One centimetre is one kilometre
Tonight's idea
A map is a picture of the ground from above, made much smaller. Everything on it is shrunk by the same amount. So shapes stay true. If one place is twice as far away as another in real life, it is twice as far on the map.
The scale says how much the world was shrunk. This map has the scale 1 cm : 1 km. Read the two dots as "stands for". One centimetre on the paper stands for one kilometre on the ground.
Real distance = centimetres on the map × what one centimetre stands for.
How big is that shrink? 1 km is 1000 m, and 1 m is 100 cm. So 1 km is 100 000 cm. This map makes the world 100 000 times smaller.
Watch one: Home to the Lake
Walk from Home to School, then on to the Lake. On the map that is \(3 + 4 = 7\) cm. Each centimetre stands for 1 km, so the walk is 7 km.
The straight path from Home to the Lake is 5 cm, so 5 km. It saves 2 km.
Lake to Hill is 2.5 cm. That is 2.5 km, which is 2 km and 500 m. Parts of a centimetre count too.
Your turn
- Use the map above. (a) How far is it from School to the Lake? (b) How far is Home to the Lake to the Hill, by the straight paths? (c) You walk Home to School to Lake and straight back Home. How far is that? You walk 4 km each hour. How long does it take?
- A different map has the scale 1 cm : 2 km. (a) Two towns are 6 cm apart on this map. How far apart are they really? (b) A river is 9 km long. How long is it on the map? Draw a straight line that long with a ruler.
- A plan of a town has the scale 1 cm : 100 m. (a) The park is 3.5 cm from the station. How far is that really? (b) The main street is 1 km long. How long is it on the plan? (c) Which shows more detail, this plan or the map above? Why?
- An old map has lost its scale. You know the bridge and the church are really 10 km apart. On the map they are 4 cm apart. (a) What does 1 cm stand for? (b) The farm is 6 cm from the church on the map. How far is it really?
Stretch: a square on the map
On a map with scale 1 cm : 2 km, a forest covers a square 1 cm by 1 cm. How many square kilometres is the real forest? Explain why the answer is not 2.
Answers
- (a) 4 cm, so 4 km. (b) \(5 + 2.5 = 7.5\) cm, so 7.5 km. (c) \(3 + 4 + 5 = 12\) cm, so 12 km. At 4 km each hour that takes \(12 \div 4 = 3\) hours.
- (a) \(6 \times 2 = 12\) km. (b) Each centimetre uses up 2 km, so \(9 \div 2 = 4.5\) cm. Your line should be 4 and a half centimetres long.
- (a) \(3.5 \times 100 = 350\) m. (b) 1 km is 1000 m, and \(1000 \div 100 = 10\) cm. (c) The plan. On the map 1 cm stands for 1000 m. On the plan it stands for only 100 m, so everything is drawn 10 times longer and there is room for small things.
- (a) 4 cm stands for 10 km, so 1 cm stands for \(10 \div 4 = 2.5\) km. (b) \(6 \times 2.5 = 15\) km.
Stretch. Each side of the square is 1 cm, which stands for 2 km. So the real forest is 2 km by 2 km. Its area is \(2 \times 2 = 4\) square kilometres. The scale stretches the length and the width, so the area grows twice over.