Functional Skills: Maps and Scale Drawings

Skill 1: Understanding Scale Keys and Scale Factors

Scale factors are used to accurately scale up or down an image. Scale drawings will come with a key, or a scale factor, that tells you what a dimension in the drawing is equal to in real life.

They are usually represented as ratios, with an $=$ sign or as a line drawing, as seen on the $1$ cm grid below.

Note: These all mean the same thing!

Skill 2: Calculating Distances by Measuring

Example: The scale drawing below shows a section of coastline. Calculate the distance between point A and point B.

We first need to measure the length of the scale, using a ruler. It is $1$ cm long. Therefore $1$ cm on the drawing represents $5$ km in real life.

Then, measure the distance between A and B on the drawing, using a centimetre ruler:

Since $1$ cm on the drawing represents $5$ km in real life, the distance between A and B in real life is:

$8.5 times 5 = 42.5$ km

Skill 3: Calculating Distances on a Grid

Example: Below is a map of Africa. Calculate the real-life distance between Dakar and Khartoum, marked on the map.

We are given the scale as a line drawing on a grid, so we do not need to use a ruler.

$1$ square on the grid is equal to $500$ miles in real life

Count the number of squares between the two cities on the map:

There are $5.5$ squares between Dakar and Khartoum on the map.

To find the real-life distance between Dakar and Khartoum, multiply the distance represented by $1$ square by the number of squares between the two cities:

$5.5 times 500 = 2750$ miles

Skill 4: Working out the Scale

You may be asked to find the scale on a map or drawing, given a distance.

Example: The diagram below is a scale drawing of a classic car. The length of the car in real life is $textcolor{limegreen}{3.2}$ m.

Calculate the scale used in the drawing. Give your answer as a ratio.

We need to measure the length of the drawing, using a centimetre ruler:

The length of the car is $textcolor{red}{8}$ cm on the drawing.

Both measurements need to be in the same units, so convert the length of the car in real life to cm:

Real-life length $= textcolor{limegreen}{3.2}$ m $= textcolor{limegreen}{320}$ cm

So, we can write this as a ratio:

Drawing length : Real-life length $= textcolor{red}{8} : textcolor{limegreen}{320}$

and then simplify the ratio by dividing both sides by $8$:

$textcolor{red}{1} : textcolor{limegreen}{40}$

This means that $1$ cm on the drawing represents $40$ cm in real life.

Skill 5: Making Scale Drawings

To make a scale drawing, you will need to work out the dimensions first.

Example: Draw a rectangle, on the grid below, of height $2.5$ m and width $3$ m.

Use the scale $1:50$. Each square is $1$ cm by $1$ cm.

The grid is in cm, so convert the dimensions of the rectangle in to cm:

$textcolor{red}{text{real height} = 2.5 times 100 = 250 text{ cm}}$

$textcolor{blue}{text{real width} = 3 times 100 = 300 text{ cm}}$

$1:50$ means that $1$ cm on the grid represents $50$ cm in real life.

Divide the real dimensions by $50$ to find the dimensions of the scale drawing:

$textcolor{red}{text{drawing height} = 250 div 50 = 5 text{ cm}}$

$textcolor{blue}{text{drawing width} = 300 div 50 = 6 text{ cm}}$

Finally, we can draw the rectangle on the grid, of height $textcolor{red}{5 text{ cm}}$ and width $textcolor{blue}{6 text{ cm}}$

Skill 6: Using Bearings and Maps Together

Sometimes you will need to use a map to describe the distance between two places and what direction one is in respect to the other.

To do this you will need to use a map scale and then measure the distance and bearing. Make sure you revise the Angles and Bearings page first.