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A lot of the time, it's not really the best idea to have things full size.

A map would be useless if it was full size, and a toy car doesn't really want to be the same size as a normal car, does it?

When we have an issue like this in maths, we use a scale diagram or a scale model.

What Is a Scale Diagram / Model?

A scale diagram is just a diagram where everything has been reduced by the same factor

It could be half the size, a tenth of the size, or anything else, but every element must be reduced by exactly the same factor.

How Are Scales Written?

Scales are written as ratios, such as 1: 100 or 1:50,000.

What Does a Scale Mean?

Scales are read from left to right.

For example, the scale 1:100 would mean that every 1 unit of length on the scale is the same as 100 units in real life.

So an element that was 2 cm long on a scale diagram, would be 200 cm long in real life.

Let's look at this concept in action with some examples now.

e.g. A model car is 1.5 cm tall. If the scale used to create it is 1:100, how tall would the car be in real life?

All we need to do here is multiply by the scale factor:

1.5 × 100 = 150 cm

So the car would be 150 cm or 1.5 m tall in real life.

e.g. A model is made of a 2 m tall man. If the model is 4 cm tall, what scale has been used?

The first thing we should notice here is that the units used are different, so we need to make them the same before we start:

There are 100 cm in 1 m, so 2 m = 200 cm.

Now, we need to write these numbers as a ratio (remember that the model comes first):

4:200

Our final step is to simplify this ratio:

4:200 ÷ 4

1:50

In this activity, we will apply scale factors to find the real life scale values of specific scaled elements or calculate the scale which has been used to create a scale diagram or model.

10 questions