Solve problems involving percentages in a range of contexts | Maths

Starter quiz

Match each percentage amount to the value of 100% e.g. If 10% = 1.8 then 100% = ___

10% = 1.8

⇔

100% = 18 ✓

25% = 35

⇔

100% = 140 ✓

50% = 82.5

⇔

100% = 165 ✓

1% = 2.7

⇔

100% = 270 ✓
What is the new price of the sunglasses? £______

'12' ✓
What is the new price of the hat? £______

'16.50' ✓
Which item is the most expensive?

The cap ✓

The sunglasses
What was the original price of this T-shirt? £______

'30' ✓
What was the original price of this T-shirt? £______

'20' ✓

Exit quiz

If 100% = 1,100 match these percentages to the answers.

10%

⇔

110 ✓

5%

⇔

55 ✓

15%

⇔

165 ✓

40%

⇔

440 ✓

90%

⇔

990 ✓
Work out the new price of the toy robot. £______

'16.80' ✓
Work out the new price of the toy panda. £______

'13.50' ✓
Lucas thinks of a number and says that 4% of his number is 160 What is his number?

'4,000' ✓
Sofia has read 70% of her book which is 210 pages. How long is her book in total? ______ pages

'300' ✓
Laura has cycled for 72 km which is 75% of her race. The total length of the race is ______ km

'96' ✓

Worksheet

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Lesson Details

Key learning points

If I know the value of the whole, I can calculate the value of a part.
If I know the value of a part, I can calculate the value of the whole.
Addition, subtraction, multiplication and division can be used to calculate a new percentage from known percentages.

Common misconception

When finding a price has reduced by 25%, pupils may give the answer as 25% of the number, rather than seeing it as 75% of the whole.

Emphasise that '25% off' means that the price has been reduced by 25%. The whole, subtract 25%, is equal to 75% of the whole. Bar models are useful for showing this.

Keywords

Percentage - A percentage is a proportion of a whole.