The Order of Operations (BOMDAS/BIMDAS)

Active learning makes the abstract rules of BOMDAS memorable and meaningful. When students physically match expressions or rotate through stations, they see why the order matters rather than just hearing it. Calculations become less about memorizing steps and more about reasoning through real examples together.

• 5th Class
• Mathematical Mastery: Exploring Patterns and Logic
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the result of multi-step arithmetic expressions using the BOMDAS/BIMDAS order of operations.
2. Compare the outcomes of calculations when brackets are placed in different positions within an expression.
3. Explain the necessity of a standardized order of operations for consistent mathematical results.
4. Identify the correct sequence of operations (Brackets, Orders, Division/Multiplication, Addition/Subtraction) in given expressions.

Stations Rotation

⏱ 25 min·Pairs

Pairs Game: Expression Matching

Provide cards with expressions on one set and correct results on another. Pairs apply BOMDAS to match them, then swap and check partners' work. Discuss any mismatches as a class.

Prepare & details

Explain why a universal order of operations is necessary in mathematics.

Facilitation Tip: During the Pairs Game, circulate and listen for students debating answers; this is where the most powerful learning happens.

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·Small Groups

Small Groups: Bracket Challenge Stations

Set up stations with expressions missing brackets. Groups insert brackets to achieve given targets, test calculations, and rotate. Share strategies at the end.

Prepare & details

Analyze how changing the position of brackets can alter the outcome of a calculation.

Facilitation Tip: In Bracket Challenge Stations, place a timer for each round to create urgency and focus the group’s attention on accuracy.

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

⏱ 30 min·Whole Class

Whole Class: Error Detective Relay

Write expressions with deliberate mistakes on the board. Teams race to spot and correct order of operations errors, explaining their fixes aloud.

Prepare & details

Predict what would happen to scientific data if everyone used their own order of operations.

Facilitation Tip: For the Error Detective Relay, assign roles clearly so students rotate tasks and stay engaged throughout the activity.

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

⏱ 20 min·Individual

Individual: Prediction Puzzles

Students receive expression cards, predict results before calculating with BOMDAS, then verify. Collect and review predictions to highlight patterns.

Prepare & details

Explain why a universal order of operations is necessary in mathematics.

Facilitation Tip: During Prediction Puzzles, ask students to sketch the sequence of steps they plan to take before they calculate.

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 BOMDAS by starting with simple expressions and gradually adding complexity. Avoid rushing to rules; instead, build understanding through examples where the order visibly changes outcomes. Use visual cues like highlighting brackets or circling orders to make the sequence explicit. Research shows students grasp the logic of BOMDAS better when they first experience the consequences of ignoring the rules, so design activities that make those consequences obvious and discussable.

What to Expect

Successful learning looks like students confidently applying BOMDAS to unfamiliar expressions without hesitation. They explain their steps aloud, justify each move, and correct peers when rules are misapplied. You will notice students shifting from guessing answers to analyzing the structure of each problem.

Watch Out for These Misconceptions

Common Misconception

During the Pairs Game: Expression Matching, watch for students who calculate left to right regardless of brackets or orders, leading to mismatched pairs.

What to Teach Instead

Circulate and ask pairs to explain why their matched expressions produce the same result. If they disagree, prompt them to recalculate using BOMDAS and compare the outcomes.

Common Misconception

During Bracket Challenge Stations, watch for students who assume multiplication always comes before division, even when the expression requires division first.

What to Teach Instead

Challenge groups to create their own examples where division precedes multiplication. Have them present their findings to the class to reinforce left-to-right application within the same precedence level.

Common Misconception

During Prediction Puzzles, watch for students who evaluate powers after multiplication, ignoring the correct order entirely.

What to Teach Instead

Ask students to cross out each step as they complete it, starting with orders, then multiplication/division, and finally addition/subtraction. Use a class poster to model this process step by step.

Assessment Ideas

Exit Ticket

After the Pairs Game, provide an exit ticket with two expressions: 8 – 2 × 3 and (8 – 2) × 3. Ask students to calculate both and write one sentence explaining the difference in their answers.

Quick Check

During the Bracket Challenge Stations, collect one completed expression from each group. Check that they have written each step with the correct justification referencing BOMDAS/BIMDAS.

Discussion Prompt

After the Error Detective Relay, pose the question: 'What if mathematicians disagreed on the order of operations for calculating the cost of building a bridge?' Facilitate a brief discussion on the importance of consistent rules, then have students write a reflection on why standardization matters.

Extensions & Scaffolding

• Challenge: Invite students to create two different expressions that both equal 10 using BOMDAS, one with and one without brackets.
• Scaffolding: Provide partially completed worked examples for students to finish step by step.
• Deeper exploration: Ask students to write a short paragraph explaining why BOMDAS is necessary for real-world professions like engineering or programming.

Key Vocabulary

BOMDAS/BIMDAS	An acronym representing the order of operations: Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
Order of Operations	A set of rules that dictates the sequence in which mathematical operations should be performed to ensure a consistent result.
Brackets	Symbols such as (), [], or {} used to group parts of a mathematical expression, indicating that the operations within them should be performed first.
Precedence	The priority given to certain mathematical operations over others, as defined by the order of operations rules.