Use knowledge of calculating common percentages of a number to solve problems in a range of contexts | Maths

Starter quiz

Match the percentages and fractions that are equivalent.
- 50%
  
  ⇔
  
  ${1} \over {2}$ ✓
- 10%
  
  ⇔
  
  ${1} \over {10}$ ✓
- 1%
  
  ⇔
  
  ${1} \over {100}$ ✓
100% of a number is 240 Use this to match the percentages to the value.
- 1% of 240
  
  ⇔
  
  2.4 ✓
- 50% of 240
  
  ⇔
  
  120 ✓
- 10% of 240
  
  ⇔
  
  24 ✓
One of the stages of the Tour de France race is 205 km long. Match the percentage of the race to the number of km.
- 100% of 205 km
  
  ⇔
  
  205 km ✓
- 50% of 205 km
  
  ⇔
  
  102.5 km ✓
- 10% of 205 km
  
  ⇔
  
  20.5 km ✓
- 1% of 205 km
  
  ⇔
  
  2.05 km ✓
A rider has completed 50% of a different stage of the race. If they have ridden 88 km, what is the length of the whole race? ______ km
- '176' ✓
If 100% of a number is 110, what is 1% of the number? ______
- '1.1' ✓
If 10% of a number is 46.5, what is 100% of the number? ______
- '465' ✓

Exit quiz

Match the fractions and the percentages.
- one-half
  
  ⇔
  
  50% ✓
- one-quarter
  
  ⇔
  
  25% ✓
- one whole
  
  ⇔
  
  100% ✓
- three-quarters
  
  ⇔
  
  75% ✓
What is one half of 50%? ______%
- '25' ✓
Find 25% of these numbers.
- 25% of 100
  
  ⇔
  
  25 ✓
- 25% of 88
  
  ⇔
  
  22 ✓
- 25% of 200
  
  ⇔
  
  50 ✓
- 25% of 160
  
  ⇔
  
  40 ✓
- 25% of 140
  
  ⇔
  
  35 ✓
$75% is three one-quarters or <Math> {3} \over {4} </Math> so what is 75% of 240 km? <span class="blank">______</span> km$

75% is three one-quarters or ${3} \over {4}$ so what is 75% of 240 km? ______ km
- '180' ✓
Use this fact to calculate other percentages. 100% is 120 km
- 50 % of 120 km
  
  ⇔
  
  60 km ✓
- 10% of 120 km
  
  ⇔
  
  12 km ✓
- 70% of 120 km
  
  ⇔
  
  84 km ✓
- 20% of 120 km
  
  ⇔
  
  24 km ✓
- 5% of 120 km
  
  ⇔
  
  6 km ✓
If 100% is 250 km, use an efficient method to find 20% of 250 km ______ km
- '50' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Addition, subtraction, multiplication and division can be used to calculate a new percentage from known percentages.
For example, if I know 10% of a number, I can halve it to find 5%
If I know 10% and 5% of a number, I can add them to find 15%

Common misconception

Pupils may find calculating 75% of a number difficult.

First focus on teaching one strategy for finding 75% of a number. Pupils may find it easiest to add 50% and 25% together. Show representations of this (e.g. bar models showing the proportion of the whole) alongside calculations.

Keywords

Efficient - Efficient means working in an organised way without wasting time or effort.
Percentage - A percentage is a proportion of a whole.