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Year 8

Finding the original amount after a decrease

I can calculate the original value, given the final value after a stated percentage decrease.

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Year 8

Finding the original amount after a decrease

I can calculate the original value, given the final value after a stated percentage decrease.

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Lesson details

Key learning points

  1. A bar model can be used to find the original amount after a percentage decrease.
  2. A double number line can be used to find the original amount after a percentage decrease.
  3. A ratio table can be used to find the original amount after a percentage decrease.
  4. In all of these representations a single multiplier can be used to find the original amount after a percentage decrease.

Keywords

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Common misconception

A single digit percentage is incorrectly worked out by dividing by 10 and not 100 e.g 3% = 0.3. This error continues when increasing amounts e.g increase 40 by 3% has a multiplier of 1.3

Remind pupils that to covert a percentage into a decimal we divide by 100. This applies with increase too e.g 120% has a multiplier of 1.2


To help you plan your year 8 maths lesson on: Finding the original amount after a decrease, download all teaching resources for free and adapt to suit your pupils' needs...

Before starting on the second learning cycle assess their understanding of multipliers using MWBs. Ask them questions such as, '0.7 is my multiplier what percentages could I be finding?'. Here you could be finding 70% or a decrease of 30%.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of the following is the correct calculation for finding 20% of 300?
300 + 0.2
300 − 0.2
Correct answer: 300 × 0.2
300 ÷ 0.2
Q2.
A number is increased by 25%. 1 part is equal to 25%. What will be the total number of parts representing the new number?
3
4
Correct answer: 5
6
Q3.
The cost of a TV increases by 20%. The new price is £420. What was the cost of the TV before the price increase? Without calculating the answer, decide whose answers cannot possibly be correct?
Correct answer: Andeep says the answer is £525
Correct answer: Izzy says the answer is £502
Aisha says the answer is £350
Jacob says the answer is £226
Q4.
Jun thinks of a number and increases it by 20%. Jun's new number is 720. What was his original number?
900
864
Correct answer: 600
576
Q5.
The cost of a TV increases by 20%. The new price is £420. The cost of the TV before the price increase is £ .
Correct Answer: 350, £ 350, £350, 350.00, £350.00
Q6.
The cost of a concert ticket is £80. This is an increase of 25% on last year. The cost of the ticket last year was £ .
Correct Answer: 64, £ 64, £64, £64.00, 64.00

Exit quiz

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6 Questions

Q1.
Which of the following words indicate an increase?
depreciate
discount
Correct answer: interest
loss
Correct answer: profit
Q2.
Which of the following is the correct calculation for finding 3% of 300?
300 + 0.03
300 − 0.03
Correct answer: 300 × 0.03
300 ÷ 0.03
Q3.
Match each percentage question to the correct multiplier.
Correct Answer:Increase by 2%,1.02
tick

1.02

Correct Answer:Increase by 30%,1.3
tick

1.3

Correct Answer:Decrease by 20%,0.8
tick

0.8

Correct Answer:Decrease by 3%,0.97
tick

0.97

Q4.
A t-shirt costs £12 in a sale offering a 25% discount. The cost of the t-shirt before the discount was £ .
Correct Answer: 16, £ 16, £16, £16.00, 16.00
Q5.
The value of a motorbike depreciates by 14% each year. It is now worth £5590. Last year the motorbike was worth £ .
Correct Answer: 6500, 6,500, £6500, £6,500, 6 500
Q6.
Mr. Oak sells a vase is sold for £102. This gives him a profit of 20%. Mr. Oak originally purchased the vase for £ .
Correct Answer: 85, £ 85, 85.00, £85, £85.00