Seeing the Math You Teach, Grades K-6

An Elementary Teacher’s Quick-Guide to Meaningful Mathematical Strategies and Representations
First Edition
Seeing the Math You Teach, Grades K-6
April 2025 | 224 pages | Corwin
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eBook
ISBN: 9781071984512
Available from January 0001
Spiral
ISBN: 9781071984666
Available from May 2025

Description

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.

Contents

Whole Numbers & Decimal Place Value

Whole Numbers & Decimal Place Value

Math Symbols & Properties

Math Symbols & Properties

Estimation (including rounding)

Estimation (including rounding)

Addition & Subtraction Using Place Value

Addition & Subtraction Using Place Value

Multiplication & Division Using Place Value

Multiplication & Division Using Place Value

Special Topics with Whole Numbers

Special Topics with Whole Numbers

Negative & Positive Numbers

Negative & Positive Numbers

Fraction Basics

Fraction Basics

Add, Subtract, Multiply, & Divide Fractions

Add, Subtract, Multiply, & Divide Fractions

Relationships Between Fractions, Decimals, & Percents

Relationships Between Fractions, Decimals, & Percents

Ratios & Rates

Ratios & Rates

Algebraic Expression, Equations, & Inequalities

Algebraic Expression, Equations, & Inequalities

Coordinate Planes

Coordinate Planes

Geometry

Geometry

Measurement

Measurement

Data

Data

Description

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.

Contents

Whole Numbers & Decimal Place Value

Whole Numbers & Decimal Place Value

Math Symbols & Properties

Math Symbols & Properties

Estimation (including rounding)

Estimation (including rounding)

Addition & Subtraction Using Place Value

Addition & Subtraction Using Place Value

Multiplication & Division Using Place Value

Multiplication & Division Using Place Value

Special Topics with Whole Numbers

Special Topics with Whole Numbers

Negative & Positive Numbers

Negative & Positive Numbers

Fraction Basics

Fraction Basics

Add, Subtract, Multiply, & Divide Fractions

Add, Subtract, Multiply, & Divide Fractions

Relationships Between Fractions, Decimals, & Percents

Relationships Between Fractions, Decimals, & Percents

Ratios & Rates

Ratios & Rates

Algebraic Expression, Equations, & Inequalities

Algebraic Expression, Equations, & Inequalities

Coordinate Planes

Coordinate Planes

Geometry

Geometry

Measurement

Measurement

Data

Data

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Seeing the Math You Teach, Grades K-6

An Elementary Teacher’s Quick-Guide to Meaningful Mathematical Strategies and Representations


April 2025 | 224 pages | Corwin

Format Published Date ISBN Price
Spiral 01/02/2026 9781071984666 $40.95
Lifetime 16/03/2026 9781071984512 $37.00

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

Recent Product Reviews:

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.
Peter Liljedahl, Building Thinking Classrooms
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.
Fawn Nguyen, STEM Initiatives
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.
Pam Seda
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!
Graham Fletcher
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.
Melynee Naegele, Osage County Interlocal Cooperative

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