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Kimberly Morrow-Leong & Sara Delano Moore 
Mathematize It! [Grades K-2] 
Going Beyond Key Words to Make Sense of Word Problems, Grades K-2

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‘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 San Giovanni
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! 



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Содержание

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

Об авторе

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.
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язык английский ● Формат PDF ● страницы 232 ● ISBN 9781071811320 ● Размер файла 16.3 MB ● издатель SAGE Publications ● город Thousand Oaks ● Страна US ● опубликованный 2020 ● Издание 1 ● Загружаемые 24 месяцы ● валюта EUR ● Код товара 7437637 ● Защита от копирования Adobe DRM
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