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.Dianne Soltess, BA, PBDE, is a curriculum coordinator K–8 for the St. James-Assiniboia School Division in Winnipeg, Manitoba. She has practised in the education field for more than 30 years, teaching grades 1–6 before becoming a math/science coordinator. Dianne has taught undergraduate and post-baccalaureate courses for the Faculty of Education at the University of Manitoba in Winnipeg, Manitoba. She has been involved in math and science curriculum development and document writing for Manitoba Education and has contributed to the Hands-On Math series.Meagan Mutchmor, BEd, PBCE, is the K–8 mathematics consultant for Winnipeg School Division. She provides professional learning workshops on a variety of topics including mathematics, assessment for learning, and reflective practice. Meagan has also contributed to several educational resources as an author, advisor, and consultant. As an educator for 25 years Meagan believes that successful learners are active participants in their learning. This belief guides her practice with all learners, including children and adults.Tina Jagdeo BAH, BEd, MA, is the Learning Strategies Coordinator of the Wernham West Centre for Learning at Upper Canada College in Toronto, Ontario. In this role, she teaches boys from kindergarten to grade 7 to help them understand and develop strategies for their unique learning profiles. She enjoys leading school-based workshops on best practices in literacy, mathematics, differentiation, and social, and emotional learning. Tina has co-written two workbooks, Centred for Learning, volumes 1 and 2, on how to create inclusive learning environments.Lara Jensen, BEd, BA, BPHE, has been a classroom teacher, specialist teacher, ICT integrator, curriculum coordinator, and librarian for the past 18 years at K–8 schools in Canada, Germany, and Switzerland. She holds a certificate in Outdoor and Experiential Education and has worked to incorporate inquiry-based teaching and learning into every classroom. Lara has conducted teacher’s workshops on such topics as mathematics, literacy, international-mindedness, and inquiry.Denise MacRae, BHEc, EdCert, is a former primary school teacher who taught nursery to grade 3 for 29 years in the inner city of Winnipeg. She currently works as a faculty advisor for the University of Manitoba. She lives in Winnipeg, Manitoba.

• Introduction to Hands-On Problem Solving Grade 3 1Program 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? 5 Best Practices in Teaching Problem Solving 5 Routine Problems 5 Non-Routine Problems 6 Extended Exploration Problems 7 Implementing the Hands-On Problem-SolvingProgram 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 Blackline Masters to Guide and Support Learning – Problem Solving 10 Mathematics Correlation 11 Grade 3 Correlation Chart 11 The Hands-On Problem Solving Assessment Plan 13Assessment for Learning 13 Assessment as Learning 13 Assessment of Learning 14 Performance Assessment 14 Portfolios 14 Assessment Blackline Masters 16 Routine Problems 25Implementation of Routine Problems 26 Problem Types 26 Teaching Routine Problems 27 1A Jamie Counts his Money 32 2A Mohammed and Andy Watch a Movie 34 3A Scrambling Eggs for Breakfast 36 4A The Greatest Sum 38 5A The Best Price for Pens 40 6A How Many Grade Threes Are at School? 42 7A Jared Picks Apples 44 8A How Many Candies? 46 9A How Much Change? 48 10A Carrots for Rabbits 50 11A Gumballs for Lootbags 53 12A How Much Money Does April Have? 55 13A Viking Ships 57 14A Animals With Legs 59 15A Nickels and Dimes 61 16A Sharing Pizza 63 17A Collecting Shells 65 18A Going on a Field Trip 67 19A One-on-One Basketball 69 20A Adding Seeds 71 21A Magic Square Mystery 73 22A Greatest Sum Wins 76 23A Morgan Saves for an MP3 Player 78 24A Marvin Magician’s Magic Math Machine 80 25A Digging Up Dinosaur Bones 83 26A What Is the Dot Pattern? 86 27A Leap-Year Puzzler 88 28A Counting Quarters 90 29A Filling the Sandbox 92 30A Growing an Amaryllis Plant 94 31A A Caterpillar Crawling 96 32A Yasser Reads for One Hour 98 33A Building a Pen for the Pony 100 34A How Far from Home Plate? 102 35A Sorting Scraps of Wood 104 36A Building a Three-Dimensional (3-D) Object 107 37A How Many Faces Are Triangles? 109 38A Favourite Pets 111 39A Balls in Mr. Woods’s Store 114 40A Which Type of Fish Is the Most Common? 