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Your Mathematics Standards Companion, Grades 6-8
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Your Mathematics Standards Companion, Grades 6-8
What They Mean and How to Teach Them

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August 2017 | 336 pages | Corwin

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.

 
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

Supplements

Sample Materials & Chapters

At a Glance

Part 3

US Standards Map

Index


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ISBN: 9781506382258
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