Activity 01
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.
Analyze the difference between finding a percentage of an amount and a percentage change.
Facilitation TipDuring Station Rotation: Percentage Changes, rotate groups every 8 minutes so students experience both increase and decrease stations before fatigue sets in.
What to look forProvide students with two scenarios: 1) A price tag showing a £20 item is now £15. Ask: 'What is the percentage decrease?' 2) A savings account starts with £100 and grows by 5%. Ask: 'What is the new balance?'
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Activity 02
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.
Explain how to calculate the original amount after a percentage change.
Facilitation TipIn Pair Challenge: Discount Design, provide scissors, glue, and price tags so pairs can physically cut and paste to see the effect of successive discounts.
What to look forPresent students with a problem: 'A town's population increased from 50,000 to 55,000 in one year. Calculate the percentage increase.' Observe students' methods and identify common errors in calculation or concept.
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Activity 03
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.
Design a problem involving a percentage increase or decrease.
Facilitation TipDuring 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.
What to look forPose the question: 'If a shopkeeper says an item is 'half price', is that the same as a 50% discount? Explain your reasoning.' Facilitate a class discussion comparing these two statements and their mathematical equivalence.
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Activity 04
Individual: Error Hunt
Provide worksheets with mixed calculations; students identify and correct errors in percentage changes. Follow with self-explanation of fixes.
Analyze the difference between finding a percentage of an amount and a percentage change.
Facilitation TipIn Error Hunt, use common errors written on cards so students identify and explain mistakes before fixing them.
What to look forProvide students with two scenarios: 1) A price tag showing a £20 item is now £15. Ask: 'What is the percentage decrease?' 2) A savings account starts with £100 and grows by 5%. Ask: 'What is the new balance?'
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Generate Complete Lesson→A few notes on teaching this unit
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.
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
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.
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.
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.
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.
During Growth Tracker, watch for students who believe a 50% increase followed by a 50% decrease will return to the original value.
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.
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