Indexes Cross-Referencing Your State Standards

Quick Reference Guide

Acknowledgments

Letter to Grades 6–8 Teachers

Letter to Middle School Principals

Introduction

A Brief History of Current State Standards

College and Career Ready Standards for Mathematics

Terminology Used in This Book

Effective Teaching Practices

Part 1. Ratios and Proportional Relationships

Suggested Materials for This Domain

Grade 6

Cluster A: Understand ratio concepts and use ratio reasoning to solve problems.

Sample Planning Page: Ratios and Proportional Relationships, Grade 6, Cluster A

Grade 7

Cluster A: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Sample Planning Page: Ratios and Proportional Relationships, Grade 7, Cluster A

Reflection Questions: Ratios and Proportional Relationships

Part 2. The Number System

Suggested Materials for This Domain

Grade 6

Cluster A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Cluster B: Compute fluently with multi-digit numbers and find common factors and multiples.

Cluster C: Apply and extend previous understandings of numbers to the system of rational numbers.

Sample Planning Page: The Number System, Grade 6, Cluster C

Grade 7

Cluster A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Sample Planning Page: The Number System, Grade 7, Cluster A

Grade 8

Cluster A: Know that there are numbers that are not rational, and approximate them by rational numbers.

Sample Planning Page: The Number System, Grade 8, Cluster A

Reflection Questions: The Number System

Part 3. Expressions and Equations

Suggested Materials for This Domain

Grade 6

Cluster A: Apply and extend previous understandings of arithmetic to algebraic expressions.

Cluster B: Reason about and solve one-variable equations and inequalities.

Cluster C: Represent and analyze quantitative relationships between dependent and independent variables.

Sample Planning Page: Expressions and Equations, Grade 6, Cluster C

Grade 7

Cluster A: Use properties of operations to generate equivalent expressions.

Cluster B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Sample Planning Page: Expressions and Equations, Grade 7, Cluster A

Grade 8

Cluster A: Work with radicals and integer exponents.

Cluster B: Understand the connections between proportional relationships, lines, and linear equations.

Cluster C: Analyze and solve linear equations and pairs of simultaneous linear equations.

Sample Planning Page: Expressions and Equations, Grade 8, Cluster A

Reflection Questions: Expressions and Equations

Part 4. Functions

Suggested Materials for This Domain

Grade 8

Cluster A: Define, evaluate, and compare functions.

Cluster B: Use functions to model relationships between quantities.

Sample Planning Page: Functions, Grade 8, Cluster A

Reflection Questions: Functions

Part 5. Geometry

Suggested Materials for This Domain

Grade 6

Cluster A: Solve real-world and mathematical problems involving area, surface area, and volume.

Sample Planning Page: Geometry, Grade 6, Cluster A

Grade 7

Cluster A: Draw, construct, and describe geometrical figures and describe the relationships between them.

Cluster B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Sample Planning Page: Geometry, Grade 7, Cluster B

Grade 8

Cluster A: Understand congruence and similarity using physical models, transparencies, or geometry software.

Cluster B: Understand and apply the Pythagorean Theorem.

Cluster C: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Sample Planning Page: Geometry, Grade 8, Cluster A

Reflection Questions: Geometry

Part 6. Statistics and Probability

Suggested Materials for This Domain

Grade 6

Cluster A: Develop understanding of statistical variability.

Cluster B: Summarize and describe distributions.

Sample Planning Page: Statistics and Probability, Grade 6, Cluster B

Grade 7

Cluster A: Use random sampling to draw inferences about a population.

Cluster B: Draw informal comparative inferences about two populations.

Cluster C: Investigate chance processes and develop, use, and evaluate probability models.

Sample Planning Page: Statistics and Probability, Grade 7, Cluster C

Grade 8

Cluster A: Investigate patterns of association in bivariate data.

Sample Planning Page: Statistics and Probability, Grade 8, Cluster A

Reflection Questions: Statistics and Probability

Resources

Table 1. Standards for Mathematical Practice

Table 2. Effective Teaching Practices

Reproducibles

Reproducible 1. Percent Wheel

Reproducible 2. Frayer Model

Reproducible 3. Net of a Cube

Reproducible 4. Example for MAD (Mean Absolute Deviation)

Additional Resources

About the Authors