Mathematics · Year 7

Active learning ideas

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.

• ACARA Content Descriptions
• AC9M7N01

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Present students with three expressions, each with a different complexity level requiring BODMAS/PEMDAS. Ask them to solve each one on mini-whiteboards and hold them up. Observe for common errors related to specific steps.

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

Activity 02

• 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.

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.

What to look for

Provide students with the expression: 5 + 3 x (6 - 2)^2. Ask them to solve it step-by-step, showing their work. Then, ask: 'What would the answer be if the parentheses were removed?'

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

Activity 03

• 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.

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.

What to look for

Pose the question: 'Imagine you and a friend are calculating the cost of buying 4 items at $5 each, with a $2 discount. Why is it important that you both agree on the order of operations to get the same final price?' Facilitate a brief class discussion.

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

Activity 04

• 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.

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.

What to look for

Present students with three expressions, each with a different complexity level requiring BODMAS/PEMDAS. Ask them to solve each one on mini-whiteboards and hold them up. Observe for common errors related to specific steps.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Escape Room