Mathematics · Year 9

Active learning ideas

Profit and Loss

Active learning is essential for profit and loss calculations because it grounds abstract percentages in tangible business decisions. When students actively engage with scenarios, they move beyond rote memorization to develop a practical understanding of financial concepts.

• ACARA Content Descriptions
• AC9M9N04

• 25–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Problem-Based Learning
• 45 min · Small Groups

Business Simulation: Markup Mania

Students are given a list of products with their cost prices. In small groups, they decide on a percentage markup for each product, calculate the selling price, and then determine the profit. They then present their pricing strategy and justify their markups.

How do businesses use percentage markups to ensure they cover costs and generate profit?

Facilitation Tip

During the Problem-Based Learning activity 'Business Simulation: Markup Mania,' encourage groups to document their pricing strategies and justify their markup percentages based on perceived market factors, fostering analytical reasoning.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 30 min · Pairs

Discount Dilemma: Original Price Recovery

Provide students with items on sale, showing the discounted price and the percentage discount. Students work in pairs to calculate the original price of each item, reinforcing their understanding of working backwards with percentages.

What is the mathematical difference between a discount and a rebate?

Facilitation Tip

In the Decision Matrix activity 'Discount Dilemma: Original Price Recovery,' guide students to explicitly state the criteria they used to evaluate which original prices were most likely, prompting systematic thinking about the relationship between discount and original value.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 25 min · Whole Class

Profit/Loss Percentage Debate

Present a scenario where profit is calculated as a percentage of selling price. Facilitate a whole-class discussion or debate where students must justify why calculating profit/loss as a percentage of cost price is often preferred in business analysis.

Justify why calculating profit/loss as a percentage of cost price is often preferred.

Facilitation Tip

During the Debate activity 'Profit/Loss Percentage Debate,' ensure students not only argue their points but also actively listen to and respond to counterarguments, reinforcing the critical distinction between profit margin and profit percentage based on cost price.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

This topic benefits from a scaffolded approach, starting with concrete examples before moving to more abstract calculations. Avoid simply presenting formulas; instead, use activities that allow students to discover the relationships between cost, selling price, profit, and percentage change through exploration and discussion.

Students will demonstrate a clear understanding of how cost price and selling price interact to determine profit or loss. They will confidently calculate percentage changes and original values, articulating the reasoning behind their answers in real-world contexts.

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Watch Out for These Misconceptions

• During 'Profit/Loss Percentage Debate,' watch for students who consistently calculate profit as a percentage of the selling price, confusing it with profit margin.

  Redirect students by having them use the provided scenario's cost price data to recalculate the profit as a percentage of cost, then compare this to the profit margin they initially calculated, highlighting the difference.

• During 'Discount Dilemma: Original Price Recovery,' watch for students who assume a 10% discount followed by a 10% markup will always return an item to its original price.

  Use the sale price and discount percentage data from the activity to have students work backward and calculate the original price, then have them apply a 10% markup to the discounted price and compare the result to the original price they found.

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Methods used in this brief

• Problem-Based Learning