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# Your Mathematics Standards Companion, Grades 6-8

**By:**
Ruth Harbin Miles, Lois A. Williams

*Common Core Mathematics Companions*provides indexes for states implementing state-specific mathematics standards and shows which are the same as CCSS-M, which differ and how.

**Grade Level:**PreK-12**ISBN:**9781506382258**Published By:**Corwin**Series:**Corwin Mathematics Series**Year:**2017**Page Count:**336**Publication date:**June 23, 2017

**Price: $39.95**

### For Instructors

### Tools

## Description

*Transforming the standards into learning outcomes just got a lot easier*

In this resource, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, allowing you to see and understand which page number to turn to for standards-based teaching ideas.

It’s all here, page by page:

- Get the inside scoop on which standards connect, what key vocabulary means, and time-saving tables showing where to focus instruction for each grade
- Write curriculum for: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics & probability
- Use the What to Teach pages to deliver powerful standards-based lessons
- Learn effective techniques to create an environment where all students can experience math break-throughs
- Incorporate the Standards for Mathematical Practice to improve students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more
- Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state

*Your Mathematics Standards Companion* is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

## Author(s)

### Ruth Harbin Miles

**Ruth Harbin Miles** coaches rural, suburban, and inner-city school mathematics teachers. Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginia’s Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics. Ruth is a co-author of five Corwin books including A *Guide to Mathematics Coaching*, *A Guide to Mathematics Leadership*, *Visible Thinking in the* *K-8 Mathematics Classroom, The Common Core Mathematics Standards, and Realizing Rigor in the Mathematics Classroom. *As co-owner of Happy Mountain Learning, Ruth specializes in developing teachers’ content knowledge and strategies for engaging students to achieve high standards in mathematics.

### Lois A. Williams

After teaching mathematics in grades K-8 for 20 years, Lois served as the middle school mathematics specialist for the Virginia Department of Education. Here she worked on curriculum and teacher professional learning. She served the Virginia Council of Teachers of Mathematics and was a board member for the local Jefferson Council of Teachers of Mathematics. After receiving her doctorate in curriculum and instruction at The University of Virginia, she began serving as adjunct faculty to Mary Baldwin College and is in her 15^{th} year working with pre-service teachers. Currently Lois is an International Fellow with the Charles A. Dana Center working with classroom teachers in the Department of Defense Schools helping them implement their College and Career Readiness Standards. Among her recognitions are a Fulbright Teacher Exchange and Virginia Middle School Mathematics Teacher of the Year.

## Table of Contents

**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**