Percentage Increase and Decrease

Active learning works for percentage increase and decrease because students need to see the multiplicative effect on quantities, not just memorize formulas. Hands-on tasks make the abstract concrete, helping students connect calculations to real decisions like pricing and budgeting.

• Primary 6
• Mathematics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Calculate the new value after a percentage increase or decrease is applied to an original value.
2. Analyze why a percentage increase followed by an equal percentage decrease results in a different final value than the original.
3. Construct a formula to find the original value when given a percentage change and the final value.
4. Evaluate the effect of successive percentage changes on a quantity in a financial context.

Case Study Analysis

⏱ 45 min·Small Groups

Market Stall Simulation: Price Changes

Groups set up stalls selling items at base prices. Apply successive percentage increases or decreases based on customer negotiations, recording original, new prices, and profits. Rotate roles as buyer and seller, then graph changes.

Prepare & details

Analyze why a percentage increase followed by an equal percentage decrease does not return to the original value.

Facilitation Tip: In the Market Stall Simulation, circulate with a calculator to catch students who accidentally use the new price as the base when calculating increases or decreases.

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 Calculation Challenge: Mystery Prices

Provide cards with final prices and percentage changes. Pairs work backwards to find originals using equations like original = final / (1 + change/100). Share methods and verify with whole class.

Prepare & details

Evaluate the impact of percentage changes on financial decisions.

Facilitation Tip: During the Reverse Calculation Challenge, provide students with price tags they can physically mark up or down to reinforce the original base concept.

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·Small Groups

Profit Impact Relay: Scenario Cards

Teams relay-race to stations with business scenarios involving percentage changes on costs and revenues. Calculate net profit/loss at each, passing batons with answers. Debrief patterns in impacts.

Prepare & details

Construct a method to calculate the original value given a percentage change and the new value.

Facilitation Tip: For the Profit Impact Relay, time the relay to create urgency while allowing time for peer explanations of each step in the profit calculation.

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·Individual

Savings Tracker: Personal Finance

Individuals track a starting savings amount, applying monthly percentage increases from interest or decreases from expenses. Plot on graphs and predict future values after multiple changes.

Prepare & details

Analyze why a percentage increase followed by an equal percentage decrease does not return to the original value.

Facilitation Tip: In the Savings Tracker, model how to record percentage changes in a two-column table to track original and adjusted 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

Teaching This Topic

Teach this topic by focusing on the original amount as the anchor for all calculations, using visuals like number lines or bar models to show the shift. Avoid rushing to shortcuts; instead, require students to write out each step to build accuracy. Research shows that students benefit from repeated exposure to the same scenario with different percentage values to internalize the process.

What to Expect

Successful learning shows when students confidently explain why a 20% increase followed by a 20% decrease does not return to the original amount, and when they use consistent base values in calculations. Students should also justify their answers with clear steps and peer feedback.

Watch Out for These Misconceptions

Common Misconception

During Market Stall Simulation, watch for students who apply the percentage change to the new price instead of the original price.

What to Teach Instead

Have students label their price tags with 'Original Price' and 'New Price' before calculating, and ask peers to verify the base used in each calculation.

Common Misconception

During Reverse Calculation Challenge, watch for students who assume the percentage change applies to the final unknown amount.

What to Teach Instead

Ask students to write the equation with the original price as the variable, then solve step-by-step while explaining why the original price must be the base.

Common Misconception

During Profit Impact Relay, watch for students who confuse profit with revenue or cost.

What to Teach Instead

Have students present their scenario cards to the class, using the terms 'cost price,' 'selling price,' and 'profit' in context to clarify the relationships.

Assessment Ideas

Quick Check

After Market Stall Simulation, give each pair a scenario like: 'A bookstore buys a book for $40 and sells it for $50. What is the percentage profit? If the bookstore then offers a 10% discount, what is the new selling price?' Collect and check calculations for both steps.

Discussion Prompt

During Reverse Calculation Challenge, pose this question: 'A jacket costs $80 after a 20% discount. What was the original price? Compare your methods with a partner and explain why using the original price as the base matters.' Facilitate a class discussion on different approaches.

Exit Ticket

After Profit Impact Relay, give each student a card with a problem like: 'A shopkeeper marks up a shirt by 25% to $125. What was the original cost? Show your method and write one sentence explaining your steps.' Collect and review responses to identify misconceptions about the base value.

Extensions & Scaffolding

• Challenge students to create a 15% discount followed by a 10% service fee on a $200 item, then calculate the final price and explain each step to a partner.
• Scaffolding: Provide a partially completed table for the Market Stall Simulation with some values filled in to guide students who struggle with setting up calculations.
• Deeper: Ask students to research and compare the impact of a 5% price increase on a small business versus a large corporation, using real examples from local news or advertisements.

Key Vocabulary

Percentage Increase	The amount by which a value grows, expressed as a percentage of the original value.
Percentage Decrease	The amount by which a value shrinks, expressed as a percentage of the original value.
Original Value	The starting amount before any percentage change is applied.
New Value	The amount after a percentage increase or decrease has been applied.
Profit	The financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something, often calculated as a percentage of cost price.
Loss	The financial disadvantage, especially the difference between the amount earned and the amount spent when the expenses exceed the revenue, often calculated as a percentage of cost price.