Introduction to Hands-On Problem Solving, Grade 5 1

• Program Introduction 2
• Program Principles 2
• Big Ideas in Mathematics 2
• Communication 2
• Connections 3
• Mental Math 3
• Estimation 3
• Reasoning 4
• Technology 4
• Visualization 4
• Problem Solving 4
• What Is Problem Solving? 4
• Best Practices in Teaching
• Problem Solving 5
• Routine Problems 5
• Non-Routine Problems 5
• Extended Exploration Problems 7
• Implementing the Hands-On
• Problem-Solving Program 7
• Program Format 7
• Planning Your Year of Problem Solving 7
• Curricular Connections 8
• Supporting Literacy During Problem
• Solving 8
• The Questioning Process 8
• Additional Resources 8
• A Note About Pennies 8
• Guiding and Supporting Learning:
• Problem Solving 10
• Mathematics Correlation 11
• Grade 5 Correlation Chart 11

The Hands-On Problem Solving Assessment Plan 13

• Assessment for Learning 13
• Assessment as Learning 13
• Assessment of Learning 14
• Performance Assessment 14
• Portfolios 14
• Assessment Reproducibles 15

Routine Problems 23

• Implementation of Routine Problems 24
• Problem Types 24
• Teaching Routine Problems 25
  • 1A The Super-Duper Six-Dice Game 30
  • 2A Estimating the Number of Seeds 33
  • 3A Debating Groups 36
  • 4A Stacking Loonies 38
  • 5A Pelican Eggs 41
  • 6A If Colin Filled Five Albums 44
  • 7A Collecting Money 46
  • 8A Paddling Puzzler 48
  • 9A Youngest to Oldest 50
  • 10A Evaporating Water 52
  • 11A Picking Blueberries 54
  • 12A One Million Eggs 56
  • 13A Lilac Bush Buds 58
  • 14A Building a Sandbag Dike 60
  • 15A Replacing Boards on the Boardwalk 62
  • 16A Gestation Period: Humans vs. Rabbits 64
  • 17A Playground Perimeter 67
  • 18A Don’t Forget the Sunblock! 69
  • 19A Running Long-Jump Total 72
  • 20A How Many Mosquitoes? 74
  • 21A Spiders Weigh-In 76
  • 22A Chocolate Brownies 78
  • 23A Many Grains of Rice 80
  • 24A Mr. Mekanic’s Alphabet Patterns 83
  • 25A What Did He Say? 85
  • 26A The “Run for Heart Health” Race 87
  • 27A Yan’s Rectangular Chicken Coop 89
  • 28A Spray Painting a Graffiti Wall 91
  • 29A Knit-Wit Scarves 93
  • 30A Geocaching 95
  • 31A Buying an Aquarium Pump 97
  • 32A Building a Birdhouse 100
  • 33A Painting the Pool 102
  • 34A Smoking the Beehives 104
  • 35A Shapes With Parallel Lines 106
  • 36A Reflected Image 108
  • 37A Shapes in the Sand 111
  • 38A Two Weeks of Physical Activity 115
  • 39A Bouncing Balls 120
  • 40A Heads or Tails? 122

Non-Routine Problems 125

• Implementation of Non-Routine Problems 126
• Teaching Non-Routine Problems 129
• An Additional Resource for Solving Non-Routine Problems 131
• Guiding and Supporting Learning: Non-Routine Problems 132
  • 1B Venetian Blind Riddle 133
  • 2B How Many Handshakes? 135
  • 3B The Order of the Coins 137
  • 4B The Sequence of Shapes on
  • the String 140
  • 5B Multiplication Patterns With 36
  • as a Factor 142
  • 6B Let’s Make a Comic-Book Deal 145
  • 7B Who Rides Which Bus? 147
  • 8B One of These Nets is Not Like
  • the Others 149
  • 9B Number Sentence Challenge 151
  • 10B Individual Point Scores 154
  • 11B The Best Cellphone Plan 156
  • 12B Spring Picnic Food Tickets 160
  • 13B Rolling Lucky Seven 163
  • 14B A Baby’s Mass 166
  • 15B Opening Day at the Film Festival 169
  • 16B How Many Songs are on Ravi’s
  • MP3 Player? 171
  • 17B Making Waterproof Sleeping-Bag
  • Covers 173
  • 18B Making a Slideshow 175
  • 19B How Many Fewer Strides? 177
  • 20B Seating at Ted’s Bistro 179
  • 21B A Cube Number Palindrome 182
  • 22B Charm Challenge 184
  • 23B Along the Edges of a Cube 186
  • 24B Less Than $1 188
  • 25B A Total of 41 190
  • 26B The Cambridge Falls Canoe Challenge 192
  • 27B Sam’s Sister’s Grass-Cutting
  • Business 194
  • 28B Andy’s Travels 196
  • 29B Mr. Banerjee’s Ladder 198
  • 30B Jellybean Countdown 200
  • 31B Amanda’s Darts Scores 202
  • 32B Delivering Surveys 204
  • 33B Using Only the Number 5 206
  • 34B 1 Through 9 208
  • 35B Returning Pennies to the Bank 210
  • 36B A Sum of 86 212
  • 37B Halloween Costume Combinations 214
  • 38B Half of Half of Half... 216
  • 39B Edible Mushrooms 218
  • 40B Combinations of Support 220

Extended Exploration Problems 223

• Implementation of Extended Exploration Problems 224
• Teaching Extended Exploration Problems 224
• Guiding and Supporting Learning: Extended Exploration Problems 228
  • 1C How Many Football Fields? 229
  • 2C My Dream Bedroom 232
  • 3C Fractions of a Tangram 234
  • 4C Estimating the Number of Words on a Page 238
  • 5C The Last Chip 240
  • 6C Opening Day Giveaways 242
  • 7C An Old Record Collection 244
  • 8C Jason’s Stained-Glass Design 246
  • 9C Jonas’s Five-Layered 3-D Block Structure 248
  • 10C Flushing Water Down the Toilet 250

Appendix 253
References 258
About the Authors 259