## Bigger means faster

Teaching Guidance for 5-11 11-14

#### Units for speed

**Wrong Track: **60 km/h is faster than 40 mph 'cos it's bigger.

**Right Lines: ** A speed has two parts, a value and a unit. Speeds are much easier to compare if they have the same unit.

#### Converting units

**Thinking about the learning**

A car travelling at 60 must be going faster than a car travelling at 40.

This kind of statement is very common and reflects what we see around us. Speed limit signs are 30

or 50

with no attention paid to units.

Of course bigger numbers give a bigger

message. A younger child offered the choice between 100 pence or one pound might be seduced by the larger number of pence into thinking that it was somehow worth more. In this example, pence and pounds are examples of two different units of measurement. There is a conversion factor between them (100 p is £1).

And so it is with speed. However, in the 60 kilometre / hour and 40 mph example it is not altogether obvious which of the two speeds mentioned above is greater. In fact they are almost the same speed, quoted in different ways.

**Thinking about the teaching**

A car travelling at 60 kilometre / hour will be going faster than a car travelling at 40 kilometre / hour.

However, a car travelling at 60 kilometre / hour is not going faster than a car travelling at 40 mph. It is important that pupils realise from the outset the importance of specifying units, so that comparisons can be made. Numbers on their own are meaningless.

To illustrate this in another context, imagine that you were told that John is 1420, Max is 150 and Ian is 1.6 tall. Is John the tallest?

Including the units we see that if John is 1420 millimetre, Max is 150 centimetre and Ian is 1.6 metre tall, then Ian is the tallest. Mathematics often concentrates on numbers and relationships between numbers. Science rarely deals with pure numbers but with quantities. A quantity is a number multiplied by a unit. For example 56 is a number but 56 metre / second is a quantity. An education in science must make this distinction in a formal sense. This will not be the first time that pupils have met the challenge of different units. One approach is to ensure that most examples given to pupils are quoted in metres and seconds in the first instance. Hence try to avoid early questions which have objects moving at speeds such as 22 millimetre / second or 47 kilometre / hour. It is far better to use examples such as people walking at 3 metre / second or cars travelling at 12 metre / second or sound travelling at 330 metre / second.