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

Abstract inverse proportion

Maths

Checking and securing understanding of direct proportion graphs

Checking and securing understanding of inverse proportion graphs

Abstract direct proportion

Finding the constant of proportionality for direct proportion

Finding the constant of proportionality for directly proportional relationships

Finding the constant of proportionality for inverse proportion

Proportion modelled algebraically

Problem solving with direct and inverse proportion

In the linear graphs unit, pupils learnt to recognise and interpret graphs that illustrate direct and inverse proportion. In this unit, pupils learn how to represent these relationships algebraically.

In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.

Direct and inverse proportion

Match the equations with the correct proportions.

Converting euros to dollars or vice versa

The hours you work and the salary received

The taps to fill a water bucket and the time it takes to fill the bucket

The number of robots to complete a job and the time to complete the job

Which of the following are examples of inverse proportion?

$$p\propto \frac{1}{q}$$, match the correct values for A, B and C.

It takes 10 workers 6 hours to build a wall. They all work at the same rate. Firstly, all workers build for 2 hours, then 6 workers leave. How many hours will it take the 4 workers to finish the wall?

$$y\propto \frac{1}{\sqrt{x}}$$, when $$x=25, y=16$$. Work out the value of $$y$$ when $$x=400$$.

$$y\propto \frac{1}{\sqrt[3]{x}}$$, when $$x=125, y=0.15$$. Work out the value of $$y$$ when $$x=0.008$$.

Two variables are {{}} proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other. 

Pair up the reciprocals with the following numbers. 

What is the single multiplier that connects 9 to 54?

What is the single multiplier that connects 15 to 10?

What is the single multiplier that connects 24 to 9.6?

$$y\propto \sqrt{x}$$, when $$x=64, y=6$$. Work out the value of $$y$$ when $$x=400$$.

Abstract inverse proportion

Lesson outcome