Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
You cannot draw your house at full size on a sheet of paper! To represent the real world on paper, we shrink every length in the same way: that is the idea of scale. A floor plan, a road map or a scale model all use this idea.
A scale is written like a fraction, for example 1/100. Read it like this: 1 cm on the plan represents 100 cm in real life, that is 1 m. On a 1/25000 map, each centimetre represents 25000 real centimetres, which is 250 m.
Behind the scale hides your old friend proportionality: every length on the plan is multiplied by the same number to get the real lengths. To go from the plan to reality, you multiply by the denominator of the scale. To go from reality to the plan, you divide.
Trap number one is units: the multiplication gives you a result in centimetres, often huge. Remember to convert it to metres or kilometres so it makes sense (100 cm = 1 m, 100000 cm = 1 km).
Architects, geographers, hikers: they all read scales every day. Your turn to master this round trip between paper and the real world!
On a plan at scale 1/100, a wall measures 5 cm. What is its real length in metres?
1 cm (plan) = 100 cm (réel)
I translate the scale: each centimetre on the plan represents 100 cm in real life.
5 × 100 = 500
I multiply the plan length by 100: the wall is 500 cm in real life.
500 cm = 5 m
I convert to metres so the result makes sense: 100 cm = 1 m.
Result: The wall is 5 m long in real life.
On a 1/25000 map, two villages are 4 cm apart. What is the real distance in kilometres?
4 × 25000 = 100000
I multiply by the denominator of the scale: the real distance is 100000 cm.
100000 cm = 1000 m
I convert to metres: I divide by 100.
1000 m = 1 km
Then to kilometres: 1000 m = 1 km. The villages are 1 km apart.
Result: The real distance is 1 km.