# Hands-on, Practical Guidance for Educators

From math,
literacy, equity, multilingual learners, and SEL, to assessment, school counseling,
and education leadership, our books are research-based and authored by experts
on topics most relevant to what educators are facing today.

# Mathematize It! [Grades 3-5]

**shares a reasoning approach that takes the initial focus off specific numbers and computations and puts it on the actions and relationships expressed in the word problem.**

*Mathematize It!***Grade Level:**3-5**ISBN:**9781506395272**Published By:**Corwin**Series:**Corwin Mathematics Series**Year:**2019**Page Count:**224**Publication date:**September 16, 2019

**Price: $35.95**

### Review Copies

Review copies may be requested by individuals planning to purchase 10 or more copies for a team or considering a book for adoption in a higher ed course. To request a review copy, contact sales@corwin.com.

## Description

*“The list of math books to truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently add *Mathematize It* to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving. *Mathematize It* will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!”
*

Suni Singh

Author of P

*i of Life: the Hidden Happiness of Mathematics*and

*Math Recess: Playful Learning in an Age of Disruption*

**Help****students reveal the math behind the words**“I don’t get what I’m supposed to do!” This is a common refrain from students when asked to solve word problems.

Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them.

**shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of**

*Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5**mathematizing*, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem.

Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades 3–5

• Offers a systematic mathematizing process for students to use when solving word problems • Gives practice opportunities and dozens of problems to leverage in the classroom • Provides specific examples of questions and explorations for all four operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, and decimals • Demonstrates the use of concrete manipulatives to model problems with dozens of short videos • Includes end-of-chapter activities and reflection questions

*Mathematize it!*

## Key features

Includes:

- Dozens of word problems for teacher practice and classroom use
- More than 35 brief videos demonstrating how to use concrete manipulatives to model word problems
- Student work samples
- Teacher workspace for practice
- End-of-chapter activities and reflection questions

## Author(s)

### Sara Delano Moore

Sara Delano Moore is an independent mathematics education consultant at SDM Learning. A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in *Mathematics Teaching in the Middle School*, *Teaching Children Mathematics*, *Science & Children*, and *Science Scope*.

### Kimberly Morrow-Leong

**Kimberly Morrow-Leong** is an adjunct instructor at George Mason University in Fairfax, Virginia, a part-time researcher at American Institutes for Research, and a consultant for Math Solutions. She is a former grade 5–9 classroom teacher, K–8 mathematics coach, and coordinator of elementary professional development for the National Council of Teachers of Mathematics (NCTM). She recently completed an elected term as vice president and 2018 program chair for NCSM, Leadership in Mathematics Education. She holds a BA in French language and a masters in linguistics (TESOL). She also holds an MEd and PhD in mathematics education leadership from George Mason University. Kim is the 2009 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) from Virginia. She is happiest when working with teachers and students, putting pencils down and getting messy with manipulatives!

### Linda M. Gojak

**Linda M. Gojak**directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and 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.

## Table of Contents

**Video List**

**Preface**

**Chapter 1 Introduction: Why You Need to Teach Students to Mathematize**

Problem Solving Strategies Gone Wrong

What is Mathematizing? Why Is It Important?

Teaching Students to Mathematize

Final Words Before You Dive In

**Part 1 Addition and Subtraction**

**Chapter 2: Add-To and Take-From: Locating the Change**

Thinking About Active Addition and Subtraction Situations

Moving Beyond Whole Numbers

Key Ideas

Try It Out!

Reflect

**Chapter 3: Part-Part-Whole: Understanding the Relationship**

Thinking About Part-Part-Whole Situations

Moving Beyond Whole Numbers

Key Ideas

Try It Out!

Reflect

**Chapter 4: Additive Comparisons: Another Kind of Relationship**

Thinking About Additive Comparison Situations

Moving Beyond Whole Numbers

Key Ideas

Try It Out!

Reflect

**Part 2: Multiplication and Division**

**Chapter 5: Equal Groups Multiplication: Two Factors, Different Jobs**

Thinking About Equal Groups Situations

Moving Beyond Whole Numbers

Key Ideas

Try it Out!

