Mathematics · Year 7

Active learning ideas

Factorising into Single Brackets

Active learning works well for factorising into single brackets because students need to move between concrete and abstract representations. Handling physical or written expressions helps them see patterns in numbers and letters that aren’t obvious when working mentally alone.

• National Curriculum Attainment Targets
• KS3: Mathematics - Algebra

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Jigsaw
• 30 min · Pairs

Card Match: Expanded to Factorised

Prepare cards with expanded expressions on one set and factorised forms on another. Pairs match them, such as 5x + 10 with 5(x + 2), then justify choices verbally. Extend by having pairs create new pairs for the class to match.

Analyze the relationship between expanding and factorising expressions.

Facilitation Tip

During Card Match, provide answer cards with both correct and incorrect factorisations so students must justify their choices rather than rely on guesswork.

What to look for

Present students with a list of expressions (e.g., 8x + 12, 5y - 10, 3a + 7b). Ask them to circle the expressions that can be factorised into a single bracket and underline the HCF for each.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 02

• Jigsaw
• 35 min · Small Groups

Factor Race: Small Groups

Divide class into small groups with expression sheets. First group to factor all correctly wins a point; rotate roles as timer and checker. Discuss strategies after each round to highlight common factors.

Differentiate between an expanded and a factorised expression.

Facilitation Tip

In Factor Race, circulate and listen for students naming the HCF aloud as they work, reinforcing the vocabulary of highest common factor.

What to look for

Give each student an expression like 9m + 15. Ask them to factorise it into a single bracket. Then, ask them to write one sentence explaining how they found the HCF.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 03

• Jigsaw
• 25 min · Whole Class

Error Hunt: Whole Class

Project expressions with deliberate mistakes in factorisation. Class votes on errors via mini-whiteboards, then whole class corrects and explains using HCF rules. Follow with individual practice on similar items.

Construct an expression that can be factorised into a single bracket.

Facilitation Tip

In Error Hunt, ask students to present their corrected versions on the board so the class can see multiple solutions and reasoning paths.

What to look for

Pose the question: 'If you expand 4(3x + 2), you get 12x + 8. How does understanding the reverse process, factorising, help you check your expansion?' Facilitate a brief class discussion on the inverse relationship.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Activity 04

• Jigsaw
• 40 min · Individual

Build and Factor: Individual then Pairs

Students individually expand brackets to create expressions, then swap with a partner to factorise. Pairs verify each other's work and refine if needed, building a shared set of examples.

Analyze the relationship between expanding and factorising expressions.

Facilitation Tip

In Build and Factor, give students algebra tiles first so they physically see the common parts before moving to symbolic writing.

What to look for

Present students with a list of expressions (e.g., 8x + 12, 5y - 10, 3a + 7b). Ask them to circle the expressions that can be factorised into a single bracket and underline the HCF for each.

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers should start with numerical expressions before introducing variables, so students grasp the concept of common factors without distraction. Avoid rushing to abstract symbols; use visual models like area diagrams or algebra tiles to show shared parts. Research shows that students who manipulate physical or visual representations before symbolic work retain understanding longer and make fewer errors when letters appear.

Students will confidently identify the highest common factor in an expression and rewrite it as a single bracket. They will explain their reasoning clearly and verify their answers by expanding back. Missteps in variable or coefficient selection will be caught and corrected through discussion.

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Watch Out for These Misconceptions

• During Card Match, watch for students picking the smallest number as the HCF instead of finding the largest shared factor across all terms.

  Have students list all factors of each coefficient and circle the largest one common to every term before matching cards.

• During Build and Factor, watch for students ignoring common variable factors, such as factoring 3x + 6 as 3(x + 2) but missing 3(x + 2) when the expression is x^2 + 3x.

  Use algebra tiles to build expressions and ask students to physically separate the shared x from x^2 + 3x, writing x(x + 3) before moving to symbols.

• During Error Hunt, watch for students assuming factorised form is always simpler and rejecting expanded equivalents.

  Ask groups to expand their corrected factorised forms and compare with the original to confirm equality, reinforcing that both forms are valid and useful.

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Methods used in this brief

• Jigsaw