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5. THE RESULTS: COLLEGE AND CAREER READINESS STANDARDS FOR MATHEMATICS 46 The CCSS for Mathematics have two central parts: the Standards for Mathematical Practice and the Standards for Mathematical Content. The Standards for Mathematical Practice (the Practices)—accepted in their entirety by the panel— describe habits of mind that mathematics educators at all levels of learning should seek to develop in their students. These practices rest on “processes and proficiencies” with established significance in mathematics education, including such skills as complex problem solving, reasoning and proof, modeling, precise communication, and making connections. The Standards for Mathematical Content are a balanced combination of procedural fluency and conceptual understanding intended to be connected to the Practices across domains and at each level. The Practices define ways students are to engage with the subject matter as they grow in mathematical maturity and expertise across levels. Content expectations that begin with the word “understand” highlight the relationship between the two parts of the CCSS for Mathematics and connect the practices and content standards. Modeling is directly addressed in the Practices (MP.4 Model with mathematics) and also in the content standards. Since modeling is best understood in relation to the content and the context, the content standards addressing mathematical modeling can be found in Number and Quantity, Algebra, Functions, and Geometry and are indicated by an asterisk (*). In the CCSS document, when a star appears on a heading for a cluster of standards, it applies to all standards in that group. The grades K–8 mathematics standards are organized by grade level, with four or five domains within each level. Under each domain are overarching standard statements followed by a cluster of related standards. For high school, the CCSS are organized by conceptual categories, which together portray a coherent view of high school mathematics and span traditional high school course boundaries. These conceptual categories include: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability. Under each conceptual category there is an organizing structure similar to that used in K–8: domains with overarching standard statements, with each followed by a cluster of related standards. Each grade level and conceptual category has an overview page that indicates the domain, their related standard statements, and the associated Mathematical Practices.

5. THE RESULTS: COLLEGE AND CAREER READINESS STANDARDS FOR MATHEMATICS 47 Mathematics Standards Key The citation at the end of each standard identifies the CCSS grade, domain, and standard number (or standard number and letter, where applicable). So, 6.NS.6a, for example, stands for Grade 6, Number Sense domain, Standard 6a, and 5.OA.2 stands for Grade 5, Operations and Algebraic Thinking domain, Standard 2. The CCSS domains for K–8 are: NBT: Number and Operations in Base Ten (K–5) NS: The Number System (6–8) NF: RP: Number and Operations—Fractions (3–5) Ratios and Proportional Relationships (6–7) OA: Operations and Algebraic Thinking (K–5) EE: Expressions and Equations (6–8) F: Functions (8) G: Geometry (K–8) MD: Measurement and Data (K–5) SP: Statistics and Probability (6–8) The CCSS domains for high school are: N.RN: N.Q: A.SSE: The Real Number System Number and Quantity Algebra: Seeing Structure in Expressions A.APR: Algebra: Arithmetic with Polynomials and Rational Expressions A.CED: Algebra: Creating Equations A.REI: F.IF: F.BF: F.LE: G.CO: G.SRT: Algebra: Reasoning with Equations and Inequalities Functions: Interpreting Functions Functions: Building Functions Functions: Linear, Quadratic, and Exponential Models Geometry: Congruence Geometry: Similarity, Right Triangles, and Trigonometry G.GMD: Geometry: Geometric Measurement and Dimension G.MG: S.ID: Geometry: Modeling with Geometry Statistics and Probability: Interpreting Categorical and Quantitative Data

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