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…mehr
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.
Jennifer E. Lawson, PhD, is the creator of the Hands-On books published by Portage & Main Press. As senior writer and editor for the series, she has contributed to more than 50 publications for teachers and students. Jennifer provides professional development workshops for educators locally, nationally, and virtually, and is a Workplace Wellness Advisor. Her most recent book is a collective effort called Teacher, Take Care: A Guide to Well-Being and Workplace Wellness for Educators. She is also one of the founders of Mission to Mexico, an organization that supports schools in some of the most impoverished communities in Puerto Vallarta. Throughout her extensive career in education, Jennifer has worked as a classroom teacher, resource and special education teacher, consultant, principal, university instructor, and school trustee. She lives with her family in Winnipeg, Manitoba.
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Introduction to Hands-On Problem Solving, Grade 6 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 6 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 1. Implementation of Routine Problems 24 2. Problem Types 24 3. Teaching Routine Problems 25 * 1A Number Stumper 30 * 2A Debating Numbers 33 * 3A Fruit Ratio 36 * 4A Movie Ticket Sales 38 * 5A Payment Plan Premium 40 * 6A Order of Operations 42 * 7A Amusing Multiples 44 * 8A Tips Towards Ice Time 46 * 9A Charting Baby Enoch’s Sleep 48 * 10A Riding the School Bus 50 * 11A Ice-Tea Ratio 52 * 12A Percent of Marbles 54 * 13A Avital’s Stamp Collection 56 * 14A Complimentary T-Shirts 58 * 15A Glee Club Arrangement 60 * 16A Buying Badminton Racquets and Birdies 63 * 17A Decorating Mira’s Locker 65 * 18A Adopting a Polar Bear 67 * 19A Ordering Pizza 70 * 20A Calling Mexico 72 * 21A Bar Mitzvah Seating 75 * 22A Onion Rings at Orion’s Onion Ring Diner 77 * 23A What’s With the Width? 79 * 24A Painting a Purple Stripe 81 * 25A Building a Model Soddie 83 * 26A Podium Puzzle 85 * 27A Tomás’s Stained-Glass Window 87 * 28A Designing the Barn Door 89 * 29A Jonathan’s Snow-Removal Business 91 * 30A Sahrish’s Vegetable Garden 93 * 31A The Volume of a Backpack 95 * 32A Triangle Tattoos 97 * 33A Scrapbooking Shapes 99 * 34A Transformation Design 101 * 35A Regular and Irregular Polygons 104 * 36A The Price of a Canadian Stamp 107 * 37A Cory’s Height 111 * 38A Who Will Come Back? 113 * 39A Prize Probabilities 115 * 40A Number Cube Probabilities 119 Non-Routine Problems 121 4. Implementation of Non-Routine Problems 122 5. Teaching Non-Routine Problems 125 6. An Additional Resource for Solving 7. Non-Routine Problems 127 8. Guiding and Supporting Learning – Non-Routine Problems 128 * 1B Make 48 Number Cube 129 * 2B Sari’s Six-Level Mayan Pyramid 132 * 3B Seating at the Breakfast Nook 134 * 4B Pizza Toppings 136 * 5B Pet-Sitting Offers 138 * 6B Leeville Family Centre Library Fines 140 * 7B Populations of Canadian Cities 142 * 8B Kittens and Mice for Sale 144 * 9B How Many Children’s Tickets Sold? 146 * 10B Restaurant Food Combinations 148 * 11B Seats at the Movie Theatre 151 * 12B Outfit Combinations 154 * 13B Three-Legged Stools and Four-Legged Chairs 156 * 14B Evens and Odds 158 * 15B JP’s Begonia and Cactus Sale 161 * 16B Vincent’s Shopping Spree 163 * 17B Smoothies for Five 165 * 18B Getting Home 167 * 19B Bake Sale Goodies 169 * 20B What Is the Mystery Number? 171 * 21B How Many Floors? 173 * 22B Mr. Oliver’s Towing Rope 175 * 23B Trading Hockey Cards 177 * 24B Arranging Lettered Tiles 179 * 25B Delivering Flyers 181 * 26B Chen Buys 10 Comics 183 * 27B Upstairs, Downstairs... 185 * 28B How Many Games of Chess? 187 * 29B Missing Pages 189 * 30B Seating Arrangement for 150 191 * 31B Which Lawyer, Which Office? 193 * 32B The Square With the Star 196 * 33B Cartwheel Conundrum 198 * 34B The Hamster Did It! 200 * 35B Measures of Size 202 * 36B The End of the Concert 204 * 37B Fieldtrip to the Bata Shoe Museum 206 * 38B Mr. Clark’s Venus Fly Traps 208 * 39B Paying for a New MacBook 210 * 40B Deluxe Snow Forts 212 Extended Exploration Problems 215 9. Implementation of Extended 10. Exploration Problems 216 11. Teaching Extended Exploration Problems 216 12. Guiding and Supporting Learning – Extended Exploration Problems 220 * 1C Recycled Basketball 221 * 2C Apartment Design 225 * 3C Dream House Design 229 * 4C Factor Trees 231 * 5C Family Vacation 235 * 6C Planning Your Birthday Party 239 * 7C Poster Project 241 * 8C Using a Line Graph to Write a Story 245 * 9C Order of Operations Mobile 248 * 10C Restaurant Menu Creation 250 Appendix 253 References 259 About the Authors 260
