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Year 8

Securing understanding of percentages

I can manipulate percentages of an amount with a representation.

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New

Year 8

Securing understanding of percentages

I can manipulate percentages of an amount with a representation.

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Share activities with pupils

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Lesson details

Key learning points

Percentages of amounts can be found by combining known percentages
Percentages of amounts can be represented and found using a bar model
Percentages of amounts can be represented and found using double number lines
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

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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

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

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?

49%

89%

Correct answer: 99%

Q5.

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

Correct Answer: 315

Q6.

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

Correct Answer: 842.8