Commutative Multiplication
Understand and apply the commutative property of multiplication and recognise that division is not commutative
Share and support
Teaching Table
Set out your lesson
Use rotated arrays for commutative multiplication and show why division differs.
Ask for an example of one prerequisite idea; revisit if needed. Historical graph coverage does not establish this learner’s readiness.
Use dots, a paper array or the structured matrices; no screen animation needed.
Use supplied stage sheets on screen or scrap paper; keep adult keys separate.
Use the fictional scenarios. Passing is allowed. Do not ask for private money amounts, account details, family conflict, identity or health information. Keep only minimal local learning notes.
Supplied data are explicitly practice data, not observations. Record only what is actually attempted; absent equipment, consent, partner or repeated observations means that part remains pending.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
Finite products and fractional division contrasts; prerequisite fraction readiness may require support.
Use the fictional scenarios. Passing is allowed. Do not ask for private money amounts, account details, family conflict, identity or health information. Keep only minimal local learning notes.
Supplied data are explicitly practice data, not observations. Record only what is actually attempted; absent equipment, consent, partner or repeated observations means that part remains pending.
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Use rotated arrays for commutative multiplication and show why division differs.
Use rotated arrays for commutative multiplication and show why division differs.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
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The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
Check understanding
- Explain that 3 × 5 = 5 × 3 and show this with an array rotated
- Use commutativity to choose the easier calculation
- Demonstrate that 12 ÷ 3 ≠ 3 ÷ 12
“Does your child know that 4 × 7 gives the same answer as 7 × 4 — so they can choose whichever order is easier to remember from their times tables?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Multiplication & Division
- Age range
- Ages 6–7
Standards