About the Book
Because when you see the math, they can see it too.
The role of today’s classroom teacher has evolved from being a disseminator of information to a facilitator of learning. As an elementary teacher, you can guide student thinking to deeper levels of understanding by making connections between and among physical, visual, symbolic, verbal and contextual representations.
Seeing the Math You Teach, Grades K-6 is intended to help you help your students. It is an accessible guide for elementary teachers that focuses on making mathematics meaningful through multiple strategies and representations to help foster a love for mathematics in their students. The authors have written this book based on the deep belief that everyone can be good at math. It illustrates the most commonly seen and used visual models of each of the elementary mathematical content areas the way children think about them. Rather than a book full of prescribed problem solving strategies, this book will help you and your students literally "see" the structure of mathematical concepts–how and why they work–and make connections among various representations and topics.
This is not the kind of book to be read cover-to-cover. It is organized in a flexible format to inform the math teaching and learning going on in a classroom at a given moment. Enhancing teachers’ own clarity and understanding in mathematics, or in other words, "to see the math they teach," this book:
- Provides 16 color-coded chapters–and a Topic Index–that can be used to quickly locate specific topics such as "place value", "unit fractions" or "equivalent ratios"
- Incorporates videos of how to use manipulatives to connect physical models to other visual representations
- Can be used as a planning tool with your PLC, a desk-reference, a teaching tool, and a family support tool.
This guide equips you to help your students derive meaning, sense, and joy out of their mathematics learning. It helps them see math as more than "just numbers"--illustrating the ways they think and focusing on their understanding of how and why math works.
Table of Contents:
Whole Numbers & Decimal Place Value
Math Symbols & Properties
Estimation (including rounding)
Addition & Subtraction Using Place Value
Multiplication & Division Using Place Value
Special Topics with Whole Numbers
Negative & Positive Numbers
Fraction Basics
Add, Subtract, Multiply, & Divide Fractions
Relationships Between Fractions, Decimals, & Percents
Ratios & Rates
Algebraic Expression, Equations, & Inequalities
Coordinate Planes
Geometry
Measurement
Data
About the Author :
Kimberly Rimbey is an author, inventor, entrepreneur, speaker, consultant, coach, mentor, advocate, and, proudest of all, a teacher through and through. Kim currently serves as the Chief Learning Officer and CEO at KP® Mathematics and an Official Building Thinking Classrooms Consultant alongside Peter Liljedahl. A life-long teacher and learner, her heart’s work centers on equipping teachers and helping them fall in love with teaching and learning over and over again.
Always a teacher at heart, Kim has held several leadership positions, including Executive Director of Curriculum and Instruction, Chief Learning Officer, and Mathematica Program Area Coordinator. That said, everything Kim has done in her career is based on what she learned during her 18 years as a mathematics coach and classroom teacher.
Kim is National Board Certified in Early Adolescent Mathematics, and she is a recipient of the Presidential Award for Excellence in Mathematics Teaching. Kim is the co-inventor of KP® Ten-Frame Tiles and has authored and co-authored several publications, including the Mastering Math Manipulatives and Meaningful Small Groups in Math for Corwin, Math Power: Simple Solutions for Mastering Math for the Rodel Foundation of Arizona, and, most recently, The Amazing Ten Frame series for KP Mathematics.
Kim earned her BA in Elementary Education and Mathematics from Grand Canyon University, her M.Ed. degrees in Early Childhood Education and Educational Leadership from Arizona State University and Northern Arizona University, and her Ph.D. in Curriculum and Instruction from Arizona State University. Kim lives in Phoenix, Arizona, where she continues to inspire teachers and their leaders.
Katie Basham is an aggressive Scrabble player, avid reader, affectionate mother and wife. She is also an Instructional Specialist in the Pacific NorthWest where she leads professional development and works to advance the learning of teachers both in the classroom as well as in collaborative groups. She is a former classroom teacher, elementary math specialist, and assessment coordinator. Katie strives to support teachers and teacher- leaders in their efforts to improve mathematics learning opportunities for all students. She is active in state and national mathematics organizations and has served on the Arizona Math Leaders Board of Directors. She received her Master’s Degree from Northern Arizona University and her Bachelor’s Degree from Boston College. Katie is a self-proclaimed “nerd” and proud of it; in addition to her love of numbers she is also an avid reader and enjoys walks on the beach with “Honey”, the family′s Silver Labrador.
