Multiplicative Strategies — Fencing
Progression 2 (Years 3–4) Number | Applying doubling/halving, tidy groups, and compensation to × facts in enclosure fencing contexts.
Learning Intentions & Success Criteria
Te Mātaiaho: use multiplicative strategies (emerging)
NZC L2–3: multiplication strategies (doubling/halving, tidy groups)
Key idea: transform the fact
Ākonga are learning to:
- Use structure to solve × facts (e.g., 6×9 → 6×10 − 6).
- Apply doubling/halving (e.g., 4×8 from 2×8 doubled).
- Choose a strategy and explain why it fits.
Success looks like:
- I can solve unfamiliar facts by transforming them.
- I can show the strategy on an array or line.
- I can compare two strategies for the same fact.
Teacher prompts
- “Which fact do you already know?”
- “How can you adjust it?”
- “Show the change on the array.”
Kupu / Vocabulary
- double / takirua
- halve / haurua
- tidy group / rōpū tōtika
- compensate / whakatika
- factor / tauwehe
- transform / whakarerekē
Materials
- Strategy cards (doubling/halving, tidy group ±1/±2, break apart).
- Array grids; panel count contexts.
- A5 Handout: Progression 2 core (multiplication) or generator “Multiplication facts (2–10).”
Lesson Flow
Hook (5 mins)
- Fence panels: 6 rows of 9 panels; how to solve quickly?
Teach/Model (12 mins)
- Model tidy group: 6×9 as 6×10 − 6; draw array, shade minus one column.
- Model doubling: 4×8 from 2×8 doubled; halving partner facts (e.g., 8×6 from 4×6 doubled).
- Model break apart: 7×6 as (5×6)+(2×6).
Guided Practice (15 mins)
- Station A: Tidy ±1/±2 facts (×9, ×11 style).
- Station B: Doubling/halving chains (2→4→8 facts).
- Station C: Break-apart facts (near 5s and 10s).
Independent/Extension (10–12 mins)
- Choose 4 facts; solve with two strategies; note which is fastest.
- Extension: create a mini strategy guide for ×6, ×7, ×8.
- Support: focus on ×2, ×5, ×10, then ×4, ×3 with doubling.
Exit Check (5 mins)
- Prompt: 7×8—show one strategy, then check with another.
Place-based options
- Fencing panels at Hamilton Zoo; restoration stakes along tracks; seating rows.
Push flexible use of structure, not rote-only. Encourage students to articulate “I changed it to…”
Differentiation & Support
Scaffolds
- Start with ×2, ×5, ×10 before moving to ×6, ×7, ×8.
- Provide array grids with the “tidy” column highlighted.
- Use doubling chains (2× → 4× → 8×) as a visual ladder.
Extensions
- Choose the most efficient transformation and justify.
- Create a strategy poster for ×7 or ×8.
- Link to division using inverse facts.
Common Misconceptions
- Forgetting to adjust after tidying (e.g., 6×10 but not minus 6). Remedy: mark the removed column.
- Doubling the wrong factor. Remedy: point to which side changes in the array.
- Thinking only one strategy is allowed. Remedy: require two strategies for one fact.
Assessment & Evidence
- Exit strategy clarity; accuracy of transformed facts.
- Station notes: Are strategies chosen sensibly or randomly?
Whānau Connection
- Send home a “strategy swap”: solve a fact two ways and share with whānau.
- Invite whānau to share a real grouping task (seats, packs, trays).
Handout Link
Use Progression 2 core handout (multiplication) or generator “Multiplication facts (2–10).” Ask learners to annotate with strategy notes.