Mastering BODMAS Rules

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Overview

Unit Title: Numbers and Algebra Unleashed
Lesson Number: 8 of 28
Year Level: Year 7
Lesson Duration: 30 minutes
Class Size: 30 students
Curriculum Area: Mathematics – Number
Australian Curriculum Links (Version 9):

AC9M7N04 – Apply the four operations to integers using algorithms and the properties of arithmetic.
AC9M7N05 – Use order of operations to evaluate expressions involving integers, including brackets and combinations of operations.

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Lesson Title

Order of Operations with Integers

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Lesson Description

In this energetic and engaging 30-minute session, Year 7 students will deepen their understanding of the order of operations (BODMAS) through real-world challenges, collaborative problem-solving, and hands-on mini-games. The focus is on mastering integer calculations using brackets, operations, and signs, ensuring students are confident with both negative and positive numbers in complex expressions.

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Learning Intentions

By the end of the lesson, students will be able to:

• Accurately apply the BODMAS principles to evaluate mathematical expressions involving integers.
• Identify and correct errors in order of operations.
• Collaboratively explain the reasoning behind steps taken in integer calculations.

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Success Criteria

Students will:

✔ Correctly solve at least 80% of order of operation problems during the team game.
✔ Explain the steps they take in solving integer expressions.
✔ Demonstrate understanding of how integers are treated in different operation contexts.

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Resources Required

• Whiteboard and markers
• Printed "Integer Mystery Cards" (provided below)
• Mini whiteboards and whiteboard markers for each student
• BODMAS Challenge Game Cards (pre-prepared)
• Timer or stopwatch
• Sticky notes or counters

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Warm-Up (5 mins)

Activity: Human BODMAS Chain

Purpose: Engage students with kinaesthetic learning by prompting them to physically represent each part of a mathematical problem.

Instructions:

1. Display a complex expression on the board:
   6 ÷ (−3) + 2 × (−4)

2. Select 7 volunteers, each representing one part of the expression ("6", "÷", "−3", "+", "2", "×", "−4").

3. Have the class direct the volunteers to rearrange themselves in the correct operational order based on BODMAS.

4. Ask students watching to vote using thumbs up/down to show whether the chain is in the right order.

5. Solve the expression as a class — address misconceptions around division and negative signs especially.

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Main Activity (15 mins)

Activity: Integer BODMAS Showdown!

Structure: Students will work in teams of 3–4 in a high-paced competitive game focused on correct stepwise solving of order of operation problems.

Round 1: Integer Decode

1. Each group gets a set of 5 pre-prepared BODMAS Challenge Cards:
   • Each card has a multi-step expression involving negative numbers and operations (see examples below).
2. Groups must:
   • Step 1: Solve it,
   • Step 2: Write the steps taken (including bracket simplification),
   • Step 3: Choose one team member to bring the answer and explanation to the teacher for checking.
3. If correct, the team earns a counter. If incorrect, teacher returns the card with a clue or question.
4. Rotate through problems with the goal of each team getting at least 4 correct answers out of 5.

Example Card:

Card #3: Evaluate using BODMAS
−8 + (3 × −2) ÷ [6 ÷ (−3)]
Include clear working!

Round 2: Faulty Maths Detective (Verbal option – 2 mins)

• Teacher writes an incorrect worked solution on the board.
• Students in teams must find three errors and explain the correct steps.
• Bonus counter for the team that explains it using mathematical language.

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Consolidation / Reflection (5 mins)

Quick Write: Exit Slip on a Sticky Note

Each student answers:

• “One thing I understand better about BODMAS is…”
• “One thing I’m still unsure of is…”

Have them place their sticky notes on the designated BODMAS Bump Board as they exit.

As a class, wrap up by reinforcing:

“Brackets come first – but don’t forget that negative numbers act like invisible brackets in some expressions!”

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Differentiation

• Support: Students needing extra scaffolding can work from a step-by-step breakdown sheet of BODMAS processes using colour-coded examples.
• Extension: Challenge finishers with “Reverse Engineering” – given a final answer, can they create a complex expression using BODMAS rules that evaluates to that answer?

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Assessment Opportunities

• Formative assessment through team activity participation and verbal reasoning.
• Observation checklists for team strategy and procedural fluency.
• Exit slip used to inform planning for Lesson 9 (Challenging Equations with Integers).

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Teacher Reflection Prompt (Post-Lesson)

• Which students demonstrated procedural fluency versus conceptual understanding?
• How effectively did students articulate their mathematical reasoning in small groups?
• Were misconceptions about negative numbers or fraction operations prevalent?

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Extension/Homework (Optional)

Task: Students create their own “Integer Escape Room” — a 3-step BODMAS puzzle incorporating positive and negative solutions, to challenge a peer in the next lesson.

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Final Notes

This lesson blends movement, competition, and cooperation to ensure students are not just mechanically applying rules, but truly understanding how and why the order of operations shapes their answers.

“When maths feels like a mystery to solve, students can’t wait for the next clue.”

Let the integer games begin! 💡