Ann Haltom Singleton is Associate Dean of the School of Education at Union University in Jackson Tennessee. Her research areas include leadership development and mathematics instruction, especially in inclusive settings. She has contributed to numerous articles, has made over 30 national presentations, and was recognized as the Union University 2003 Faculty of the Year. She earned her Ed.D in Special Education from the University of Memphis.

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

Drs. Tucker, Singleton, and Weaver have published numerous articles on teaching mathematics.

About the Au thors xiii

Preface xv

1 I nstructional Activities:

T he Building Blocks for Effective Instruction 1

Exploratory Developmental Activities 2

Consolidating Developmental Activities 2

Think-Time Practice Activities 3

Speed-Drill Practice Activities 3

Classroom Applications 3

Real-World Problems 4

2 Prior Student Knowledge:

T he Basis for Learning and Instruction 8

Assessing Prior Knowledge 9

Remediation of Prerequisite Knowledge 9

Additional Classroom Scenarios 10

contents

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viii C o n t e n t s

3 L ess on Design:

Planning for Effective Instruction and Maximum Learning 12

What Is a Lesson? 12

A Traditional Lesson Plan 13

A Lesson Adapted for Diverse Learners 18

4 C ompu tation with Whole Nu mbers:

A Review of Addition and Subtraction 23

Number Sense 23

Foundations of Algebra 24

Basic Concepts and Skills 24

The Meaning of the Operation 24

The Basic Facts 24

The Algorithm(s) 25

Relationships among the Addition Facts 26

Remediation of the Easy Basic Addition Facts 28

Remediation of the Hard Basic Addition Facts 29

Understanding the Addition Algorithm 31

The First Big Idea 33

The Second Big Idea 35

Use of the Developmental Sequence to Remediate Addition 35

Remediation of Student Difficulties with Whole Number Addition 36

Developing the Meaning of Subtraction 37

Remediation of the Easy Basic Subtraction Facts 37

Remediation of the Hard Basic Subtraction Facts 38

Remediation of the Subtraction Algorithm 39

The Big Ideas for the Subtraction Algorithm 39

Use of the Developmental Sequence for Remediation of Subtraction 40

Remediation of Student Difficulties with Whole Number Subtraction 41

Translate Word Problems into Situations 41

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C o n t e n t s ix

5 C ompu tation with Whole Nu mbers:

D evelopment of Multiplication and Division 45

Developing the Meaning of Multiplication 45

Developing the Easy Basic Multiplication Facts 48

Developing the Hard Basic Multiplication Facts 53

Teaching the Multiplication Algorithm 58

Use of the Developmental Sequence for Remediation of Multiplication 70

Remediation of Multiplication 71

The Meaning of Division 77

Developing the Easy Basic Division Facts 80

Developing the Hard Basic Division Facts 82

Remediating the Division Algorithm 84

Use of the Developmental Sequence for Remediation of Division 96

Remediation of Division 96

Adapting a Division Lesson 96

6 Fractions:

W orking with Units Smaller Than One 102

Three Sides of Fractions 103

Beyond Unit Fractions 106

Adapting a Lesson on Fractions 135

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x C o n t e n t s

Problem-Solving Strategies 138

7 D ecimals and percents:

W orking with Base-Ten Units Smaller Than One and Using Hundredths

as a Common Denominator 142

Adding and Subtracting Activities 154

Adapting a Lesson on Decimals 168

8 M easu rement:

A ssigning a Number to a Quantity 175

The Big Idea for Developing Area Formulas 182

Adapting a Lesson on Volume 199

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C o n t e n t s xi

9 Geometry:

Using the Big Ideas to Study Geometric Shapes 205

Straightness 206

Congruence 206

Similarity 207

Parallelism 208

Perpendicularity 209

Symmetry 210

Rectangles in Middle School 210

Circles in Middle School 211

Angles in the Fifth through Eighth Grades 212

Prisms in Middle School 213

10 D ata Analysis And Probability:

G etting Information from Data and Measuring Likelihood 220

Emphasizing the Big Ideas of Data Analysis 221

Adapting a Data Analysis Lesson 226

Using Data Analysis to Solve Problems 231

Emphasizing the Big Ideas of Probability 231

Adapting a Probability Lesson 237

Using Probability to Solve Problems 240

11 Foundations of Algebra:

Properties of Operations on Integers, Rational Numbers,

and Irrational Numbers 243

The Closure Property 244

The Associative Property 245

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xii C o n t e n t s

The Commutative Property 246

The Distributive Property 246

The Identity Elements 247

The Inverse Elements 247

The Order of Operations 253

Evaluating Algebraic Expressions 255

12 Eff ective Practice:

G ames and Activities for Practice and Fun 263

A ctivities to Take to Your Class room 279

I ndex 281

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