Order of Operations (PEMDAS/BODMAS)

Active learning works for order of operations because it turns abstract rules into visible, tactile steps. Students who manipulate symbols and check each other’s work see why BODMAS exists rather than just memorizing it.

• 4th Class
• Mastering Mathematical Thinking: 4th Class
• 4 activities
• 20 min–45 min

Learning Objectives

1. Evaluate numerical expressions involving integers, fractions, and decimals using the order of operations (BODMAS).
2. Explain the necessity of a consistent order of operations for unambiguous mathematical communication.
3. Analyze common errors students make when applying BODMAS, such as incorrect sequencing of operations.
4. Construct a multi-step numerical expression and demonstrate its step-by-step evaluation using BODMAS.
5. Compare the results of calculations performed with and without strict adherence to the order of operations.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: BODMAS Challenges

Prepare four stations with expression cards at increasing difficulty: integers only, add fractions, include decimals, mix all. Groups solve one expression per station, showing steps on mini-whiteboards, then rotate. End with a class share-out of tricky ones.

Prepare & details

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

Facilitation Tip: During Station Rotation, place a timer at each station and require students to record the order they applied before moving to the next station.

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

Flipped Classroom

⏱ 30 min·Pairs

Partner Relay: Expression Race

Pairs line up at board. First student solves first step of BODMAS expression, tags partner for next step. Include 5-7 step problems with fractions and decimals. Time teams and discuss variations.

Prepare & details

Analyze common errors made when applying the order of operations.

Facilitation Tip: In Partner Relay, stagger the expressions so groups cannot overhear the previous pair’s steps, forcing them to rely on the rules.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Flipped Classroom

⏱ 25 min·Whole Class

Whole Class: Error Detective Game

Project expressions with deliberate BODMAS errors. Class votes on correct step-by-step fixes via thumbs up/down or digital polls. Reveal official solution and vote on most common slip-ups.

Prepare & details

Construct a complex numerical expression and evaluate it step-by-step using the order of operations.

Facilitation Tip: In Error Detective Game, hand out red pens so students can mark errors directly on peers’ work, normalizing error analysis.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Flipped Classroom

⏱ 20 min·Individual

Individual: Build Your Own

Students create three original BODMAS expressions using given numbers and operations, including one with fractions or decimals. Swap with a partner to evaluate and check steps.

Prepare & details

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

Facilitation Tip: For Build Your Own, provide blank expression cards so students build both correct and incorrect versions, practicing precision.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Teaching This Topic

Start with real-world tasks where order matters, like calculating total cost with discounts applied before tax. Avoid teaching mnemonics alone; anchor each step to a concrete example. Research shows students retain the concept longer when they create and evaluate expressions themselves rather than just solving given ones.

What to Expect

Successful learning looks like students explaining which operation happens first in any expression, using precise language and handling mixed operations without left-to-right guessing. They justify each step aloud or in writing.

Watch Out for These Misconceptions

Common Misconception

During Partner Relay, watch for students who ignore the relay order and begin calculating before their partner tags them.

What to Teach Instead

Have each pair write the first operation they will perform on a sticky note and place it on the expression before starting, ensuring they follow the relay sequence.

Common Misconception

During Station Rotation, watch for students who perform multiplication before division regardless of their position in the expression.

What to Teach Instead

At each station, ask students to use colored tiles to mark each operation, then physically reorder the tiles to show left-to-right progression for same-level operations.

Common Misconception

During Error Detective Game, watch for students who skip or misread nested brackets.

What to Teach Instead

Provide expressions with nested brackets in different colors and require students to circle each bracket pair before evaluating any steps inside.

Common Misconception

Assessment Ideas

Quick Check

Present students with a mixed expression like 10 + 2 × (6 - 3). Ask them to write down the first step they would perform according to BODMAS and explain their reasoning in one sentence.

Exit Ticket

Give each student an expression such as 15 ÷ 3 + 4 × 2. Ask them to evaluate it step-by-step, showing each calculation. Collect these to check for correct application of BODMAS.

Discussion Prompt

Pose the question: 'Imagine two people calculate 5 + 3 × 2. One gets 16, the other gets 11. How is this possible, and which answer is correct according to the order of operations? Explain why.' Facilitate a class discussion on the importance of consistent rules.

Extensions & Scaffolding

• Challenge students to write two different expressions that give the same result using BODMAS, then trade with a partner to verify.
• Scaffolding: Provide partially completed expressions with some steps filled in, asking students to fill the missing operations or numbers.
• Deeper exploration: Introduce nested fractions within brackets and ask students to design a story problem that requires the expression for its solution.

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 can contain numbers, variables, and operators, but does not have an equals sign.
Evaluate	To calculate the numerical value of a mathematical expression.
Integer	A whole number (not a fractional number) that can be positive, negative, or zero.
Fraction	A number that represents a part of a whole, written as one number over another separated by a line.