Mastering Operations

Overview

Lesson Title: Combining Operations: Division, Multiplication, and Subtraction
Unit Title: Mastering Division and Multiplication (Lesson 4 of 4)
Curriculum Area: Mathematics and Statistics
Level: Level 4 of The New Zealand Curriculum
Time: 50 minutes
Class Size: 18 students (Years 9–10)

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Learning Intention

Students will solve multi-step number problems that require the combined use of long division, multiplication, and subtraction with values up to 1,000,000. They will focus on accuracy, logical reasoning, and showing the complete process behind their solutions.

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Success Criteria

By the end of this lesson, students will:

• Identify and apply the correct order of operations in complex problems
• Solve multi-step problems involving all three operations
• Show full working and explain the relationships between operations
• Reflect on strategies used and evaluate their efficiency

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Key Competencies

• Thinking: Applying logical reasoning in problem-solving situations
• Using language, symbols, and texts: Interpreting and communicating mathematical ideas
• Managing self: Staying focused on multistep tasks and managing problem-solving strategies
• Participating and contributing: Collaborating in pairs and sharing explanations

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Materials Needed

• Whiteboard and markers
• A4 paper and pencils for each student
• Individual mini whiteboards
• Multi-step problem cards (printed beforehand)
• Calculator (only to be used after manual solution for checking)

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Prior Knowledge

This lesson builds on:

• Skill in long division and multiplication with large numbers
• Subtraction involving up to 7-digit numbers
• Use of estimation and rounding
• Understanding of the relationships between operations (inverse operations)

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Lesson Sequence (50 minutes)

⏱ 0–5 mins: Warm-Up Challenge – Operation Relay

Activity: In pairs, students are given a quick 3-step arithmetic relay:

1. Multiply 324 × 12
2. Subtract 1,200
3. Divide the result by 6

Fastest accurate pair wins. This energises students and sets the tone for blending operations.

Purpose: Reactivates prior knowledge and introduces transition to multitiered problem-solving.

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⏱ 5–12 mins: Revisiting Strategy – Operation Mapping

Teacher-Led Discussion:
Use the whiteboard to model a complex problem:

A local whānau grows 878,400 apples. They want to distribute them equally into 24 crates. Each crate has a storage fee of $15. After paying the crate fees, how much profit is left from selling all apples for $2 each?

Break this into steps with student input on:

• What operations are involved?
• In which order should they be done?
• What’s the inverse of each operation?

Link to Curriculum:
This models AO Number level 4: "Use a range of multiplicative strategies when operating on whole numbers."

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⏱ 12–22 mins: Paired Activity – Operation Trails

Students solve handouts containing 3 multi-part problems. Each problem has:

• A real-world context (e.g. budgeting, packing, distributing)
• Prompts for students to show each calculation step
• A reasoning box: “Explain why you did this step”

Differentiation Tips:

• Support learners with visual flow charts for operation order
• Extension students can create their own scenario to challenge a friend

Teacher circulates, prompts with questions like:

• “What’s the first thing you know?”
• “Could we check that estimate before solving?”
• “Do the numbers make sense?”

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⏱ 22–35 mins: Class Challenge – Real-World Problem Solve

Scenario-Based Task:

A small business in Rotorua prints 624,000 brochures in a year. They sell them in packs of 48. Each pack costs $6 to produce and sells for $10. Calculate total revenue, total costs, and overall profit.

On mini-whiteboards, students:

1. Decide first steps in solving
2. Solve sequentially, presenting final answer
3. Flip boards for a "gallery walk" (rotate to view, not judge)

Integration of Skills: This task requires students to identify and connect all three operations—like real decision-making in managing resources.

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⏱ 35–43 mins: Class Discussion – Look Under the Hood

As a class, unpack the business problem. Display one group’s solution on the board. Ask classmates:

• “Why do we subtract this step?”
• “Could you have done it another way?”
• “What makes this method efficient?”

Celebrate diverse approaches to solving!

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⏱ 43–48 mins: Reflection – Operation Connections

Students complete an exit reflection:

• Name a maths strategy you used today
• Describe how multiplication and division are connected
• What would you do differently next problem?

Teacher collects responses to identify learning gaps or areas to revisit in future learning.

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⏱ 48–50 mins: Wrap-Up – Division Domino

Finishing fun! One student starts with a number and an operation (e.g. 120, divided by 5). The next student must take that result and apply a new operation. This continues around the class for a spontaneous, cumulative problem.

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Assessment Opportunities

• Formative: Observation during pair problem-solving, verbal reasoning, and gallery walk responses
• Summative: Reflection papers revealing depth of understanding and method application

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Extension / Next Steps

• Introduce BEDMAS formal structure for order of operations
• Create real-life budgeting projects where students buy, divide, sell and calculate profit/loss
• Link to Statistics by analysing data from calculation-based surveys

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Teacher Notes

• Encourage flexible thinking: not just solving, but understanding the why
• Emphasise clear mathematical communication—students should not only do the maths but speak it and write it clearly
• Incorporate te ao Māori contexts where relevant e.g. harvest, whānau budgeting, local resource sharing

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Curriculum Link

Mathematics Strand: Number and Algebra
Sub-strand: Number Strategies and Knowledge
New Zealand Curriculum Level 4 Achievement Objective:

• Use a range of multiplicative strategies when operating on whole numbers

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“He waka eke noa – We’re all in this together.”
Today’s lesson reminded students that solving problems is a journey, one operation at a time.