#
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

Series Creator: Jim Burke

*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

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## Free resources

### Place Value Lesson

Students extend their understanding of place value by bundling tens with this lesson from *The Common Core Mathematics Companion, K-2*. (Elementary)

*"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!"*

**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." *

**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." *

**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."*

**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."*

**Portland State University, Portland, OR**

"This practical, exemplary resource provides teachers support 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."

**University of Nevada, Las Vegas**

*"This book is a must go-to for classroom teachers and coaches and leaders who support teachers in implementation of the Common Core Mathematics Standards. Connecting the Common Core Mathematics Standards (both content standards and practice standards) together with the effective teaching practices (*Principles to Actions*, NCTM, 2014), the authors provide the practical resources to support teachers in deepening their understanding of the mathematics in the Standards in ways that will enable them to bring these Standards alive for all students. It is a book that will be the cornerstone of our professional development."*

**Denver Public Schools Denver, CO**

*"At the end of the day, it's our students who matter most. Have we made them feel great about themselves as learners or not? It's that simple. So it's with a huge sigh of relief —and a round of applause—that I recommend *The Common Core Math Companion, K-2.* Linda Gojak and Ruth Harbin Miles bring to this book a deep understanding of the developmental needs of children in the primary grades. Let's face it, the CCSS are challenging, perhaps especially at K-2, and we have to be extra vigilant about how they influence instruction in the early grades. These two experts also deliver the goods needed for successfully implementing the standards day-day-day, including key vocabulary, models, lists of manipulatives, reproducibles for kids. I especially admire the recurring sections on students' misconceptions and common errors, so that teachers have a clear sense of what to watch for, and more importantly, the kind of skills and understandings to teach into in future lessons."*

*“I appreciate the comprehensiveness of [The Common Core Mathematics Companion: The Standards Decoded, Grades K–2]. It compiles the standards, progressions, math practices, and more into one resource. . . . This is a reference resource to have read¬ily available for planning units and lessons, increasing content knowledge, and understand¬ing math. It will be a valuable companion on the path to increasing teacher efficacy and student learning. After I shared this resource with my colleagues, all of them requested copies for a book study.”*

**Schuyler Achievement Academy, Albany, New York**

**Teaching Children Mathematics**