Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.2
• NCCA: Junior Cycle - Algebra - A.1

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

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.

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

Activity 02

• 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.

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.

What to look for

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.

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

Activity 03

• 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.

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.

What to look for

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.

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

Activity 04

• 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.

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.

What to look for

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.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

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

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Methods used in this brief

• Stations Rotation
• Flipped Classroom