Divide and Conquer

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👩‍🏫 Lesson Overview

Unit: Numbers and Algebra Unleashed
Lesson Number: 7 of 28
Lesson Title: Division of Integers
Year Level: Year 7
Duration: 30 minutes
Class Size: 30 students
Teacher: Secondary Maths Teacher, Queensland

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🎯 Australian Curriculum Alignment (v9.0)

Curriculum Area: Mathematics – Number
Strand: Number – Number operations – ACMN1080

Content Description: Use the four operations with integers, using multiple strategies to solve problems involving the addition, subtraction, multiplication and division of integers.

General Capabilities:

• Numeracy: Understanding and using mathematical operations
• Critical and Creative Thinking: Applying logic through order of operations
• Personal and Social Capability: Working collaboratively in pair and group tasks

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🧠 Learning Intentions

By the end of this 30-minute lesson, students will be able to:

• Explain the rules of dividing integers (positive ÷ negative, etc)
• Apply integer division to solve number problems
• Work with expressions that combine multiple operations including division
• Understand and correctly apply order of operations involving integers

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✅ Success Criteria

Students will demonstrate success when they:

• Correctly solve integer division problems with justification or reasoning
• Follow correct order of operations (BODMAS) in expressions involving integers
• Collaborate effectively in class activities and contribute to class discussion

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🧰 Materials Required

• Mini whiteboards and markers (one per student)
• Slide presentation (visual prompts and worked examples)
• Prepared integer flashcards (for warm-up)
• "Integer Island Challenge" worksheet (1 per student)
• Stopwatch (for timed group challenge)
• Sticky notes (exit ticket responses)

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🗺️ Lesson Sequence

⏱️ 0:00–0:05 – Ignition: Integer Flash Duel

Purpose: Activate prior knowledge, build energy

1. Distribute mini whiteboards and markers to each student.
2. Teacher flashes prepared integer division problems (e.g., −24 ÷ 6, 15 ÷ -3).
3. Students quickly write their answers on whiteboards and hold them up as fast as possible.
4. Quick discussion on accuracy – highlight any misconceptions.
5. Introduce today’s focus and learning intention.

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⏱️ 0:05–0:10 – Explicit Teaching: Integer Division Rules

Purpose: Build understanding through visuals and pattern recognition

Use a short, clear slide presentation to visually demonstrate:

• Rule patterns:
  • Positive ÷ Positive = Positive
  • Negative ÷ Positive = Negative
  • Positive ÷ Negative = Negative
  • Negative ÷ Negative = Positive
• Model example problems step-by-step (e.g., −36 ÷ −6 = 6)

🧠 Teacher Tip: Ask students to predict the sign before revealing each answer.

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⏱️ 0:10–0:17 – Collaborative Activity: Integer Island Challenge 🌴

Purpose: Apply learning cooperatively in a game-style format

Instructions:

1. Students work in pairs – each pair receives an “Integer Island Challenge” sheet.
2. The sheet contains 6 problems increasing in complexity:
   • 2 basic division
   • 2 mixed operations applying BODMAS
   • 2 worded/real-life context problems (e.g., temperature changes, debt, gaming scores)
3. Students solve and receive a sticker or token (placed on their desk) for each correct problem.
4. Timer challenge: 7 mins max

🔁 Differentiation: Struggling students can focus on first 3 problems; extension students attempt a bonus expression from the "Stormy Waters" challenge (e.g., (-8 + 4) × (-3) ÷ 2).

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⏱️ 0:17–0:24 – Guided Discussion: Crack the Code

Purpose: Deepen understanding and tackle any misconceptions

• Class reviews ONE complex expression from the challenge (teacher-led).
• Invite students to offer explanations of the reasoning and how they approached the order of operations.
• Discuss: What happens if order is ignored? Use humour and real-life metaphor (e.g., “making a cake before preheating oven”).

👀 Watch for: common mistakes and invite students to ‘debug’ incorrect sample solutions together.

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⏱️ 0:24–0:29 – Exit Ticket: Integer Snap!

Purpose: Check for understanding individually

1. Each student receives a sticky note.
2. On board: (-18 ÷ 3) + (-2 × 4) – students must solve, write final answer AND a one-line justification.
3. Students stick their answers at the door as they leave.
4. Teacher quickly reviews post-lesson to assess class understanding and plan next step.

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⏱️ 0:29–0:30 – Wrap-Up & Fun Fact

• Recap major takeaway: When dividing integers, signs matter – just like your password! One wrong symbol, and it’s all wrong!
• Quick quirky fun fact: “Negative numbers weren’t accepted in mathematics until the 19th century in Europe – but ancient Chinese mathematicians used red and black rods to show negative and positive over 2000 years ago!”

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🎒 Differentiation & Support

• Mini whiteboards encourage low-stakes error correction for all levels
• Translation scaffolds for EALD students: use number lines, visual cues
• Extension students challenged with nested operations
• Peer pairing to support mixed-ability learners

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🔍 Assessment for Learning

• Observation during flash duel and group challenge
• Sticky note exit tickets → review individual understanding
• Group collaboration and discussion used to form judgements on mathematical reasoning

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💡 Teacher Reflection Prompts (Post-Lesson)

• Were students confidently applying integer division rules?
• Did students rely on memorised rules or grasp underlying logic?
• Who needs more consolidation with order of operations?
• Who needs extension into real-world algebraic contexts?

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📅 Coming Up Next…

Lesson 8 Preview:

Multiplying and dividing integers in algebraic expressions. Transitioning from arithmetic to algebraic fluency while keeping context relevant to students’ lives.

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This lesson invites curiosity, connection and creativity while staying strongly aligned with the Australian Curriculum. Engage your students with clear routines, conceptual clarity – and a little bit of mathematical magic!