Order of Operations with Whole NumbersActivities & Teaching Strategies
Active learning turns abstract rules into concrete understanding. When students physically sort operations, build expressions, and race through computations, they see why BODMAS matters. Whole-number practice up to 100,000 keeps the focus on structure, not calculation fatigue.
Learning Objectives
- 1Calculate the value of number sentences involving whole numbers using the BODMAS order of operations.
- 2Explain the purpose of BODMAS in ensuring a consistent order for solving arithmetic expressions.
- 3Compare the results of calculations when brackets are present versus absent in a number sentence.
- 4Identify the correct sequence of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction) within a given expression.
- 5Construct a number sentence that requires the application of BODMAS to solve a given problem.
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Card Game: BODMAS Relay
Prepare cards with mixed-operation expressions and answer cards. In small groups, one student solves the first step aloud, passes to the next for the following step, until complete. Groups race to match all expressions to answers correctly. Debrief on errors as a class.
Prepare & details
What does BODMAS mean, and in what order do you carry out the operations?
Facilitation Tip: During the Digital Expression Dash, monitor for students who skip brackets or misapply left-to-right rules.
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
Bracket Builder Challenge
Give pairs expression cards without brackets and possible bracket placements. Pairs insert brackets to match target answers, testing multiple options. They justify choices and share with the class. Extend by creating their own puzzles.
Prepare & details
How do brackets change the answer when you calculate a number sentence?
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
Operation Station Rotation
Set up stations: one for powers, one for ×/÷, one for +/-. Students rotate, completing partial expressions following BODMAS. Record steps on worksheets. Whole class shares one tricky station.
Prepare & details
Can you work out the value of a number sentence with mixed operations and explain each step?
Setup: Groups at tables with problem materials
Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric
Digital Expression Dash
Use tablets or online tools for timed multi-step problems. Individually solve, then pairs compare and explain differences. Teacher projects common errors for group correction.
Prepare & details
What does BODMAS mean, and in what order do you carry out the operations?
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 BODMAS through multiple modalities: hands-on card sorts for priority, verbal rehearsal for left-to-right rules, and group debates to resolve conflicts. Avoid premature practice with large numbers—master the order first with smaller values, then scale up. Research shows peer explanation beats teacher explanation for retention.
What to Expect
By the end of these activities, students will evaluate multi-step expressions correctly, explain each step using BODMAS language, and catch common misconceptions before they become habits. Success looks like students verbalizing the priority of operations and defending their choices.
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 BODMAS Relay, watch for students who add first in expressions like 2 + 3 × 4 instead of multiplying first.
What to Teach Instead
Pause the relay and have students sort their operation cards by priority. Ask them to verbalize why multiplication comes before addition, using the card order as proof.
Common MisconceptionDuring the Bracket Builder Challenge, watch for students who treat brackets as decorative rather than priority-changers.
What to Teach Instead
Have students swap their bracket cards with peers to see how the outcome changes. Ask groups to present why (5 + 3) × 2 is not the same as 5 + 3 × 2.
Common MisconceptionDuring Operation Station Rotation, watch for students who divide before multiplying regardless of left-to-right order.
What to Teach Instead
At the station, ask students to vocalize each step in 12 ÷ 3 × 2, emphasizing that division and multiplication have equal priority and proceed left to right.
Assessment Ideas
After the BODMAS Relay, present a worksheet with four expressions: one with brackets, one with division and addition, one with multiplication and subtraction, and one with nested brackets. Ask students to solve each and label each step with the BODMAS rule applied.
During the Digital Expression Dash, give each student a card with 10 + 4 × 2 - 6 ÷ 3. Ask them to write the first operation they would perform and why, then compute the final answer on the back.
After the Bracket Builder Challenge, pose: 'In 5 + 3 × 2, would you add 5 and 3 first or multiply 3 and 2 first? Ask students to use their bracket-building experience to explain their reasoning using BODMAS language.
Extensions & Scaffolding
- Challenge early finishers to create their own BODMAS relay cards with numbers up to 100,000.
- Scaffolding for struggling students: provide colored cards for each operation tier (brackets, orders, division/multiplication, addition/subtraction) to sort before calculating.
- Deeper exploration: introduce nested brackets like (2 + (3 × 4)) ÷ 5 and ask students to diagram the step sequence.
Key Vocabulary
| BODMAS | An acronym that stands for the order of operations: Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). |
| Order of Operations | A set of rules that tells us which calculation to perform first when there are several different operations in one number sentence. |
| Brackets | Symbols used in mathematics to group numbers and operations, indicating that the calculation inside them must be performed first. |
| Expression | A mathematical phrase that can contain numbers, variables, and operation symbols, but does not have an equals sign. |
Suggested Methodologies
Planning templates for Mathematics
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
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RubricMath Rubric
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