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Year 8

Multiplicative relationships and direct proportion

I can appreciate the connection between multiplicative relationships and direct proportion.

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New
New
Year 8

Multiplicative relationships and direct proportion

I can appreciate the connection between multiplicative relationships and direct proportion.

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Lesson details

Key learning points

  1. Direct proportion can be represented on a graph.
  2. Direct proportion can be represented on a double number line.
  3. Direct proportion can be represented with a ratio table.
  4. Direct proportion is a multiplicative relationship.

Keywords

  • Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.

Common misconception

Incorrectly drawing or interpreting the scales on axes.

Use the approach where pupils count the number of intervals of the scale and divide the difference between the intervals. For example, if there are 5 intervals and the difference is between 20 and 30, they divide 10 by 2, so each interval is 2


To help you plan your year 8 maths lesson on: Multiplicative relationships and direct proportion, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils can come up with their own examples of variables that are directly proportional. They can they create their own double number lines, ratio tables and graphs based on their situations.
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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.
When you use a ratio table, you are using __________ relationship.
an additive
a difference
Correct answer: a multiplicative
Q2.
100% = 40 and 70% = 28. The percentage change is %.
Correct Answer: 30, 30 %, 30%
Q3.
The cost of a laptop increases from £540 to £702. What is the percentage change?
130%
77%
Correct answer: 30%
23%
Q4.
Jun thinks of a number and increases it by a percentage. The number Jun thought of was 80 and his new number is 100. Jun has increased his original number by %.
Correct Answer: 25, 25 %, 25%
Q5.
Jacob’s score on a game increases from 2450 to 2744. The percentage that Jacob's original score has changed by is %.
Correct Answer: 12, 12 %, 12%
Q6.
A reduced fat bag of crisps contains 3 g of fat. The normal bag of crisps contains 2 g more of fat. The percentage that the fat has been reduced by is %.
Correct Answer: 40%, 40 %, 40

6 Questions

Q1.
Two variables are in direct proportion if they have a multiplicative relationship.
Correct Answer: constant, same
Q2.
Which of the following show a directly proportional relationship between A and B?
Correct Answer: An image in a quiz
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
Q3.
A and B are directly proportional. The missing value of B is .
An image in a quiz
Correct Answer: 11
Q4.
A and B are directly proportional. The missing value of B is .
An image in a quiz
Correct Answer: 7.5
Q5.
The graph shows the relationship between cost and number of boxes bought. Can you spend exactly £5 on boxes?
An image in a quiz
No, reading off the graph at £5 shows you can buy between 2 and 3 boxes.
Correct answer: Yes, reading off the graph at £5 shows you can buy exactly 2 boxes.
Q6.
This graph shows that A and B are in direct proportion. The proportional relationship between A and B is B = A × .
An image in a quiz
Correct Answer: 0.5