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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

A Joint Publication of Corwin Mathematics and the National Council of Teachers of Mathematics, NCTM Stock Number 15463



June 2017 | 336 pages | Corwin

Transforming the standards into learning outcomes just got a lot easier

In this expansion of the original popular Common Core Mathematics Companion, 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, showing which of your standards are the same as CCSS-M, which differ and how—and 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

Sample Materials & Chapters

At a Glance

Part 3


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