Mathematics · Year 7

Active learning ideas

Expanding Single Brackets

Expanding single brackets relies on students seeing multiplication as an operation applied to every part of an expression, not just the first term. Active tasks let learners manipulate symbols physically or collaboratively, turning abstract rules into visible, correctable steps. This hands-on approach fixes errors early by making misconceptions public and correctable in real time.

• National Curriculum Attainment Targets
• KS3: Mathematics - Algebra

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Peer Teaching
• 25 min · Pairs

Card Match: Distribute and Pair

Prepare cards with unexpanded expressions on one set and expanded forms on another. In pairs, students match them, writing justifications using the distributive law. Pairs then swap sets with neighbours to verify and discuss any mismatches.

Explain how the distributive law works in expanding brackets.

Facilitation Tip

During Card Match, circulate and ask pairs to justify their matches aloud so you can catch partial explanations before they take root.

What to look for

Present students with the expression 5(2y + 3). Ask them to write down the steps they would take to expand this expression and then write the final expanded form. Check for correct application of the distributive law.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 02

• Peer Teaching
• 35 min · Small Groups

Area Model Stations: Small Groups

Set up stations with grid paper for drawing area models of expansions like 5(x + 3). Groups rotate, create models, label areas, and expand algebraically. Each group presents one model to the class for feedback.

Compare expanding brackets to multiplying numbers.

Facilitation Tip

At Area Model Stations, provide colored tiles and insist groups label each part of their diagram before writing the algebra, forcing attention to all terms.

What to look for

Give each student a card with an expression like 3(a - 4). Ask them to expand the expression and then write one sentence comparing their method to how they would calculate 3 x 16. Collect responses to gauge understanding of the distributive principle.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 03

• Peer Teaching
• 20 min · Whole Class

Bracket Relay: Whole Class

Divide class into teams. Project an expression; first student from each team runs to board, expands part of it, tags next teammate. First team to fully expand correctly wins. Review as class.

Design an expression that requires expanding a single bracket.

Facilitation Tip

In Bracket Relay, stand at the halfway point to listen for teams correcting missed terms or signs before they move on.

What to look for

Pose the question: 'Imagine you are designing a new video game level and need to calculate the total score for a player who earns points in a specific way. How could expanding brackets help you write a formula for their score?' Facilitate a brief class discussion on how algebraic expressions can model real-world scenarios.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 04

• Peer Teaching
• 30 min · Individual

Expression Creator: Individual

Students design three original single-bracket expressions, expand them, and explain the distributive law in their own words. Collect and share two examples per student in a class gallery walk for peer feedback.

Explain how the distributive law works in expanding brackets.

Facilitation Tip

For Expression Creator, check individual work after 10 minutes to redirect students who treat expansion as simply removing brackets.

What to look for

Present students with the expression 5(2y + 3). Ask them to write down the steps they would take to expand this expression and then write the final expanded form. Check for correct application of the distributive law.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with concrete models like algebra tiles or grid drawings so students see how expansion covers the whole area, not just the first term. Move quickly to structured group tasks where students must explain their steps to peers, because teaching others reveals gaps in understanding. Avoid rushing to rules before students have tested multiple cases themselves; the distributive law makes sense when they see it working repeatedly.

Success looks like students applying the distributive law correctly in every context, including negative terms and variables. They should explain their steps verbally or in writing, showing they understand why each term changes. Peer feedback during group tasks confirms shared understanding across the class.

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Watch Out for These Misconceptions

• During Card Match, watch for pairs who only match the first term of each expression and ignore the rest.

  Ask each pair to state the full expanded form aloud before confirming the match, ensuring all terms are addressed.

• During Card Match, watch for students who assume a negative sign outside flips every sign inside the bracket.

  Have them test each negative pair with colored tiles to see that -2(x - 3) becomes -2x + 6, not -2x - 6.

• During Bracket Relay, watch for teams that remove brackets without changing the terms inside.

  Pause the race and ask the team to build the expanded form with tiles before continuing, reinforcing the multiplication step.

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Methods used in this brief

• Peer Teaching