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Lesson 15 of 16
  • Year 8

Inverse proportion in context

I can recognise inverse proportion graphically and use inverse proportionality in a range of contexts.

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Lesson 15 of 16
New
New
  • Year 8

Inverse proportion in context

I can recognise inverse proportion graphically and use inverse proportionality in a range of contexts.

Lesson details

Key learning points

  1. Inverse proportion can be represented on a graph.
  2. Key features can be used to recognise inverse proportion on a graph.
  3. Inverse proportion can be used in a number of contexts.

Keywords

  • Inverse proportion - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Common misconception

The graph representing a inversely proportional relationship is of the form x + y = a and will eventually meet the axes.

The dimensions of the rectangle are ideal for highlighting this, particularly the latter part as a you cannot have a rectangle with a length of 0 cm.


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

Use a dynamic graphing package to show the area of the rectangle problem. Question: 'Can I have a rectangle with a width 0f 0.005cm?' you can use the graph to show that you can.
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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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Prior knowledge starter quiz

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6 Questions

Q1.
Two variables are in proportion if they have a __________.

constant additive relationship
changing multiplicative relationship
different relationship
changing additive relationship
Correct answer: constant multiplicative relationship

Q2.
5 miles = 8 kilometres. So 12 miles is kilometres.

Correct Answer: 19.2, 19.2km, 19.2 km, 19.2 kilometres

Q3.
Convert 1 m³ into cm³.

1000 cm³
10 000 cm³
100 000 cm³
1 000 000 cm³
Correct answer: 1 000 000 cm³

Q4.
The cost of a box of pens is £4.80. Five boxes of pens cost £ .

Correct Answer: 24, £24.00, £24, 24.00, £ 24

Q5.
If $20 = £15.20, which of the following are true?

$100 = £95.20
$10 = £5.20
Correct answer: $50 = £38
Correct answer: $5 = £3.80
Correct answer: $6 = $4.56

Q6.
A recipe needs 180 ml of milk to make 15 scones. You can make scones using 15 litres of milk.

Correct Answer: 1250, 1,250, 1 250

Assessment exit quiz

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6 Questions

Q1.
Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the __________ of the other variable.

different
division
opposite
Correct answer: reciprocal

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 scones made and the amount of milk needed.
The time taken to read a book and the number of pages.
Correct answer: The time taken to complete a lap of a track and the speed.
Correct answer: The number of pieces a plank of wood is cut into and the length of the pieces.
The height of a wall and the number of bricks used.

Q4.
A and B are inversely proportional. The missing value is .

An image in a quiz
Correct Answer: 15, fifteen

Q5.
A and B are inversely proportional. The missing value is .

An image in a quiz
Correct Answer: 4, four

Q6.
It takes 3 people 4 days to build a wall. It should take 5 people days to build the same wall.

Correct Answer: 2.4, 2.4 days