PROPORTIONAL REASONING

Find the Real Distance

Jamuni has an interest in map reading and a curiosity to find distance between two places using different possible routes. She likes reading her world Atlas and uses the scale factor given in the map to calculate the exact distance between two places.

Task 1

Carefully look at the map-scale (scale given in the map). What do you see? Compare 1 unit of the map-scale with 1 unit of the ruler (scale) you have. Now fill the following table and put correct unit-name.

map

	Map scale	Real distance
1 unit	__________	__________

Write your observation. One unit of map scale represents how much real distance?

____________________________________________________________________________________________

Similarly, Two units of map scale will represent how much of a real distance?

_________________________________________________________________________________________

(Write in your notebook)

Task 2

The ratio between map-scale and real distance can be written as ___:___. This ratio is called the “scale factor” for a given map. It is a matter of convenience that we choose different scaling factors for showing or calculating distance between places. Now use the above scale factor to find distance between any two cities of your choice on the map. Think about different ways of doing this task. Fill in the following table :

Hint: Use a thread to measure the circuitous route and using a ruler and the given map-scale, find the actual distance between these two cities.

Map-scale	Length of the thread used	Real distance
1 cm = 12 km	_______________	_______________
1 cm = 12 km	_______________	_______________
1 cm = 12 km	_______________	_______________

(Write in your notebook)

Task 3

The other way in which a map-scale is shown on a map is by expressing a unit distance and a real distance, for example, 1 cm = 50 km which indicates that 1 cm in the map distance is equivalent to 50 km in actual distance.

Map scale	Distance of the map	Real distance
1 cm = 15 km	6 cm
1 cm = 12 km	10.5 cm
1 cm = 20 km	1/2 cm

What is the relationship between the distance on the map and the real distance?

(Write in your notebook)

note