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.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.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.

• Introduction to Hands-On Problem Solving, Grade 5 1Program Introduction 2Program Principles 2Big Ideas in Mathematics 2Communication 2Connections 3Mental Math 3Estimation 3Reasoning 4Technology 4Visualization 4Problem Solving 4What Is Problem Solving? 4Best Practices in TeachingProblem Solving 5Routine Problems 5Non-Routine Problems 5Extended Exploration Problems 7Implementing the Hands-OnProblem-Solving Program 7Program Format 7Planning Your Year of Problem Solving 7Curricular Connections 8Supporting Literacy During ProblemSolving 8The Questioning Process 8Additional Resources 8A Note About Pennies 8Guiding and Supporting Learning:Problem Solving 10Mathematics Correlation 11Grade 5 Correlation Chart 11The Hands-On Problem Solving Assessment Plan 13Assessment for Learning 13Assessment as Learning 13Assessment of Learning 14Performance Assessment 14Portfolios 14Assessment Reproducibles 15Routine Problems 23Implementation of Routine Problems 24Problem Types 24Teaching Routine Problems 251A The Super-Duper Six-Dice Game 302A Estimating the Number of Seeds 333A Debating Groups 364A Stacking Loonies 385A Pelican Eggs 416A If Colin Filled Five Albums 447A Collecting Money 468A Paddling Puzzler 489A Youngest to Oldest 5010A Evaporating Water 5211A Picking Blueberries 5412A One Million Eggs 5613A Lilac Bush Buds 5814A Building a Sandbag Dike 6015A Replacing Boards on the Boardwalk 6216A Gestation Period: Humans vs. Rabbits 6417A Playground Perimeter 6718A Don’t Forget the Sunblock! 6919A Running Long-Jump Total 7220A How Many Mosquitoes? 7421A Spiders Weigh-In 7622A Chocolate Brownies 7823A Many Grains of Rice 8024A Mr. Mekanic’s Alphabet Patterns 8325A What Did He Say? 8526A The “Run for Heart Health” Race 8727A Yan’s Rectangular Chicken Coop 8928A Spray Painting a Graffiti Wall 9129A Knit-Wit Scarves 9330A Geocaching 9531A Buying an Aquarium Pump 9732A Building a Birdhouse 10033A Painting the Pool 10234A Smoking the Beehives 10435A Shapes With Parallel Lines 10636A Reflected Image 10837A Shapes in the Sand 11138A Two Weeks of Physical Activity 11539A Bouncing Balls 12040A Heads or Tails? 122Non-Routine Problems 125Implementation of Non-Routine Problems 126Teaching Non-Routine Problems 129An Additional Resource for Solving Non-Routine Problems 131Guiding and Supporting Learning: Non-Routine Problems 1321B Venetian Blind Riddle 1332B How Many Handshakes? 1353B The Order of the Coins 1374B The Sequence of Shapes onthe String 1405B Multiplication Patterns With 36as a Factor 1426B Let’s Make a Comic-Book Deal 1457B Who Rides Which Bus? 1478B One of These Nets is Not Likethe Others 1499B Number Sentence Challenge 15110B Individual Point Scores 15411B The Best Cellphone Plan 15612B Spring Picnic Food Tickets 16013B Rolling Lucky Seven 16314B A Baby’s Mass 16615B Opening Day at the Film Festival 16916B How Many Songs are on Ravi’sMP3 Player? 17117B Making Waterproof Sleeping-BagCovers 17318B Making a Slideshow 17519B How Many Fewer Strides? 17720B Seating at Ted’s Bistro 17921B A Cube Number Palindrome 18222B Charm Challenge 18423B Along the Edges of a Cube 18624B Less Than $1 18825B A Total of 41 19026B The Cambridge Falls Canoe Challenge 19227B Sam’s Sister’s Grass-CuttingBusiness 19428B Andy’s Travels 19629B Mr. Banerjee’s Ladder 19830B Jellybean Countdown 20031B Amanda’s Darts Scores 20232B Delivering Surveys 20433B Using Only the Number 5 20634B 1 Through 9 20835B Returning Pennies to the Bank 21036B A Sum of 86 21237B Halloween Costume Combinations 21438B Half of Half of Half... 21639B Edible Mushrooms 21840B Combinations of Support 220Extended Exploration Problems 223Implementation of Extended Exploration Problems 224Teaching Extended Exploration Problems 224Guiding and Supporting Learning: Extended Exploration Problems 2281C How Many Football Fields? 2292C My Dream Bedroom 2323C Fractions of a Tangram 2344C Estimating the Number of Words on a Page 2385C The Last Chip 2406C Opening Day Giveaways 2427C An Old Record Collection 2448C Jason’s Stained-Glass Design 2469C Jonas’s Five-Layered 3-D Block Structure 24810C Flushing Water Down the Toilet 250Appendix 253References 258About the Authors 259

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.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.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.

