Mathematics · Year 8

Active learning ideas

Percentage Increase and Decrease

Active learning works for percentage increase and decrease because students often confuse percentage changes with simple addition or subtraction. Hands-on activities let them manipulate multipliers, see scaling effects, and correct errors through immediate feedback from peers and materials.

• ACARA Content Descriptions
• AC9M8N03

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

Activity 01

• Case Study Analysis
• 45 min · Small Groups

Market Stall: Successive Discounts

Price everyday items with AUD tags. Groups apply two successive discounts, such as 20% then 10%, and calculate final prices using calculators. Rotate roles: seller quotes, buyer verifies, accountant records multipliers. Discuss predictions versus actuals.

Differentiate between calculating a percentage of a number and calculating a percentage increase.

Facilitation Tip

During Market Stall, circulate to ensure students record each discount as a multiplier and verify their final prices against the originals.

What to look for

Present students with a scenario: 'A video game console originally cost 500 and is now on sale for 400. What is the percentage decrease?' Ask students to show their calculation using a multiplier and write the percentage decrease.

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

Activity 02

• Case Study Analysis
• 30 min · Pairs

Reverse Price Puzzle: Pairs Challenge

Provide final sale prices after known percentage decreases. Pairs work backwards using the formula original = final / (1 - percent/100), then verify by reapplying change. Swap puzzles with another pair for peer checking.

Justify the steps involved in finding the original amount after a percentage change.

Facilitation Tip

For Reverse Price Puzzle, give pairs only one price tag at a time to encourage step-by-step reasoning rather than guessing.

What to look for

Give students two problems: 1. Calculate the price of a 60 shirt after a 25% discount. 2. A jacket is now 90 after a 10% increase. What was the original price? Students write their answers and one sentence explaining their method for the second problem.

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

Activity 03

• Case Study Analysis
• 35 min · Whole Class

Interest Growth Relay: Whole Class

Divide class into teams. Each student calculates one step of compound interest over years, passes baton with updated amount. First team to correct final amount wins. Debrief multipliers.

Predict the final price of an item after multiple percentage discounts are applied.

Facilitation Tip

In Interest Growth Relay, provide calculators only after teams have set up the multipliers to reinforce the algorithm first.

What to look for

Pose the question: 'If an item is discounted by 20% and then by another 20%, is that the same as a 40% discount? Why or why not?' Facilitate a class discussion where students use examples to justify their reasoning.

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

Activity 04

• Case Study Analysis
• 25 min · Individual

Percentage Strip Builder: Individual Start

Students cut and label strips for 100 units, shade percentages, then extend or shrink for increases/decreases. Combine in pairs to model successive changes visually.

Differentiate between calculating a percentage of a number and calculating a percentage increase.

Facilitation Tip

With Percentage Strip Builder, ask students to label each strip with the multiplier and the percentage change to make the connection explicit.

What to look for

Present students with a scenario: 'A video game console originally cost 500 and is now on sale for 400. What is the percentage decrease?' Ask students to show their calculation using a multiplier and write the percentage decrease.

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

A few notes on teaching this unit

Teach percentage changes by emphasizing multipliers as scaling factors, not as added or subtracted percentages. Avoid starting with formulas; instead, let students derive the multiplier concept through visual and concrete activities. Research shows that students grasp successive changes better when they see the multiplicative relationship first, then abstract to the formula.

Successful learning looks like students confidently using multipliers to model changes, explaining why successive changes multiply rather than add, and accurately reversing percentage changes to find original amounts. They should justify each step with mathematical reasoning.

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Watch Out for These Misconceptions

• During Percentage Strip Builder, watch for students who treat percentage changes as additions to the original amount rather than scaling the entire strip.

  Ask students to fold their strips into sections representing the multiplier (e.g., 1.15 for 15% increase) and compare the scaled length to the original to highlight the difference between scaling and adding.

• During Market Stall, watch for students who add successive discounts (e.g., 20% then 10% equals 30%) instead of applying sequential multipliers.

  Have teams present their step-by-step calculations on the board and compare with a calculator result to show the discrepancy, prompting them to correct their method collaboratively.

• During Reverse Price Puzzle, watch for students who subtract the percentage from the new amount to reverse a change (e.g., 110 minus 10% equals 99).

  Provide price tags with the original and new amounts visible, then ask students to test their subtraction method by calculating forward to see if it returns to the original, revealing the error.

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Methods used in this brief

• Case Study Analysis