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 this issue like this in maths, we use a **scale diagram** or a** scale model**.

**What Is a Scale D****iagram / 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** 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 real car is 300 cm tall. A model of the car is created using a scale of 1:100. How tall would the model car be?**

The scale tells us that every **1 cm** on the model car will represent **100 cm** in real life.

So all we need to do is to **divide** the real height by the scale factor, to find the height of the model:

300 ÷ 100 = 3 cm

So the height of the model car is 3 cm.

**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 scale values of specific, real life elements or calculate the scale which has been used to create a scale diagram or model.