a-bf9e-e7b810c497ea","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/8614b4a2-6952-4b5a-bf9e-e7b810c497ea","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context). (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"25d0078a-a20b-11e7-a507-54aff85f6624","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/25d0078a-a20b-11e7-a507-54aff85f6624"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:40-04:00"},{"identifier":"20720b42-85af-4a6a-bcf7-abd61ec467b3","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/20720b42-85af-4a6a-bcf7-abd61ec467b3","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"9abd40da-a20b-11e7-abde-ce7f1d539ef5","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/9abd40da-a20b-11e7-abde-ce7f1d539ef5"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:48-04:00"},{"identifier":"ea0f7d90-06a0-4320-8841-535446c3e4d7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/ea0f7d90-06a0-4320-8841-535446c3e4d7","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.8a 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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"b7885524-a20b-11e7-90f1-4ef8485da350","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/b7885524-a20b-11e7-90f1-4ef8485da350"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:03:55-04:00"},{"identifier":"e42d2b71-23d8-42b4-9087-966dfca17f27","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/e42d2b71-23d8-42b4-9087-966dfca17f27","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.9 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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"d8883546-a20b-11e7-8def-d70d05ce1649","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d8883546-a20b-11e7-8def-d70d05ce1649"},"destinationNodeURI":{"title":"A.FGR.7 Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"6ea1f43a-6699-4e75-bac8-fa720c32d401","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/6ea1f43a-6699-4e75-bac8-fa720c32d401"},"lastChangeDateTime":"2022-04-21T21:04:01-04:00"},{"identifier":"f21d767f-75ba-43dc-802b-a46397593073","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/f21d767f-75ba-43dc-802b-a46397593073","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"bb761582-9fe9-11e7-834e-e60853ae2fb9","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/bb761582-9fe9-11e7-834e-e60853ae2fb9"},"destinationNodeURI":{"title":"A.PAR.8 Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"0ca0640d-94ae-4d59-a49d-75c6203ea78f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ca0640d-94ae-4d59-a49d-75c6203ea78f"},"lastChangeDateTime":"2022-04-21T21:22:29-04:00"},{"identifier":"cd689477-10bd-4e8c-98eb-33571c3f8955","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/cd689477-10bd-4e8c-98eb-33571c3f8955","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"d4ac143e-9fe9-11e7-95dd-a1063590f785","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d4ac143e-9fe9-11e7-95dd-a1063590f785"},"destinationNodeURI":{"title":"A.PAR.8 Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"0ca0640d-94ae-4d59-a49d-75c6203ea78f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ca0640d-94ae-4d59-a49d-75c6203ea78f"},"lastChangeDateTime":"2022-04-21T21:22:36-04:00"},{"identifier":"54f62a28-306a-4c65-8260-ef2c85954e8a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/54f62a28-306a-4c65-8260-ef2c85954e8a","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors. 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Include equations arising from linear, quadratic, ~~simple rational,~~ and exponential functions (integer inputs only). (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"03a48c22-a1fb-11e7-801b-bea2cddcf849","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/03a48c22-a1fb-11e7-801b-bea2cddcf849"},"destinationNodeURI":{"title":"A.PAR.8 Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"0ca0640d-94ae-4d59-a49d-75c6203ea78f","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/0ca0640d-94ae-4d59-a49d-75c6203ea78f"},"lastChangeDateTime":"2022-04-21T21:24:25-04:00"},{"identifier":"eddb318f-8b1b-42d5-bd6f-a9c4d9b5bbfc","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/eddb318f-8b1b-42d5-bd6f-a9c4d9b5bbfc","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.LE.5 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:28:19-04:00"},{"identifier":"2963a3d8-d969-498c-86a1-999756ecd030","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/2963a3d8-d969-498c-86a1-999756ecd030","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:28:46-04:00"},{"identifier":"2b2dfe21-b055-4ca0-b331-f458b111d020","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/2b2dfe21-b055-4ca0-b331-f458b111d020","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.IF.9 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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"d8883546-a20b-11e7-8def-d70d05ce1649","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/d8883546-a20b-11e7-8def-d70d05ce1649"},"destinationNodeURI":{"title":"A.FGR.9 Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:28:54-04:00"},{"identifier":"15980a73-636b-48e1-a83c-3ac67d418e98","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/15980a73-636b-48e1-a83c-3ac67d418e98","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.BF.1a 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 (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"f1bc30e8-a20c-11e7-8f0d-f5d0dad17dde","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f1bc30e8-a20c-11e7-8f0d-f5d0dad17dde"},"destinationNodeURI":{"title":"A.FGR.9 Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:29:28-04:00"},{"identifier":"bd334180-b05d-43c0-98a8-8e2cb61215b7","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/bd334180-b05d-43c0-98a8-8e2cb61215b7","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.BF.2 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. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:29:38-04:00"},{"identifier":"25086b69-5c6e-43c7-961b-f9654703a201","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/25086b69-5c6e-43c7-961b-f9654703a201","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"80e27ad4-a20d-11e7-a6dc-12d98e9dac8e","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/80e27ad4-a20d-11e7-a6dc-12d98e9dac8e"},"destinationNodeURI":{"title":"A.FGR.9 Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. (:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"1a9d774f-2b8d-4875-8c52-451ccabf6b8c","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/1a9d774f-2b8d-4875-8c52-451ccabf6b8c"},"lastChangeDateTime":"2022-04-21T21:31:00-04:00"},{"identifier":"8c580122-52f0-4c0a-8242-de299bdd2fed","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/8c580122-52f0-4c0a-8242-de299bdd2fed","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE9-12.F.LE.1a 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). (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"a1ba5376-a20d-11e7-b924-1534f0ade996","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/a1ba5376-a20d-11e7-b924-1534f0ade996"},"destinationNodeURI":{"title":"A.FGR.9 Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. 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(:e9dd7229-3558-4df2-85c6-57b8938f6180:)","identifier":"ec6d422b-9a9c-402c-beb4-0c1842da4015","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/ec6d422b-9a9c-402c-beb4-0c1842da4015"},"lastChangeDateTime":"2022-04-21T21:51:02-04:00"},{"identifier":"14ec4636-94e1-437f-b80c-491503483968","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFAssociations/14ec4636-94e1-437f-b80c-491503483968","associationType":"isRelatedTo","originNodeURI":{"title":"MGSE8.G.5 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.* (:23a8e45a-9d5a-11e7-81bc-064e21a83c7c:)","identifier":"f5d2c10c-9d60-11e7-9285-37eec92a2b6a","uri":"https://case.georgiastandards.org/ims/case/v1p1/CFItems/f5d2c10c-9d60-11e7-9285-37eec92a2b6a"},"destinationNodeURI":{"title":"G.GSR.4 Establish facts between angle relations and generate valid arguments to defend facts established. 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