Tom Bassarear
Cengage Learning | 2011 - 5ª edição | 317 páginas | rar - pdf | 3,9 Mb
link (password: matav)
This manual contains open-ended activities for the student to practice and apply the knowledge they learn from the main text. When students begin teaching, they can use the activities as models in their own classrooms.
CONTENTS
Preface xi
1 Foundations for Learning Mathematics 1
EXPLORATION 1.1 Patterns, Problem Solving, and Representations 2
EXPLORATION 1.2 Patterns in Multiplication 5
EXPLORATION 1.3 Real-life Problems 8
EXPLORATION 1.4 Patterns and Proof 9
EXPLORATION 1.5 Magic Squares 12
EXPLORATION 1.6 Magic Triangle Puzzles 17
2 Fundamental Concepts 21
SECTION 2.1 Exploring Sets 21
EXPLORATION 2.1 Understanding Venn Diagrams 22
EXPLORATION 2.2 Gathering and Interpreting Data 23
SECTION 2.2 Exploring Algebraic Thinking 24
EXPLORATION 2.3 Exploring Equivalence 24
EXPLORATION 2.4 Relationships Between Variables 27
EXPLORATION 2.5 Connecting Graphs and Words 29
EXPLORATION 2.6 Growth Patterns 32
SECTION 2.3 Exploring Numeration 37
EXPLORATION 2.7 Alphabitia 37
EXPLORATION 2.8 Different Bases 43
EXPLORATION 2.9 A Place Value Game 46
EXPLORATION 2.10 How Big Is Big? 47
3 The Four Fundamental Operations of Arithmetic 49
EXPLORATION 3.1 Computation in Alphabitia 49
SECTION 3.1 Exploring Addition 51
EXPLORATION 3.2 Mental Addition 51
EXPLORATION 3.3 Addition: Children’s Algorithms and Alternative Algorithms 52
EXPLORATION 3.4 Addition and Number Sense 54
SECTION 3.2 Exploring Subtraction 55
EXPLORATION 3.5 Mental Subtraction 55
EXPLORATION 3.6 Subtraction: Children’s Algorithms and Alternative Algorithms 56
EXPLORATION 3.7 Subtraction and Number Sense 58
SECTION 3.3 Exploring Multiplication 59
EXPLORATION 3.8 Patterns in the Multiplication Table 59
EXPLORATION 3.9 Mental Multiplication 63
EXPLORATION 3.10 Differences Between Multiplication and Addition 64
EXPLORATION 3.11 Cluster or String Problems 65
EXPLORATION 3.12 Understanding the Standard Multiplication Algorithm 66
EXPLORATION 3.13 Alternative Algorithms for Multiplication 67
EXPLORATION 3.14 Multiplication and Number Sense 69
SECTION 3.4 Exploring Division 70
EXPLORATION 3.15 Different Models of Division 70
EXPLORATION 3.16 Understanding Division Computation 71
EXPLORATION 3.17 Mental Division 72
EXPLORATION 3.18 Dealing with Remainders 73
EXPLORATION 3.19 The Scaffolding Algorithm 74
EXPLORATION 3.20 Understanding the Standard Algorithm 75
EXPLORATION 3.21 Division and Number Sense 76
EXPLORATION 3.22 Developing Operation Sense 77
EXPLORATION 3.23 Operation Sense in Games 78
EXPLORATION 3.24 How Many Stars? 79
4 Number Theory 81
SECTION 4.1 Exploring Divisibility and Related Concepts 81
EXPLORATION 4.1 Taxman 82
SECTION 4.2 Exploring Prime and Composite Numbers 85
EXPLORATION 4.2 Factors 85
EXPLORATION 4.3 Finding All Factors of a Number 91
SECTION 4.3 Exploring Greatest Common Factor and Least Common Multiple 92
EXPLORATION 4.4 African Sand Drawings 92
EXPLORATION 4.5 Cycles 94
5 Extending the Number System 97
SECTION 5.1 Exploring Integers 97
EXPLORATION 5.1 Understanding Integer Addition 98
EXPLORATION 5.2 Understanding Integer Subtraction 99
EXPLORATION 5.3 Understanding Integer Multiplication 100
