Fact Families — Keeper Kits
Progression 2 (Years 3–4) Number | Building multiplication/division fact families to strengthen basic facts.
Learning Intentions & Success Criteria
Te Mātaiaho: use place value to operate with whole numbers; connect ×/÷
NZC L2–3: basic multiplication/division facts (2–10)
Key idea: facts live in families
Ākonga are learning to:
- Create fact families from a context or array.
- Use inverse relationships to solve division.
- Fluently recall 2, 5, 10, then 3, 4 facts.
Success looks like:
- I can write 4 facts from one array (2 × 5 = 10; 5 × 2 = 10; 10 ÷ 2 = 5; 10 ÷ 5 = 2).
- I can use a multiplication fact to solve a division quickly.
Teacher prompts
- “What are the four facts in this family?”
- “Which fact helps you solve the division?”
- “Show the array that matches.”
Kupu / Vocabulary
- inverse / tauaro
- factor / tauwehe
- product / hua
- quotient / hua whakawehe
- divide / whakawehe
- family / whānau
🎥 Media Anchor (8 mins)
Video: Examples relating multiplication to division | 3rd grade | Khan Academy
Before — Predict
Start with 3 × 4 = 12. What division question can the same array answer?
During — Watch with a job
Watch the full 3:26 clip. Record multiplication and division facts that share the same total.
| Multiplication fact | Related division fact | Shared total | Array labels |
|---|---|---|---|
| … | … | … | … |
| … | … | … | … |
Kaiako moves
- Keep the total, number of groups, and group size labelled to prevent divisor and quotient reversal.
- Ask learners to point from each factor or quotient to the matching part of the array.
After — Pair process
Expand one captured multiplication/division pair into the complete four-fact family with a partner.
Immediate use
Use that family at the array and triangle-card stations before creating an original family.
Support + stretch
- Support: Use a labelled fact-family triangle and facts for 2, 5, and 10.
- Stretch: Begin with a division fact and reconstruct both multiplication facts.
Materials
- Triangle fact cards; array tiles; bar models.
- Context cards (kit items packed in equal groups).
- A5 Handout: Progression 2 core (facts) or generator “Multiplication/Division facts.”
Lesson Flow
Hook (5 mins)
- Keeper kits: 4 kits with 5 torches; how many torches? Build fact family.
Teach/Model (12 mins)
- Build array, write two × facts and two ÷ facts; highlight inverse.
- Do the same with 3×4; show bar model for division.
Guided Practice (15 mins)
- Station A: Array to fact family (2, 5, 10 then 3, 4, 12).
- Station B: Triangle cards—fill missing numbers.
- Station C: Context cards—write and solve fact family equations.
Independent/Extension (10–12 mins)
- Create 2 fact families of your own; include a division fact first.
- Extension: mix 6, 7, 8 facts; use doubling/halving strategies.
- Support: stick to 2, 5, 10; visual arrays provided.
Exit Check (5 mins)
- Fact family for 3×5; write all four equations.
Place-based options
- Zealandia/Tiritiri equipment kits; Hamilton Zoo keeper bags; Otago Peninsula trap sets.
Emphasise inverse thinking: every division fact is “undoing” a multiplication. Keep arrays visible.
Differentiation & Support
Scaffolds
- Focus on 2, 5, 10 families first.
- Use triangle cards with one number missing.
- Keep arrays visible while writing facts.
Extensions
- Introduce 6, 7, 8 facts with doubling/halving.
- Create a fact family riddle for peers.
- Connect to division with remainders (conceptually only).
Common Misconceptions
- Swapping divisor and dividend. Remedy: label “total” and “groups”.
- Writing only the multiplication facts. Remedy: require both division facts.
- Confusing factor with product. Remedy: point to array dimensions.
Assessment & Evidence
- Exit fact family correctness; fluency with 2,5,10 and intro 3,4.
- Note if students reverse divisor/dividend; adjust support.
Whānau Connection
- Send home a fact-family card set for quick practice.
- Invite whānau to share a grouping task (packs of 5, 10).
Handout Link
Use Progression 2 core handout (facts) or generator “Multiplication/Division facts (2–10),” 24–28 items.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 1 (Years 0–3) · Number (Knowledge): “- Multiplication involves combining equal groups. - Division involves equal grouping or sharing. - Counting objects in equal groups can be used to multiply (combining) or divide (sharing).”
- NZC (2007) · Mathematics and Statistics · Level 3: “Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.”
📋 Kaiako Planning Snapshot
Teacher planning support for this resource — learning intentions, success criteria, and inclusive practice guidance are summarised below.
Inclusion Guidance
- ESOL / ELL learners: Pre-teach key vocabulary (numeracy, number, fact) using visual word walls or bilingual glossaries before the lesson. Reduce language load with diagrams and visual models. Partner-share and think-pair-share strategies encouraged.
- Neurodiverse learners / ADHD: Break the lesson into clear segments with visual checkpoints. UDL principle: offer ākonga a choice in how they demonstrate understanding (verbal, written, visual/drawn). Provide anchor charts or reference cards for numeracy number p2 l5 concepts throughout.
- Dyslexia: Provide audio-text alternatives for written materials. Use high-contrast fonts and generous line spacing. Allow voice recording as an alternative to written responses where possible.