BODMAS Mastery

Overview

In this final lesson of the unit, students consolidate the order of operations using BODMAS/BIDMAS. They will solve interactive challenges that mix brackets, powers, multiplication and division, and addition and subtraction, moving from routine practice to more complex expressions.

Learning intentions

• Students will apply BODMAS/BIDMAS to evaluate expressions correctly.
• Students will substitute values into expressions and simplify step-by-step.
• Students will explain why each operation is performed in the correct order.
• Students will persevere through multi-step problems, checking for errors.

Success criteria

• I can evaluate expressions using BODMAS/BIDMAS with correct intermediate steps.
• I can handle brackets and powers before multiplication/division, then addition/subtraction.
• I can substitute values for variables and simplify accurately.
• I can justify the order I used in my final answer.

Curriculum links

• Working mathematically: become fluent with increasingly complex problems through varied and frequent practice.
• Working mathematically: select and use appropriate calculation strategies to solve increasingly complex problems.
• Working mathematically: substitute values in expressions, rearrange and simplify expressions, and solve equations.
• Working mathematically: solve problems by breaking them into a series of simpler steps and persevering.

Lesson structure (60 minutes)

1. 0–5 min · Retrieval warm-up. Teacher displays 4 quick “pick the next step” expressions on the board (no solutions shown). Students work silently, then hold up A/B/C/D for which operation to do next.

2. 5–15 min · Mini-recap and modelling. Teacher models 2 worked examples: one with brackets and one with powers, explicitly verbalising BODMAS/BIDMAS and highlighting common mistakes (e.g., doing addition before multiplication). Students copy the structure of the working into books using “Step 1, Step 2…” headings.

3. 15–30 min · Interactive challenge: “Operation Sort.” Teacher hands out cards (or a printable slide) with parts of expressions and a separate set of operation labels: Brackets, Indices, Multiply/Divide, Add/Subtract. In pairs, students:

• sort the cards into the correct order,
• then evaluate 2 full expressions as a pair (teacher circulates, checking that they follow the same order they sorted).

4. 30–45 min · Puzzles: “Find the value.” Teacher gives each student a short worksheet with 3–4 expressions involving substitution (e.g., evaluate when (x=3), (y=2)). Students calculate one expression at a time, showing substitution first, then applying BODMAS/BIDMAS to simplify. Teacher prompts: “What should you do first, and why?”

5. 45–55 min · Class quiz: “BODMAS Beat the Clock.” Teacher runs a rapid-fire quiz (single round, 8 questions). Students answer on mini-whiteboards. After each question, teacher quickly checks 1–2 strategies and corrects misconceptions (especially order between multiplication and division, and between addition and subtraction).

6. 55–60 min · Exit ticket: justify the step. Students complete a final mixed expression and add a one-sentence explanation: “I did ___ first because ___.” Teacher collects and checks for correct ordering and reasoning.

Resources

• Mini-whiteboards and pens
• Student worksheet: Operation Sort (or cards) plus “Find the value” substitution questions
• Teacher board slides or printed problem set for the quiz
• Card set or labels for operation sorting (Brackets, Indices, Multiply/Divide, Add/Subtract)
• Worked examples model sheet (optional)
• Timer for the quiz
• Exit ticket slips

Assessment

• Observe pair work during Operation Sort: check that students follow the same ordered stages they chose when sorting.
• During teacher modelling and circulation, use quick questions: “What’s first? What comes next?” to check conceptual understanding, not just answers.
• Check mini-whiteboards in the quiz for common errors (e.g., ignoring brackets or performing addition before multiplication).

Differentiation

• Support:
• Provide sentence starters: “First I look at ___, then I do ___, because…”
• Offer a step-by-step scaffold box on the worksheet: Brackets → Indices → Multiply/Divide → Add/Subtract.
• Include one “worked example of the same type” on the sheet for students who need extra structure.
• Challenge/extension (without leaving the topic):
• Add an extra puzzle line where students must compare two answers and identify which step violates BODMAS/BIDMAS.
• Include expressions with nested brackets (still within Year 7 complexity).
• SEN/EAL:
• Keep language consistent: always refer to “order of operations” and the exact stages (Brackets, Indices, Multiply/Divide, Add/Subtract).
• Use colour coding on the worksheet (e.g., brackets shaded) to reduce visual load while students practise the same reasoning.
• Reasoning:
• Require the one-sentence justification on the exit ticket so students demonstrate understanding of order, not just computation.