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Teaching Mathematics in Diverse Classrooms for Grades K-4: Practical Strategies and Activities That Promote Understanding and Problem Solving Ability

By Benny F. Tucker, Ann H. Singleton, Terry L. Weaver

Published by Pearson

Published Date: May 23, 2012


Teaching Mathematics in Diverse Classrooms for Grades K-4 emphasizes that effective mathematics teaching promotes understanding which provides a sound basis for skill development, all resulting in better learning retention. In a user-friendly format, presenting language consistent with the language used to teach children, the authors of this resource stress that when mathematical information is connected to what students already know about mathematics, it is easier for them to learn and recall. To that end they present the development of mathematical content based on a small number of easy-to-understand and easy-to-teach “big ideas.”

Table of Contents

v >

About the authors x

Preface xi

1 Instructional Activities:

T he Building Blocks for Effective Instruction 1

What Are the Students Learning? 1

Developmental Activities 2

Exploratory Developmental Activities 2

Consolidating Developmental Activities 2

Practice Activities 2

Think-Time Practice Activities 3

Speed-Drill Practice Activities 3

Application Activities 3

Classroom Applications 3

Real-World Problems 4

Assessment Activities 4

Varied Assessment Methods 4

Monitoring and Assessment 4

Level of Involvement 6

Flexible Use of Activities and Materials 7

Exercises and Activities 7

References and Related Readings 8

Websites 9

2 Less on Design:

C reating Lessons That Meet the Needs of a Diverse Classroom 10

Combining Activities into a Lesson 10

What Is a Lesson? 10

A Traditional Lesson Plan 11

The Nature of Standard Traditional Lessons 13

Adapting Lessons for Diverse Learning Needs 13

A Lesson Adapted for Diverse Learners 16

Adapting Another Lesson 19

The Planning Process and “Official” Lesson Plans 21


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vi C o n t e n t s

The Planning Process and Teaching Notes 22

Exercises and Activities 22

References and Related Readings 23

Websites 24

3 Beginnings:

M athematics Learning in Early Childhood 25

A Common Misconception 25

About Young Children 25

Teaching Classification 27

Pattern Recognition 28

Teaching Comparison and Seriation 29

Comparison 29

Seriation 32

Matching and Prenumber Comparisons 33

Matching and Prenumber Seriation 33

The Beginning of Geometric Concepts: Relative Position 34

A Revised Lesson 37

Exercises and Activities 40

References and Related Readings 40

Websites 41

4 Whole Nu mbers and Nu meration:

N aming and Writing Quantity 42

Number Sense 42

Foundations of Algebra 43

Building on What Children Already Know 43

The Big Picture 45

Development of Numbers and Numeration 45

One-Digit Numbers 46

Two-Digit Numbers 51

Three or More Digits 56

Rounding Numbers 59

Adapting a Lesson 61

Adapting the Lesson for a Diverse Group of Students 61

Exercises and Activities 64

References and Related Readings 64

Websites 64

5 Adding and Subtracting Whole Nu mbers:

C ombining and Separating Quantities 65

An Overview of the Development of Computation 65

The Meaning of the Operation 65

The Basic Facts 66

The Algorithm(s) 66

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C o n t e n t s vii

Teaching Addition of Whole Numbers 67

Developing the Meaning of Addition 67

Developing the Easy Basic Addition Facts 69

Activities for Exploring Relationships 73

Developing the Hard Basic Addition Facts 76

Teaching the Addition Algorithm 82

Summary of the Developmental Sequence for Addition 85

Teaching Subtraction of Whole Numbers 86

Developing the Meaning of Subtraction 86

Developing the Easy Basic Subtraction Facts 87

Developing the Hard Basic Subtraction Facts 90

Teaching the Subtraction Algorithm 92

Summary of the Developmental Sequence for Subtraction 93

Adapting a Lesson 94

Teaching Problem Solving Using Addition and Subtraction 96

Exercises and Activities 99

References and Related Readings 100

Websites 100

6 Mu ltiplying and Dividing Whole Nu mbers:

C ombining Equal-Sized Groups and Separating Quantities

into Equal-Sized Groups 101

Teaching Multiplication of Whole Numbers 101

Developing the Meaning of Multiplication 101

Developing the Easy Basic Multiplication Facts 103

Developing the Hard Basic Multiplication Facts 107

Teaching the Multiplication Algorithm 111

Summary of the Developmental Sequence for Multiplication 121

Adapting a Multiplication Lesson 121

Teaching Division of Whole Numbers 127

Developing the Meaning of Division 127

Developing the Easy Basic Division Facts 129

Developing the Hard Basic Division Facts 131

Teaching the Division Algorithm 133

Adapting a Division Lesson 144

Teaching Problem Solving Using Multiplication and Division 147

Exercises and Activities 147

References and Related Readings 148

Websites 149

7 Fractions:

Working with Units Smaller Than One 150

Defining Fractions 150

Three Sides of Fractions 151

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viii C o n t e n t s

Fractional Units 152

Beyond Unit Fractions 154

Fractions of a Set 155

Equivalent Fractions 156

Using the Laboratory Approach 158

Comparison of Fractions 159

Adding Fractions 161

Subtracting Fractions 163

Addition and Subtraction Activities 163

Improper Fractions and Mixed Numbers 165

Adapting a Lesson on Fractions 167

Solving Problems Using Fractions 170

Exercises and Activities 171

References and Related Readings 171

Websites 171

8 Decimals:

Working with Base-Ten Units Smaller Than One 172

Decimals 172

Place Value for Decimals 174

Comparing Decimals 178

Adding and Subtracting Decimals 181

Adapting a Lesson on Decimals 184

Using Decimals to Solve Problems 187

Exercises and Activities 187

References and Related Readings 188

Websites 188

9 Measu rement:

A ssigning a Number to a Quantity 189

