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Teaching Mathematics in Diverse Classrooms for Grades 5 - 8


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Table of Contents

vii About the Au thors xiii Preface xv 1 I nstructional Activities: T he Building Blocks for Effective Instruction 1 Instructional Activities 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 Flexible Use of Activities and Materials 5 Exercises and Activities 5 References and Related Readings 6 Websites 7 2 Prior Student Knowledge: T he Basis for Learning and Instruction 8 Building on Prior Knowledge 8 Assessing Prior Knowledge 9 Remediation of Prerequisite Knowledge 9 Additional Classroom Scenarios 10 Exercises and Activities 11 contents A01_TUCK7266_01_SE_FM.indd 7 8/1/12 2:55 PM viii C o n t e n t s 3 L ess on Design: Planning for Effective Instruction and Maximum Learning 12 Combining Activities into a Lesson 12 What Is a Lesson? 12 A Traditional Lesson Plan 13 The Nature of Standard Traditional Lessons 15 Adapting Lessons for Diverse Learning Needs 15 A Lesson Adapted for Diverse Learners 18 The Planning Process and "Official" Lesson Plans 21 The Planning Process and Teaching Notes 21 Exercises and Activities 21 References and Related Readings 22 Websites 22 4 C ompu tation with Whole Nu mbers: A Review of Addition and Subtraction 23 Three Important Considerations 23 Number Sense 23 Foundations of Algebra 24 Basic Concepts and Skills 24 An Overview of the Development of Computation 24 The Meaning of the Operation 24 The Basic Facts 24 The Algorithm(s) 25 Review and Remediation of Whole Number Addition 26 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 Review and Remediation of Whole Number Subtraction 37 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 Teaching Problem Solving Using Addition and Subtraction 41 Translate Word Problems into Situations 41 Exercises and Activities 42 A01_TUCK7266_01_SE_FM.indd 8 8/1/12 2:55 PM C o n t e n t s ix References and Related Readings 44 Websites 44 5 C ompu tation with Whole Nu mbers: D evelopment of Multiplication and Division 45 Teaching Multiplication of Whole Numbers 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 Teaching Division of Whole Numbers 77 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 Teaching Problem Solving Using Multiplication and of Division 99 Exercises and Activities 99 References and Related Readings 101 Websites 101 6 Fractions: W orking with Units Smaller Than One 102 Defining Fractions 102 Three Sides of Fractions 103 Fractional Units 104 Beyond Unit Fractions 106 Fractions of a Set 107 Equivalent Fractions 108 Using the Laboratory Approach 110 Comparison of Fractions 112 Adding Fractions 116 Subtracting Fractions 117 Least Common Denominators 118 Addition and Subtraction Activities 119 Improper Fractions and Mixed Numbers 121 Multiplying Fractions 123 Dividing Fractions 127 Multiplication and Division Activities 131 Adapting a Lesson on Fractions 135 A01_TUCK7266_01_SE_FM.indd 9 8/1/12 2:55 PM x C o n t e n t s Solving Problems Using Fractions 137 Problem-Solving Strategies 138 Exercises and Activities 140 References and Related Readings 141 Websites 141 7 D ecimals and percents: W orking with Base-Ten Units Smaller Than One and Using Hundredths as a Common Denominator 142 Decimals 142 Place Value for Decimals 144 Comparing Decimals 149 Adding and Subtracting Decimals 152 Adding and Subtracting Activities 154 Multiplying Decimals 156 Dividing Decimals 161 Multiplication and Division Activities 163 Fraction Comparison Revisited 167 Defining Percent 168 Adapting a Lesson on Decimals 168 Using Decimals to Solve Problems 171 Exercises and Activities 173 References and Related Readings 174 Websites 174 8 M easu rement: A ssigning a Number to a Quantity 175 Measurement and Geometry 175 Defining Measurement 175 Measuring Length 176 Measuring Area 178 The Big Idea for Developing Area Formulas 182 Measuring Volume 187 Measuring Angles 195 Measuring with Indirect Units 198 Measuring Weight 198 Measuring Temperature 198 Measuring Value 198 Adapting a Lesson on Volume 199 Using Measurement to Solve Problems 201 Exercises and Activities 203 References and Related Readings 204 Websites 204 A01_TUCK7266_01_SE_FM.indd 10 8/1/12 2:55 PM C o n t e n t s xi 9 Geometry: Using the Big Ideas to Study Geometric Shapes 205 The Big Ideas of Middle School Geometry 205 Straightness 206 Congruence 206 Similarity 207 Parallelism 208 Perpendicularity 209 Symmetry 210 Using the Big Ideas to Study Geometric Shapes 210 Rectangles in Middle School 210 Circles in Middle School 211 Angles in the Fifth through Eighth Grades 212 Prisms in Middle School 213 Adapting a Geometry Lesson 215 Using Geometry to Solve Problems 216 Exercises and Activities 218 References and Related Readings 219 Websites 219 10 D ata Analysis And Probability: G etting Information from Data and Measuring Likelihood 220 Data Analysis and Probability: Two Distinct but Related Areas of Mathematics 220 Data Analysis 221 Emphasizing the Big Ideas of Data Analysis 221 Adapting a Data Analysis Lesson 226 Using Data Analysis to Solve Problems 231 Probability 231 Emphasizing the Big Ideas of Probability 231 Adapting a Probability Lesson 237 Using Probability to Solve Problems 240 Exercises and Activities 241 References and Related Readings 242 Websites 242 11 Foundations of Algebra: Properties of Operations on Integers, Rational Numbers, and Irrational Numbers 243 Emphasizing the Big Ideas of Algebra 243 The Closure Property 244 The Associative Property 245 A01_TUCK7266_01_SE_FM.indd 11 8/1/12 2:55 PM 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 Computation with Integers 248 The Order of Operations 253 Evaluating Algebraic Expressions 255 Using Properties of Equality to Solve Equations 255 Exponents 257 Exercises and Activities 261 References and Related Readings 262 Websites 262 12 Eff ective Practice: G ames and Activities for Practice and Fun 263 Matching Activities 264 Ordering Activities 271 Answer or Example Construction Activities 275 Summary 278 References and Related Readings 278 A ctivities to Take to Your Class room 279 I ndex 281

About the Author

Benny F. Tucker earned his Ph.D. at the University of Illinois in 1975. He has taught mathematics in a variety of settings at every level, kindergarten through graduate school. Dr. Tucker 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. In addition 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. 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.


Relevant and useful information related to conceptualizing and practicing specific math skills. Beginning teachers often fall 'victim' to using published materials 'as is' and this book provides repeated examples of how teachers can adjust the materials that are provided to them by district-selected curricula. -Rebecca Swanson Gehrke, Professor, Arizona State University, Tempe, AZ

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