Percentage Increase and Decrease

Active learning helps students grasp percentage changes because the abstract idea of multiplying by a decimal becomes concrete when they physically adjust prices or track growth over time. Moving between hands-on steps and abstract calculations builds durable understanding better than worksheets alone.

• Year 7
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the new amount after a percentage increase or decrease.
2. Determine the percentage change between two given amounts.
3. Explain the steps required to find the original amount given a percentage change.
4. Design a word problem that requires calculating a percentage increase or decrease in a real-world context.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Percentage Changes

Prepare stations with price tags showing original and sale prices. Students calculate increases or decreases, then reverse to find originals. Rotate groups every 10 minutes, discussing methods at each station. End with a class share-out.

Prepare & details

Analyze the difference between finding a percentage of an amount and a percentage change.

Facilitation Tip: During Station Rotation: Percentage Changes, rotate groups every 8 minutes so students experience both increase and decrease stations before fatigue sets in.

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

Problem-Based Learning

⏱ 30 min·Pairs

Pair Challenge: Discount Design

Pairs create real-world problems, like clothing sales or wage rises, swapping with another pair to solve. They check answers using the reverse method. Teacher circulates to prompt equation setups.

Prepare & details

Explain how to calculate the original amount after a percentage change.

Facilitation Tip: In Pair Challenge: Discount Design, provide scissors, glue, and price tags so pairs can physically cut and paste to see the effect of successive discounts.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Problem-Based Learning

⏱ 35 min·Whole Class

Whole Class: Growth Tracker

Display a table of yearly population growth percentages. Class predicts values after 3 years using calculators, then verifies step-by-step on board. Adjust for decreases like shrinking habitats.

Prepare & details

Design a problem involving a percentage increase or decrease.

Facilitation Tip: During Growth Tracker, give each pair a different starting population and a fixed growth rate so the class can compare multiple linear-but-not-symmetric patterns side by side.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Problem-Based Learning

⏱ 20 min·Individual

Individual: Error Hunt

Provide worksheets with mixed calculations; students identify and correct errors in percentage changes. Follow with self-explanation of fixes.

Prepare & details

Analyze the difference between finding a percentage of an amount and a percentage change.

Facilitation Tip: In Error Hunt, use common errors written on cards so students identify and explain mistakes before fixing them.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Teaching This Topic

Teach this topic by first anchoring to students’ lived experiences—shopping, saving, and population—and then moving deliberately between concrete and abstract representations. Emphasize the multiplier as the core tool, not the percentage points added. Avoid rushing to the formula before students have internalized why a 20% increase means multiplying by 1.20 through repeated examples and visual tracking.

What to Expect

Successful learning looks like students confidently choosing whether to add or subtract a percentage, showing clear work with multipliers like 1.20 or 0.75, and explaining why a 50% increase followed by a 50% decrease does not return to the original value. They should also reverse changes to find original amounts without reversing the percentages themselves.

Watch Out for These Misconceptions

Common Misconception

During Station Rotation: Percentage Changes, watch for students who add the percentage directly to the original amount instead of applying the multiplier. For example, adding 20 to a £50 price rather than using 1.20 × 50.

What to Teach Instead

Have students use play money and price tags to show that adding 20 pounds to 50 pounds gives £70, but a 20% increase on £50 should give £60. Guide them to write the multiplier (1 + 20/100 = 1.20) so the connection between the percentage and the operation becomes visible.

Common Misconception

During Pair Challenge: Discount Design, watch for students who subtract the discount percentage from the new (discounted) price instead of the original price when reversing the change.

What to Teach Instead

Ask pairs to trace a single £100 item through a 20% discount to £80, then reverse by calculating 20% of the original £100 (£20) to return to £100. Use this to show why reversing must always reference the original amount.

Common Misconception

During Growth Tracker, watch for students who believe a 50% increase followed by a 50% decrease will return to the original value.

What to Teach Instead

Give each pair a starting value and have them calculate step-by-step: increase by 50%, then decrease the new amount by 50%. Ask them to compare the final value to the start and explain why the values are not equal, reinforcing the asymmetry of percentage changes.

Assessment Ideas

Exit Ticket

After Station Rotation: Percentage Changes, give students two quick problems: 1) A £30 item is reduced to £24. What is the percentage decrease? 2) A savings account starts with £200 and grows by 7%. What is the new balance? Collect responses to assess whether students apply multipliers correctly and reverse changes accurately.

Quick Check

During Growth Tracker, circulate and observe pairs as they calculate percentage increases for their assigned populations. Note if students consistently use the formula new = original × (1 + change/100) or if they default to additive thinking, then provide immediate targeted feedback.

Discussion Prompt

After Pair Challenge: Discount Design, ask pairs to present one discount scenario and explain whether a 'half price' sale is mathematically the same as a 50% discount. Use their explanations to assess if they understand the equivalence and can articulate the calculation behind it.

Extensions & Scaffolding

• Challenge: Provide compound scenarios with two successive changes (e.g., 10% increase followed by 15% decrease) and ask students to justify their final multiplier.
• Scaffolding: Offer a template with pre-labeled columns for original, percentage change, multiplier, and new amount when reversing changes.
• Deeper exploration: Explore the difference between percentage change and percentage point change using interest rate examples to highlight when each applies.

Key Vocabulary

Percentage Change	The measure of how much a quantity has changed relative to its original value, expressed as a percentage.
Percentage Increase	A calculation showing how much a value has gone up, expressed as a percentage of the original value.
Percentage Decrease	A calculation showing how much a value has gone down, expressed as a percentage of the original value.
Original Amount	The starting value before any percentage change has been applied.
New Amount	The value after a percentage increase or decrease has been applied.