Mathematize It! [Grades K-2]
Purchase
Description
“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!
Contents
Publisher's Acknowledgements
Publisher's Acknowledgements
Table of Contents
Table of Contents
Video List
Video List
About the Authors
About the Authors
Introduction: Why You Need to Teach Students to Mathematize
Introduction: Why You Need to Teach Students to Mathematize
Problem Solving Strategies Gone Wrong
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
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
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
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
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
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
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
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
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
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
Additional materials
Description
“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!
Contents
Publisher's Acknowledgements
Publisher's Acknowledgements
Table of Contents
Table of Contents
Video List
Video List
About the Authors
About the Authors
Introduction: Why You Need to Teach Students to Mathematize
Introduction: Why You Need to Teach Students to Mathematize
Problem Solving Strategies Gone Wrong
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
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
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
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
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
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
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
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
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
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
Additional materials
Reviews
Mathematize It! [Grades K-2]
Going Beyond Key Words to Make Sense of Word Problems, Grades K-2
April 2020 | 232 pages | Corwin
| Format | Published Date | ISBN | Price |
|---|---|---|---|
| Paperback | 01/02/2026 | 9781544389851 | $37.95 |
| Lifetime | 01/02/2026 | 9781071811313 | $35.00 |
“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!
Table Of Contents:
- 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