EXPLORATION 5.4 Understanding Integer Division 101
SECTION 5.2 Exploring Fractions and Rational Numbers 102
EXPLORATION 5.5 Making Manipulatives 102
EXPLORATION 5.6 Sharing Brownies 103
EXPLORATION 5.7 Partitioning 104
EXPLORATION 5.8 Equivalent Fractions 109
EXPLORATION 5.9 Developing Fraction Sense 110
SECTION 5.3 Exploring Operations with Fractions 111
EXPLORATION 5.10 Ordering Fractions 111
EXPLORATION 5.11 Adding Fractions 115
EXPLORATION 5.12 Making Sense of Wholes and Units 116
EXPLORATION 5.13 Multiplying Fractions 118
EXPLORATION 5.14 An Alternative Algorithm for Dividing Fractions 119
EXPLORATION 5.15 Remainders 120
EXPLORATION 5.16 Meanings of Operations with Fractions 121
EXPLORATION 5.17 Developing Operation Sense 122
SECTION 5.4 Exploring Beyond Integers and Fractions: Decimals, Exponents,
and Real Numbers 124
EXPLORATION 5.18 Decimals and Base Ten Blocks 124
EXPLORATION 5.19 Exploring Decimal Algorithms 125
EXPLORATION 5.20 Patterns in Repeating Decimals 126
EXPLORATION 5.21 Developing Decimal Sense 128
EXPLORATION 5.22 The Right Bucket: A Decimal Game 130
EXPLORATION 5.23 Target: A Decimal Game 133
EXPLORATION 5.24 A Real-life Problem in College 137
6 Proportional Reasoning 139
SECTION 6.1 Exploring Ratio and Proportion 139
EXPLORATION 6.1 Which Ramp Is Steeper? 140
EXPLORATION 6.2 Using Qualitative Reasoning to Develop Proportional Reasoning 141
EXPLORATION 6.3 Using Proportional Reasoning to Interpret Data 142
EXPLORATION 6.4 Unit Pricing and Buying Generic 145
EXPLORATION 6.5 Proportional Reasoning and Functions 146
SECTION 6.2 Exploring Percents 147
EXPLORATION 6.6 Percents 147
EXPLORATION 6.7 Do You Get What You Pay For? 149
EXPLORATION 6.8 Reducing, Enlarging, and Percents 150
EXPLORATION 6.9 Mice on Two Islands 152
7 Uncertainty: Data and Chance 153
SECTION 7.1 The Process of Collecting and Analyzing Data 153
EXPLORATION 7.1 Population Growth and Density 154
EXPLORATION 7.2 Collecting Data to Understand a Population: Typical Person 155
EXPLORATION 7.3 Exploring the Concept of Average 156
EXPLORATION 7.4 Explorations for Gathering and Analyzing Data 159
SECTION 7.2 Going Beyond the Basics 161
EXPLORATION 7.5 How Many Drops of Water Will a Penny Hold? 161
EXPLORATION 7.6 How Accurate Can You Get the Whirlybird to Be? 162
EXPLORATION 7.7 Exploring Relationships Among Body Ratios 163
EXPLORATION 7.8 Collecting Data to Make a Decision:
What Container Best Keeps Coffee Hot? 165
EXPLORATION 7.9 Explorations for Comparing Two Sets of Data 166
EXPLORATION 7.10 Collecting Data of Your Choice 169
EXPLORATION 7.11 Designing and Conducting a Survey 170
SECTION 7.3 Exploring Concepts Related to Chance 171
EXPLORATION 7.12 Heads and Tails and Probability 171
EXPLORATION 7.13 What Is the Probability of Having the Same Number of Boys and Girls? 172
EXPLORATION 7.14 What Is the Probability of Rolling Three Doubles in a Row? 173
EXPLORATION 7.15 What’s in the Bag? 174
EXPLORATION 7.16 How Many Boxes Will You Probably Have to Buy? 176
EXPLORATION 7.17 More Simulations 177
EXPLORATION 7.18 Using Sampling to Estimate a Whole Population 178
EXPLORATION 7.19 Fair Games 179
SECTION 7.4 Exploring Counting and Chance 181
EXPLORATION 7.20 License Plates 181
EXPLORATION 7.21 Native American Games 182
