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.

• Year 8
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the new amount after a percentage increase or decrease using decimal multipliers.
2. Explain the inverse relationship between percentage increase and decrease when finding an original value.
3. Compare the final price of an item after sequential percentage discounts versus a single combined discount.
4. Justify the steps taken to determine the original price of an item given its price after a percentage change.

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.

Prepare & details

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.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with case materials

Materials: Case study packet (3-5 pages), Analysis framework worksheet, Presentation template

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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).

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Interest Growth Relay, give each student a quick-check slip with a $200 investment scenario and ask them to calculate the final amount after two successive 5% increases using multipliers and show their steps.

Exit Ticket

After Reverse Price Puzzle, give students two problems: one to find the final price after successive changes and another to reverse a change to find the original. Collect responses to check for correct use of multipliers and clear explanations.

Discussion Prompt

During Market Stall, pose the question: 'If an item is discounted by 20% and then taxed by 10%, should you apply the tax to the discounted price or the original price? Why?' Facilitate a class discussion where students use their stall calculations to justify their reasoning.

Extensions & Scaffolding

• Challenge students to design a two-step discount advertisement that results in the same final price as a single 30% discount, then justify their design using multipliers.
• For students who struggle, provide fraction strips to model changes like 1/10 or 1/5 before moving to decimals.
• Deeper exploration: Have students investigate how a 10% increase followed by a 10% decrease does not return to the original value, and generalize to any percentage.

Key Vocabulary

Percentage Increase	A calculation that determines how much a quantity has grown relative to its original value, expressed as a percentage.
Percentage Decrease	A calculation that determines how much a quantity has shrunk relative to its original value, expressed as a percentage.
Multiplier	A number used to multiply a quantity. For percentage changes, multipliers like 1.15 (for 15% increase) or 0.85 (for 15% decrease) simplify calculations.
Original Amount	The starting value before any percentage increase or decrease is applied.
Successive Discounts	Applying multiple percentage discounts one after another, where each discount is calculated on the reduced price, not the original.