
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