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Year 11
Higher

Proportion modelled algebraically

I can identify and solve proportion questions involving algebra.

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New
New
Year 11
Higher

Proportion modelled algebraically

I can identify and solve proportion questions involving algebra.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The question does not always state the type of proportion.
  2. The context of the question can be used to determine the type of proportion.
  3. If more than one pair of values is given, this can determine the type of proportion.

Keywords

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

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

Common misconception

The constant of proportionality shows the gradient for inversely proportional graphs.

The constant of proportionality shows the gradient for directly proportional graphs only. The constant for a reciprocal graph in the form k/x^n, shows the distance of the reciprocal from the origin.

A Desmos based lesson is an excellent opportunity to allow pupils to investigate the impact of changing the value of k for: y = kx (direct proportion), y=kx^2 (direct proportion), y=k sqrt(x) (direct proprtion) and y=k/x^n (inverse proportion).
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.
Which of the following equations of a line show the direct proportion between $$x$$ and $$y$$?
$$y = 3x + 10$$
Correct answer: $$y = 3x$$
$$y = 5x - 2$$
Correct answer: $$y = 5x$$
Q2.
Which of the following equations of a curve show the direct proportion between $$x^2$$ and $$y$$?
Correct answer: $$y=4x^2$$
$$y=(x-3)(x-4)$$
$$y=x(x-10)$$
Correct answer: $$y=2x^2$$
Q3.
Which of the following show that $$x$$ is inversely proportional to $$y$$?
Correct answer: $$y=\frac{3}{x}$$
$$y=\frac{x}{3}$$
Correct answer: $$y=\frac{3}{5x}$$
$$y=\frac{5x}{3}$$
Q4.
Given that $$y$$ is directly proportional to $$𝑥$$ and $$𝑦=30$$ when $$x=5$$, write the equation connecting $$y$$ and $$x$$.
Correct Answer: y=6x, 6x=y, y = 6x
Q5.
Given that $$y$$ is directly proportional to $$𝑥^2$$ and $$𝑦=4375$$ when $$x=25$$, write the equation connecting $$y$$ and $$x^2$$.
$$y=875x$$
Correct answer: $$y=7x^2$$
$$y=175x$$
$$y=49x^2$$
Q6.
Given that $$y\propto \frac{1}{𝑥}$$ and $$𝑦=4$$ when $$x=50$$, write the equation connecting $$y$$ and $$x$$.
$$y=\frac{400}{𝑥}$$
$$y=\frac{x}{400}$$
Correct answer: $$y=\frac{200}{x}$$
$$y=\frac{x}{200}$$

Exit quiz

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6 Questions

Q1.
Which of the following show an inversely proportional relationship between $$y$$ and $$x^n$$?
Correct answer: $$y=\frac{4}{x^2}$$
Correct answer: $$y=\frac{3}{4x}$$
$$y=\frac{3x}{4}$$
$$y=\frac{x^2}{4}$$
Q2.
Which of these graphs show direct proportion between $$y$$ and $$x^n$$?
An image in a quiz
Correct answer: C, D, E
A, B, C, D, E
A, C, D, E, F
All
None
Q3.
Match the graph with the equation.
An image in a quiz
Correct Answer:$$y=\frac{k}{x^2}$$,A

A

Correct Answer:$$y=\frac{k}{x}$$,B

B

Correct Answer:$$y=kx$$,C

C

Correct Answer:$$y=k\sqrt{x}$$,D

D

Correct Answer:$$y=kx^2$$,E

E

Correct Answer:$$y=kx+c$$,F

F

Q4.
Two variables are inversely proportional if there is a constant relationship between one variable and the reciprocal of the other.
Correct Answer: multiplicative
Q5.
Match the value of $$k$$ with the relevant graph for $$y=\frac{k}{x}$$
An image in a quiz
Correct Answer:$$k=20$$,A

A

Correct Answer:$$k=2$$,C

C

Correct Answer:$$k=10$$,B

B

Q6.
Match the value of $$k$$ with the relevant graph for $$y=\frac{k}{x^2}$$
An image in a quiz
Correct Answer:$$k=20$$,A

A

Correct Answer:$$k=2$$,C

C

Correct Answer:$$k=10$$,B

B