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)
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Teaching Table
Set out your lesson
Find the greatest common factor of the terms, write a factor times a bracket, and check by expansion.
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.
Check readiness directly. Prerequisite availability is not attainment.
Start with the readiness check. Use Show, then Guided, then a fresh Try. These linked lessons may need several short sessions; do not impose a speed target. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations are allowed but do not show independent reading or handwriting. Use as much space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the fresh Try givens available. Give no answer or target method during the first attempt. If help is needed, give it and mark the attempt supported. Review the key after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, physical experiment or real measurement is required.
Record the actual response and assistance. These tasks do not establish mastery.
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.
Only two-term expressions with a positive highest common numerical factor and at most x² are used. General factorisation, multiple variables and quadratic-factor methods are not covered.
Record the actual response and assistance. These tasks do not establish mastery.
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Teaching approaches
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1 approach
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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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