You are here

 

For our 30th Anniversary, we're celebrating all educators' courageous work on the frontlines

Our gift to you: 30 for 30

30% discount across all our books, PLUS FREE shipping, through the end of August with code 30FOR30 at checkout

 

Mathematize It! [Grades K-2]
Share

Mathematize It! [Grades K-2]
Going Beyond Key Words to Make Sense of Word Problems, Grades K-2

First Edition


May 2020 | 232 pages | Corwin

“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
Coordinator, Elementary Mathematics
Howard County Public School System, Ellicott City, MD


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.

Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades K-2 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 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 K-2

·         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 addition and subtraction of whole numbers as well as early thinking for multiplication and division

·         Demonstrates the use of concrete manipulatives to model problems with dozens of short videos

·         Includes end-of-chapter activities and reflection questions

How can you help your students understand what is happening mathematically when solving word problems? Mathematize it! 



 
Publisher's Acknowledgements
 
Table of Contents
 
Video List
 
About the Authors
 
Introduction: Why You Need to Teach Students to Mathematize
 
Problem Solving Strategies Gone Wrong
 
What is Mathematizing? Why Is It Important
Focus on Operation Sense

 
Using Mathematical Representations

 
 
Teaching Students to Mathematize
Building your Understanding of Operations and Related Problem Situations

 
Playing in the Mathematizing Sandbox: A Problem-Solving Model

 
 
Final Words Before You Dive
 
Chapter 2: Moving From Counting to Addition & Subtraction
 
Thinking About Counting, Addition, and Subtraction
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problem

 
The Development of Courting

 
Counting or Add-To?

 
Representing Problem Situations or Representing Answers

 
 
Using Children's Literature to Explore add-To and Take From Situations
Transcribe the Action or Relationship

 
 
Moving beyond Twenty
Students and Teachers Think About the Problems

 
Representing Problem Situations Multiple Ways

 
Translating the Five Relationships: Try It Out

 
Teaching Students to Use Concrete and Pictorial Models

 
 
Key Ideas
 
Try It Out!
Identify the Principle

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 3: Add-To Problems: Locating the Change
 
Thinking About Active Addition Situations
 
Thinking About Active Addition Situations
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problems

 
Finding the Unknown, Three Story Structures

 
 
Story Structures: Implications for Teaching
 
Modeling the Active Problem Situation
Model Actions

 
Distinguish Pictures from Pictorial Representation

 
Identify Important Features

 
Creatively Meet Students' Needs

 
 
Using Children's Literature to Explore Add-To Problems
Make Predictions

 
Transcribe the Action or Relationship

 
 
Digging Deeper into Start Unknown Situations
Complicating Things: The Start Unknown Variation

 
Strategies for Making Sense of Start Unknown Problem Situation

 
Separating Computation from Operation

 
Moving to Equations

 
 
Key Ideas
 
Try It Out!
Identify the Problem Situation

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 4: Take-From Problems: Locating the Change
 
Thinking About Active Subtraction Situations
Sandbox Notes: Explore Your Thinkin

 
Students and Teachers Think About the Problems

 
Finding the Unknown, Three Story Structures

 
Story Structures: Implications for Teaching

 
Modeling the Active Problem Situation

 
 
Digging Deeper into the Start and Change Unknown Situations
Moving from Concrete to Symbolic Representation

 
 
Using Children's Literature to Explore Take-From Situations
Create Another Outcome

 
Finding the Unknown Quantity

 
 
Key Ideas
 
Try It Out!
Identify the Problem Situatoon

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 5: Part-Part-While: Understanding the Relationship
 
Thinking About Part-Part-Whole Situations
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problems

 
Defining the Part-Part-Whole Situation

 
Modeling Relationships vs. Action

 
Moving from Counters to Bar Models

 
The Special Case of Both Parts Unknown

 
Modeling Measurement Problems

 
A Note About the Commutative Property

 
 
Using Children's Literature to Explore part-Part-Whole Situations
Make Predictions

 
 
Moving to Larger Whole Numbers
Students and Teachers Think about the Problems

 
Modeling Measurement Problems

 
Writing Equations: Addition or Subtraction

 
Writing Equations: Addition or Subtraction

 
Finding the Equation in the Model

 
 
Key Ideas
 
Try It Out!
Identify the Problem Sitaution

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 6: Additive Comparison: Another Kind of Relationship
 
Thinking About Additive Comparison Situation
Students and Teachers Think about the Problems

 
Early Years Comparisons

 
Additive Comparison Situations

 
 
Building Models for Comparisons
Students and Teachers Think About the Problems

 
Making Use of Models For Thinking

 
 
The Language of Comparisons
Language Can Get Tricky

 
Building Bar Models for Comparisons

 
Problem Posing as an Instructional Strategy

 
 
Using Children's Literature to Explore Additive Comparison Situations
Create Another Outcome

 
 
Key Ideas
 
Try It Out
Identify the Problem Situation

 
Write a Problem

 
Change It Up

 
 
