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Lesson 2 of 16

Securing understanding of percentages

I can manipulate percentages of an amount with a representation.

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View unit
Lesson 2 of 16
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Securing understanding of percentages

I can manipulate percentages of an amount with a representation.

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Lesson details

Key learning points

  1. Percentages of amounts can be found by combining known percentages
  2. Percentages of amounts can be represented and found using a bar model
  3. Percentages of amounts can be represented and found using double number lines
  4. Percentages of amounts can be represented and found using ratio tables

Keywords

  • Proportion - Variables are in proportion if they have a constant multiplicative relationship.

  • Equivalent fractions - Two fractions are equivalent if they have the same value.

Common misconception

When finding 10% we divide by 10, so when finding 5% we divide by 5.

Use a bar model to show the division of 10 means one tenth of the amount. When dividing by 5 it means one fifth has been found.

Using MWB pupils must draw the same question but illustrated in different ways; ratio table, double number line or bar model. E.g show 48% of 800. They can then decide which representation they prefer. Look out for efficient approaches using subtraction where appropriate.
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2026), 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.
Proportionality means two variables have a constant __________ relationship so the variables are in proportion to each other.

additive
divisive
Correct answer: multiplicative
subtractive

Q2.
40% of 440 is .

Correct Answer: 176

Q3.
1% of 780 is .

Correct Answer: 7.8

Q4.
Which of the following are correct strategies to find 75% of 200?

Correct answer: $$200\div10\times7 + 10$$
Correct answer: $$200 \div 4\times3$$
Correct answer: $$\frac{3}{4}\times200$$
Correct answer: $$\frac{1}{4}\times200 + 100$$
$$75\times200$$

Q5.
Match each percentage question to its answer.

Correct Answer:15% of 700,105

105

Correct Answer:25% of 600,150

150

Correct Answer:20% of 800,160

160

Correct Answer:90% of 140,126

126

Correct Answer:35% of 900,315

315

Correct Answer:1% of 6000,60

60

Q6.
Starting with the calculation with the largest answer, put these percentage calculations in descending order.

1 - 1% of 50 000
2 - 20% of 800
3 - 5% of 3000
4 - 50% of 280
5 - 100% of 90
6 - 35% of 40

Assessment exit quiz

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6 Questions

Q1.
__________ means two variables have a constant multiplicative relationship.

Equality
Equivalent
Positivity
Correct answer: Proportionality

Q2.
Match each representation of proportion to its advantages.

Correct Answer:Bar model,Good visual representation. Bars can be split in any way needed.

Good visual representation. Bars can be split in any way needed.

Correct Answer:Double number line,Good visual representation with scaled lines.

Good visual representation with scaled lines.

Correct Answer:Ratio table,Concise without visual representation and quick to construct.

Concise without visual representation and quick to construct.

Q3.
What percentage of 800 is represented by the calculation: 800 ÷ 2 − 8?

40%
Correct answer: 49%
50%
59%
90%

Q4.
What percentage of 650 is represented by the calculation: 650 − 6.5?

1%
9%
49%
89%
Correct answer: 99%

Q5.
Use the double number line to work out 45% of 700.

An image in a quiz
Correct Answer: 315

Q6.
Using the ratio table or another representation, work out 98% of 860.

An image in a quiz
Correct Answer: 842.8

Lesson appears in

UnitMaths / Understanding multiplicative relationships: percentages and proportionality

Maths

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