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Year 10
Foundation

Graphs showing inverse proportion

I can recognise inverse proportion graphically and can interpret graphs that illustrate inverse proportion.

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New
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Year 10
Foundation

Graphs showing inverse proportion

I can recognise inverse proportion graphically and can interpret graphs that illustrate inverse proportion.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Inverse proportion can be recognised graphically.
  2. The equation of an inverse proportion graph is of the form y = k/x
  3. An alternative way of writing the equation is y α 1/x

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

Solutions for context-based problem can be listed as coordinate pairs with units e.g. 6 workers, 60 hours.

Solutions should always be fully interpreted in relation to the context e.g. It would take 6 workers 60 hours to paint the building.

k is used in the notation to prepare pupils for the Year 11 unit where k is formally referred to as the constant of proportionality.
Teacher tip

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).

Lesson video

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Starter quiz

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6 Questions

Q1.
If it takes 2 hours to walk 6 miles, 3 hours to walk 9 miles, and 4 hours to walk 12 miles then the variables time and distance are said to ...
Correct answer: be in direct proportion to each other.
be unrelated.
have a changing rate of change.
Q2.
Which of these graphs shows a directly proportional relationship?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
This time distance graph shows the relationship between the hours walked and the distance travelled in miles. What do the coordinates (5, 20) show?
An image in a quiz
It takes 5 hours to walk 20 km.
It takes 20 hours to walk 5 km.
Correct answer: It takes 5 hours to walk 20 miles.
It takes 20 hours to walk 5 miles.
Q4.
What is the equation of the line in this distance-time graph? Use $$d$$ for distance travelled and $$t$$ for time taken.
An image in a quiz
$$d=5t$$
$$t=5d$$
Correct answer: $$d=4t$$
$$4d=t$$
$$d=t+4$$
Q5.
For the equation $$s={30\over{t}}$$, when $$t=7.5$$, $$s=$$ .
Correct Answer: 4, s=4
Q6.
For the equation $$s={30\over{t}}$$, when $$s=7.5$$, $$t=$$
Correct Answer: 4, t=4

Exit quiz

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6 Questions

Q1.
When two variables are indirectly proportional, as one variable increases the other ...
increases.
Correct answer: decreases.
remains constant.
Q2.
Inversely proportional relationships are modelled by the relationship ...
$$ky=x$$
$$y=kx$$
$$y={x\over{k}}$$
Correct answer: $$y={k\over{x}}$$
Q3.
Which of these graphs shows a relationship of indirect 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
Q4.
Why can this not be a graph of indirect proportion?
An image in a quiz
Correct answer: Indirect proportion graphs do not intersect either axis.
It is not a straight line.
It is decreasing as the horizontal variable decreases.
Correct answer: Indirect graphs have the form $$y={k\over{x}}$$ , dividing by zero is undefined.
Q5.
This graph plots the time taken ($$t$$) in days for a varying number of people ($$p$$) to dig a hole. How long would it take 3 people?
An image in a quiz
3
5
5 people
Correct answer: It would take 3 people 5 days to dig the hole.
It would take 5 people 3 days to dig the hole.
Q6.
This graph shows the relationship between people and time required to build a wall. The point marked shows that 10 people would take 3 days. It would take 3 people days to build the wall.
An image in a quiz
Correct Answer: 10, Ten