The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5: What They Say, What They Mean, How to Teach Them

by Jennifer M.D . Berman, Ruth Harbin Miles

Overview

Your user’s guide to the mathematics standards

In the 12 short months since the ELA versions of The Common Core Companions, Grades K-2 and 3-5, burst on the scene, they’ve already assisted tens of thousands of teachers with the day-to-day “what you do.” Teachers’ one big criticism: what about mathematics? Luckily NCTM past-president Linda Gojak and mathematics coach Ruth Harbin Miles stepped up to the task. The result? That version of the mathematics standards you wish you had.

Page by page, The Common Core Mathematics Companions clearly lay out:

• The mathematics embedded in each standard for a deeper understanding of the content
• Examples of what effective teaching and learning look like in the classroom
• Connected standards within each domain so teachers can better appreciate how they relate
• Priorities within clusters so teachers know where to focus their time
• The three components of rigor: conceptual understanding, procedural skills, and applications
• Vocabulary and suggested materials for each grade-level band with explicit connections to the standards
• Common student misconceptions around key mathematical ideas with ways to address them

Don’t spend another minute poring over the mathematics standards. Gojak and Miles have already done the heavy-lifting for you. Focus instead on how to teach them, using The Common Core Mathematics Companion as your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, and director of John Carroll University’s Center for Mathematics and Science Education, Linda Gojak has spent 28 years teaching elementary and middle school mathematics and 15 years working with K–8 teachers. She has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics.

Ruth Harbin Miles is a mathematics coach, with special expertise in developing teachers’ content knowledge and strategies for engaging students to achieve high standards in mathematics. She has served on the Board of Directors for the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.

Also From Corwin:

• Gojak & Miles/Common Corwin Mathematics Companion, Grades 3-5
• Taberski/The Common Core Companion, K-2
• Hull/The Common Core Mathematics Standards

Product Details

ISBN-13:	9781483381602
Publisher:	SAGE Publications
Publication date:	07/14/2015
Series:	Photos of Idaho
Edition description:	New Edition
Pages:	320
Sales rank:	46,212
Product dimensions:	8.70(w) x 10.90(h) x 0.90(d)

About the Author

Linda Gojak has spent 28 years teaching elementary and middle school mathematics and 15 years working with K–8 teachers. She currently directs the Center for Mathematics and Science Education at John Carroll University. She has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics. She has written several publications on problem solving and working with struggling students. Among her awards is the Presidential Award for Excellence in Science and Mathematics Teaching.

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.

