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Learning Intention:
Understand how to use scale to measure distances accurately on a topographic map.
Success Criteria:
Explain what map scale is and why it is important.
Use the scale on a topographic map to measure distances between two points accurately.
Convert map distances to real-world distances using the given scale.
Demonstrate the ability to use a ruler or string to measure distances on a map and calculate the actual distance.
A scale is a statement of the relationship between distances on a map and distances in real life. A drawing that is made according to scale will be an exact copy of the real object but will be smaller or larger than the real object. Scale drawings are often used in real life because they are very accurate, including maps, blueprints, and architectural models.
There are three different ways to write a scale:
as a statement (in words)
as a ratio or representative fraction
as a linear scale
Smallest vs Largest Scale
Copy down the following tips:
1:5,000 is large scale. 1:50,000,000 is small scale. The larger the denominator, the smaller the scale.
Small-scale maps cover a large area with little detail
Zoomed out is smallest
Large-scale maps cover smaller areas with great detail.
Zoomed in is largest
Small Scale Map
Large Scale Map
Distance
The distance between two points on a map can be found by measuring the distance on the map and then converting it from centimetres to kilometres and/or metres. You can do this by using the map’s linear scale, which works for both printed and digital documents.
There are several ways to measure the distance between two points on a map:
Using a straight line: Place the edge of a paper between two points or use a ruler. Mark the points on the paper, then align it with the map’s scale to find the distance.
Using a curved line: Place a paper or string at the starting point and trace the curve, marking each section. When you reach the end point, measure the length using the map's scale.
Converting units of measurement according to the scale
Copy down the following formular
Example Question:
On a map, the distance between City A and City B is 5 cm. If the map scale is 1:100,000, what is the actual distance between these two cities in kilometres?
Understand the Scale:
The map scale of 1:100,000 means that 1 cm on the map represents 100,000 cm in real life.
Set Up the Calculation:
Since the distance on the map is 5 cm, we need to multiply this by the scale to find the real distance:
5 cm × 100,000 = 500,000 cm
Convert to Meters:
Now, convert the result from centimetres to meters. We know that there are 100 cm in a meter, so we divide by 100:
500,000 cm ÷ 100 = 5,000 m
Convert to Kilometres:
To express the distance in kilometres, we need to convert from meters to kilometres. Since 1 km = 1,000 m, we divide by 1,000:
5,000 m ÷ 1,000 = 5 km
State the Answer:
The actual distance between City A and City B is 5 kilometres.
Practice converting scale
If the distance between point A and point B is 8 cm on a map, and the map scale is 1:50,000, what is the real distance between the two points in kilometres?
The distance from town X to town Y is 12 cm on the map. If the map scale is 1:100,000, what is the actual distance between these two towns in kilometres?
A river runs 15 cm on a map between two points. If the map scale is 1:25,000, what is the real distance of the river in kilometres?
The distance from city C to city D is shown as 5 cm on the map. With a map scale of 1:200,000, calculate the actual distance between the two cities in kilometres.
On a map, the distance between a mountain and a lake is 10 cm. If the map scale is 1:75,000, what is the true distance between them in kilometres?
The distance between point A and point B on a map is 7 cm, with a map scale of 1:10,000. What is the actual distance in meters?
On a map, the distance from city X to city Y is 3 cm. If the scale is 1:250,000, what is the actual distance in kilometres?
The distance between a park and a school is 20 cm on a map. If the map scale is 1:5,000, what is the real distance between them in meters?
A road is shown as 6 cm long on a map with a scale of 1:50,000. What is the actual distance of the road in kilometres?
The map distance between a river and a mountain is 2 cm. If the scale of the map is 1:2,000, what is the real distance between the river and mountain in meters?
Answers
Answer: 4 km
Answer: 12 km
Answer: 3.75 km
Answer: 10 km
Answer: 7.5 km
Answer: 700 m
Answer: 7.5 km
Answer: 1,000 m (or 1 km)
Answer: 3 km
Answer: 40 m
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