Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Order of Operations (PEMDAS/BODMAS)

Active learning works well for order of operations because students often get stuck in procedural rules without truly understanding how to apply them. Hands-on games and peer discussions push students to articulate their steps, catch their own mistakes, and internalize why grouping and priority matter in calculations.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.8

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 25 min · Small Groups

Relay Race: BODMAS Challenge

Divide the class into teams of four. Write multi-step expressions on the board; each team member solves one operation in sequence, racing to the finish. Review answers as a class, highlighting bracket impacts. Adapt with visuals for simpler levels.

Justify the importance of following a specific order when evaluating expressions.

Facilitation Tip

During the Relay Race, require every student to verbalize the next step before passing the marker to keep the focus on sequencing.

What to look for

Present students with a short expression like 5 + 2 x 3. Ask them to write down the first step they would take and why. Collect responses to gauge understanding of initial steps.

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

Activity 02

• Collaborative Problem-Solving
• 20 min · Pairs

Pairs Sort: Operation Order Cards

Provide pairs with cards showing numbers and operations. Students arrange them into expressions following BODMAS, solve, and swap to check partners' work. Discuss how changing bracket positions alters results.

Analyze how parentheses change the outcome of an expression.

Facilitation Tip

In Pairs Sort, circulate and listen for students using terms like ‘brackets first’ or ‘division before addition’ to confirm correct reasoning.

What to look for

Give each student an expression with brackets, such as 3 x (4 + 2). Ask them to solve it and then write one sentence explaining why the brackets were important for their answer.

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

Activity 03

• Collaborative Problem-Solving
• 30 min · Whole Class

Whole Class: Error Detective Game

Project expressions with deliberate mistakes, like ignoring brackets. Students raise hands to spot and correct errors, justifying with BODMAS steps. Tally points for teams with most accurate fixes.

Critique common errors made when applying the order of operations.

Facilitation Tip

In the Error Detective Game, allow students to challenge the ‘detective’s’ solution only after they provide a cited rule from BODMAS.

What to look for

Write two different solutions to the same problem on the board, one correct and one incorrect (e.g., 10 - 4 ÷ 2 = 3 vs. 10 - 4 ÷ 2 = 7). Ask students: 'Which answer is correct and why? What rule did the incorrect solution forget to follow?'

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

Activity 04

• Collaborative Problem-Solving
• 15 min · Individual

Individual: Bracket Builder Worksheet

Students draw brackets around given expressions, solve both bracketed and unbracketed versions, and note differences. Follow with sharing one pair in a class gallery walk.

Justify the importance of following a specific order when evaluating expressions.

What to look for

Present students with a short expression like 5 + 2 x 3. Ask them to write down the first step they would take and why. Collect responses to gauge understanding of initial steps.

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

A few notes on teaching this unit

Teach order of operations by modeling the thinking aloud first, then shifting responsibility to students through structured partner talk and movement. Avoid giving shortcuts like ‘PEMDAS songs’ before conceptual understanding is solid. Research shows that when students explain their steps to peers, misconceptions surface naturally and corrections stick better than when teachers correct alone.

Successful learning looks like students using BODMAS correctly without prompting, explaining each step aloud as they solve expressions, and catching errors in peer work. They should also be able to transfer this skill to new problems and explain their reasoning clearly.

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Watch Out for These Misconceptions

• During the Pairs Sort activity, watch for students arranging operations left to right without considering BODMAS priority.

  Have pairs physically move operation cards into the correct BODMAS sequence, then compute both ways to show how answers change, reinforcing why priority matters.

• During the Relay Race: BODMAS Challenge, listen for teams skipping grouping symbols when the expression is simple.

  Pause the race to remind teams that brackets always come first, even in short expressions, and require them to verbalize the bracket step before proceeding.

• During the Pairs Sort activity, watch for students assuming division and multiplication can be done in any order without checking left-to-right flow.

  Ask pairs to rearrange division and multiplication cards to test different orders, then compare answers to prove that left-to-right order changes results.

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Methods used in this brief

• Collaborative Problem-Solving