117 Non-Routine Problems 119Implementation of Non-Routine Problems 120 Teaching Non-Routine Problems 123 An Additional Resource for Solving Non-Routine Problems 125 Blackline Master to Guide and Support Learning – Non-Routine Problems 126 1B The Ants Go Marching 127 2B How Many Outfits? 130 3B Walking to School 134 4B A Trip to the Water Park 137 5B Selling Pizza 140 6B Pennies in the Gumball Machine 143 7B Animals in Line 145 8B Who Plays Which Sport? 147 9B What Are the Numbers? 149 10B Beanbag Toss Brainteaser 151 11B Birds at the Feeder 153 12B The Sum of Each Side is 12 156 13B Which Coins Are in the Bag? 159 14B Oranges and Mangos 161 15B Denise Buys Toy Dinosaurs 163 16B Pink and Orange Popsicles 165 17B How Old Are Sheryl and Yaakov? 167 18B Running Around the Block 170 19B Joel Saves His Babysitting Money 172 20B How Many Masks? 174 21B A Pattern Using the Word DOG 176 22B Balancing the Teeter-Totter 178 23B Caterpillars Meet for Dinner 180 24B Ingredients for Salsa 182 25B Bricks for a New School 184 26B How Many Times Does Afya the Leopard Roar? 186 27B Domino House Number Combinations 188 28B Plants for Sale 190 29B Collecting Coupons for a Prize 192 30B Muffins for Breakfast 194 31B What Number Am I? 196 32B What Day of the Week? 198 33B A Spider Crawls Up the Triceratops 200 34B Monkey Mystery 202 35B Games on the Shelf 204 36B Collecting Shells in Hawaii 206 37B Canoeing Along the White Hawk River 208 38B Stamps on Pierre’s Letter 210 39B Observing Crayfish and Painted Turtles 212 40B How Old Was Kevin When He Learned to Swim? 214 Extended Exploration Problems 217Implementation of Extended Exploration Problems 218 Teaching Extended Exploration Problems 218 Blackline Masters to Guide and Support Learning – Extended Explorations 222 1C Building the Number of the Day 223 2C Lego Structure Bar Graphs 228 3C Building A Garden 231 4C Carnival Menu 233 5C Book-Cover Patterns 236 6C Marching to the War Memorial 239 7C Money Collection Pattern 242 8C Making the Numbers 1–20 244 9C Animal Puzzler 246 10C More Mystery With Magic Squares 251 Appendix 253References 261About the Authors 262

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.Dianne Soltess, BA, PBDE, is a curriculum coordinator K–8 for the St. James-Assiniboia School Division in Winnipeg, Manitoba. She has practised in the education field for more than 30 years, teaching grades 1–6 before becoming a math/science coordinator. Dianne has taught undergraduate and post-baccalaureate courses for the Faculty of Education at the University of Manitoba in Winnipeg, Manitoba. She has been involved in math and science curriculum development and document writing for Manitoba Education and has contributed to the Hands-On Math series.Meagan Mutchmor, BEd, PBCE, is the K–8 mathematics consultant for Winnipeg School Division. She provides professional learning workshops on a variety of topics including mathematics, assessment for learning, and reflective practice. Meagan has also contributed to several educational resources as an author, advisor, and consultant. As an educator for 25 years Meagan believes that successful learners are active participants in their learning. This belief guides her practice with all learners, including children and adults.Tina Jagdeo BAH, BEd, MA, is the Learning Strategies Coordinator of the Wernham West Centre for Learning at Upper Canada College in Toronto, Ontario. In this role, she teaches boys from kindergarten to grade 7 to help them understand and develop strategies for their unique learning profiles. She enjoys leading school-based workshops on best practices in literacy, mathematics, differentiation, and social, and emotional learning. Tina has co-written two workbooks, Centred for Learning, volumes 1 and 2, on how to create inclusive learning environments.Lara Jensen, BEd, BA, BPHE, has been a classroom teacher, specialist teacher, ICT integrator, curriculum coordinator, and librarian for the past 18 years at K–8 schools in Canada, Germany, and Switzerland. She holds a certificate in Outdoor and Experiential Education and has worked to incorporate inquiry-based teaching and learning into every classroom. Lara has conducted teacher’s workshops on such topics as mathematics, literacy, international-mindedness, and inquiry.Denise MacRae, BHEc, EdCert, is a former primary school teacher who taught nursery to grade 3 for 29 years in the inner city of Winnipeg. She currently works as a faculty advisor for the University of Manitoba. She lives in Winnipeg, Manitoba.

