Home → Curriculum Hub → Maths Lessons → Percentages → Calculating a Percentage Change
Ready-to-teach lesson. Includes a video tutorial, printable worksheets and GCSE exam-style practice with worked solutions.
Students learn to calculate a percentage change by writing an increase or decrease as a single decimal multiplier, applying it in one calculation, and using it on problems where a quantity changes more than once. The lesson covers percentage increases, percentage decreases, worded problems and comparing offers.
Most students arrive able to find a percentage of an amount and add it on. That method works, and it is why it survives. The problem is that it does not scale. A percentage change is not two operations, it is one: multiply by a number that represents the whole quantity after the change.
Students who hold that idea can go on to repeated percentage change, compound interest and reverse percentages without learning anything new. Students who treat the multiplier as a trick for saving time have to relearn the topic each time it reappears.
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Watch this tutorial first to see how to write a percentage increase or decrease as a single decimal multiplier, then apply it. Download the handout to work along with the video, then try the worksheet below.
Key topics: writing an increase as a multiplier greater than 1, writing a decrease as a multiplier less than 1, and applying the multiplier in one calculation. Download handout.
Six questions, with full solutions. Questions 1 and 2 build fluency with percentage increases and decreases separately. Question 3 is a matching activity that pairs an increase with an equivalent decrease, for example 18 increased by 14% and 25.65 decreased by 20% both giving 20.52, which forces students to compute rather than pattern match.
Questions 4 to 6 are worded problems: a 3% pay rise on £410, a 24% sale reduction on a £98 coat, and a theme park question where the child price is defined relative to the adult price.
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The starter is a non-calculator recap built on a table of 5% and 10% of several amounts. Students use those facts to work out three progressively harder values, for example that 15% of £30 is £4.50, and that £15 is 20% of £75.
This is deliberate. The multiplier method is about to replace a method students trust, and it lands better when their existing method has just been rehearsed and shown to work. The starter also gives you the number sense you need later, because a student who knows 10% of £82 is £8.20 can tell you straight away what is a plausible answer for a 15% reduction.
Prompts / Questions to consider
When you introduce 1.2, spend time on the 1 before the 2. The 1 is the original amount, still there. The 0.2 is the extra fifth. Together they are the new quantity in a single number.
Decreases are where the idea proves itself. For a 42% decrease, ask what is left rather than what is lost. Fifty eight per cent of the original remains, so the multiplier is 0.58, and 216 decreased by 42% is 0.58 × 216 = 125.28. A student who reaches for 0.42 has answered the question “how much came off”, which is a different question.
Work through the examples in order. They move from friendly numbers, £60 increased by 20%, to money with awkward percentages, £51.30 decreased by 32%.
Prompts / Questions to consider
The most challenging question in the teaching phase is the rectangle. A length of 1.5 cm is reduced by 5% and a width of 4.8 cm is increased by 9%.
This question does something the earlier ones cannot. Two multipliers act on two different quantities and the results carry through into a third calculation. Students who have been finding the percentage and adding it on will visibly slow down here, and that slowing down is the argument for the method. It is also where the lesson quietly points at compound interest.
The plenary sets the same idea in a context students recognise. Emma can buy the same trainers from three shops, each with a different offer. The mathematics is straightforward once each offer is written as a multiplier. The value is in the justification.
Prompts / Questions to consider
More able: apply two multipliers in sequence, then compare offers and justify the best value.
Less able: rehearse finding 5% and 10% without a calculator before introducing the multiplier for a single increase.
| Phase | Focus | Time |
|---|---|---|
| Starter | Non-calculator recap using 5% and 10% facts | 5 to 10 min |
| Development | Multiplier for an increase, then for a decrease | 15 to 20 min |
| Check | Mixed set including the rectangle area question | 10 min |
| Main / stretch | Repeated change and comparing three offers | 10 to 15 min |
| Plenary | Justify which shop is best value, and why | 5 to 10 min |
Use this checklist after the lesson or as a revision self-check.
Try these GCSE-style questions on calculating a percentage change, then reveal the solutions to check your working. Select the image to view it full screen.
a) Increase £86 by 18%.
b) Decrease £560 by 20%.
a) 100% + 18% = 118% of the original.
118% = 1.18 (the multiplier).
86 × 1.18 = £101.48
b) 100% − 20% = 80% of the original.
80% = 0.80 (the multiplier).
560 × 0.80 = £448
Daniel was paid £12.00 per hour. Daniel receives a pay increase of 30%. Work out how much Daniel is now paid per hour.
100% + 30% = 130% of the original pay.
130% = 1.30 (the multiplier).
£12.00 × 1.30 = £15.60
Daniel is now paid £15.60 per hour.
Two supermarkets, A and B, have offers on the same packet of pasta.
Supermarket A: Normal price £1.60 for each packet. Special offer: buy two packets at the normal price and get a third packet for half price.
Supermarket B: Normal price £1.70 for each packet. Special offer: 10% off the normal price.
Stephen buys three packets of pasta. Which supermarket is best value for Stephen?
Supermarket A:
Buy 2 at £1.60 each = £3.20
Third packet half price = £1.60 ÷ 2 = £0.80
Total = £3.20 + £0.80 = £4.00
Supermarket B:
3 packets at £1.70 each = £5.10
10% off = × 0.90
£5.10 × 0.90 = £4.59
£4.00 < £4.59
Answer: Supermarket A
The cost of sending a child to day care is £8.80 per hour on each weekday. On Saturday the cost is 25% greater than the weekday hourly rate. A child goes to day care for:
The total cost for the three days is reduced by 12% as a special offer.
Work out the cost for the three days after the 12% reduction. You must show your working.
Weekday rate = £8.80 per hour
Saturday rate = £8.80 × 1.25 = £11.00 per hour
Total before reduction = £70.40 + £35.20 + £33.00 = £138.60
After 12% reduction, multiplier = 0.88
£138.60 × 0.88 = £121.968
Answer: £121.97
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A single decimal that represents the whole quantity after the change. An increase of 20% uses the multiplier 1.2, and a decrease of 20% uses the multiplier 0.8. Multiply the original amount by that number in one calculation.
Add the percentage to 100%, convert to a decimal, then multiply. For a 5% increase the multiplier is 1.05, so 450 increased by 5% is 1.05 × 450.
Subtract the percentage from 100%, convert to a decimal, then multiply. For a 42% decrease, 58% remains, so the multiplier is 0.58.
Because the second percentage is taken from the new amount, not the original. Multiplying by 1.2 and then by 0.8 gives 0.96, so you finish 4% below where you started.
Repeated percentage change, where the multiplier is applied more than once, then compound interest and reverse percentages.
The natural next lesson is repeated percentage change, where the multiplier is applied more than once and students meet index notation in this context for the first time. Compound interest follows from it directly, and reverse percentages follow from asking students to undo a multiplier rather than apply one. For the full topic hub, visit All Percentages Lessons.
If you want to try one thing from this lesson tomorrow, use the rectangle question as a starter with a class already partway through percentages. How quickly students reach 7.4556 cm² tells you whether the multiplier is a method they own or a rule they are reciting.
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