Percentage change and misleading discounts
KS4 · 40 minutes · Calculate percentage increase and decrease and distinguish reverse changes.
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Our learning goal
Calculate percentage increase and decrease and distinguish reverse changes.
Your turn: Choose one thing you would like to understand by the end.
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My lesson notes & project
Full teaching script
- Today: Percentage change and misleading discounts. Our goal: Calculate percentage increase and decrease and distinguish reverse changes.
- Take one idea at a time. Pause after each sentence; ask for repetition whenever you need it.
- A percentage is a fraction out of one hundred. A 20% discount on £50 is £10, so the new price is £40. A multiplier combines the steps: 50 × 0.8 = 40. A 15% increase uses 1.15, so £80 becomes £92. Be careful: a 20% decrease followed by a 20% increase does not return to the start. £50 becomes £40, then £40 × 1.2 = £48. The second percentage is taken from a different base. To reverse a 20% decrease, divide by 0.8: £40 ÷ 0.8 = £50. When comparing discounts, check the original price, final price and whether extra charges apply. Show the base amount before writing a percentage calculation.
- Together: choose one example from the explanation and show how it works. What do you notice?
- Your turn: Calculate 10%, 25% and 50% of £60 mentally. Model a 20% discount. Work out a 15% increase on £120 and a 30% decrease on £90. Explain why successive opposite percentages are not inverse operations.
- Reflect: what made sense, and what would you like explained differently?
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