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.

• Year 9
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Calculate the new price after a percentage increase or decrease, applying the correct multiplier.
2. Explain why successive percentage changes, such as a discount followed by a price increase, do not result in the original value.
3. Compare the net effect of different sequences of percentage changes on an initial amount.
4. Construct a word problem involving a real-world scenario that requires calculating successive percentage changes.
5. Analyze the impact of a given percentage increase or decrease on a specific financial quantity.

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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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

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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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 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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Multiplier Match-Up, give students a starting value of $80 and ask them to calculate the final price after a 25% increase followed by a 25% decrease. Have them write one sentence explaining the difference from the original amount.

Quick Check

During Shop Sale Simulation, present students with three items and ask them to calculate two different discount scenarios for each: one applied once, the other split into two smaller discounts. Compare final prices to assess understanding of compounding.

Discussion Prompt

After Growth Chain Relay, pose the question: 'If a population increases by 5% each year for two years, is it the same as a 10% increase over two years? Why or why not?' Facilitate a class discussion using their relay results as evidence.

Extensions & Scaffolding

• Challenge early finishers to create a real-world scenario involving two successive percentage changes, then trade with a partner to solve.
• Scaffolding for struggling students: provide partially completed multiplier calculations with missing steps to build confidence before independent work.
• Deeper exploration: invite students to research and present how percentage increase and decrease are used in business profit margins or population studies.

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 value; in percentage change, it represents the original amount plus or minus the percentage change as a decimal.
Successive Percentage Changes	Applying more than one percentage change one after another to a value, where each change is calculated on the result of the previous one.