8 Geometry as Shape 185
EXPLORATION 8.1 Geoboard Explorations 185
EXPLORATION 8.2 Tangram Explorations 191
EXPLORATION 8.3 Polyomino Explorations 197
SECTION 8.1 Exploring Basic Concepts of Geometry 203
EXPLORATION 8.4 Manhole Covers 203
EXPLORATION 8.5 Proof 207
EXPLORATION 8.6 Using Geometric Knowledge to Make Angles 208
SECTION 8.2 Exploring Two-Dimensional Figures 209
EXPLORATION 8.7 “What Do You See?” and “Make It from Memory” 209
EXPLORATION 8.8 Making Shapes from Folding a Square 213
EXPLORATION 8.9 Definitions and Language 214
EXPLORATION 8.10 The Sum of the Angles in a Polygon 216
EXPLORATION 8.11 Congruence 217
EXPLORATION 8.12 Polygons with Various Attributes 219
EXPLORATION 8.13 Polygons and Relationships 221
SECTION 8.3 Exploring Three-Dimensional Figures 225
EXPLORATION 8.14 Exploring Polyhedra 225
EXPLORATION 8.15 Relationships Among Polyhedra 227
EXPLORATION 8.16 Regular Polyhedra 228
EXPLORATION 8.17 Block Buildings 229
EXPLORATION 8.18 Cross Sections 233
EXPLORATION 8.19 Nets 234
9 Geometry as Transforming Shapes 241
EXPLORATION 9.1 Geoboard Explorations 241
EXPLORATION 9.2 Tangram Explorations 251
EXPLORATION 9.3 Polyomino Explorations 252
SECTION 9.1 Exploring Translations, Reflections, and Rotations 256
EXPLORATION 9.4 Reflections (Flips) 256
EXPLORATION 9.5 Paper Folding 263
EXPLORATION 9.6 Developing Rotation Sense 271
SECTION 9.2 Symmetry and Tessellations 275
EXPLORATION 9.7 Symmetries of Common Polygons 275
EXPLORATION 9.8 Symmetry Groups 276
EXPLORATION 9.9 Tessellations 281
EXPLORATION 9.10 Quilts 287
SECTION 9.3 Exploring Similarity 299
EXPLORATION 9.11 Similarity with Pattern Blocks 299
EXPLORATION 9.12 Similar Figures 301
10 Geometry as Measurement
SECTION 10.1 Exploring Systems of Measurement 303
EXPLORATION 10.1 How Far Is It? 303
EXPLORATION 10.2 How Tall? 305
EXPLORATION 10.3 How Thick? 306
EXPLORATION 10.4 How Much Is a Million? 307
SECTION 10.2 Exploring Perimeter and Area 308
EXPLORATION 10.5 What Does Mean? 308
EXPLORATION 10.6 Exploring the Meaning of Area 309
EXPLORATION 10.7 Exploring Area on Geoboards 310
EXPLORATION 10.8 Exploring the Area of a Circle 315
EXPLORATION 10.9 Can You Make the Quilt Pattern? 316
EXPLORATION 10.10 How Much Will the Carpet Cost? 317
EXPLORATION 10.11 Irregular Areas 318
EXPLORATION 10.12 Exploring Relationships Between Perimeter and Area 319
EXPLORATION 10.13 Functions, Geometric Figures, and Geoboards 321
SECTION 10.3 Exploring Surface Area and Volume 327
EXPLORATION 10.14 Understanding Surface Area 327
EXPLORATION 10.15 Understanding Volume 328
EXPLORATION 10.16 Determining Volumes of Irregularly Shaped Objects 330
EXPLORATION 10.17 Paper Towels 331
EXPLORATION 10.18 Measurement, Ambiguity, and Precision 332
EXPLORATION 10.19 Applying Volume Concepts 333
Endnotes E-1
Index I-1
Cutouts
BASE TEN GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
OTHER BASE GRAPH PAPER
GEOBOARD DOT PAPER
ISOMETRIC DOT PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
POLYOMINO GRID PAPER
TANGRAM TEMPLATE
REGULAR POLYGONS
EXPLORING THE AREA OF A CIRCLE
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Editora: Cengage Learning, ©2011.
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