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.

• Year 6
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Calculate the value of numerical expressions using the order of operations (BODMAS) with accuracy.
2. Compare the outcomes of mathematical expressions when the order of operations or bracket placement is altered.
3. Explain the necessity of a standardized order of operations for consistent mathematical communication.
4. Identify and correct errors in calculations that misapply the order of operations.

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

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.

What to Expect

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

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Error Hunt Stations, display a list of three expressions, two correctly solved and one with errors. Ask students to circle the incorrect one and write the corrected steps using BODMAS priorities.

Exit Ticket

After BODMAS Relay Race, give students the expression 5 + (3 × 2)² ÷ 3. Collect their written steps showing Brackets first, then Orders, followed by Division, and finally Addition, with the correct final answer.

Discussion Prompt

During Expression Creator Workshop, pose the question: ‘Two people solve the same problem, but one uses BODMAS and the other does not. What is the most likely outcome?’ Facilitate a discussion on consistency and why a standard order matters for clear mathematical communication.

Extensions & Scaffolding

• Challenge: Provide expressions with nested brackets and exponents like ((2 + 3)² × 2) - 4³ ÷ 8, asking students to create their own using dice rolls for numbers and spinners for operations.
• Scaffolding: Offer partially completed worked examples with missing steps for students to fill in, focusing on left-to-right processing within multiplication/division and addition/subtraction.
• Deeper exploration: Ask students to create a ‘BODMAS detective guide’ with annotated examples showing how ignoring the rules changes outcomes, including algebraic expressions such as 3a + 2b² when a = 2 and b = 3.

Key Vocabulary

BODMAS	An acronym representing the order of operations: Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Expression	A mathematical phrase that contains numbers, variables, and operators, but does not have an equals sign.
Operation	A mathematical process such as addition, subtraction, multiplication, or division.
Bracket	Symbols used in mathematics to group parts of an expression, indicating that the operation within them should be performed first.
Exponent	A number that shows how many times the base number is multiplied by itself.