Percentage Increase and Decrease

Active learning works for percentage increase and decrease because these concepts demand flexible thinking about changing bases. Students must repeatedly adjust their reference point as values shift, which hands-on activities make visible. Concrete examples prevent the common trap of treating percentages as fixed additions or subtractions from the original amount.

• Year 7
• Mathematics
• 4 activities
• 30 min–50 min

Learning Objectives

1. Calculate the new value after a percentage increase or decrease is applied to an initial amount.
2. Explain why successive percentage changes of the same value do not result in the original amount.
3. Analyze the impact of multiple successive percentage changes on a starting value.
4. Construct a word problem that requires calculating a discount or sales tax.
5. Compare the final amounts resulting from different sequences of percentage changes.

Case Study Analysis

⏱ 45 min·Small Groups

Shopping Spree: Discount Calculations

Provide catalogs or printed store flyers with prices. In small groups, students select items, apply successive discounts like 20% off then 10% off, and calculate final prices. Groups present one purchase scenario, justifying steps to the class.

Prepare & details

Justify why a percentage increase followed by the same percentage decrease does not return to the original value.

Facilitation Tip: During Shopping Spree, circulate and ask students to justify their discount calculations to you before moving to the next item, ensuring they use the sale price as the new base.

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

Savings Challenge: Interest Tracker

Give each pair a starting savings amount. They apply quarterly interest rates, such as 2% per quarter for four quarters, recording changes on a shared chart. Pairs compare results and discuss why the amount grows nonlinearly.

Prepare & details

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

Facilitation Tip: In Savings Challenge, provide calculators but require students to write each step—starting amount, interest calculation, new total—on paper to make the compounding visible.

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

Stations Rotation

⏱ 50 min·Small Groups

Stations Rotation: Percentage Scenarios

Set up stations for wage increases, price drops, tax additions, and mixed changes. Students rotate, solving two problems per station with calculators and recording justifications. Debrief as a whole class on common patterns.

Prepare & details

Construct a problem involving a real-world discount or tax calculation.

Facilitation Tip: For Station Rotation, place a timer at each station and limit materials to force students to adjust their approach when the base changes unexpectedly.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Case Study Analysis

⏱ 35 min·Pairs

Problem Construction: Real-Life Builds

Individually, students create a financial scenario with at least two percentage changes, such as a sale followed by tax. They swap with a partner for solving and feedback, then revise based on peer input.

Prepare & details

Justify why a percentage increase followed by the same percentage decrease does not return to the original value.

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 anchoring every new percentage to the current total, not the original amount. Use visuals like number lines that reset after each change to reinforce the shifting base. Avoid teaching percentage rules in isolation; instead, embed them in financial scenarios students recognize. Research shows that students who manipulate real quantities before abstract calculations retain the concept longer.

What to Expect

Successful learning looks like students adjusting their calculations when the base changes mid-problem without prompting. You should see them explaining why a 20% discount on a $50 item is not the same as a $10 reduction. Peer explanations during mixed-ability groups reveal deep understanding of sequential percentage changes.

Watch Out for These Misconceptions

Common Misconception

During Shopping Spree, watch for students subtracting the discount percentage directly from the original price (e.g., $60 − 15 = $45).

What to Teach Instead

Redirect them to calculate 15% of $60 first, then subtract that amount from $60 to find the sale price. Use the manipulative money provided to show the discount as a physical stack removed from the total.

Common Misconception

During Savings Challenge, watch for students applying the interest percentage to the original deposit only.

What to Teach Instead

Have them recalculate each year’s interest using the current balance shown on their tracker sheet. Ask, 'What is 5% of $126?' to guide them to use the updated base.

Common Misconception

During Station Rotation, watch for students stating that a 10% increase followed by a 10% decrease cancels out perfectly.

What to Teach Instead

Ask them to use the station’s whiteboard to show the two steps with actual numbers, then compare the final amount to the original. Highlight the pattern that the decrease is applied to a larger amount than the increase.

Assessment Ideas

Quick Check

After Shopping Spree, present students with a scenario: 'A jacket costs $80 and is discounted by 25%. What is the sale price?' Ask students to show their calculation steps and final answer on a mini-whiteboard.

Discussion Prompt

During Savings Challenge, pose the question: 'If you deposit $100 and earn 8% interest the first year but lose 8% the second year, are you back to $100? Explain using your interest tracker calculations.' Facilitate a brief class discussion to reconcile the changing base.

Exit Ticket

After Station Rotation, give each student a card with a starting price ($150) and two percentage changes (+30%, -25%). Ask them to calculate the final price and write one sentence about whether the final price is higher or lower than the original.

Extensions & Scaffolding

• Challenge early finishers to create a 3-step percentage change scenario where the final amount is less than the original, then trade with a partner to solve.
• Scaffolding: Provide a template with blanks for each step (original → after first change → after second change) for students who confuse the base.
• Deeper exploration: Have students research real-world examples of successive percentage changes, such as sales tax followed by a tip, and present their findings to the class.

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.
Original Value	The starting amount or quantity before any percentage change is applied.
Successive Percentage Changes	Applying multiple percentage increases or decreases one after another, where each change is calculated on the new amount from the previous step.