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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
New
Year 8

Securing understanding of percentages

I can manipulate percentages of an amount with a representation.

Download all resources
Share activities with pupils

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

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.

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.

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).

Video

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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

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?
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