Order of Operations (BIDMAS/BODMAS)

Active learning works for Order of Operations because students must physically manipulate symbols and justify each step aloud, turning abstract rules into visible logic. When students correct errors or build expressions themselves, they internalize priorities rather than memorize steps. Immediate peer feedback turns mistakes into teachable moments that no worksheet can replicate.

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

Learning Objectives

1. Calculate the value of complex numerical expressions by correctly applying the order of operations (BIDMAS/BODMAS).
2. Analyze how the placement of brackets alters the sequence and outcome of operations within an expression.
3. Critique a given calculation, identifying and explaining errors resulting from the misapplication of BIDMAS/BODMAS rules.
4. Compare the results of calculations performed with and without adherence to the standard order of operations to justify its necessity.

Escape Room

⏱ 30 min·Pairs

Error Hunt: Spot the BIDMAS Mistakes

Provide worksheets with 10 expressions solved incorrectly. In pairs, students identify the error, explain the correct BIDMAS application, and rewrite the solution. Pairs then swap sheets with another pair for verification.

Prepare & details

Justify the need for a specific order of operations in complex calculations.

Facilitation Tip: During Error Hunt, circulate with a red pen and mark only the first error students find, then challenge them to locate the next one to deepen scrutiny.

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

Card Sort: Build and Solve Expressions

Distribute cards with numbers, operations, and brackets. Small groups assemble expressions following BIDMAS rules, solve them, and justify their order to the class. Extend by creating challenging ones for others.

Prepare & details

Analyze how brackets alter the priority of operations within an expression.

Facilitation Tip: For Card Sort, give each pair a timer and ask them to justify their final expression’s order aloud before solving it.

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

⏱ 35 min·Small Groups

Relay Critique: Team Calculation Race

Divide class into teams. Each student solves one step of a long expression on a board, passing a baton. If a BIDMAS error occurs, the team discusses and corrects before continuing.

Prepare & details

Critique a calculation that has been performed incorrectly due to misapplication of BIDMAS.

Facilitation Tip: In Relay Critique, stand at the end of the line so you see every team’s calculation and can stop play instantly when priorities are ignored.

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·Individual

Bracket Builder: Individual Challenges

Students receive expressions without brackets and add them to achieve target answers. They test solutions using BIDMAS and share strategies in a whole-class debrief.

Prepare & details

Justify the need for a specific order of operations in complex calculations.

Facilitation Tip: Use Bracket Builder as a silent 5-minute task where students cannot speak, forcing them to rely on written notation to clarify their thinking.

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 Order of Operations by starting with simple expressions where students predict answers before learning the rule, then reveal the discrepancy to create cognitive need. Use color-coding on the board: brackets in red, indices in blue, division/multiplication in green, addition/subtraction in black. Research shows that pairing verbal explanations with written steps strengthens retention more than silent practice alone.

What to Expect

Successful learning looks like students applying BIDMAS/BODMAS automatically, explaining choices in their own words, and spotting errors in others’ work without prompting. They should justify their order with the rules and adjust calculations when peers challenge their steps. Confidence grows when students can defend their answers with clear, step-by-step reasoning.

Watch Out for These Misconceptions

Common Misconception

During Error Hunt, watch for students who mark all errors but cannot explain why one priority overrides another in their corrections.

What to Teach Instead

After they identify the first error, hand them a mini whiteboard and ask them to write the correct order using BIDMAS acronym before solving the expression step by step.

Common Misconception

During Card Sort, watch for students who group multiplication before division regardless of their position in the expression.

What to Teach Instead

Have them lay out the cards in a line and use two different colored highlighters to mark division and multiplication steps, then defend their left-to-right order to a peer.

Common Misconception

During Bracket Builder, watch for students who treat brackets as purely for addition and subtraction, ignoring divisions or multiplications inside them.

What to Teach Instead

Give them a fresh expression where brackets contain a division, then ask them to recalculate and explain why brackets must be resolved first, no matter what operation is inside.

Assessment Ideas

Quick Check

After Card Sort, display three solved expressions on the board—one correct and two with different BIDMAS errors—and ask students to identify which are right and justify their choices with the rule.

Discussion Prompt

During Relay Critique, when a team presents their answer, ask the class to vote silently on whether the order is correct, then select one student to explain the mistake using the BIDMAS acronym aloud.

Exit Ticket

After Bracket Builder, give each student an exit card with a bracketed expression and ask them to write the first operation they will perform and why, then calculate the final answer on the back.

Extensions & Scaffolding

• Challenge: Give students expressions with nested brackets and indices to create their own BIDMAS puzzles for peers to solve.
• Scaffolding: Provide a laminated BIDMAS flowchart with blanks for students to fill during calculations until they internalize the order.
• Deeper exploration: Ask students to research how BIDMAS/BODMAS applies to spreadsheets or programming languages, then present one real-world example to the class.

Key Vocabulary

BIDMAS/BODMAS	An acronym representing the order of mathematical operations: Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction.
Brackets	Symbols used to group parts of a mathematical expression, indicating that operations within them must be performed first.
Indices/Orders	Operations involving exponents, such as squares or cubes, which are performed after brackets but before multiplication, division, addition, and subtraction.
Operation Precedence	The established hierarchy that dictates the sequence in which mathematical operations should be performed to ensure a consistent result.