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Mathematize It!
Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5

First Edition

Free Online Video Included!



September 2019 | 240 pages | Corwin

“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 Pi 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.

Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5 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 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

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


 
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

“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

“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
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 Kilday
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 Jamieson

“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! 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, Mathematize It!

Hilary Kreisberg
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
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

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ISBN: 9781506395272
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