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Lesson 12 of 16
Multiplicative relationships and direct proportion
I can appreciate the connection between multiplicative relationships and direct proportion.
Lesson 12 of 16
New
New
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
- Direct proportion can be represented on a graph.
- Direct proportion can be represented on a double number line.
- Direct proportion can be represented with a ratio table.
- 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
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.
Teacher tip
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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Prior knowledge starter quiz
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6 Questions
Q1.When you use a ratio table, you are using __________ relationship.
When you use a ratio table, you are using __________ relationship.
an additive
a difference
Q2.100% = 40 and 70% = 28. The percentage change is %.
100% = 40 and 70% = 28. The percentage change is %.
Q3.The cost of a laptop increases from £540 to £702. What is the percentage change?
The cost of a laptop increases from £540 to £702. What is the percentage change?
130%
77%
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 %.
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 %.
Q5.Jacob’s score on a game increases from 2450 to 2744. The percentage that Jacob's original score has changed by is %.
Jacob’s score on a game increases from 2450 to 2744. The percentage that Jacob's original score has changed by is %.
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 %.
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 %.
Assessment exit quiz
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6 Questions
Q1.Two variables are in direct proportion if they have a multiplicative relationship.
Two variables are in direct proportion if they have a multiplicative relationship.
Q2.Which of the following show a directly proportional relationship between A and B?
Which of the following show a directly proportional relationship between A and B?
Q3.A and B are directly proportional. The missing value of B is .
A and B are directly proportional. The missing value of B is .
Q4.A and B are directly proportional. The missing value of B is .
A and B are directly proportional. The missing value of B is .
Q5.The graph shows the relationship between cost and number of boxes bought. Can you spend exactly £5 on boxes?
The graph shows the relationship between cost and number of boxes bought. Can you spend exactly £5 on boxes?
No, reading off the graph at £5 shows you can buy between 2 and 3 boxes.
Q6.This graph shows that A and B are in direct proportion. The proportional relationship between A and B is B = A × .
This graph shows that A and B are in direct proportion. The proportional relationship between A and B is B = A × .
