Properties of Operations
Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
Lesson
Set out your lesson
Practise the bounded task in Properties of Operations; see exact limits before inferring broader coverage.
Before teaching
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Knows multiplication facts; parentheses mean group these factors first.
Exact directed source edges retained; earlier authorship is not learner attainment.
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Practise the bounded task in Properties of Operations; see exact limits before inferring broader coverage.
Practise the bounded task in Properties of Operations; see exact limits before inferring broader coverage.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Valid Equalities? (Part 2)
Before you open · source notes
True-or-false equalities prompt properties of multiplication such as commutativity and distributivity. Not every property proof.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk why an equality is true or false using a property name or a quick array sketch. Sorting cards alone does not prove every property.
Opening this link does not save learning or assess mastery.
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 2026-11-11 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. “Valid Equalities? (Part 2).” 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
- Use commutativity: if 6 × 4 = 24 then 4 × 6 = 24
- Use the distributive property: 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56
- Use associativity to multiply three numbers: 2 × 3 × 5 = 6 × 5 = 30
“Can your child use tricks like breaking up a number — working out '6 × 14' as '6 × 10 + 6 × 4 = 60 + 24 = 84' — to make multiplication easier?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Multiplication & Division
- Age range
- Ages 8–13
Standards