• Introduction to Hands-On Problem Solving, Grade 5 1Program Introduction 2Program Principles 2Big Ideas in Mathematics 2Communication 2Connections 3Mental Math 3Estimation 3Reasoning 4Technology 4Visualization 4Problem Solving 4What Is Problem Solving? 4Best Practices in TeachingProblem Solving 5Routine Problems 5Non-Routine Problems 5Extended Exploration Problems 7Implementing the Hands-OnProblem-Solving Program 7Program Format 7Planning Your Year of Problem Solving 7Curricular Connections 8Supporting Literacy During ProblemSolving 8The Questioning Process 8Additional Resources 8A Note About Pennies 8Guiding and Supporting Learning:Problem Solving 10Mathematics Correlation 11Grade 5 Correlation Chart 11The Hands-On Problem Solving Assessment Plan 13Assessment for Learning 13Assessment as Learning 13Assessment of Learning 14Performance Assessment 14Portfolios 14Assessment Reproducibles 15Routine Problems 23Implementation of Routine Problems 24Problem Types 24Teaching Routine Problems 251A The Super-Duper Six-Dice Game 302A Estimating the Number of Seeds 333A Debating Groups 364A Stacking Loonies 385A Pelican Eggs 416A If Colin Filled Five Albums 447A Collecting Money 468A Paddling Puzzler 489A Youngest to Oldest 5010A Evaporating Water 5211A Picking Blueberries 5412A One Million Eggs 5613A Lilac Bush Buds 5814A Building a Sandbag Dike 6015A Replacing Boards on the Boardwalk 6216A Gestation Period: Humans vs. Rabbits 6417A Playground Perimeter 6718A Don’t Forget the Sunblock! 6919A Running Long-Jump Total 7220A How Many Mosquitoes? 7421A Spiders Weigh-In 7622A Chocolate Brownies 7823A Many Grains of Rice 8024A Mr. Mekanic’s Alphabet Patterns 8325A What Did He Say? 8526A The “Run for Heart Health” Race 8727A Yan’s Rectangular Chicken Coop 8928A Spray Painting a Graffiti Wall 9129A Knit-Wit Scarves 9330A Geocaching 9531A Buying an Aquarium Pump 9732A Building a Birdhouse 10033A Painting the Pool 10234A Smoking the Beehives 10435A Shapes With Parallel Lines 10636A Reflected Image 10837A Shapes in the Sand 11138A Two Weeks of Physical Activity 11539A Bouncing Balls 12040A Heads or Tails? 122Non-Routine Problems 125Implementation of Non-Routine Problems 126Teaching Non-Routine Problems 129An Additional Resource for Solving Non-Routine Problems 131Guiding and Supporting Learning: Non-Routine Problems 1321B Venetian Blind Riddle 1332B How Many Handshakes? 1353B The Order of the Coins 1374B The Sequence of Shapes onthe String 1405B Multiplication Patterns With 36as a Factor 1426B Let’s Make a Comic-Book Deal 1457B Who Rides Which Bus? 1478B One of These Nets is Not Likethe Others 1499B Number Sentence Challenge 15110B Individual Point Scores 15411B The Best Cellphone Plan 15612B Spring Picnic Food Tickets 16013B Rolling Lucky Seven 16314B A Baby’s Mass 16615B Opening Day at the Film Festival 16916B How Many Songs are on Ravi’sMP3 Player? 17117B Making Waterproof Sleeping-BagCovers 17318B Making a Slideshow 17519B How Many Fewer Strides? 17720B Seating at Ted’s Bistro 17921B A Cube Number Palindrome 18222B Charm Challenge 18423B Along the Edges of a Cube 18624B Less Than $1 18825B A Total of 41 19026B The Cambridge Falls Canoe Challenge 19227B Sam’s Sister’s Grass-CuttingBusiness 19428B Andy’s Travels 19629B Mr. Banerjee’s Ladder 19830B Jellybean Countdown 20031B Amanda’s Darts Scores 20232B Delivering Surveys 20433B Using Only the Number 5 20634B 1 Through 9 20835B Returning Pennies to the Bank 21036B A Sum of 86 21237B Halloween Costume Combinations 21438B Half of Half of Half... 21639B Edible Mushrooms 21840B Combinations of Support 220Extended Exploration Problems 223Implementation of Extended Exploration Problems 224Teaching Extended Exploration Problems 224Guiding and Supporting Learning: Extended Exploration Problems 2281C How Many Football Fields? 2292C My Dream Bedroom 2323C Fractions of a Tangram 2344C Estimating the Number of Words on a Page 2385C The Last Chip 2406C Opening Day Giveaways 2427C An Old Record Collection 2448C Jason’s Stained-Glass Design 2469C Jonas’s Five-Layered 3-D Block Structure 24810C Flushing Water Down the Toilet 250Appendix 253References 258About the Authors 259