Table of Contents

Acknowledgments
Letter to Teachers of Grades 3-5
Letter to Elementary School Principals
Introduction
A Brief History of the Common Core
The Common Core Standards for Mathematics
Instructional Shifts
Common Core Word Wall
The Common Core Standards for Mathematical Practice
Effective Teaching Practices
How to Use This Book
Reflection Questions
Part I. Operations & Algebraic Thinking, Grades 3-5
Domain Overview
Suggested Materials for This Domain
Key Vocabulary
Grade 3
Cluster A: Represent and solve problems involving multiplication and division
Cluster B: Understand properties of multiplication and the relationship between multiplication and division.
Cluster C: Multiply and divide within 100
Cluster D: Solve problems involving the four operations, and identify and explain patterns in arithmetic
Sample Planning Page: Operations and Algebraic Thinking, Grade 3, Cluster A
Planning Pages
Grade 5
Cluster A: Write and interpret numerical expressions
Cluster B: Analyze patterns and relationships
Sample Planning Page: Operations and Algebraic Thinking, Grade 5, Cluster A
Planning Pages
Reflection Questions
Part II: Number & Operations in Base Ten, Grades 3-5
Domain Overview
Suggested Materials for This Domain
Key Vocabulary
Grade 3
Cluster A: Use place value understanding and properties of operations to perform multi-digit arithmetic Sample Lesson: Number and Operations in Base Ten, Grade 3, Cluster A
Planning Pages
Grade 4
Cluster A: Generalize place value understanding for multi-digit whole numbers
Cluster B: Use place value understanding and properties of operations to perform multi-digit arithmetic
Sample Lesson: Number & Operations in Base Ten, Grade 4, Cluster B
Planning Pages
Grade 5
Cluster A: Understand the place value system
Cluster B: Perform operations with multi-digit whole numbers and with decimals to hundredths
Sample Planning Page: Number and Operations in Base Ten, Grade 5, Cluster B
Planning Pages
Reflection Questions
Part III: Number & Operations – Fractions, Grade 3-5
Domain Overview
Suggested Materials for This Domain
Key Vocabulary
Grade 3
Cluster A: Develop understanding of fractions as numbers
Sample Planning Page: Number & Operations – Fractions, Grade 3, Cluster A
Planning Page
Grade 4
Cluster A: Extend understanding of fraction equivalence and ordering
Cluster B: Build fractions from unit fractions
Cluster C: Understand decimal notation for fractions, and compare decimal fractions
Sample Planning Page: Number & Operations – Fractions, Grade 4, Cluster C
Planning Pages
Grade 5
Cluster A: Use equivalent fractions as a strategy to add and subtract fractions
Cluster B: Apply and extend previous understandings of multiplication and division
Sample Planning Page: Number & Operations – Fractions, Grade 5, Cluster A
Planning Pages
Reflection Questions
Part IV: Measurement & Data
Domain Overview
Suggested Materials for This Domain
Key Vocabulary
Grade 3
Cluster A: Solve problems involving measurement and estimation
Cluster B: Represent and interpret data
Cluster C: Geometric measurement: understand concepts of area and relate area to multiplication and to addition
Cluster D: Geometric measurement: recognize perimeter
Sample Planning Page: Measurement & Data, Grade 3, Cluster A
Planning Pages
Grade 4
Cluster A: Solve problems involving measurement and conversion of measurements
Cluster B: Represent and interpret data
Cluster C: Geometric measurement: understand concepts of angle and measure angles
Sample Planning Page: Measurement & Data, Grade 4, Cluster A
Planning Pages
Grade 5
Cluster A: Convert like measurement units within a given measurement system
Cluster B: Represent and interpret data
Cluster C: Geometric measurement: understand concepts of volume
Sample Planning Page: Measurement & Data, Grade 5, Cluster C
Planning Pages
Reflection Questions
Part V: Geometry
Domain Overview
Suggested Materials for This Domain
Key Vocabulary
Grade 3
Cluster A: Reason with shapes and their attributes
Sample Lesson: Geometry, Grade 3, Cluster A
Planning Pages
Grade 4
Cluster A: Draw and identify lines and angles, and classify shapes by properties of their lines and angles
Sample Lesson: Geometry, Grade 4, Cluster A
Planning Pages
Grade 5
Cluster A: Graph points on the coordinate plane to solve real-world and mathematical problems
Cluster B: Classify two-dimensional figures into categories based on their properties
Sample Lesson: Geometry, Grade 5, Cluster A
Planning Pages
Reflection Questions
Resources
Table 1
Table 2
Black Line Masters, 1-12
Standards for Mathematical Practice
Effective Teaching Practices
CCSS Where to Focus Grade 3 Mathematics
CCSS Where to Focus Grade 4 Mathematics
CCSS Where to Focus Grade 5 Mathematics
Additional Resources

Editorial Reviews

"This companion supports implementation of the Common Core Mathematics Standards with attention to the instructional shifts: focus, coherence, and rigor. The standard-by-standard examples provide an image of what the standards looks like in the classroom for both teachers and students. The attention to students’ conceptions helps teachers plan with student thinking in mind and contributes to the collaborative work of grade-level teams. "

Nicole Rigelman

"This practical, exemplary resource supports teachers in their understanding and learning of the Common Core Mathematics Standards. The book does an excellent job of unpacking what the standards mean and makes explicit connections both to the Standards for Mathematical Practice and common student misconceptions. It is an ideal choice for a book study at either the grade or school level. "

Jeffrey Shih

"This book is a ‘must-go-to’ for classroom teachers as well as coaches and leaders who support teachers in implementation of the Common Core Mathematics Standards. Connecting both the content standards and the practice standards with the effective teaching practices (Principles to Actions, NCTM, 2014), Linda Gojak and Ruth Harbin Miles provide the practical resources to enhance teachers’ understanding of the mathematics in the standards in ways that will bring them alive for all students. This is a book that will be the cornerstone of our professional development. "

Cathy Martin

"The Common Core Companion series for ELA became a runaway bestseller because it made instructional planning to address the standards manageable—and meaningful. Jim Burke and his co-authors put best practices first, equipping teachers with the 'what-it-looks-like' teaching ideas for each and every standard. Teachers have been clamoring for math version for more than a year, and now it's here! Linda Gojak and Ruth Harbin Miles do an amazing job demystifying the standards for grades 3-5. The authors have created a format and design that will have teachers dog-earing this book as they plan for instruction!"

Leslie Blauman

"I would use this book as a starting place to plan lessons because it gives a teacher a good idea of activities and some examples for each standard. It can also be used as a toolkit for understanding how standards connect across clusters and grade levels."

NCTM - Daniel Vitkus