Chryste Berda is an adventurer, traveler, teacher, coach, consultant, author, and mom of two amazing Gen Z guys. She finds joy in singing at the top of her lungs and in the art of teaching. Chryste is energized by sharing her passion for learning with her colleagues as the district math coordinator and as a Regional VP for the Arizona Association of Teachers of Mathematics. She is intensely curious about students’ thinking and spends much of her time listening to students explain their ideas. Chryste is an Honors program graduate from Western Oregon University with a Bachelor’s degree in Elementary Education and Interdisciplinary Studies with a Specialty in Mathematics. She holds two Master’s degrees from Arizona State University - one in Curriculum and Instruction, the other in Educational Leadership. She has taught mostly math to students in grades K-12, their teachers, and leaders (in addition to some other very fun courses) since 1998. Chryste is a native Oregonian who for the past twenty-ish years has lived with her family in Arizona′s Valley of the Sun. She and her husband are raising two Arizona natives and aspire to become “snowbirds” in the future.
Review :
Too often, in mathematics, we are in a rush to move from the concrete to abstract. In doing so, we overlook the visual. This book is an excellent reminder of the importance of the visual. It not only helps us understand how visuals can help students see mathematics but also helps us see what students see when they are doing mathematics. This book is a necessity for every K–6 teacher.
Seeing the Math You Teach delivers exactly what it promises—math you can actually see. The visuals are clean, clear, and do the heavy lifting, making tricky concepts far more intuitive for both students and teachers. If you’ve ever struggled to explain fractions without resorting to interpretive dance, this book is for you.
If we’re serious about equity in math, we must change how we teach it. Seeing the Math You Teach gives parents and teachers the tools to do just that—by using visual models and brain-friendly strategies that support all kids, not just those labeled as ‘high achievers,’ in developing real mathematical understanding.
Seeing the Math You Teach is an essential resource for educators looking to deepen their mathematical understanding and better support their students. Through clear visuals and a progression of conceptual development, this book helps teachers see how students think and learn, allowing them to meet each learner where they are. A must-have for building instructional confidence and fostering meaningful mathematical understanding in the classroom!
This book is a valuable resource for teachers who want to make math more accessible and meaningful for all students. With clear explanations, visual support, and practical strategies, it helps break down abstract concepts so that every learner can engage and build understanding. Grounded in how children learn, this book offers thoughtful guidance for creating lessons that support problem-solving, confidence, and a genuine connection to math.
Teachers often ask, ‘How can I ratchet up the quality of my math teaching to better engage my students in mathematical thinking and to deepen their understanding of math beyond answer-getting?’ Call this helpful book ‘A Compendium of Math Representations’ because it provides a slew of topic-specific ways to picture mathematics. By including these multiple representations in our lessons, we ensure that all the active, yet different, brains in our classrooms can ‘get it.’
Seeing the Math You Teach is an essential resource that transforms mathematics into a visual and accessible experience for all students. This comprehensive guide will undoubtedly become a favorite among teachers, showing signs of frequent use as they refer to it time and time again!
Seeing the Math You Teach is a valuable resource that brings clarity to mathematical representations. It will help you make essential concepts more accessible for all learners. The practical strategies and visual models will empower you to foster deeper understanding and greater confidence in math.
I’ve shared about the ‘Sweet Spot of the C-R-A model,’ where you do an activity that includes all 3 and the power that has with building your students’ understanding. Seeing the Math You Teach is full of representations to help you get to that ‘Sweet Spot.’
If you want to see math visually, then this is the book for you! Seeing the Math You Teach shows us what math looks like. It’s an easy-to-read reference book that will be on my desk to share with teachers (and students!)
With clear explanations and powerful visual representations, Seeing the Math You Teach is an indispensable resource for K–6 teachers looking to deepen their understanding of mathematics and how students learn it. Packed with practical strategies, this book empowers educators to guide students beyond rote memorization toward true mathematical comprehension by bridging the gap between abstract concepts and hands-on, visual learning. A must-have for any teacher committed to helping students see, explore, and master math with confidence.
Seeing the Math You Teach is an essential resource for teachers, instructional aides, special educators, and those entering the profession through alternative certification. As a district math coordinator, I appreciate how the book’s clear visuals, concise text, and embedded video clips make complex mathematical representations immediately accessible—not just for educators, but also for parents and caregivers supporting math learning at home. An eye-opening approach to visualizing mathematics!
This book is a must-read for educators and caregivers who want to foster sense-making in mathematics. The authors present clear, comprehensive visual representations that make abstract concepts understandable. A valuable resource for anyone who is eager to provide children with rich and connected mathematical experiences.
Seeing the Math You Teach is more than just a resource—it’s a toolbox for teachers, packed with practical ideas to help make math visible and meaningful. It gives you simple ways to break down big concepts and help every student truly get it.
