How_To_Be_Good_At_Math

NUMBERS • SCALING 73

Scale on maps

Scaling is useful for drawing maps. We couldn’t use a life-size map – it would

be too big to carry around! We write a map scale as a ratio, which tells us how

many units of distance in real life are equal to one unit on the map.

Scale factors

A scale factor is the

number we multiply or

divide by when we

scale up or down.

1 cm : 1 km

On this map, 1 cm represents 1 km in real

life. We can see the whole island, but not in

much detail.

If we scaled the triangle back to its original

size, we would say is was scaled by

a negative factor of −2.

LENGTH 30 cm

SCALE 1 : 40

1 cm : 100 m

This time, 1 cm on the map stands for 100 m.

We can see lots of detail, but only on a very

small part of the island.

If we scale something by a factor of 2, we make

it two times larger. So, this triangle with sides of

2.8 cm becomes a triangle with sides of 5.6 cm.

How tall is a T. rex?

This scale model of a T. rex has a scale factor

of 40. If the model’s height is 14 cm and its

length is 30 cm, can you work out the height

and length of the real dinosaur?

TRY IT OUT

Answers on page 319

HEIGHT 14

cm

This part of the

island is shown

in the map to

the right

All three sides

have doubled

SCALE FACTOR: 2 in length

SCALE FACTOR: −2

2.8 cm

2.8 cm

2.8 cm

5.6 cm

5.6 cm

5.6 cm

0 1 km 2 km 3 km

SCALE

0 100 m 200 m 300 m

SCALE

The scale bar

tells us that

1 cm on the

map stands

for 100 m

in real life

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