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Mathematize It! [Grades K-2] - Book Cover Look Inside
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Mathematize It! [Grades K-2]

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

By: Kimberly Morrow-Leong, Sara Delano Moore, Linda M. Gojak

Mathematize It! shares a reasoning approach that takes the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the word problem.


Product Details
  • Grade Level: PreK-12
  • ISBN: 9781544389851
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2020
  • Page Count: 232
  • Publication date: May 06, 2020

Price: $35.95

Price: $35.95
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Description

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! 


Author(s)

Author(s)

Kimberly Morrow-Leong photo

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!

Sara Delano Moore photo

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.

Linda M. Gojak photo

Linda M. Gojak

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.
Table of Contents

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

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