• Introduction to Hands-On Problem Solving Grade 3 1Program 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? 5 Best Practices in Teaching Problem Solving 5 Routine Problems 5 Non-Routine Problems 6 Extended Exploration Problems 7 Implementing the Hands-On Problem-SolvingProgram 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 Blackline Masters to Guide and Support Learning – Problem Solving 10 Mathematics Correlation 11 Grade 3 Correlation Chart 11 The Hands-On Problem Solving Assessment Plan 13Assessment for Learning 13 Assessment as Learning 13 Assessment of Learning 14 Performance Assessment 14 Portfolios 14 Assessment Blackline Masters 16 Routine Problems 25Implementation of Routine Problems 26 Problem Types 26 Teaching Routine Problems 27 1A Jamie Counts his Money 32 2A Mohammed and Andy Watch a Movie 34 3A Scrambling Eggs for Breakfast 36 4A The Greatest Sum 38 5A The Best Price for Pens 40 6A How Many Grade Threes Are at School? 42 7A Jared Picks Apples 44 8A How Many Candies? 46 9A How Much Change? 48 10A Carrots for Rabbits 50 11A Gumballs for Lootbags 53 12A How Much Money Does April Have? 55 13A Viking Ships 57 14A Animals With Legs 59 15A Nickels and Dimes 61 16A Sharing Pizza 63 17A Collecting Shells 65 18A Going on a Field Trip 67 19A One-on-One Basketball 69 20A Adding Seeds 71 21A Magic Square Mystery 73 22A Greatest Sum Wins 76 23A Morgan Saves for an MP3 Player 78 24A Marvin Magician’s Magic Math Machine 80 25A Digging Up Dinosaur Bones 83 26A What Is the Dot Pattern? 86 27A Leap-Year Puzzler 88 28A Counting Quarters 90 29A Filling the Sandbox 92 30A Growing an Amaryllis Plant 94 31A A Caterpillar Crawling 96 32A Yasser Reads for One Hour 98 33A Building a Pen for the Pony 100 34A How Far from Home Plate? 102 35A Sorting Scraps of Wood 104 36A Building a Three-Dimensional (3-D) Object 107 37A How Many Faces Are Triangles? 109 38A Favourite Pets 111 39A Balls in Mr. Woods’s Store 114 40A Which Type of Fish Is the Most Common? 117 Non-Routine Problems 119Implementation of Non-Routine Problems 120 Teaching Non-Routine Problems 123 An Additional Resource for Solving Non-Routine Problems 125 Blackline Master to Guide and Support Learning – Non-Routine Problems 126 1B The Ants Go Marching 127 2B How Many Outfits? 130 3B Walking to School 134 4B A Trip to the Water Park 137 5B Selling Pizza 140 6B Pennies in the Gumball Machine 143 7B Animals in Line 145 8B Who Plays Which Sport? 147 9B What Are the Numbers? 149 10B Beanbag Toss Brainteaser 151 11B Birds at the Feeder 153 12B The Sum of Each Side is 12 156 13B Which Coins Are in the Bag? 159 14B Oranges and Mangos 161 15B Denise Buys Toy Dinosaurs 163 16B Pink and Orange Popsicles 165 17B How Old Are Sheryl and Yaakov? 167 18B Running Around the Block 170 19B Joel Saves His Babysitting Money 172 20B How Many Masks? 