Factorising Expressions
Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)
Lesson
Set out your lesson
Find the greatest common factor of the terms, write a factor times a bracket, and check by expansion.
Before teaching
Use this short check, then start teaching.
Ask the learner to expand 2(x + 3). Expect 2x + 6 with both products explained. Ask what a factor of a whole number is: a whole number that divides it without a remainder. If needed, make factor pairs before starting. This lesson assumes no speed target.
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Find the greatest common factor of the terms, write a factor times a bracket, and check by expansion.
Find the greatest common factor of the terms, write a factor times a bracket, and check by expansion.
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Learning resources
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Illustrative Mathematics · Practice link — not the full lesson
Snow Day
Before you open · source notes
Snow Day supports factorising expressions. Not every worksheet pack.
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 explain one step of “Snow Day” in their own words.
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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. “Snow Day.” 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
- Identify the highest common factor of all terms in an expression
- Write the factorised form as a product of the HCF and a bracket
- Check factorisation by expanding the brackets back out
“Can your child look at an expression like "6x + 9" and rewrite it with the common factor taken out — as "3(2x + 3)"?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 12–13
Standards