Mathematics · Year 6

Active learning ideas

Applying the Order of Operations (BODMAS)

Active learning helps Year 6 students internalise BODMAS because procedural fluency requires repeated, deliberate practice with immediate feedback. When students move, discuss, and justify steps aloud, they convert abstract rules into tangible actions, reducing errors that come from passive reading or rushed calculations.

• ACARA Content Descriptions
• AC9M6A03

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 30 min · Small Groups

Simulation Game: BODMAS Relay Race

Divide the class into teams of four. Display a complex expression on the board. The first student writes the bracket step, passes the marker to the next for Orders, then Division/Multiplication, and finally Addition/Subtraction. First team with correct answer wins a point. Repeat with five expressions.

Why is a universal order of operations necessary for mathematics?

Facilitation Tip

For BODMAS Relay Race, place expressions on separate cards at stations so teams rotate with clear roles like writer, calculator, and explainer to keep everyone accountable.

What to look for

Present students with a series of expressions, some correctly solved and some with errors. Ask them to identify which expressions are solved correctly according to BODMAS and to circle the errors in the incorrect ones, explaining their reasoning briefly.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Stations Rotation
• 25 min · Pairs

Bracket Challenge Pairs

Provide pairs with expressions lacking brackets, such as 10 - 2 × 3 + 4. Partners insert brackets in two different positions, calculate both results, and explain the differences. Share one pair's work with the class for discussion.

How can changing the position of brackets alter the outcome of an expression?

Facilitation Tip

During Bracket Challenge Pairs, insist students verbalise each step before writing, so partners catch misplaced operations early.

What to look for

Give students the expression: 5 + (3 × 2)² ÷ 3. Ask them to write down each step of their calculation, showing how they applied BODMAS, and to state the final answer.

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

Activity 03

• Stations Rotation
• 40 min · Small Groups

Error Hunt Stations

Set up four stations, each with five expressions containing common BODMAS errors. Small groups visit each station, identify mistakes, correct them, and justify changes on worksheets. Rotate every seven minutes and debrief as a class.

Is the order of operations a discovery or a human invention?

Facilitation Tip

Set a timer of 2 minutes per expression in Error Hunt Stations to prevent overanalysis and encourage quick error spotting through comparison.

What to look for

Pose the question: 'Imagine two people solve the same problem, but one uses BODMAS and the other does not. What is the most likely outcome? Why is having a standard order important for mathematics?' Facilitate a class discussion on consistency and communication.

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

Activity 04

• Stations Rotation
• 35 min · Pairs

Expression Creator Workshop

Individually, students write three multi-step expressions using BODMAS, including brackets. They swap with a partner to solve and check answers together. Compile correct ones for a class BODMAS poster.

Why is a universal order of operations necessary for mathematics?

Facilitation Tip

Have students use colour coding in Expression Creator Workshop—red for Brackets, blue for Orders, green for Division/Multiplication, yellow for Addition/Subtraction—to visually reinforce priority levels.

What to look for

Present students with a series of expressions, some correctly solved and some with errors. Ask them to identify which expressions are solved correctly according to BODMAS and to circle the errors in the incorrect ones, explaining their reasoning briefly.

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

A few notes on teaching this unit

Teach BODMAS by modelling written steps with colour coding and think-alouds to make invisible priorities visible. Avoid rushing to abstract notation; anchor understanding in concrete examples where students physically group or reorder expression parts. Research shows that students who verbalise steps aloud while writing develop stronger metacognitive control over their calculations.

Students will solve multi-step expressions accurately, recording each step clearly and explaining their reasoning to peers. They will identify and correct errors in others’ work, showing confidence in applying BODMAS priorities and left-to-right processing where required.

---

Watch Out for These Misconceptions

• During BODMAS Relay Race, watch for students calculating 6 ÷ 2 × 3 as 1 instead of 9. The relay’s timed stations and peer roles push teams to compare step-by-step work immediately, prompting quick correction when mismatched answers appear.

  Circulate during Bracket Challenge Pairs and ask students to explain why 12 ÷ 3 × 4 equals 16, not 16. Partners must justify their steps aloud, reinforcing that division and multiplication are processed left to right even when multiplication feels more familiar.

• During Error Hunt Stations, watch for students calculating exponents after multiplication or division, resulting in 2 × 3² being read as 36 instead of 18. The station’s error cards and group discussions expose this gap clearly.

  After Expression Creator Workshop, have students swap their created expressions and solutions with peers. Missteps in exponent placement will surface as partners recalculate and debate, clarifying that Orders always precede multiplication and division.

---

Methods used in this brief

• Simulation Game
• Stations Rotation