Order of Operations (BODMAS/PEMDAS)

Order of operations can feel abstract to students until they see how ignoring it changes answers completely. Active tasks like relay races and puzzles make the sequence visible and memorable, turning a rule into a tool they trust. When students explain steps aloud and compare results, they internalize why the order matters, not just how to follow it.

• 6th-class
• Mastering Mathematical Reasoning
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the result of multi-step mathematical expressions using the BODMAS order of operations.
2. Compare the outcomes of calculations when operations are performed in different orders.
3. Explain the necessity of a standardized order of operations for consistent mathematical results.
4. Identify and apply the correct sequence of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction) to solve complex problems.
5. Evaluate mathematical expressions containing parentheses, exponents, and mixed operations accurately.

Problem-Based Learning

⏱ 25 min·Pairs

Card Game: BODMAS Relay

Prepare cards with multi-step expressions. In pairs, one student solves the first step aloud while the partner checks using BODMAS rules, then they switch for the next expression. First pair to finish 10 cards correctly wins. Debrief as a class on tricky steps.

Prepare & details

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

Facilitation Tip: During BODMAS Relay, circulate and listen for students verbalizing each step as they solve, not just writing answers.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Small Groups

Group Challenge: Expression Puzzles

Small groups receive jumbled operation cards and must arrange them into a correct BODMAS sequence to match a given answer. Groups present their solutions, justifying each step. Class votes on the most creative puzzle.

Prepare & details

Analyze how changing the order of operations can alter the outcome of a calculation.

Facilitation Tip: For Expression Puzzles, encourage groups to swap puzzles after solving to verify answers together before sharing with the class.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 20 min·Whole Class

Whole Class: Error Detective Hunt

Project sample calculations with deliberate BODMAS errors. Students individually spot and correct mistakes, then share in a class discussion. Tally common errors to reinforce rules.

Prepare & details

Apply BODMAS rules to solve multi-step problems and verify the solution.

Facilitation Tip: In Error Detective Hunt, model how to underline the first operation to apply and annotate why, so students adopt this habit.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 30 min·Pairs

Pairs Practice: Create and Solve

Partners invent expressions following BODMAS, swap with another pair to solve, and verify answers together. Discuss any discrepancies.

Prepare & details

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

Facilitation Tip: For Create and Solve in pairs, ask students to swap expressions and solve them aloud to rehearse the sequence.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Teachers often start by modeling a worked example on the board, thinking aloud as they decide which operation to tackle first. Avoid rushing to the answer: pause after each step and ask students to predict what comes next. Research shows that students learn order of operations best when they create their own expressions and explain the reasoning to others, so pair practice and puzzle tasks are essential. Keep drill worksheets brief and use them only after students have built confidence through active tasks.

What to Expect

By the end of these activities, students will solve multi-step problems correctly, justify each step using BODMAS vocabulary, and spot errors in their own or peers' work. They will also explain in their own words why left-to-right matters for equal-priority operations and why brackets come first.

Watch Out for These Misconceptions

Common Misconception

During BODMAS Relay, watch for students performing operations strictly left to right, ignoring the rule.

What to Teach Instead

In the relay, hand each team a card with a problem like 2 + 3 × 4. Require them to write each step on a whiteboard and invite a volunteer to explain why 14 is correct, tracing the multiplication first.

Common Misconception

During BODMAS Relay, watch for students assuming multiplication always comes before division regardless of position.

What to Teach Instead

Include cards like 12 ÷ 3 × 2 and ask teams to write both possible answers then debate which is correct, referencing the left-to-right rule before moving to the next card.

Common Misconception

During Expression Puzzles, watch for students ignoring brackets when they seem simple.

What to Teach Instead

Provide puzzles where removing brackets changes the answer dramatically, such as (6 + 2) × 3 versus 6 + 2 × 3. Ask students to build both expressions with counters or drawings to see the impact before solving.

Common Misconception

Assessment Ideas

Quick Check

Present students with a worksheet containing 3-4 multi-step problems. Ask them to solve each problem, showing each step clearly and circling their final answer. Review for accuracy in applying BODMAS.

Discussion Prompt

Write two solutions to the same problem on the board, one correct and one incorrect due to a wrong order of operations. Ask students: 'Which solution is correct and why? What rule did the incorrect solution break?' Facilitate a class discussion on the importance of consistency.

Exit Ticket

Give each student a card with a simple expression like '5 + 3 x 2'. Ask them to write down the answer and then write one sentence explaining the order of operations they used to get that answer.

Extensions & Scaffolding

• Challenge early finishers to design a BODMAS scrambled expression that requires all four steps and trade with a partner.
• Scaffolding for struggling students: provide expressions with color-coded brackets and equal-priority operations marked with arrows to guide left-to-right flow.
• Deeper exploration: invite students to write a one-page explanation of BODMAS for a younger classmate, including two examples with common mistakes and fixes.

Key Vocabulary

BODMAS	An acronym representing the order of operations: Brackets, Orders (powers and square roots), Division, Multiplication, Addition, and Subtraction.
Parentheses	Symbols used to group parts of a mathematical expression, indicating that the operations within them should be performed first.
Exponents	A number showing how many times the base number is multiplied by itself; also referred to as 'Orders' in BODMAS.
Order of Operations	A set of rules that dictates the sequence in which mathematical operations should be performed to ensure a consistent and correct answer.