Introduction to Hands-On Mathematics1

• Program Introduction 1
• Program Principles 1
• The Big Ideas of Mathematics 1
• Hands-On Mathematics Learning Outcomes 5
• Program Implementation 8
• Classroom Environment 9
• Timelines 9
• Classroom Management 9
• Planning Guidelines 10

Assessment 13

• The Hands-On Mathematics Assessment Plan 13

Mental Math 26

• Introduction to Mental Math – Grade 3 26
• Grade 3 Mental Math Strategies 28

Websites 53

Module 1: Patterns and Relations 57

• Books for Children 58
• Introduction 60
• 1 Ongoing Patterns and Relations Activities 61
• 2 Repeating Linear Patterns 65
• 3 Increasing and Decreasing Patterns 72
• 4 Number-Sequence Patterns 78
• 5 Patterns in Addition and Subtraction 86
• 6 Patterns in Multiplication 91
• 7 Patterns in Structures 97
• 8 Addition Equations Involving Symbols 103
• 9 Subtraction Equations Involving Symbols 107
• Problem-Solving Reproducible: Patterns and Relations 108
• References for Teachers 110

Module 2: Statistics and Probability 113

• Books for Children 114
• Introduction 115
• 1 Literature Connections 116
• 2 TV Time 120
• 3 Classroom Carnival 125
• 4 Looking at Names 130
• 5 The Typical Grade Three Student 133
• 6 Weather or Not... 137
• 7 Symbolic Graphs 143
• 8 A Year in Time 146
• 9 Line Plots 149
• Problem-Solving Reproducible: Statistics and Probability 151
• References for Teachers 153

Module 3: Shape and Space 155

• Books for Children (Measurement) 156
• Books for Children (3-D Objects and 2-D Shapes) 157
• Introduction 158
• 1 Measuring the Passage of Time 159
• 2 Measuring the Passage of Time in Standard Units 162
• 3 Days in a Month, Months of the Year 166
• 4 Introducing Standard Measurement: Metre and Centimetre 171
• 5 Measuring Objects by Height, Length, and Width 177
• 6 Comparing and Ordering Objects by Mass 180
• 7 Investigating Mass 184
• 8 Perimeter 189
• 9 More About Perimeter 192
• 10 Exploring Two-Dimensional Shapes 196
• 11 Regular and Irregular Polygons 203
• 12 Identifying the Faces of Geometric Solids (Three-Dimensional Objects) 207
• 13 Identifying, Comparing, and Contrasting Geometric Solids 211
• 14 Investigating Nets 215
• 15 Skeletons and Pictorial Representations of Three-Dimensional Solids 219
• Problem-Solving Reproducible: Shape and Space 222
• References for Teachers 223

Module 4: Number Concepts 225

• Books for Children 226
• Introduction 227
• 1 Personal Numbers 228
• 2 Rote Counting to 1 000 231
• 3 Number Paths and Number Charts 236
• 4 Skip Counting 245
• 5 Skip Counting by 25s 249
• 6 How Much is 1 000? 252
• 7 Walk to 1 000 257
• 8 One Hundred Pennies 260
• 9 $1 000 Budget 263
• 10 Doubling 266
• 11 Numeral and Number-Word Chains 269
• 12 Fractions 273
• 13 More Fractions: Halves 276
• 14 More Fractions: Fourths 279
• 15 More Fractions: Thirds 281
• 16 Still More Fractions 282
• 17 Comparing Fractions 286
• Problem-Solving Reproducible: Number Concepts 288
• References for Teachers 290

Module 5: Number Operations 291

• Books for Children 292
• Introduction 294
• 1 Addition and Subtraction Facts to 18 295
• 2 More Addition and Subtraction Facts 298
• 3 One- and Two-Digit Addition and Subtraction 302
• 4 Addition and Subtraction with a Calculator 306
• 5 Addition of Hundreds 308
• 6 Compatible Numbers 311
• 7 Addition with Three-Digit Numbers 316
• 8 More Addition with Three-Digit Numbers 319
• 9 Solving Multiple-Step Problems 322
• 10 Subtraction with Three-Digit Numbers 323
• 11 More Subtraction with Three-Digit Numbers 325
• 12 Choosing a Method for Solving Problems 329
• 13 Exploring Multiplication – Part One 331
• 14 Exploring Multiplication – Part Two 333
• 15 Exploring Multiplication – Part Three 335
• 16 Exploring Multiplication – Part Four 339
• 17 More Multiplication 341
• 18 Commutative Property of Multiplication 345
• 19 Multiplying by 1 and by 0 348
• 20 Multiplication Facts 351
• 21 Exploring Division – Part One 353
• 22 Exploring Division – Part Two 354
• 23 Exploring Division – Part Three 355
• 24 The Inverse Relationship Between Multiplication and Division 358
• Problem-Solving Reproducible: Number Operations 362
• References for Teachers 364

Access Digital Resources 365