Ratios and Proportional Relationships 6.RP Major Clusters

• Understand ratio concepts and use ratio reasoning to solve problems. (6.RP.1–3 )

The Number System 6.NS Major Clusters

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions. (6.NS.1 )

• Apply and extend previous understandings of numbers to the system of rational numbers.

(6.NS.5–8 )

Additional/Supporting Clusters

• Compute uently with multi-digit numbers and nd common factors and multiples. (6.NS.2–4)

Expressions and Equations 6.EE Major Clusters

• Apply and extend previous understandings of arithmetic to algebraic expressions. (6.EE.1–4 )

• Reason about and solve one-variable equations and inequalities. (6.EE.5–8 )

• Represent and analyze quantitative relationships between dependent and independent variables.

(6.EE.9 )

Geometry 6.G Additional/Supporting Clusters

• Solve real-world and mathematical problems involving area, surface area, and volume. (6.G.1–4)

Statistics and Probability 6.SP Additional/Supporting Clusters

• Develop understanding of statistical variability. (6.SP.1–3) • Summarize and describe distributions. (6.SP.4–5)

Ratios and Proportional Relationships 7.RP Major Clusters

• Analyze proportional relationships and use them to solve real-world and mathematical problems. (7.RP.1–3 )

The Number System 7.NS Major Clusters

• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (7.NS.1–3 )

Expressions and Equations 7.EE Major Clusters

• Use properties of operations to generate equivalent expressions. (7.EE.1–2 )

• Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (7.EE.3–4 )

Geometry 7.G Additional/Supporting Clusters

• Draw, construct, and describe geometrical gures and describe the relationships between them. (7.G.1–3)

• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.4–6)

Statistics and Probability 7.SP Additional/Supporting Clusters

• Use random sampling to draw inferences about a population.1 (7.SP.1–2) • Draw informal comparative inferences about two populations.2 (7.SP.3–4)

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Investigate chance processes and develop, use, and evaluate probability models. (7.SP.5–8)

The Number System 8.NS Additional/Supporting Clusters

• Know that there are numbers that are not rational, and approximate them by rational numbers.1 (8.NS.1–2)

Expressions and Equations 8.EE Major Clusters

• Work with radicals and integer exponents. (8.EE.1–4 )

• Understand the connections between proportional relationships, lines, and linear equations. (8.EE.5–6 ) • Analyze and solve linear equations and pairs of simultaneous linear equations. (8.EE.7–8 )

Functions 8.F Major Clusters

• De ne, evaluate, and compare functions. (8.F.1–3 ) Additional/Supporting Clusters

• Use functions to model relationships between quantities.2 (8.F.4–5)

Geometry 8.G Major Clusters

• Understand congruence and similarity using physical models, transparencies, or geometry software. (8.G.1–5 )

• Understand and apply the Pythagorean Theorem. (8.G.6–8 ) Additional/Supporting Clusters

• Solvereal-worldandmathematicalproblemsinvolvingvolumeofcylinders,cones,andspheres.(8.G.9)

Statistics and Probability 8.SP Additional/Supporting Clusters

• Investigate patterns of association in bivariate data.3 (8.SP.1–4)