Full Description
Hands-On Problem Solving is essential to learning mathematics. When actively engaged in problem solving, students use all the mathematical processes they need in order to achieve the goals of mathematics education and to support lifelong learning. In Hands-On Problem Solving, students are exposed to a wide range of problems in all areas of mathematics. They solve these problems by applying a combination of mathematical knowledge, tools, and strategies. They also explore a variety of methods for solving and confirming their solutions.
The ability to use mathematical knowledge to solve problems is the goal for all students. Hands-On Problem Solving is an easy-to-use resource that helps teachers plan and implement best practices to meet this goal. In this book, you will find
problem-solving activities to incorporate into daily mathematics classes for an entire school year
a correlation chart identifying the math concepts presented in each lesson
tasks designed for specific outcomes and learning expectations from Canadian curriculum documents
problems integrating other curricular areas such as language arts, science, and social studies
materials lists, reproducibles, assessment suggestions, and much more!
Download the FREE digital resources that accompany this book by following the instructions printed on the first page of the Appendix.
Contents
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
