Order of Operations (BODMAS/PEMDAS)

Active learning works because the order of operations is a procedural skill best mastered through repeated, immediate practice with feedback. Students solidify their understanding when they see how ignoring BODMAS changes answers, making abstract rules concrete through hands-on challenges.

• Year 7
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Evaluate numerical expressions using the order of operations (BODMAS/PEMDAS) with accuracy.
2. Analyze how the placement of parentheses and operations affects the final result of an expression.
3. Create a mathematical expression that requires specific application of the order of operations to solve.
4. Justify the necessity of a standardized order of operations for clear mathematical communication.

Escape Room

⏱ 35 min·Small Groups

Relay Race: BODMAS Challenges

Divide class into teams of four. Each student solves one expression following BODMAS on a card, then tags the next teammate who builds on it. Teams compare final answers and explain steps. Debrief as a class on common pitfalls.

Prepare & details

Justify the importance of a consistent order of operations in mathematics.

Facilitation Tip: During Relay Race, have each team member solve one step before passing the board marker to avoid groupthink and ensure individual accountability.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Escape Room

⏱ 45 min·Small Groups

Error Hunt Stations

Set up four stations with expressions solved incorrectly. Groups rotate, identify the error, rewrite correctly, and justify using BODMAS. Record findings on a shared class chart for discussion.

Prepare & details

Analyze how a single misplaced operation can drastically alter the outcome of an expression.

Facilitation Tip: At Error Hunt Stations, provide answer keys so students can immediately verify their corrections and focus on reasoning rather than guessing.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Escape Room

⏱ 25 min·Pairs

Expression Builder Pairs

Pairs create two expressions with the same digits and operations but different results due to order. Swap with another pair to solve both ways and add brackets for clarity. Share and vote on most ambiguous.

Prepare & details

Construct an expression that requires careful application of the order of operations to solve.

Facilitation Tip: For Expression Builder Pairs, require pairs to write two different expressions with the same answer by rearranging operations, reinforcing flexibility within the rules.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Escape Room

⏱ 30 min·Whole Class

BODMAS Bingo Whole Class

Give students bingo cards with expressions. Call out answers; students mark if their expression matches after computing. First to line wins, then verify all calculations together.

Prepare & details

Justify the importance of a consistent order of operations in mathematics.

Facilitation Tip: Run BODMAS Bingo slowly at first, pausing after each number to discuss why it matches a specific BODMAS step before moving on.

Setup: Group tables with puzzle envelopes, optional locked boxes

Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards

• Remember
• Apply
• Analyze
• Relationship Skills
• Self-Management

Teaching This Topic

Teach with a mix of urgency and patience. Start with quick diagnostic mini-whiteboard checks to surface misconceptions early, then use station rotations to isolate and practice troublesome steps like nested brackets or left-to-right division/multiplication. Avoid lengthy lectures; instead, rely on peer discussion and immediate feedback loops to build automaticity. Research shows that students retain order of operations best when they repeatedly correct errors in real time rather than re-reading rules.

What to Expect

Students will confidently apply BODMAS/PEMDAS to multi-step expressions, explain their reasoning clearly, and recognize the impact of misapplied steps. Success looks like correct solutions paired with verbal justifications about why each operation was performed in sequence.

Watch Out for These Misconceptions

Common Misconception

During Relay Race, watch for students performing operations strictly left to right, ignoring priority.

What to Teach Instead

Before starting the relay, present a simple example like 8 ÷ 2 x 4 and have teams solve it two ways: left-to-right and following BODMAS. Ask them to compare answers and identify which matches the given rules, reinforcing that DM and AS are left-to-right only.

Common Misconception

During Error Hunt Stations, watch for students assuming multiplication always comes before division.

What to Teach Instead

At each station, include a pair of expressions where division and multiplication appear in different orders, such as 12 ÷ 3 x 2 versus 12 x 2 ÷ 3. Ask students to compute both and graph the results, highlighting that the answers are the same when operations are performed left to right.

Common Misconception

During Relay Race, watch for students forgetting to resolve inner brackets first.

What to Teach Instead

Include expressions with nested brackets like (3 + (2 x 4)) - 5. When a team’s partial solution is incorrect, ask them to re-examine the innermost brackets first and trace the steps backward, building habits of step-by-step verification.

Assessment Ideas

Quick Check

After Relay Race, present three expressions of varying complexity on the board and ask students to solve them on mini-whiteboards. Observe for errors related to brackets, orders, or left-to-right rules for DM/AS.

Exit Ticket

During BODMAS Bingo, collect each student’s bingo card with their solutions to the called expressions. Review their work to assess whether they applied BODMAS correctly and identify any recurring errors.

Discussion Prompt

After Expression Builder Pairs, facilitate a class discussion using the prompt: 'Your expressions had the same answer but different orders. Why is it important to agree on the order before comparing results?' Listen for students to connect BODMAS to clear mathematical communication.

Extensions & Scaffolding

• Challenge: Provide expressions with multiple sets of nested brackets and ask students to create a visual flowchart showing the order of operations.
• Scaffolding: Give students a color-coded reference strip with BODMAS steps and allow them to use it during early activities until they internalize the sequence.
• Deeper exploration: Introduce expressions with exponents and fractions, asking students to justify each step in writing while solving for an unknown variable.

Key Vocabulary

Order of Operations	A set of rules that dictates the sequence in which mathematical operations should be performed to ensure a consistent result.
Parentheses/Brackets	Symbols used to group parts of an expression, indicating that the operations within them must be performed first.
Indices/Orders	Exponents or powers, which are typically performed after parentheses but before multiplication and division.
BODMAS/PEMDAS	Mnemonics used to remember the order of operations: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right).