Reflect
 
Chapter 7: Early Multiplication and Division: Patterns and Predictions
 
Thinking about Early Multiplicative Thinking
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problem

 
Modeling Even and Odd Numbers

 
Equal Groups Problem Situation

 
Using Patterns to Identify Even and Odd Numbers

 
 
Using Children's Literature to Explore Early Multiplication
Transcribe the Action or Relationship

 
 
Bringing Another Dimension with Arrays
Recognizing Area/Array as a Problem Situation

 
Building an Understanding of Arrays as Structures

 
 
Using Children's Literature to Explore Arrays
Transcribe the Action or Relationship

 
 
Setting the Stage Division
Equipartitioning

 
Two Models for Division

 
 
Using Children's Literature to Explore Early Division
Transcribe the Action or Relationship

 
 
Key ideas
 
Try It Out
Identify the Problem Situation

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 8: Changing How You Teach Word Problems
 
Getting into the Mathematizing Sandbox
 
8 Shifts in Instruction for Building Students' Problem-Solving Skills
Do Word Problems for Sense-Making

 
Treat Context and Computation Separately

 
Create More and Varied Representations

 
Explore All the Work Operations can Do

 
Add Operation Sense Routines with a Variety of Problem Situatons

 
Listen to Students and Be Curious

 
Make Time for Mathematizing in the Sandbox

 
 
Guidance for Moving Forward: FAQ's
Finding Unexpected Mathematics in Stories

 

Free resources

Moving From Counting to Addition and Subtraction

Moving From Counting to Addition and Subtraction

This excerpt from chapter two of Mathematize It!, Grades K-2  explains how to move from counting to adding and subracting.

 

Download

Why You Need to Teach Students to Mathematize

Why You Need to Teach Students to Mathematize

This excerpt from chapter one of Mathematize It!, Grades K-2 introduces why you should teach students to mathematize.

 

Download

“One of the most important goals of K–2 math education should be developing a robust understanding of addition and subtraction that can serve as a foundation for later learning. In Mathematize It! Morrow-Leong, Moore, and Gojak help teachers transform solving word problems from an activity focused on getting answers to an activity that supports students’ understanding of the mathematical principles of the operations. Teaching
suggestions are integrated throughout the book in a manner that allows teachers to make adaptations to meet the needs of their students. This book belongs on every primary grade teachers’ bookshelf.”

Linda Levi
Director, CGI Math Teacher Learning Center, LLC

“Kim Morrow-Leong, Sara Delano Moore, and Linda Gojak have written an essential guide for teachers of grade K–2 mathematics—both those new to the field and those with many years of experience. Read this book and learn how to help students develop a deep understanding of the mathematical principles behind each operation—in other words, effectively help students learn to mathematize problem situations.”

Beth Skipper
Elementary Education Consultant, Reston, VA

“Help your students get into the messy fun of true problem solving, where the goal is to make sense of the world—not just arrive at an answer! Mathematize It! will engage you in the nuance and power of teaching through context. You’ll be surprised and delighted by the student examples, inspired by the teacher commentary, and ready to craft story problems that uncover the big ideas of your grade.”

Berkeley Everett
UCLA Mathematics Project (University of California, Los Angeles Mathematics Project)

“Mathematize It! is a must-have resource for teachers and teacher leaders. In this comprehensive resource the authors not only introduce a new verb—mathematize—to the primary teacher’s vocabulary, they also provide teachers with a ‘go-to guide’ for teaching problem solving. Features such as the Mathematizing Sandbox as a problem-solving model, the emphasis on the use of multiple representations, and the integration of children’s literature provide teachers with instructional tools to help students develop a strong operation sense.”

Latrenda Knighten
Elementary Mathematics Instructional Specialist, Baton Rouge, LA

“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 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!”

Sunil Singh
Author of Pi of Life: The Hidden Happiness of Mathematics and Math Recess: Playful Learning in an Age of Disruption

“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
National Board Certified Teacher Co-Founder & CEO, KP Mathematics

“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 Kilday
Math Interventionist and MTSS Coordinator Metcalf Elementary School, Exeter, RI Presidential Award for Excellence in Mathematics and Science Teaching Awardee, Former Member of the NCTM Board of Directors

“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 Jamieson
Past President, Virginia Council for Mathematics Supervision (VCMS), Mathematics Specialist for Virginia Council of Teacher of Mathematics (VCTM)

“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
Mathematics Coach, 2004 Presidential Award for Excellence in Mathematics and Science Teaching Awardee, Riffa Views International School, Bahrain

“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
Principal Researcher American Institutes for Research, Washington, DC

Sample Materials & Chapters

Preface (PDF)

Chapter 1 (PDF)

TOC + Video List (PDF)


Preview this book

Purchasing options

Volume Discounts Available

contact corwin

Please select a format:

ISBN: 9781544389851
$32.95  $26.95*
*Includes a 20% everyday educator discount!

For instructors