Mathematics · Year 9

Active learning ideas

Percentage Increase and Decrease

Active learning makes percentage increase and decrease concrete because students manipulate real quantities and observe outcomes directly. Calculating with multipliers moves students beyond rote formulas to see how changes compound, which is essential for accurate financial and scientific reasoning.

• ACARA Content Descriptions
• AC9M9N04

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Case Study Analysis
• 25 min · Pairs

Pairs: Multiplier Match-Up

Provide cards with percentage changes (e.g., +20%, -10%) and initial values. Pairs match sequences to final outcomes, compute using multipliers, and predict results before calculating. Discuss patterns in why successive changes compound differently.

Why is a 10 percent increase followed by a 10 percent decrease not the same as the original price?

Facilitation Tip

During Multiplier Match-Up, circulate and prompt pairs to explain their matching process aloud to uncover reasoning gaps.

What to look for

Provide students with a starting price of $50. Ask them to calculate the final price after a 10% increase followed by a 10% decrease. Then, ask them to write one sentence explaining why the final price is not $50.

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

Activity 02

• Case Study Analysis
• 40 min · Small Groups

Small Groups: Shop Sale Simulation

Groups receive store inventory lists with original prices. Apply successive percentage changes from customer scenarios, like 15% off then 10% tax. Record final prices and present one misleading 'sale' to the class.

Analyze the impact of successive percentage changes on an initial value.

Facilitation Tip

In Shop Sale Simulation, provide calculators but ask students to estimate first to build number sense before computing exact values.

What to look for

Present students with two scenarios: Scenario A: A $100 item is increased by 20%, then decreased by 20%. Scenario B: A $100 item is decreased by 20%, then increased by 20%. Ask students to calculate the final price for each scenario and identify which scenario results in a higher final price.

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

Activity 03

• Case Study Analysis
• 35 min · Whole Class

Whole Class: Growth Chain Relay

Line up students; first computes a percentage increase on a starting value and passes to next for a decrease. Chain continues with class-chosen percentages. Graph results to analyze net change after 5-6 steps.

Construct a problem involving a percentage increase or decrease in a real-world context.

Facilitation Tip

For Growth Chain Relay, assign roles so every student calculates, records, and hands off results to reinforce shared responsibility.

What to look for

Pose the question: 'Imagine a shop owner increases the price of a popular video game by 15% due to high demand, and then a month later, they put it on sale for 15% off. Is the sale price the same as the original price? Why or why not?' Facilitate a class discussion using student responses.

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

Activity 04

• Case Study Analysis
• 20 min · Individual

Individual: Problem Creator

Each student constructs a real-world problem with successive percentage changes, like phone plan costs. Swap with a partner to solve and verify using multipliers. Share one class example.

Why is a 10 percent increase followed by a 10 percent decrease not the same as the original price?

Facilitation Tip

In Problem Creator, require students to write both the problem and the solution key to practice clear mathematical communication.

What to look for

Provide students with a starting price of $50. Ask them to calculate the final price after a 10% increase followed by a 10% decrease. Then, ask them to write one sentence explaining why the final price is not $50.

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

A few notes on teaching this unit

Teach this topic by focusing on the multiplier method from the start, using visual representations like bar models to show the base amount before and after change. Avoid teaching percentage change as addition or subtraction unless the context explicitly requires it, such as tax added to a bill. Research shows that when students practice with varied contexts early, their misconceptions about base amounts and compounding are reduced over time.

Successful learning shows when students use multipliers correctly to compute final values and explain why successive percentage changes do not cancel out. They should also articulate the base amount for each calculation and justify their reasoning with evidence from activities.

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Watch Out for These Misconceptions

• During Multiplier Match-Up, watch for students who treat a 10% increase followed by a 10% decrease as returning to the original value.

  Ask pairs to record their starting value and each step’s multiplier on a shared sheet, then compare the final value to the original. Circulate and ask, ‘Why is the final value less?’ to guide them toward noticing the larger base for the decrease.

• During Shop Sale Simulation, watch for students who base the discount on the sale price instead of the original tag price.

  Provide price tags with original values clearly labeled and ask groups to write the original and sale prices side by side. Ask, ‘Is the discount taken from the sticker price or the new price?’ to refocus on the consistent base.

• During Growth Chain Relay, watch for students who add percentages instead of multiplying.

  Have the class pause after two steps and ask, ‘Is the new amount larger or smaller than the original? What does that tell us about the operation we used?’ to highlight the multiplicative nature of change.

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Methods used in this brief

• Case Study Analysis