Order of Operations with IntegersActivities & Teaching Strategies
Active learning works well for order of operations with integers because it forces students to confront their misconceptions through immediate feedback. When students see their peers solve the same problem differently, they must justify their steps aloud, which strengthens their understanding of BODMAS rules.
Learning Objectives
- 1Calculate the value of complex integer expressions using BODMAS/PEMDAS with accuracy.
- 2Analyze common errors in applying BODMAS/PEMDAS to integer expressions, particularly with negative numbers.
- 3Compare the results of correctly and incorrectly applying BODMAS/PEMDAS to identify critical steps.
- 4Construct a multi-step integer expression that requires careful application of BODMAS/PEMDAS and solve it step-by-step.
- 5Explain the rationale behind each step in solving an integer expression according to the order of operations.
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Pairs: Error Hunt Challenge
Provide pairs with 10 expressions containing common BODMAS errors involving integers. Students circle mistakes, rewrite correctly step-by-step, and justify changes. Pairs then exchange papers with another pair for peer review and class discussion of top errors.
Prepare & details
Evaluate the importance of following the order of operations in integer calculations.
Facilitation Tip: During the Error Hunt Challenge, circulate to listen for pairs debating why the order of operations matters, stepping in only when they reach an impasse.
Setup: Group tables with puzzle envelopes, optional locked boxes
Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards
Small Groups: Expression Relay
Divide class into small groups and line them up. Give the first student a simple integer expression; they solve one operation and pass to the next, who continues until complete. Groups race, then verify answers as a class.
Prepare & details
Critique common errors made when applying BODMAS/PEMDAS with negative numbers.
Facilitation Tip: For the Expression Relay, set a timer no longer than 3 minutes per problem to maintain urgency and focus.
Setup: Group tables with puzzle envelopes, optional locked boxes
Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards
Individual: BODMAS Puzzle Cards
Distribute cards with mixed integer expressions to individuals. Students solve independently, match to answer cards, then pair up to check and discuss discrepancies using BODMAS posters.
Prepare & details
Construct a complex integer expression and solve it step-by-step.
Facilitation Tip: With BODMAS Puzzle Cards, observe students matching pieces to check if they prioritize brackets and operations correctly before allowing them to move to the next card.
Setup: Group tables with puzzle envelopes, optional locked boxes
Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards
Whole Class: Build and Solve Chain
Project a starting integer expression. Students suggest operations one by one, teacher adds to chain. Class votes on next step, solves collectively, tracking on board to model BODMAS.
Prepare & details
Evaluate the importance of following the order of operations in integer calculations.
Setup: Group tables with puzzle envelopes, optional locked boxes
Materials: Puzzle packets (4-6 per group), Lock boxes or code sheets, Timer (projected), Hint cards
Teaching This Topic
Teach BODMAS by anchoring it in real mistakes students make, then using guided practice to rebuild their understanding. Start with simple expressions and gradually introduce negatives and brackets to avoid overwhelming learners. Research shows that students retain rules better when they teach them to others, so design activities that require verbal explanations.
What to Expect
Successful learning looks like students confidently explaining each step of an expression, using correct terminology for operations, and catching their own errors before moving forward. They should be able to articulate why multiplication comes before subtraction in a problem like 8 - 3 × 2.
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 Error Hunt Challenge, watch for students who incorrectly prioritize subtraction over multiplication in expressions like 10 - 2 × 3.
What to Teach Instead
Have them rewrite the problem with brackets showing the correct order, then compare their rewritten version with the original to see the difference in results.
Common MisconceptionDuring the Expression Relay, watch for teams ignoring negative signs in multiplication or division steps.
What to Teach Instead
Ask the team to pause and verbally explain each operation’s sign result before proceeding, using the whiteboard to track changes.
Common MisconceptionDuring BODMAS Puzzle Cards, watch for students overlooking brackets or misapplying the left-to-right rule for operations of the same priority.
What to Teach Instead
Prompt them to physically move the puzzle pieces to match the correct order, then justify each move using BODMAS rules aloud to a partner.
Assessment Ideas
After the Error Hunt Challenge, present students with -5 + 3 × (-2) and ask them to write down only the first operation they would perform and why, then the final answer.
After the Expression Relay, present two different solutions to the problem 7 - (-2) × 3, one correct and one with a common error. Ask students to discuss which is correct and why, identifying the specific BODMAS rule broken in the incorrect one.
During the Build and Solve Chain, give students 10 - (-4) × 2 + 6 and ask them to solve it step-by-step, clearly showing each operation and its result along with the BODMAS rule applied at each step.
Extensions & Scaffolding
- Challenge early finishers to create their own error-hunt worksheet for a peer, intentionally embedding common mistakes for others to find.
- Scaffolding for struggling students: provide a colored-coded BODMAS chart with each operation highlighted in a different color to match expression steps.
- Deeper exploration: invite students to design a game board where each space requires solving an order of operations problem with integers to advance.
Key Vocabulary
| BODMAS/PEMDAS | A mnemonic rule for the order in which mathematical operations should be performed: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right). |
| Integers | Whole numbers and their opposites, including positive numbers, negative numbers, and zero (e.g., -3, 0, 5). |
| Order of Operations | The set of rules that dictates the sequence in which mathematical operations must be performed to ensure a consistent and correct result. |
| Expression | A mathematical phrase that contains numbers, variables, and operation symbols, but does not have an equals sign. |
Suggested Methodologies
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