174 21B A Pattern Using the Word DOG 176 22B Balancing the Teeter-Totter 178 23B Caterpillars Meet for Dinner 180 24B Ingredients for Salsa 182 25B Bricks for a New School 184 26B How Many Times Does Afya the Leopard Roar? 186 27B Domino House Number Combinations 188 28B Plants for Sale 190 29B Collecting Coupons for a Prize 192 30B Muffins for Breakfast 194 31B What Number Am I? 196 32B What Day of the Week? 198 33B A Spider Crawls Up the Triceratops 200 34B Monkey Mystery 202 35B Games on the Shelf 204 36B Collecting Shells in Hawaii 206 37B Canoeing Along the White Hawk River 208 38B Stamps on Pierre’s Letter 210 39B Observing Crayfish and Painted Turtles 212 40B How Old Was Kevin When He Learned to Swim? 214 Extended Exploration Problems 217Implementation of Extended Exploration Problems 218 Teaching Extended Exploration Problems 218 Blackline Masters to Guide and Support Learning – Extended Explorations 222 1C Building the Number of the Day 223 2C Lego Structure Bar Graphs 228 3C Building A Garden 231 4C Carnival Menu 233 5C Book-Cover Patterns 236 6C Marching to the War Memorial 239 7C Money Collection Pattern 242 8C Making the Numbers 1–20 244 9C Animal Puzzler 246 10C More Mystery With Magic Squares 251 Appendix 253References 261About the Authors 262

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.Dianne Soltess, BA, PBDE, is a curriculum coordinator K–8 for the St. James-Assiniboia School Division in Winnipeg, Manitoba. She has practised in the education field for more than 30 years, teaching grades 1–6 before becoming a math/science coordinator. Dianne has taught undergraduate and post-baccalaureate courses for the Faculty of Education at the University of Manitoba in Winnipeg, Manitoba. She has been involved in math and science curriculum development and document writing for Manitoba Education and has contributed to the Hands-On Math series.Meagan Mutchmor, BEd, PBCE, is the K–8 mathematics consultant for Winnipeg School Division. She provides professional learning workshops on a variety of topics including mathematics, assessment for learning, and reflective practice. Meagan has also contributed to several educational resources as an author, advisor, and consultant. As an educator for 25 years Meagan believes that successful learners are active participants in their learning. This belief guides her practice with all learners, including children and adults.Tina Jagdeo BAH, BEd, MA, is the Learning Strategies Coordinator of the Wernham West Centre for Learning at Upper Canada College in Toronto, Ontario. In this role, she teaches boys from kindergarten to grade 7 to help them understand and develop strategies for their unique learning profiles. She enjoys leading school-based workshops on best practices in literacy, mathematics, differentiation, and social, and emotional learning. Tina has co-written two workbooks, Centred for Learning, volumes 1 and 2, on how to create inclusive learning environments.Lara Jensen, BEd, BA, BPHE, has been a classroom teacher, specialist teacher, ICT integrator, curriculum coordinator, and librarian for the past 18 years at K–8 schools in Canada, Germany, and Switzerland. She holds a certificate in Outdoor and Experiential Education and has worked to incorporate inquiry-based teaching and learning into every classroom. Lara has conducted teacher’s workshops on such topics as mathematics, literacy, international-mindedness, and inquiry.Denise MacRae, BHEc, EdCert, is a former primary school teacher who taught nursery to grade 3 for 29 years in the inner city of Winnipeg. She currently works as a faculty advisor for the University of Manitoba. She lives in Winnipeg, Manitoba.

