Lesson Notes By Weeks and Term v5 - Grade 11
Measurement: scale, maps and plans – Week 6 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Measurement: scale, maps and plans – Week 6 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 11
Term: 3rd Term
Week: 6
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This week, we delve into the crucial topic of scale, maps, and plans. Understanding scale is fundamental to interpreting maps, building plans, and other scaled representations of real-world objects and spaces. In a country like South Africa, where access to resources and infrastructure planning is vital, being able to accurately interpret and use maps and plans is a valuable life skill. From navigating your neighbourhood using a street map to understanding architectural plans for a new school building, this topic equips you with the tools to engage with the world around you more effectively.
2.1 Understanding Scale Definition: Scale is the ratio between the distance on a map or plan and the corresponding distance on the ground. It represents how much the real world has been reduced (or sometimes enlarged) to fit on the map or plan.
Types of Scale: Ratio Scale (Representative Fraction): Expressed as a ratio, e.g., 1:
5
0
0. This means that 1 unit on the map represents 500 units on the ground. The units must be the same on both sides of the ratio.
Verbal Scale: A statement that describes the relationship between map distance and ground distance, e.g., "1 cm represents 1 km." Bar Scale (Graphical Scale): A visual representation of the scale, usually a line divided into segments that represent specific distances on the ground. This is especially useful as it remains accurate even if the map is photocopied or resized.
Converting Between Scale Types: It's essential to be able to convert between these different representations. For example, converting a verbal scale to a ratio scale: If the verbal scale is "1 cm represents 2 km", we need to convert 2 km to cm: 2 km = 2 1000 m = 2000 m = 2000 * 100 cm = 200,000 cm.
Therefore, the ratio scale is 1:200,000. 2.2 Calculating Actual Distances Using Ratio Scale: If the scale is 1:10,000 and the distance on the map is 5 cm, then the actual distance is 5 cm 10,000 = 50,000 cm. Convert this to a more appropriate unit like meters: 50,000 cm = 500 m, or kilometers: 500 m = 0.5 km.
Using Verbal Scale: If the verbal scale is "1 cm represents 5 km" and the distance on the map is 3.5 cm, then the actual distance is 3.5 cm 5 km/cm = 17.5 km.
Using Bar Scale: Measure the distance on the map using a ruler and then compare it to the bar scale to determine the corresponding distance on the ground. 2.3 Calculating Actual Areas Understanding Area Scale: When dealing with areas, the scale factor needs to be squared.
If the linear scale is 1:100, then the area scale is 1 2 :100 2 or 1:10,
0
0
0. This means that 1 square cm on the map represents 10,000 square cm on the ground.
Calculation: If a rectangular park measures 4 cm x 2 cm on a map with a scale of 1:5,000, the area on the map is 4 cm 2 cm = 8 cm 2 .
The area scale is 1: (5,000) 2 = 1:25,000,
0
0
0. Therefore, the actual area is 8 cm 2 * 25,000,000 = 200,000,000 cm 2 .
Convert this to square meters: 200,000,000 cm 2 = 20,000 m 2 .
Convert this to hectares: 20,000 m 2 = 2 hectares (since 1 hectare = 10,000 m 2 ). 2.4 Practical Considerations: Map Projections: Different map projections distort the Earth's surface in different ways. This can affect the accuracy of distances and areas, especially over large areas. Be aware of the map projection used and its limitations.
Terrain: Maps represent a two-dimensional view of a three-dimensional surface. Slopes and elevation changes are not directly represented in horizontal distances on a map.
Therefore, distances may appear shorter on a map than they are in reality, especially in mountainous areas.
Example 1: A map of Kruger National Park has a scale of 1:250,
0
0
0. The distance between Skukuza Rest Camp and Satara Rest Camp measures 15 cm on the map. What is the actual distance between the two camps?
Solution:
Scale: 1:250,000
Map Distance: 15 cm
Actual Distance: 15 cm 250,000 = 3,750,000 cm
Convert to km: 3,750,000 cm = 37,500 m = 37.5 km
Answer: The actual distance between Skukuza and Satara is 37.5 km.
Example 2: A building plan uses a scale of 1:
5
0. A room measures 8 cm by 6 cm on the plan. What are the actual dimensions and area of the room?
Solution:
Scale: 1:50
Plan Dimensions: 8 cm x 6 cm
Actual Length: 8 cm 50 = 400 cm = 4 m
Actual Width: 6 cm 50 = 300 cm = 3 m
Actual Area: 4 m 3 m = 12 m 2
Answer: The room is 4 m long, 3 m wide, and has an area of 12 m 2 .
Example 3: On a street map with a bar scale where 1 cm on the map represents 500 meters, two landmarks are 6.8 cm apart. Calculate the real-world distance between the landmarks in kilometers.
Solution:
Map distance: 6.8 cm
Scale: 1 cm represents 500 meters
Real-world distance in meters: 6.8 cm 500 meters/cm = 3400 meters
Convert meters to kilometers: 3400 meters / 1000 meters/km = 3.4 km
Answer: The real-world distance between the landmarks is 3.4 kilometers.
Guided Practice (With Solutions)
Question 1: A map has a scale of 1:20,
0
0
0. A road measures 7.5 cm on the map. What is the actual length of the road in meters?
Solution:
Scale: 1:20,000
Map Distance: 7.5 cm
Actual Distance: 7.5 cm 20,000 = 150,000 cm
Convert to meters: 150,000 cm = 1500 m
Answer: The actual length of the road is 1500 meters. The key here is to understand that the scale means 1 cm on the map represents 20,000 cm in reality. Then, we need to convert centimeters to a more usable unit like meters.