Explain how to solve problems where the percentage part and size is known but the whole is unknown | Maths

Starter quiz

If 100% of an amount is 320 km, find these percentages.
- 50% of 320 km
  
  ⇔
  
  160 km ✓
- 10% of 320 km
  
  ⇔
  
  32 km ✓
- 1% of 320 km
  
  ⇔
  
  3.2 km ✓
- 25% of 320 km
  
  ⇔
  
  80 km ✓
- 75% of 320 km
  
  ⇔
  
  240 km ✓
10% of a race is 1.5 km Calculate these percentages of the race.
- 20% of the race
  
  ⇔
  
  3 km ✓
- 30% of the race
  
  ⇔
  
  4.5 km ✓
- 60% of the race
  
  ⇔
  
  9 km ✓
- 5% of the race
  
  ⇔
  
  0.75 km ✓
- 80% of the race
  
  ⇔
  
  12 km ✓
Aisha’s battery has 61% of 600 minutes left. Complete each step of the table to calculate 61% of 600 minutes. ______ minutes
- '366' ✓
Lucas needs to find the number of children who cycled to school. Look at the pie chart and complete each step of the table to calculate 21% of 400 children ______
- '84' ✓
Look at the table and find the missing percentage. 18 = ______% of 60
- '30' ✓
Use the table to calculate the missing percentage. 440 = ______% of 800
- '55' ✓

Exit quiz

If I know a part, I can work out the whole. Match the parts of the sentence correctly.
- If I know 10%
  
  ⇔
  
  I can multiply by 10 to calculate 100% ✓
- If I know 25%
  
  ⇔
  
  I can multiply by 4 to calculate 100% ✓
- If I know 50%
  
  ⇔
  
  I can multiply by 2 to calculate 100% ✓
- If I know 20%
  
  ⇔
  
  I can multiply by 5 to calculate 100% ✓
Lucas has read 25% of his book. He has read 64 pages. His book is ______ pages long.
- '256' ✓
Aisha thinks of a number. 20% of her number is 104 What is her number?
- '520' ✓
Lucas has read 75% of his book. This is 90 pages. How many pages are in his book? ______ pages
- '120' ✓
Aisha thinks of a number. 40% of her number is 72 What number is Aisha thinking of?
- '180' ✓
Lucas takes part in a race. He has run 30% of the race which is 600 m What is the distance of the whole race? ______ m
- '2,000' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

If I know about a part, I can work out the whole from that part.
If I know what 10% is, I can multiply by 10 to calculate 100%.
If the part is a factor of 100, I can multiply the part by the other factor to calculate the whole.

Common misconception

Pupils may not always instantly recognise that a percentage part is a factor of 100

Discuss factors of 100 with the pupils, for example, as factor pairs. Allow them to keep these displayed to refer to throughout the lesson if needed to help make this connection.

Keywords

Percentage - A percentage is a proportion of a whole.