Mathematics · Year 7

Active learning ideas

Addition and Subtraction Strategies

Active learning works for this topic because students need to physically manipulate the order of operations to see how small changes in grouping or sequencing can produce dramatically different results. When students debate, investigate, and teach each other, they transform abstract rules into concrete understanding that sticks far longer than passive note-taking.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Formal Debate
• 20 min · Whole Class

Formal Debate: The Viral Equation

Present a controversial 'internet' maths problem (e.g., 8 ÷ 2(2+2)). Divide the class into teams to argue for different answers based on their interpretation of BIDMAS, eventually reaching a consensus through logical proof.

Differentiate between various addition strategies and assess their efficiency.

Facilitation Tip

During the Viral Equation debate, assign specific roles so that every student must articulate a clear position and respond to counterarguments, preventing quiet observers from slipping through.

What to look for

Present students with three addition problems: 45 + 67, 132 + 89, 567 + 234. Ask them to solve the first using partitioning, the second by bridging, and the third using a written method, then state which strategy they found most efficient for each and why.

• Analyze
• Evaluate
• Create
• Self-Management
• Decision-Making

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Target Number

Give small groups four numbers and a target total. Students must use brackets and different operations to create an expression that equals the target, testing their understanding of how operation priority changes the outcome.

Explain how inverse operations can be used to check subtraction calculations.

Facilitation Tip

In Target Number, provide each group with a whiteboard and marker so they can physically draw brackets and arrows to show their thinking as they rearrange the numbers.

What to look for

Give students the calculation 73 - 28. Ask them to solve it using a mental strategy and then write one sentence explaining how they could use addition to check their answer.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Peer Teaching
• 25 min · Pairs

Peer Teaching: Error Detectives

Provide pairs with 'completed' worksheets full of common BIDMAS errors. Students must act as teachers to find the mistakes, explain why they happened, and provide the correct solution using a step-by-step breakdown.

Construct a scenario where estimation is more appropriate than exact calculation for addition.

Facilitation Tip

In Error Detectives, give each pair a red pen so they can mark corrections directly on the worked examples, making their feedback visible and immediately usable.

What to look for

Pose the scenario: 'You need to buy ingredients for a bake sale. You have a list of 15 items with prices ranging from £0.50 to £4.00. Would you calculate the exact total cost or estimate it? Explain your reasoning, considering the purpose of the calculation.'

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

A few notes on teaching this unit

Teachers approach this topic by starting with simple expressions and gradually increasing complexity, always asking students to verbalise the rule they are applying. Avoid teaching acronyms alone without context, as students often memorise BIDMAS without understanding why division and multiplication share priority. Research suggests that students benefit from seeing the same problem solved multiple ways (e.g., mentally, written, calculator) to build flexible thinking and check for consistency.

Successful learning looks like students confidently applying BIDMAS/BODMAS without prompting, explaining their reasoning aloud, and justifying their steps when challenged by peers. You will hear students referencing the hierarchy naturally and catching errors in each other’s work during collaborative tasks.

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Watch Out for These Misconceptions

• During the Structured Debate: The Viral Equation, watch for students insisting that addition must always come before subtraction because 'A' comes before 'S' in BIDMAS.

  Use the debate script to model left-to-right calculation on a projected number line, physically moving a counter to show how the result depends on order rather than the letter sequence in the acronym.

• During Collaborative Investigation: Target Number, watch for students ignoring brackets or treating them as decorative rather than structural.

  Have two groups solve the same numbers with different bracket placements, then present their totals side by side so the class sees how brackets shift where the calculation starts, making the priority visible.

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Methods used in this brief

• Formal Debate
• Inquiry Circle
• Peer Teaching