MathematicsMultiplication & DivisionAges 8–12

Factor Pairs & Commutativity

Recognise and use factor pairs and commutativity in mental calculations

Lesson

Set out your lesson

List factor pairs systematically and separate reordering from regrouping.

Before teaching

Use this short check, then start teaching.

Activity

Inferred, not a taxonomy edge: learner can access the supplied prompt with agreed support and can explain or mark a response. If earlier skills are unfamiliar, use the prerequisite topic for teaching; an authored prerequisite is not proof this learner is ready.

Printer, credit, and teaching notes

Sequence

Keep the two adult-only cards off the learner screen. Have a pencil and scrap paper if useful; oral pointing/typing/AAC can replace handwriting unless spelling or composition is the target. No printing, cutting, account or purchase is required.
Open Show first, read the explanation together, and pause to check the central idea. Then do Guided Try together.
For Try, close earlier models and the adult keys unless the task explicitly supplies a reference. Record any hints, read-aloud help or model reopening; do not call supported work independent.
Use only the active learner card. Keep the private key closed until an attempt is recorded. Stop or take a break on request; practical claims stay not observed unless actually done.

No Printer

Use on screen; read aloud or recreate a tactile model only with declared support. No printer or purchased kit.

Privacy

Never display adult keys or dictation spellings with a learner task; no family financial, identity or conflict disclosure.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

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Teaching approaches

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List factor pairs systematically and separate reordering from regrouping.

Family records and proof options

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Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

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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

You Can Multiply Three Numbers in Any Order

Open practice(new tab)

Before you open · source notes

Multiplying three numbers in any order supports factor pairs and commutativity. Not every prime sieve.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask the learner to regroup factors in a different order and show the product matches.

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 2026-11-12 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. “You Can Multiply Three Numbers in Any Order.” 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

List all factor pairs of a given number (e.g. 24: 1×24, 2×12, 3×8, 4×6)
Use commutativity to reorder a multiplication for easier mental calculation
Explain what a factor pair is and how commutativity helps

“If your child needs to multiply '4 × 15', can they spot that splitting it into '4 × 5 × 3 = 20 × 3 = 60' is a clever shortcut — using factor pairs to make it easier?”

Curriculum record

Type: Conceptual
Subject: Mathematics
Domain: Multiplication & Division
Age range: Ages 8–12

Standards

acara-v9:AC9M5N02the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-B2.6uk-nc-2013:Ma/KS2/Y4/MD/3