Order of Operations (PEMDAS/BODMAS)Activities & Teaching Strategies
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.
Learning Objectives
- 1Calculate the result of simple numerical expressions using the order of operations (BODMAS/PEMDAS).
- 2Compare the outcomes of numerical expressions with and without grouping symbols.
- 3Identify common errors students make when applying the order of operations.
- 4Explain why a consistent order of operations is necessary for mathematical communication.
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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.
Prepare & details
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.
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
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.
Prepare & details
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.
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
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.
Prepare & details
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.
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
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.
Prepare & details
Justify the importance of following a specific order when evaluating expressions.
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
Teaching This Topic
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.
What to Expect
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.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring the Pairs Sort activity, watch for students arranging operations left to right without considering BODMAS priority.
What to Teach Instead
Have pairs physically move operation cards into the correct BODMAS sequence, then compute both ways to show how answers change, reinforcing why priority matters.
Common MisconceptionDuring the Relay Race: BODMAS Challenge, listen for teams skipping grouping symbols when the expression is simple.
What to Teach Instead
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.
Common MisconceptionDuring the Pairs Sort activity, watch for students assuming division and multiplication can be done in any order without checking left-to-right flow.
What to Teach Instead
Ask pairs to rearrange division and multiplication cards to test different orders, then compare answers to prove that left-to-right order changes results.
Assessment Ideas
After the Pairs Sort activity, present a short expression like 5 + 2 × 3 and have students write the first step they would take and why, then collect responses to check understanding of initial priority.
After the Bracket Builder Worksheet, give each student an expression with brackets, such as 3 × (4 + 2). Ask them to solve it and write one sentence explaining why the brackets were essential for their answer.
During the Error Detective Game, 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 to identify the correct answer and explain which BODMAS rule the incorrect solution forgot to follow.
Extensions & Scaffolding
- Challenge students to create a complex expression with all operations and brackets that equals a target number, then swap with a partner to solve.
- For students who struggle, provide expressions with missing brackets that students fill in to match a given answer, like 8 _ 2 _ 4 = 16.
- Deeper exploration: Introduce nested brackets (e.g., ((3 + 2) × 4) + 1) and ask students to invent a mnemonic for the new layers.
Key Vocabulary
| BODMAS/PEMDAS | A rule that gives the order in which to perform calculations: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). |
| Brackets/Parentheses | Symbols like () or [] that group numbers and operations together, indicating that the calculation inside should be done first. |
| Operation | A mathematical process such as addition, subtraction, multiplication, or division. |
| Expression | A combination of numbers, symbols, and operations that represents a mathematical value. |
Suggested Methodologies
Planning templates for Foundations of Mathematical Thinking
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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