New
New
Solve problems where the known percentage part and size represents a change to the whole
I can solve percentage problems where the whole is changed.
Lesson 9 of 10
New
New
- Year 6
Solve problems where the known percentage part and size represents a change to the whole
I can solve percentage problems where the whole is changed.
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.
Keywords
Percentage - A percentage is a proportion of a 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)
The second learning cycle deepens understanding of percentages relating to change and calculates the change as a percentage. Pupils need to be confident in their understanding of, and calculation of, percentages before moving to this cycle in the lesson.
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
6 Questions
Q1.Match the percentage amount to 100%
Match the percentage amount to 100%
Q2.Lucas has read 25% of his book. He has read 73 pages. His book is pages long.
Lucas has read 25% of his book. He has read 73 pages. His book is pages long.
Q3.Aisha thinks of a number. 20% of her number is 95 What is her number?
Aisha thinks of a number. 20% of her number is 95 What is her number?
Q4.Lucas has read 75% of his book. This is 99 pages. How many pages are in his book? pages
Lucas has read 75% of his book. This is 99 pages. How many pages are in his book? pages
Q5.Aisha thinks of a number. 60% of her number is 78 What number is Aisha thinking of?
Aisha thinks of a number. 60% of her number is 78 What number is Aisha thinking of?
Q6.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
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
Assessment exit quiz
6 Questions
Q1.When items cost less in a sale, match the ways that you can calculate a new price.
When items cost less in a sale, match the ways that you can calculate a new price.
Q2.What is the new price of the sunglasses? £
What is the new price of the sunglasses? £
Q3.What is the new price of the hat? £
What is the new price of the hat? £
Q4.Which item is the cheapest?
Which item is the cheapest?
The cap
Q5.What was the original price of this T-shirt? £
What was the original price of this T-shirt? £
Q6.What was the original price of this T-shirt? £
What was the original price of this T-shirt? £
