A rate is a relationship between two units. For example miles per hour (mph) is a rate called speed which relates distance and time.

An exchange rate is the rate at which one currency is exchanged for another. The two currencies are in proportion because they have a constant multiplicative relationship.

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

Checking and further securing understanding of direct proportion in context

Maths

Compound measures for speed

Compound measures for density

Compound measures for pressure

Converting between metric speed measures

Converting between metric and imperial speed measures

Converting between other compound measures

Combining speeds

Combining densities

Advanced problem solving with compound measures

In this unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from the prior unit will aid understanding. There are also links to the volume units as volume is required for the density formula.

In this unit, pupils explore the multiplicative relationship between different compound meaures and units such as speed, rates of pay, density and pressure.

Compound measures

Which of these ratios represents this sentence?  For every 1 dollar you get 56 pence

Izzy says, "I changed £200 and got $254".  What is this as a unit ratio in pounds?

Andeep says, "I changed £300 and got €400".  What is this as a unit ratio in euros?

A tap fills at a rate of 16 litres per minute.  How long will it take to fill a paddling pool with a capacity of 400 litres?

Calculate the cost of electricity.  Give your answer to the nearest penny.

An {{ }} rate is the rate at which one currency is exchanged for another. The two currencies are in proportion because they have a constant multiplicative relationship.

For every 1 nugget you get 3 chips.  Use this statement to decide which of the following are true?

The ratio of A : B is 1 : 6.  What is the multiplicative relationship between A and B?

The ratio of A : B is 2 : 3.  What is the multiplicative relationship between A and B?

What is the missing value in this ratio table?

Checking and further securing understanding of direct proportion in context

Lesson outcome