Commutative Multiplication
Understand and apply the commutative property of multiplication and recognise that division is not commutative
Lesson
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Use rotated arrays for commutative multiplication and show why division differs.
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Use rotated arrays for commutative multiplication and show why division differs.
Use rotated arrays for commutative multiplication and show why division differs.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Picturing Factors in Different Orders
Before you open · source notes
Factor pictures in different orders support commutative multiplication. Not every prime-factorization drill.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to show the same product with factors swapped and say why the total matches.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Picturing Factors in Different Orders.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
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 6–9
Standards