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New
Year 6

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

I can solve problems where a percentage part is known but the whole is unknown.

New
New
Year 6

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

I can solve problems where a percentage part is known but the whole is unknown.

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Lesson details

Key learning points

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

Keywords

  • Percentage - A percentage is a proportion of a 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.


To help you plan your year 6 maths lesson on: Explain how to solve problems where the percentage part and size is known but the whole is unknown, download all teaching resources for free and adapt to suit your pupils' needs...

To access this lesson, pupils must have familiarity with working out percentages of numbers. Pupils may find bar models and ratio tables helpful. Bar models help in understanding the structure of each problem. Ratio tables help in clearly setting the information out to see what needs calculating.
Teacher tip

Licence

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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Prior knowledge starter quiz

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6 Questions

Q1.
If 100% of an amount is 320 km, find these percentages.
Correct Answer:50% of 320 km,160 km

160 km

Correct Answer:10% of 320 km,32 km

32 km

Correct Answer:1% of 320 km,3.2 km

3.2 km

Correct Answer:25% of 320 km,80 km

80 km

Correct Answer:75% of 320 km,240 km

240 km

Q2.
10% of a race is 1.5 km Calculate these percentages of the race.
Correct Answer:20% of the race ,3 km

3 km

Correct Answer:30% of the race ,4.5 km

4.5 km

Correct Answer:60% of the race ,9 km

9 km

Correct Answer:5% of the race ,0.75 km

0.75 km

Correct Answer:80% of the race ,12 km

12 km

Q3.
Aisha’s battery has 61% of 600 minutes left. Complete each step of the table to calculate 61% of 600 minutes. minutes
An image in a quiz
Correct Answer: 366
Q4.
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
An image in a quiz
Correct Answer: 84
Q5.
Look at the table and find the missing percentage. 18 = % of 60
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Correct Answer: 30
Q6.
Use the table to calculate the missing percentage. 440 = % of 800
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Correct Answer: 55

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
If I know a part, I can work out the whole. Match the parts of the sentence correctly.
Correct Answer:If I know 10% ,I can multiply by 10 to calculate 100%

I can multiply by 10 to calculate 100%

Correct Answer:If I know 25% ,I can multiply by 4 to calculate 100%

I can multiply by 4 to calculate 100%

Correct Answer:If I know 50% ,I can multiply by 2 to calculate 100%

I can multiply by 2 to calculate 100%

Correct Answer:If I know 20% ,I can multiply by 5 to calculate 100%

I can multiply by 5 to calculate 100%

Q2.
Lucas has read 25% of his book. He has read 64 pages. His book is pages long.
An image in a quiz
Correct Answer: 256
Q3.
Aisha thinks of a number. 20% of her number is 104 What is her number?
Correct Answer: 520
Q4.
Lucas has read 75% of his book. This is 90 pages. How many pages are in his book? pages
An image in a quiz
Correct Answer: 120
Q5.
Aisha thinks of a number. 40% of her number is 72 What number is Aisha thinking of?
An image in a quiz
Correct Answer: 180
Q6.
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
Correct Answer: 2,000