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.

• Year 7
• Mathematics
• 3 activities
• 20 min–30 min

Learning Objectives

1. Compare the efficiency of different mental addition strategies, such as partitioning and bridging, for whole numbers up to 1000.
2. Explain how the inverse relationship between addition and subtraction can be used to verify the accuracy of subtraction calculations.
3. Calculate the sum or difference of integers, including negative numbers, using a chosen strategy.
4. Construct a word problem where estimation is a more appropriate method for finding an approximate sum than exact calculation.

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.

Prepare & details

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.

Setup: Two teams facing each other, audience seating for the rest

Materials: Debate proposition card, Research brief for each side, Judging rubric for audience, Timer

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

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

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Structured Debate: The Viral Equation, give students three calculations (e.g., 7 + 3 × 2, 15 – 4 + 2, 8 × (2 + 3)) and ask them to solve and justify each using the order of operations rules they debated.

Exit Ticket

During Collaborative Investigation: Target Number, ask each student to write one sentence explaining why their group’s target number required specific brackets or operation order, then collect these to check for accurate use of terminology.

Discussion Prompt

After Peer Teaching: Error Detectives, pose a new calculation with a common error (e.g., 12 ÷ 2 × 3 = 2 instead of 18) and ask students to discuss in pairs how the error violates BIDMAS before sharing with the class.

Extensions & Scaffolding

• Challenge students to create their own viral equation with brackets and operations that deliberately trick peers, then swap and solve.
• Scaffolding: Provide partially completed worked examples with missing brackets for students to finish, focusing on where parentheses would change the outcome.
• Deeper exploration: Have students research historical mathematical ambiguities caused by unclear order of operations and present their findings to the class.

Key Vocabulary

Mental Mathematics	Performing calculations in your head without the use of written methods or calculators.
Partitioning	Breaking down a number into its place value components (e.g., 345 becomes 300, 40, and 5) to simplify addition or subtraction.
Bridging	Adding or subtracting to the nearest multiple of 10 or 100 to make calculations easier, often used in mental strategies.
Inverse Operation	An operation that reverses the effect of another operation, such as addition reversing subtraction.
Estimation	Finding an approximate answer to a calculation by rounding numbers to make them easier to work with.