• Introduction to Hands-On Problem Solving Grade 3 1Program 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? 5 Best Practices in Teaching Problem Solving 5 Routine Problems 5 Non-Routine Problems 6 Extended Exploration Problems 7 Implementing the Hands-On Problem-SolvingProgram 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 Blackline Masters to Guide and Support Learning – Problem Solving 10 Mathematics Correlation 11 Grade 3 Correlation Chart 11 The Hands-On Problem Solving Assessment Plan 13Assessment for Learning 13 Assessment as Learning 13 Assessment of Learning 14 Performance Assessment 14 Portfolios 14 Assessment Blackline Masters 16 Routine Problems 25Implementation of Routine Problems 26 Problem Types 26 Teaching Routine Problems 27 1A Jamie Counts his Money 32 2A Mohammed and Andy Watch a Movie 34 3A Scrambling Eggs for Breakfast 36 4A The Greatest Sum 38 5A The Best Price for Pens 40 6A How Many Grade Threes Are at School? 42 7A Jared Picks Apples 44 8A How Many Candies? 46 9A How Much Change? 48 10A Carrots for Rabbits 50 11A Gumballs for Lootbags 53 12A How Much Money Does April Have? 55 13A Viking Ships 57 14A Animals With Legs 59 15A Nickels and Dimes 61 16A Sharing Pizza 63 17A Collecting Shells 65 18A Going on a Field Trip 67 19A One-on-One Basketball 69 20A Adding Seeds 71 21A Magic Square Mystery 73 22A Greatest Sum Wins 76 23A Morgan Saves for an MP3 Player 78 24A Marvin Magician’s Magic Math Machine 80 25A Digging Up Dinosaur Bones 83 26A What Is the Dot Pattern? 86 27A Leap-Year Puzzler 88 28A Counting Quarters 90 29A Filling the Sandbox 92 30A Growing an Amaryllis Plant 94 31A A Caterpillar Crawling 96 32A Yasser Reads for One Hour 98 33A Building a Pen for the Pony 100 34A How Far from Home Plate? 102 35A Sorting Scraps of Wood 104 36A Building a Three-Dimensional (3-D) Object 107 37A How Many Faces Are Triangles? 109 38A Favourite Pets 111 39A Balls in Mr. Woods’s Store 114 40A Which Type of Fish Is the Most Common? 117 Non-Routine Problems 119Implementation of Non-Routine Problems 120 Teaching Non-Routine Problems 123 An Additional Resource for Solving Non-Routine Problems 125 Blackline Master to Guide and Support Learning – Non-Routine Problems 126 1B The Ants Go Marching 127 2B How Many Outfits? 130 3B Walking to School 134 4B A Trip to the Water Park 137 5B Selling Pizza 140 6B Pennies in the Gumball Machine 143 7B Animals in Line 145 8B Who Plays Which Sport? 147 9B What Are the Numbers? 149 10B Beanbag Toss Brainteaser 151 11B Birds at the Feeder 153 12B The Sum of Each Side is 12 156 13B Which Coins Are in the Bag? 159 14B Oranges and Mangos 161 15B Denise Buys Toy Dinosaurs 163 16B Pink and Orange Popsicles 165 17B How Old Are Sheryl and Yaakov? 167 18B Running Around the Block 170 19B Joel Saves His Babysitting Money 172 20B How Many Masks? 174 21B A Pattern Using the Word DOG 176 22B Balancing the Teeter-Totter 178 23B Caterpillars Meet for Dinner 180 24B Ingredients for Salsa 182 25B Bricks for a New School 184 26B How Many Times Does Afya the Leopard Roar? 186 27B Domino House Number Combinations 188 28B Plants for Sale 190 29B Collecting Coupons for a Prize 192 30B Muffins for Breakfast 194 31B What Number Am I? 196 32B What Day of the Week? 198 33B A Spider Crawls Up the Triceratops 200 34B Monkey Mystery 202 35B Games on the Shelf 204 36B Collecting Shells in Hawaii 206 37B Canoeing Along the White Hawk River 208 38B Stamps on Pierre’s Letter 210 39B Observing Crayfish and Painted Turtles 212 40B How Old Was Kevin When He Learned to Swim? 214 Extended Exploration Problems 217Implementation of Extended Exploration Problems 218 Teaching Extended Exploration Problems 218 Blackline Masters to Guide and Support Learning – Extended Explorations 222 1C Building the Number of the Day 223 2C Lego Structure Bar Graphs 228 3C Building A Garden 231 4C Carnival Menu 233 5C Book-Cover Patterns 236 6C Marching to the War Memorial 239 7C Money Collection Pattern 242 8C Making the Numbers 1–20 244 9C Animal Puzzler 246 10C More Mystery With Magic Squares 251 Appendix 253References 261About the Authors 262