What to Look For: Facilitator's Guide

Table of Contents

Acknowledgements … vi

Introduction … viii

  • Making Use of What to Look For Resources … viii
  • Facilitation Tips … ix
  • Before the Session … ix
  • Your Preparation … x
  • Pacing … x
  • Repeated Components of Each Session … xi
  • Physical Considerations … xiii
  • How This Book Is Organized … xiv
  • The Challenge … xvi

1 | Starting at the Beginning: Early Addition … 1

  • Day 1 at a Glance … 2
  • Getting Started (Slides 1–5) … 4
  • Why learn more than the facts and procedures? (Slides 6–15) … 8
  • The Addition Strategies Continuum to 20 (Slides 16–26) … 13
  • Games: Consolidating and Moving Students Forward (Slides 27–28) … 23
  • Moving on from Counting On: Beginning to Work with Numbers (Slides 29–37) … 25
  • Games: Consolidating and Moving Students Forward (Slides 38–40) … 33
  • Introducing Models: The Five-Frame and the Ten-Frame (Slides 41–48) … 36
  • Wrapping Up (Slide 49) … 48

2 | Later Addition and Early Subtraction … 49

  • Day 2 at a Glance … 50
  • Welcome Back (Slides 1–5) … 52
  • Working Toward an Alternative Algorithm for Addition (Slides 6–11) … 54
  • Riley’s Learning Pathways and Using the Continuum (Slides 12–15) … 60
  • What will proficiency look like for subtraction? (Slides 16–18) … 63
  • Beginning Subtraction: From Counting Three Times to Think Addition (Slides 19–28) … 67
  • Moving On: Working with the Numbers (Slides 29–34) … 74
  • Developing Our Own Mathematical Understanding (Slides 35–39) … 77
  • Wrapping Up (Slide 40) … 84

3 | Later Subtraction: Continuum Pathways and Algorithms … 85

  • Day 3 at a Glance … 86
  • Welcome Back (Slides 1–4) … 88
  • Deepening Our Own Mathematical Understanding of Subtraction (Slides 5–11) … 90
  • A Subtraction Pathway That Leads to the Number Line and Mental Math (Slides 12–18) … 102
  • A Subtraction Pathway That Leads to Splitting and Algorithms (Slides 19–25) … 108
  • An Alternative Subtraction Algorithm: Partial Differences (Slides 26–30) … 113
  • The Decomposition and Accessible Decomposition Algorithms for Subtraction (Slides 31–34) … 118
  • The Equal Additions Subtraction Algorithm (Slides 35–36) … 124
  • How do we want our students to subtract? (Slides 37–38) … 127
  • Wrapping Up (Slide 39) … 128

4 | Problem Structures and Number Line Pathway Activities … 129

  • Day 4 at a Glance … 130
  • Welcome Back (Slides 1–4) … 132
  • Introducing Addition and Subtraction Problem Structures (Slides 5–10) … 134
  • Why Use Different Problem Structures? (Slides 11–16) … 141
  • Supporting Students’ Progress Along the Number Line Pathway (Slides 17–25) … 150
  • Introducing the Open Number Line (Slides 26–29) … 161
  • Modelling and Scribing Student Thinking (Slides 30–31) … 167
  • Wrapping Up (Slide 32) (Use after slide 31 or after slide 38 if introducing the algebraic pathway.) … 170
  • An Algebraic Pathway (Slides 33–38) (Use if time and participant energy levels permit.) … 171

5 | Early Multiplication and Division 175

  • Day 5 at a Glance … 176
  • Getting Started (Slides 1–3) … 178
  • Beginning to Consider Children’s Development of Multiplicative Reasoning (Slides 4–9) … 180
  • The Shift from Additive to Multiplicative Reasoning (Slides 10–17) … 184
  • Developing Multiplicative Reasoning: The Importance of Unitizing (Slides 18–30) … 189
  • The Multiplication Continuum: Early Strategies (Slides 31–37) … 194
  • Introducing Division: Two Models of Division (Slides 38–40) … 198
  • The Division Continuum: Early Strategies (Slides 41–46) … 201
  • The Further Development of Multiplicative Reasoning (Slides 47–53) … 205
  • Activity: Modelling Students’ Strategies (Slide 54) (Optional if Using Day 6) … 210
  • Is there an order for learning multiplication facts that best supports children? (Slides 55–57) … 211
  • Wrapping Up (Slide 58) … 214

6 | A Pathway to Multiplicative Reasoning and Fact Proficiency … 215

  • Day 6 at a Glance … 216
  • Welcome Back (Slides 1–3) … 218
  • A Multiplicative Pathway (Slides 4–7) … 220
  • Supporting Students’ Progress Along the Multiplicative Pathway, Part I (Slides 8–17) … 227
  • A Short Break to Play a Game (Slide 18) … 235
  • Supporting Students’ Progress Along the Multiplicative Pathway, Part II (Slides 19–25) … 236
  • Wrapping Up (Slide 26) … 242

7 | Math with Mel: Sharing the Learning, from One Coach to Another … 243

  • My Learning Journey as a Coach: Where It All Began … 243
  • The Nature of a Coach’s Work … 244
  • From Professional Development to Classroom Practice … 244
  • Be Prepared: The Importance of Knowing Your Content … 244
  • Preparing to Move into the Classroom … 245
  • First Steps: Making Contact with the School … 245
  • Co-Planning: An Integral Part of Collaborating with a Teacher … 246
  • The Co-Planning Process … 246
  • The Coach in the Classroom … 251
  • My Math Coach Kit: What do I bring to the classroom? … 251
  • Coaching Etiquette: Honouring the Classroom Space … 253
  • Supporting Teachers as They Engage in Assessment for Learning … 253
  • Sample Co-Teaching Plans … 256

References … 263
Index … 264
Credits … 268