Reflect

**Chapter 6: Equal Groups Division: When a Factor Is Missing**

Thinking About Equal Groups Division

Moving Beyond Whole Numbers

Key Ideas

Try it Out!

Reflect

**Chapter 7: Multiplicative Comparisons: Another Asymmetric Relationship**

Thinking About Multiplicative Comparisons

Moving Beyond Whole Numbers

Key Ideas

Try It Out!

Reflect

**Chapter 8: Area and Array: Two Factors, Same Job**

Thinking About Area and Array Situations

Moving Beyond Whole Numbers

Key Ideas

Try It Out!

Reflect

**Chapter 9: Changing How You Teach Word Problems**

Getting into the Mathematizing Sandbox

8 Shifts in Instruction for Building Students’ Problem-Solving Skills

Guidance for Moving Forward: FAQ’s

**Appendix A – Situation Tables**

**References**

**Index**

## Reviews

*Mathematize It!*to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving.

*Mathematize It!*will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!”

“The list of generational math books to come along and truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently addSunil SinghMathematize It!to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving.Mathematize It!will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!”

*“Mathematize It!*is a must-read for anyone who has struggled to teach word problems and is ready to figure out what really works. The authors present a plethora of strategies that help students focus on the thinking part of the problem-solving process while gently helping the reader understand that so many of our ‘tried-and-true’ methods, such as key words, really don’t work. They help us realize that the real work of solving word problems is in the sense-making phase—once students have made sense of a problem, calculating the solution is the simpler part of the process.”

Kimberly Rimbey“Mathematize It!is a must-read for anyone who has struggled to teach word problems and is ready to figure out what really works. The authors present a plethora of strategies that help students focus on the thinking part of the problem-solving process while gently helping the reader understand that so many of our ‘tried-and-true’ methods, such as key words, really don’t work. They help us realize that the real work of solving word problems is in the sense-making phase—once students have made sense of a problem, calculating the solution is the simpler part of the process.”

KP Matheamtics

*Mathematize It!*addresses the complexity of problem solving more completely than any other individual resource. It is easy to say that we must teach students to ‘mathematize situations’ but this book helps us to actually help students learn to do it. The challenge and reflection pieces at the end of each chapter are a game changer for unveiling teaching opportunities, prompting discussion in your PLC, and moving this from a book on the professional shelf to a powerful tool to impact instruction.

Gina KildayMathematize It!addresses the complexity of problem solving more completely than any other individual resource. It is easy to say that we must teach students to ‘mathematize situations’ but this book helps us to actually help students learn to do it. The challenge and reflection pieces at the end of each chapter are a game changer for unveiling teaching opportunities, prompting discussion in your PLC, and moving this from a book on the professional shelf to a powerful tool to impact instruction.

Metcalf Elementary School, Exeter, RI

*Mathematize It!*is a book that should be on the shelf of every classroom teacher and division leader who supports mathematics teaching and leading. This valuable resource helps educators to think about the what, why, and the how to make sense of word problems. It gives a framework and visuals on how to support teachers’ understanding around problem types and solving problems and excels in assisting teachers in how to make a commitment to teaching for greater understanding.”

“Spencer JamiesonMathematize It!is a book that should be on the shelf of every classroom teacher and division leader who supports mathematics teaching and leading. This valuable resource helps educators to think about the what, why, and the how to make sense of word problems. It gives a framework and visuals on how to support teachers’ understanding around problem types and solving problems and excels in assisting teachers in how to make a commitment to teaching for greater understanding.”

Virginia Council of Teacher of Mathematics

“This is a game changer… even after 20 years of supporting students and their sensemaking of word problems, I am thrilled to learn even more from this trio of authors. They offer practical suggestions, opportunities for practice, and relevant research in order to increase awareness of best practices surrounding word problems. The only key word in this case is MATHEMATIZE! To have this resource in your hands is to have an invitation to the ‘mathematizing sandbox’.”Beth Terry

