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.

• Year 7
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the expanded form of algebraic expressions involving single brackets using the distributive law.
2. Explain the distributive law as it applies to multiplying a term by an expression within brackets.
3. Compare the process of expanding single brackets to multiplying a whole number by a two-digit number.
4. Design an algebraic expression that requires expanding a single bracket to simplify.

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.

Prepare & details

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.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

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.

Prepare & details

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.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

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.

Prepare & details

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.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

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.

Prepare & details

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.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Quick Check

After Card Match, present 5(2y + 3) and ask students to write the expanded form on mini-whiteboards, checking for correct steps.

Exit Ticket

During Area Model Stations, give each student 3(a - 4) and ask them to expand it, then write one sentence comparing their method to mental math with 3 x 16.

Discussion Prompt

After Bracket Relay, pose the scenario about designing a video game score formula and facilitate a 3-minute class discussion on how expanding brackets models the situation.

Extensions & Scaffolding

• Challenge early finishers to create three expressions with negative terms outside the bracket, then expand and check each other’s work.
• Scaffolding for strugglers includes using two-color counters to mark negative and positive terms during Area Model Stations.
• Deeper exploration asks students to design a word problem where expanding brackets calculates a real-world quantity, then solve it algebraically.

Key Vocabulary

Distributive Law	A rule in algebra stating that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. For example, a(b + c) = ab + ac.
Expand	To rewrite an algebraic expression by removing brackets, typically by applying the distributive law.
Term	A single number or variable, or numbers and variables multiplied together. Terms are separated by '+' or '-' signs.
Coefficient	The numerical factor of a term containing a variable. For example, in 3x, the coefficient is 3.