The Common Core Mathematics Companion: The Standards Decoded, Grades K-2

What They Say, What They Mean, How to Teach Them
Linda M. Gojak - Mathematics Consultant, NCTM Past-President
Ruth Harbin Miles - Mary Baldwin College, VA
The Common Core Mathematics Companion: The Standards Decoded, Grades K-2
March 2015 | 256 pages | Corwin
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ISBN: 9781483381558
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Description

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

 

Contents

Acknowledgments

Acknowledgments

Letter to K-2 Teachers

Letter to K-2 Teachers

Letter to Elementary School Principals

Letter to Elementary School Principals

Introduction

Introduction

1. Counting and Cardinality

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Reflection Questions

2. Operations and Algebraic Thinking

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

3. Number and Operations in Base Ten

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Key Vocabulary
  • Grade 1
  • Grade 2
  • Reflection Questions

4. Measurement and Data

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

5. Geometry

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

Resources

Resources

Description

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

 

Contents

Acknowledgments

Acknowledgments

Letter to K-2 Teachers

Letter to K-2 Teachers

Letter to Elementary School Principals

Letter to Elementary School Principals

Introduction

Introduction

1. Counting and Cardinality

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Reflection Questions

2. Operations and Algebraic Thinking

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

3. Number and Operations in Base Ten

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Key Vocabulary
  • Grade 1
  • Grade 2
  • Reflection Questions

4. Measurement and Data

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

5. Geometry

  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions

Resources

Resources

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The Common Core Mathematics Companion: The Standards Decoded, Grades K-2

What They Say, What They Mean, How to Teach Them


March 2015 | 256 pages | Corwin

Format Published Date ISBN Price
Spiral 01/02/2026 9781483381565 $40.95
Lifetime 01/02/2026 9781483381558 $37.00

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

 


Table Of Contents:

  • Acknowledgments
  • Letter to K-2 Teachers
  • Letter to Elementary School Principals
  • Introduction
  • 1. Counting and Cardinality
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Reflection Questions
  • 2. Operations and Algebraic Thinking
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions
  • 3. Number and Operations in Base Ten
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Key Vocabulary
  • Grade 1
  • Grade 2
  • Reflection Questions
  • 4. Measurement and Data
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions
  • 5. Geometry
  • Domain Overview
  • Suggested Materials for This Domain
  • Key Vocabulary
  • Kindergarten
  • Grade 1
  • Grade 2
  • Reflection Questions
  • Resources

Recent Product Reviews:

"The Common Core State Standards in Math needed to be deciphered! After reading this book, teachers will have acquired an abundance of realistic steps to achieve fantastic outcomes! Well done!"
Susan E. Schipper, Elementary Teacher, Charles Street School, Palmyra, NJ
"I loved this book. It is a must have for K-2 teachers. The breakdown and explanation of the math skills is excellent. As a teacher who has been teaching Common Core for a few years, I wish I had had something like this to help guide me from the beginning. I will definitely recommend it for my school. This book is a winner for classroom teachers."
Donna Adkins, First Grade Teacher, Perritt Primary, Arkadelphia, AR
"I love the user-friendly organization of this book. Teachers in K-2 can easily check the prior grade level standards to see how each standard builds off of another. Teachers who have multi-age primary classrooms will appreciate the easy-to-follow examples. All teachers will value the clear “I do, you do” format presented in the book as well as the common misconceptions sections which will help teachers plan accordingly."
Renee J. Nealon, Second Grade Teacher, McDowell Elementary School, Petaluma, CA
"This book is worth its weight in gold, for states following the Common Core and for states who don’t. States not using the Common Core can use this book for a better perspective of what is meant by rigor and how students can master the standards, which are very similar to individual state standards . . . The importance of the book is immeasurable."
Pat Baker, Retired Elementary Teacher, NBCT, Culpeper, VA
"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 teachers with 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, Associate Professor, Portland State University, Portland, OR

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