Riffa Views International School, Baharain

“This dynamic author trio brings years of classroom experiences to one of the central problems of teaching and learning mathematics: making sense of word problems. Focusing on the construct of “mathematizing”—drawing, constructing, describing, representing, and making sense of situations— this clear and practical guide needs to be required reading and discussion fodder for every elementary teacher of mathematics. It’s just that clear, informative and insightful!”Steve Leinwand

American Institutes for Research, Washington, DC

“As our students begin to mathematize the world around them, it becomes extremely important that we listen to their thinking so that we can continue to move their understanding forward. What makes Mathematize It! such a useful tool for teachers is that it thoughtfully unpacks student strategies, which helps inform and guide our next move as a classroom teacher.”Graham Fletcher

Atlanta, GA

*Mathematize It!*”

“Mathematize It! engages readers deeply in the mathematics content through an easy-to-use visual analogy: playing in a sandbox. The authors have found a way to make problem-solving seem like a fun task—one that is akin to something we’ve all been doing forever: playing. Their clever and applicable problem-solving model of thinking provides a structure teachers can use to support students in tackling word problems and actually enjoying the process. It’s time for you to play in the sandbox and more importantly,Hilary KreisbergMathematize It!”

Lesley University, Cambridge, MA

“The authors provide a detailed and practical guide on how to take a word problem, uncover the mathematics embedded in it, carefully consider representations, and use it all to solve the problem. The reader begins to realize that all models are not created equal. The authors’ careful attention to the nuances within mathematical relationships illustrates how mathematizing differs from answer getting, yet shows us that ideas like operation sense and computation are related. The authors’ plain language explanations empower us to leverage those relationships in order to help students become better mathematicians.”Paul Gray

Consenza & Associates, LLC

“I can’t wait to use Mathematize It! in my work with teachers and students! The excellent examples, including actual student work and teacher commentaries, highlight the complexity of the problem situations in a way that is clear and usable for classroom teachers and for those of us who support them. The focus on operation sense, understanding the role that each quantity plays, and connecting representations to problems makes this a must read for anyone helping students become successful problem-solvers. I especially appreciate the inclusion of non-whole number examples!”Julie McNamara

California State University, East Bay, Hayward, CA

“This book is a must-have for anyone who has faced the challenge of teaching problem solving. The ideas to be learned are supported with a noticeably rich collection of classroom-ready problems, examples of student thinking, and videos. Problem solving is at the center of learning and doing mathematics. And so, Mathematize It! should be at the center of every teacher’s collection of instructional resources.”John Sangiovanni

Howard County Public School System, Ellicott City, MD

*Mathematize It!*clarifies the challenges in problem solving and gives concrete steps and advice on understanding problem contexts and the mathematics involved. The examples, student work, and videos throughout the book bring ideas to life, and make their implementation doable. This is a must-read for every math teacher who desires their students to truly understand the role of mathematics in the world.”

“Finally! An answer for equipping students in making sense of word problems.Nanci N. SmithMathematize It!clarifies the challenges in problem solving and gives concrete steps and advice on understanding problem contexts and the mathematics involved. The examples, student work, and videos throughout the book bring ideas to life, and make their implementation doable. This is a must-read for every math teacher who desires their students to truly understand the role of mathematics in the world.”

Arizona Christian University, Glendale, AZ

*Mathematize It!*will effectively help develop teachers’ understanding of problem types and the pedagogical techniques necessary to teach students how to solve problems through understanding. Using comprehension strategies and varied representations are key to student success with contextualized computation. The sandbox notes, structured techniques, and videos make this book very teacher friendly. The ideas are easily transferable to the mathematics classroom.”

“Leaving behind the procedures and the gimmicks,Natalie CristMathematize It!will effectively help develop teachers’ understanding of problem types and the pedagogical techniques necessary to teach students how to solve problems through understanding. Using comprehension strategies and varied representations are key to student success with contextualized computation. The sandbox notes, structured techniques, and videos make this book very teacher friendly. The ideas are easily transferable to the mathematics classroom.”

Baltimore County Public Schools

### Review Copies

Review copies may be requested by individuals planning to purchase 10 or more copies for a team or considering a book for adoption in a higher ed course. To request a review copy, contact sales@corwin.com.

### Related Resources

- Why You Need to Teach Students to Mathematize [Lessons and Strategies]