Measurement and Geometry 189

Defining Measurement 189

Measuring Length 190

Teaching Area Measurement 199

Teaching Volume Measurement 204

Measuring Time 208

Measuring Weight 210

Measuring Temperature 210

Measuring Value 210

Adapting a Lesson on Volume 211

Using Measurement to Solve Problems 214

Exercises and Activities 214

References and Related Readings 215

Websites 215

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C o n t e n t s ix

10 Geometry:

L earning the Names and Characteristics of Shapes 216

The Big Ideas of Elementary School Geometry 216

Straightness 217

Congruence 217

Similarity 218

Parallelism 218

Perpendicularity 219

Symmetry 220

Using the Big Ideas to Study Geometric Shapes 220

Rectangles in Elementary School 220

Circles in Elementary School 225

Angles in Elementary School 228

Prisms in Elementary School 230

Adapting a Geometry Lesson 231

Exercises and Activities 235

References and Related Readings 236

Websites 236

11 Data Analysis and Probability:

G etting Information from Data and Measuring Likelihood 237

Data Analysis and Probability–Two Distinct but Related Areas of Mathematics 237

Data Analysis 238

Emphasizing the Big Ideas of Data Analysis 238

From Exploratory Experiences toward Conceptual Understanding:

A Typical K—4 Development of Data Analysis 238

Adapting a Data Analysis Lesson 245

Using Data Analysis to Solve Problems 250

Probability 250

Emphasizing the Big Ideas of Probability 250

From Exploratory Experiences toward Conceptual Understanding:

A Typical K—4 Development of Probability 251

Using Probability to Solve Problems 256

Exercises and Activities 256

References and Related Readings 257

Websites 257

A ctivities to Take to Your Class room 258

I ndex 260

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about the authors

Benny F. Tucker earned his Ph.D. at the University of Illinois in 1975. He has authored

or co-authored more than 50 books, on topics ranging from teaching methods for elementary

school mathematics to the use of instructional activities in the mathematics

classroom. He has authored or co-authored more than 20 articles in professional journals

and has made more than 30 presentations at professional conferences.

Ann Haltom Singleton is Associate Dean of the School of Education at Union University

in Jackson Tennessee. She earned her Ed.D. in Special Education from the University

of Memphis. Her research areas include leadership development and mathematics

instruction, especially in inclusive settings. She has contributed to numerous articles and

has made over 30 national presentations. She was recognized as the Union University

2003 Faculty of the Year.

Terry L. Weaver honed his teaching skills in the Miami-Dade County School System.

He received his Ph.D. in Special Education from George Peabody College for Teachers

at Vanderbilt University. Dr. Weaver then shared his teaching skills at Carson-Newman

College and Union University where he continues to teach. Dr. Weaver has served as an

item writer for and participated in the revalidation of the Praxis II Specialty Area Test

in SE (Core Knowledge). He is a co-author of Teaching Mathematics to All Children:

Designing and Adapting Instruction to Meet the Needs of Diverse Learners, has presented

on differentiated instruction and assessment, universal design, inclusion, and adapting

instruction for diverse learners, and recently lead the revision of a chapter on mathematics

in Vaughn’s and Bos’s Strategies for Teaching Students with Learning and Behavior



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Why This Book?

The diversity of students in K—4 classrooms is extensive. The children in a typical classroom

are diverse in gender, diverse in race and ethnicity, and diverse in religion and

culture. They are diverse in ability, diverse in interests, and diverse in preferred learning

styles. And they are diverse in family background, and diverse with respect to resources

in the home such as books and technology. In the face of such diversity, how can the

teacher expect to plan for effective instruction?

Although teachers must certainly be aware of student diversity and the need to

accommodate that diversity, it is perhaps more important for K—4 teachers to be aware of

the ways in which their students are alike. For example, almost universally, children are


learners. It is natural for them to be active and move around. They love classroom

activities that allow (even require) them to be energetic and animated. Children

are also naturally inquisitive. They are interested in what, why, and how. It is the nature

of children to be curious about things. They like to talk to one another, to exchange

ideas, and to discuss the things that they are experiencing and learning. Children are

concrete learners. They enjoy handling things, seeing how things are related. They

like to understand.

In this text, we provide an approach to the planning and teaching of K—4 mathematics

that is based on the nature of children. We believe that the teaching suggestions in

this text will help teachers be more effective as they plan and teach mathematics in diverse

classrooms, grades K—4.

Structure of the Book

The book begins with two introductory chapters that provide a basic understanding

of instructional activities and lesson planning. Then there are nine chapters devoted to

teaching the content that most commonly appears in K—4 mathematics textbooks. We

do not attempt to provide comprehensive coverage of every topic that might appear in

a K—4 textbook. Rather, our intent is to emphasize a way of teaching effectively that

will result in learning, understanding, retention of important concepts and skills, and

an ability to apply those concepts and skills to solve problems. Important to that way of

teaching is effective planning. Therefore, we have made planning for effective teaching

an important part of this text.