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.