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Year 8

Problem solving with percentages and proportionality

I can use my knowledge of percentages and proportionality to solve problems.

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New
New
Year 8

Problem solving with percentages and proportionality

I can use my knowledge of percentages and proportionality to solve problems.

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Lesson details

Key learning points

  1. Representations can support problem solving.
  2. Direct proportion can be used to solve real life problems.
  3. Inverse proportion can be used to solve real life problems.

Keywords

  • Proportion - If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.

Common misconception

Forgetting to find the percentage change.

Emphasise the word change. Encourage pupils to write down the 2 percentages with their relevant values. Go back to the question and calculate the actual change they should notice that this is neither of the 2 values but the difference between them.


To help you plan your year 8 maths lesson on: Problem solving with percentages and proportionality, download all teaching resources for free and adapt to suit your pupils' needs...

When completing task A in the first learning cycle the shapes could be printed out and pupils could make various correct original shapes.
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Licence

This content is © Oak National Academy Limited (2025), 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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6 Questions

Q1.
Two variables are inversely proportional if there is a multiplicative relationship between one variable and the reciprocal of the other.
Correct Answer: constant, same
Q2.
Which of the following is a graph representing inverse proportion?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q3.
Which of the following situations illustrate an inversely proportional relationship?
The number of coaches needed for a school trip and the number of people.
Correct answer: The time taken to to paint a wall and the number of people painting.
The number of pounds and the number of dollars exchanged.
Correct answer: The time taken to drive to Liverpool and speed of the car.
Correct answer: Number of buckets needed to fill a paddling pool and the size of the buckets.
Q4.
A and B are inversely proportional. The missing value is .
An image in a quiz
Correct Answer: 21
Q5.
A and B are inversely proportional. The missing value is .
An image in a quiz
Correct Answer: 10
Q6.
It takes 3 people 4 days to build a wall. It should take 2 people days to build the same wall.
Correct Answer: 6, 6 days

6 Questions

Q1.
Variables which are in proportion share a __________ relationship.
additive
different
Correct answer: multiplicative
Q2.
Here is part of a larger shape. Which of the following could be the whole shape?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
If 100% = 45, 130% = 58.5 then the percentage change is %.
Correct Answer: 30, 30 %, 30%
Q4.
Calculate the percentage profit on a watch bought for £40 and sold for £50.
125%
80%
Correct answer: 25%
20%
Q5.
Calculate the percentage loss on a mobile phone bought for £300 and sold for £240.
Correct answer: 20%
25%
80%
120%
125%
Q6.
A, B and C are 3 different numbers. C is two-fifths of B. C is 3 times A. The total of A & C is 32. The value of B is .
Correct Answer: 60, sixty