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

- Ruth Harbin Miles - Mary Baldwin College, VA
- Lois A. Williams - Owner, C&I Mathematics Consulting

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

*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.

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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 |

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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 |

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 |

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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 |

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 |

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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

Sample Planning Page: Geometry, Grade 6, Cluster A |

Planning Page |

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 |

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 |

Domain Overview |

Suggested Materials for This Domain |

Key Vocabulary |

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 |

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 |

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 |

Table 1. Standards for Mathematical Practice |

Table 2. Effective Teaching Practices |

Reproducible 1. Percent Wheel |

Reproducible 2. Frayer Model |

Reproducible 3. Net of a Cube |

Reproducible 4. Example for MAD (Mean Absolute Deviation) |

### Supplements

HEOA Compliance

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**Available formats**

ISBN: 9781506382258 | Spiral | Suggested Retail Price: $34.95 | Bookstore Price: $27.96 |

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