**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

Instructional Shifts

Terminology Used in This Book

Effective Teaching Practices

How to Use This Book

Reflection Questions

**Part 1. Ratios and Proportional Relationships**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**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

Planning Page

**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

Planning Page

Reflection Questions: Ratios and Proportional Relationships

**Part 2. The Number System**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**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

Planning Pages

**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

Planning Page

**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

Planning Page

Reflection Questions: The Number System

**Part 3. Expressions and Equations**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**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

Planning Pages

**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

Planning Pages

**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

Planning Pages

Reflection Questions: Expressions and Equations

**Part 4. Functions**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**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

Planning Pages

Reflection Questions: Functions

**Part 5. Geometry**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**Grade 6**

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

Sample Planning Page: Geometry, Grade 6, Cluster A

Planning Page

**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

Planning Pages

**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

Planning Pages

Reflection Questions: Geometry

**Part 6. Statistics and Probability**

Domain Overview

Suggested Materials for This Domain

Key Vocabulary

**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

Planning Pages

**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

Planning Pages

**Grade 8**

Cluster A: Investigate patterns of association in bivariate data.

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

Planning Page

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**