Mathematics · Year 9

Active learning ideas

Factorising into Single Brackets

Actively manipulating algebraic expressions helps Year 9 students internalise the relationship between expansion and factorisation. Working with physical tiles and timed challenges turns abstract coefficients and variables into something they can rearrange, test, and correct in real time, strengthening both fluency and conceptual understanding.

• National Curriculum Attainment Targets
• KS3: Mathematics - Algebra

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Pairs

Pair Match-Up: Expression Pairs

Provide cards with 20 expanded expressions and their single-bracket factorised forms. Pairs match them, then expand their pairs to check accuracy. Circulate to prompt discussions on HCF choices.

Justify why factorisation is considered the inverse process of expansion.

Facilitation Tip

During Pair Match-Up, circulate and listen for pairs that verbalise their choice of HCF before matching, ensuring they connect the coefficient and variable parts.

What to look for

Provide students with the expression 15a + 20b. Ask them to: 1. Identify the HCF of the terms. 2. Factorise the expression into a single bracket. 3. Expand their answer to check their work.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 45 min · Small Groups

Small Group Tiles: HCF Builds

Distribute paper algebra tiles or cutouts representing terms. Groups physically group tiles by HCF, factorise, and photograph their setups for a class gallery walk. Compare methods to refine techniques.

Construct a systematic approach to finding the highest common factor of algebraic terms.

Facilitation Tip

In Small Group Tiles, ask one student in each group to record each trial factorisation on mini-whiteboards so everyone sees the progression.

What to look for

Display several expressions on the board, such as 8x - 12, 9y + 18, and 4c² + 16c. Ask students to write down the HCF for each expression on mini-whiteboards. Review answers as a class, focusing on common errors with coefficients and variables.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 25 min · Whole Class

Whole Class Relay: Factor Chain

Divide class into teams lining up at the board. First student factorises a given expression, tags next who verifies by expanding and adds another. Fastest accurate team wins.

Evaluate the importance of identifying common factors for simplifying expressions.

Facilitation Tip

For the Whole Class Relay, insist teams write both the HCF and the fully factorised expression before the next runner starts to prevent rushing.

What to look for

Pose the question: 'Why is factorising considered the opposite of expanding?' Encourage students to use examples like 3(x + 2) and 3x + 6 to explain their reasoning and discuss the role of the HCF in this inverse relationship.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 20 min · Individual

Individual Hunt: Spot the Factors

Give worksheets with jumbled terms. Students list factors for each, factorise solo, then pair-share to peer-assess. Collect for targeted feedback.

Justify why factorisation is considered the inverse process of expansion.

Facilitation Tip

During Individual Hunt, ask students to jot down the divisor they used for each term directly above the original expression to make their division step visible.

What to look for

Provide students with the expression 15a + 20b. Ask them to: 1. Identify the HCF of the terms. 2. Factorise the expression into a single bracket. 3. Expand their answer to check their work.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with concrete examples using algebra tiles so students see how grouping common pieces mirrors the numerical HCF process. Emphasise systematic checks—listing factors or using prime decomposition—before moving to purely symbolic work. Avoid rushing to shortcuts; spend time on full re-expansions to embed the inverse relationship. Research shows that students who practise verification steps retain procedures longer and make fewer careless errors later.

Students will confidently identify the highest common factor of terms and rewrite expressions with one common factor outside a bracket. They will justify each step by re-expanding and will articulate why using the HCF matters for later algebraic work.

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Watch Out for These Misconceptions

• During Small Group Tiles, watch for students who group all the x-tiles together without checking whether the coefficients share a common factor.

  Prompt them to list the factors of the coefficients first, then select only the tiles that match the HCF before grouping, using the tiles to confirm the division step visually.

• During Whole Class Relay, watch for teams that stop at any common factor rather than the highest one.

  Have the next runner pause and ask the team to justify why that factor is the largest possible, using the factorisation they wrote on the board to test alternatives.

• During Pair Match-Up, watch for pairs who place the HCF outside but do not divide the original terms by it inside the bracket.

  Ask them to re-expand their matched pair to check if it returns the original expression, guiding them to correct the division step before finalising the match.

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Methods used in this brief

• Gallery Walk