Mathematics · 3rd Class

Active learning ideas

Order of Operations (PEMDAS/BODMAS)

Active learning works because students need to physically manipulate symbols and see immediate consequences of their choices. For order of operations, moving expressions around or racing to correct answers makes abstract rules concrete. This hands-on approach reduces confusion between symbols and teaches them that ignoring BODMAS changes the meaning of an entire problem.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.6
• NCCA: Junior Cycle - Algebra - A.1

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

Activity 01

• Outdoor Investigation Session
• 35 min · Pairs

Card Build: BODMAS Expressions

Provide cards with numbers, operations, parentheses, and exponents. In pairs, students build three expressions then evaluate using BODMAS, swapping to check partner's work. Discuss how rearranging changes results. End with sharing one creative expression per pair.

Evaluate the importance of following the order of operations to get a unique answer.

Facilitation Tip

During Card Build, circulate and ask pairs to explain why they placed a certain operation before another, focusing their attention on the hierarchy.

What to look for

Provide students with the expression: 5 + (3 x 4) - 2^2. Ask them to calculate the value, showing each step according to BODMAS/PEMDAS. Then, ask: 'What would the answer be if you ignored the parentheses?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Order Challenges

Set up stations: one for bracket sorts, one for exponent drills, one for full expressions with fractions/decimals, one for error spotting. Small groups rotate every 7 minutes, recording solutions on mini-whiteboards. Debrief as a class.

Explain how parentheses change the order of calculation in an expression.

Facilitation Tip

For Station Rotation, place a timer at each station so students practice speed without sacrificing accuracy.

What to look for

Present students with a series of expressions on the board, some correctly evaluated and some with errors. Ask students to identify which expressions are correct and explain the specific error made in the incorrect ones, referencing BODMAS/PEMDAS rules.

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

Activity 03

• Outdoor Investigation Session
• 25 min · Small Groups

Puzzle Race: Target Answers

Give teams expression templates with missing parentheses or operations. They insert elements to reach a target answer using BODMAS. First team done checks others. Repeat with decimals and fractions.

Design an expression that requires careful application of the order of operations.

Facilitation Tip

In Puzzle Race, assign roles such as recorder or speaker to ensure all students participate and articulate their reasoning.

What to look for

Pose the question: 'Imagine you and a friend are calculating the same problem, but you get different answers. What is the most likely reason for the difference, and how can you both ensure you get the same, correct answer?' Guide the discussion towards the importance of the order of operations.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 20 min · Whole Class

Whole Class: Expression Chain

Project a starter expression. Students add one operation or bracket per turn, evaluating aloud as a class. Correct BODMAS use keeps the chain going; errors prompt group fixes.

Evaluate the importance of following the order of operations to get a unique answer.

Facilitation Tip

During the Whole Class Expression Chain, deliberately include an error in one step and pause to let students correct the peer who reads it aloud.

What to look for

Provide students with the expression: 5 + (3 x 4) - 2^2. Ask them to calculate the value, showing each step according to BODMAS/PEMDAS. Then, ask: 'What would the answer be if you ignored the parentheses?'

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Start with simple expressions that only include addition and multiplication, then gradually layer in parentheses and exponents. Use color-coding on whiteboards to match each BODMAS step with a different color. Avoid teaching left-to-right as a default; instead, show how ignoring the rules changes the meaning of the problem. Research shows that students grasp exponents better when they visualize repeated multiplication with towers or grids before moving to symbolic forms.

By the end, students should confidently explain why parentheses come first and why multiplication before addition matters. They should also recognize that following the rules produces one correct answer, while ignoring them leads to multiple wrong answers. Clear articulation of each step in their calculations demonstrates true understanding.

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Watch Out for These Misconceptions

• During Card Build, watch for students arranging operations strictly from left to right instead of grouping parentheses and exponents first.

  Remind students to sort operations by BODMAS layers before sequencing left-to-right. Ask them to place the parentheses cards or exponent cards down first, then fill in the rest to show the hierarchy.

• During Station Rotation, watch for students treating parentheses only as grouping for addition or subtraction, ignoring multiplication or division inside them.

  At the station with parentheses expressions, have students circle the innermost parentheses and label the operation inside. If it’s multiplication, ask them to explain why that operation still follows BODMAS even inside brackets.

• During Puzzle Race, watch for students treating exponents the same as multiplication, calculating left-to-right instead of powering the base first.

  Provide visual exponent towers at this station and ask students to write out 3^2 as 3 x 3 before solving, so they see why exponents come before multiplication in the sequence.

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Methods used in this brief

• Outdoor Investigation Session
• Stations Rotation