Grades 1 to 3 Number Sense and Numeration Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where a particular product is used by teachers in schools across Ontario, that product is identified by its trade name, in the interests of clarity. Reference to particular products in no way implies an endorsement of those products by the Ministry of Education. Ministry of Education Printed on recycled paper ISBN 978-1-4606-8920-2 (Print) ISBN 978-1-4606-8921-9 (PDF) © Queen’s Printer for Ontario, 2016 Contents Introduction ......................................................................................... 1 Purpose and Features of This Document ................................................ 2 “Big Ideas” in the Curriculum for Grades 1 to 3 ..................................... 2 The “Big Ideas” in Number Sense and Numeration ........................... 5 Overview ............................................................................................... 5 General Principles of Instruction ............................................................ 7 Counting .............................................................................................. 9 Overview ............................................................................................... 9 Key Concepts of Counting .................................................................... 11 Instruction in Counting ......................................................................... 12 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 13 Grade 1 ............................................................................................ 13 Grade 2 ............................................................................................ 15 Grade 3 ............................................................................................ 17 Operational Sense ............................................................................... 19 Overview ............................................................................................... 19 Understanding the Properties of the Operations .................................... 24 Instruction in the Operations ................................................................. 25 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 25 Grade 1 ............................................................................................ 25 Grade 2 ............................................................................................ 27 Grade 3 ............................................................................................ 29 Une publication équivalente est disponible en français sous le titre suivant : Guide d’enseignement efficace des mathématiques, de la 1re à la 3e année – Numération et sens du nombre. Quantity ............................................................................................... 33 Overview ............................................................................................... 33 Understanding Quantity ........................................................................ 35 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 37 Grade 1 ............................................................................................ 37 Grade 2 ............................................................................................ 39 Grade 3 ............................................................................................ 41 Relationships ....................................................................................... 45 Overview ............................................................................................... 45 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 49 Grade 1 ............................................................................................ 49 Grade 2 ............................................................................................ 50 Grade 3 ............................................................................................ 51 Representation .................................................................................... 53 Overview ............................................................................................... 53 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 55 Grade 1 ............................................................................................ 55 Grade 2 ............................................................................................ 57 Grade 3 ............................................................................................ 58 References ........................................................................................... 60 Learning Activities for Number Sense and Numeration ..................... 63 Introduction .......................................................................................... 65 Appendix A: Grade 1 Learning Activities ............................................ 67 Counting: Healing Solutions .................................................................. 69 Blackline masters: C1.BLM1 – C1.BLM3 Operational Sense: Train Station ............................................................ 75 Blackline masters: OS1.BLM1 – OS1.BLM7 Quantity: The Big Scoop ....................................................................... 83 Blackline masters: Q1.BLM1 – Q1.BLM7 Relationships: Ten in the Nest ................................................................ 89 Blackline masters: Rel1.BLM1 – Rel1.BLM6 iv A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Number Sense and Numeration Representation: The Trading Game ........................................................ 95 Blackline masters: Rep1.BLM1 – Rep1.BLM4 Appendix B: Grade 2 Learning Activities ............................................ 103 Counting: The Magician of Numbers .................................................... 105 Blackline masters: C2.BLM1 – C2.BLM3 Operational Sense: Two by Two ............................................................ 111 Blackline masters: OS2.BLM1 Quantity: What’s Your Estimate? ............................................................ 119 Blackline masters: Q2.BLM1 – Q2.BLM2 Relationships: Hit the Target .................................................................. 125 Blackline masters: Rel2.BLM1 – Rel2.BLM5 Representation: Mystery Bags ................................................................ 131 Blackline masters: Rep2.BLM1 – Rep2.BLM9 Appendix C: Grade 3 Learning Activities ............................................ 141 Counting: Trading up to 1000 ............................................................... 143 Blackline masters: C3.BLM1 – C3.BLM5 Operational Sense: What Comes in 2’s, 3’s, and 4’s? .............................. 149 Blackline masters: OS3.BLM1 – OS3.BLM2 Quantity: Estimate How Many ............................................................... 155 Blackline masters: Q3.BLM1 – Q3.BLM6 Relationships: What’s the Relationship?.................................................. 161 Blackline masters: Rel3.BLM1 – Rel3.BLM3 Representation: What Fraction Is It? ....................................................... 167 Blackline masters: Rep3.BLM1 – Rep3.BLM5 Appendix D: Correspondence of the Big Ideas and the Curriculum Expectations in Number Sense and Numeration ................................ 173 Overall Expectations .............................................................................. 175 Specific Expectations in Relation to the Big Ideas ................................... 175 Glossary ............................................................................................... 185 Contents v Introduction This document is a practical guide that teachers will find useful in helping students to achieve the curriculum expectations for mathematics outlined in the Number Sense and Numeration strand of The Ontario Curriculum, Grades 1–8: Mathematics, 2005. The expectations outlined in the curriculum documents describe the knowledge and skills that students are expected to acquire by the end of each grade. In Early Math Strategy: The Report of the Expert Panel on Early Math in Ontario (Expert Panel on Early Math, 2003), effective instruction is identified as critical to the successful learning of mathematical knowledge and skills, and the components of an effective program are described. As part of the process of implementing the panel’s vision of effective mathematics instruction for Ontario, A Guide to Effective Instruction in Mathematics, Grades 1 to 3 provides a framework for teaching mathematics. This framework includes specific strategies for develop- ing an effective program and for creating a community of learners in which students’ mathematical thinking is nurtured. The strategies focus on the “big ideas” inherent in the expectations;