Solve problems where the known percentage part and size represents a change to the whole
Lesson details
Learning outcome
I can solve percentage problems where the whole is changed.
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)
Teacher tip
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Match the percentage amount to 100%
100% = 150
100% = 160
100% = 154
100% = 165
Q2.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?
Q4.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?
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
Assessment exit quiz
6 Questions
Q1.When items cost less in a sale, match the ways that you can calculate a new price.
is 80% of the original price.
is 60% of the original price.
is 70% of the original price.
is 85% of the original price.
Q2.What is the new price of the sunglasses? £
Q3.What is the new price of the hat? £
Q4.Which item is the cheapest?
Q5.What was the original price of this T-shirt? £
Q6.What was the original price of this T-shirt? £
To help you plan your 6 maths lesson on: Solve problems where the known percentage part and size represents a change to the whole, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 6 maths lesson on: Solve problems where the known percentage part and size represents a change to the whole, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 2 maths lessons from the Understanding percentages unit, dive into the full primary maths curriculum, or learn more about lesson planning.