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

About the Author

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 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!

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, 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.

Reviews

"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*

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*

"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*

"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*

"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*

"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*

"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*

"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*

"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*

"Finally! An answer for equipping students in making sense of word problems. 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."
*Nanci N. Smith*

"Leaving behind the procedures and the gimmicks, 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."
*Natalie Crist*