Solve problems where the known percentage part and size represents a change to the whole | Maths

Starter quiz

Match the percentage amount to 100%
- 10% = 15
  
  ⇔
  
  100% = 150 ✓
- 25% = 40
  
  ⇔
  
  100% = 160 ✓
- 50% = 77
  
  ⇔
  
  100% = 154 ✓
- 1% = 1.65
  
  ⇔
  
  100% = 165 ✓
Lucas has read 25% of his book. He has read 73 pages. His book is ______ pages long.
- '292' ✓
Aisha thinks of a number. 20% of her number is 95 What is her number?
- '380' ✓
Lucas has read 75% of his book. This is 99 pages. How many pages are in his book?______ pages
- '132' ✓
Aisha thinks of a number. 60% of her number is 78 What number is Aisha thinking of?
- '130' ✓
Lucas takes part in a race. He has run 70% of the race which is 840 m What is the distance of the whole race? ______ m
- '1,200' ✓

Exit quiz

When items cost less in a sale, match the ways that you can calculate a new price.
- 20% off the price
  
  ⇔
  
  is 80% of the original price. ✓
- 40% off the price
  
  ⇔
  
  is 60% of the original price. ✓
- 30 % off the price
  
  ⇔
  
  is 70% of the original price. ✓
- 15% off the price
  
  ⇔
  
  is 85% of the original price. ✓
What is the new price of the sunglasses? £______
- '13.50' ✓
What is the new price of the hat? £______
- '14.40' ✓
Which item is the cheapest?
- The cap
- The sunglasses ✓
What was the original price of this T-shirt? £______
- '24' ✓
What was the original price of this T-shirt? £______
- '8' ✓

Worksheet

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Lesson Details

Key learning points

Identify the part and how it relates to the whole.
If the percentage part is a factor of 100, you can multiply the other part to calculate the whole.
If the percentage part is not a factor of 100, you can use division and multiplication to calculate the whole.

Common misconception

Pupils may make mistakes in the second cycle, where they find the whole after a percentage change. They may think the part given (e.g. the new cost) is represented by the percentage change.

Use bar models to help make it clear that the price given is the part remaining after the percentage change. If pupils are struggling with this, simplify the problem by giving numbers easy to calculate with (e.g. 30% off; new price £7)

Keywords

Percentage - A percentage is a proportion of a whole.