Lesson Notes By Weeks and Term v5 - Grade 11
Measurement: scale, maps and plans – Week 9 focus
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Measurement: scale, maps and plans – Week 9 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: 9
Theme: General lesson support
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This week, we delve into the crucial skill of interpreting and using scales, maps, and plans. Understanding these tools is vital for navigating our world, making informed decisions about distances, areas, and proportions, and even planning construction or gardening projects. In South Africa, where access to reliable transportation and resources can vary greatly, the ability to understand maps and plans becomes even more essential for everyday life and informed citizenship. For example, understanding scale allows you to calculate travel times using a map, budget for fencing a plot of land from a plan, or even follow directions accurately.
2.1 Understanding Scale: A scale is a ratio that compares a distance on a map, plan, or model to the corresponding distance in the real world. It allows us to represent large areas or objects in a smaller, manageable format.
There are several ways to represent scale: Ratio Scale: This is expressed as a ratio, such as 1:
5
0
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0. This means that 1 unit of measurement on the map or plan represents 5000 of the same units in reality. For example, 1 cm on the map represents 5000 cm (or 50 meters) in the real world.
Representative Fraction (RF): The RF is similar to a ratio scale, but it doesn't specify units. It's often expressed as a fraction, like 1/
5
0
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0. The interpretation is the same as the ratio scale: 1 unit on the map represents 5000 of the same units in reality.
Bar Scale (Graphical Scale): This is a visual representation of the scale, usually a line divided into segments, each representing a specific distance on the ground. It allows for quick estimation of distances directly from the map. The advantage of a bar scale is that it remains accurate even if the map is photocopied and enlarged or reduced, unlike numerical scales.
Statement Scale (Verbal Scale): This expresses the relationship between map distance and ground distance in words, such as "1 cm represents 1 kilometer". 2.2 Converting Between Scales: It's essential to be able to convert between different types of scales.
Here's how: Ratio Scale to Statement Scale: Let's say the ratio scale is 1:100,
0
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0. This means 1 unit on the map represents 100,000 of the same units on the ground. If the unit on the map is centimeters (cm), then 1 cm represents 100,000 cm. To convert to kilometers, divide by 100,000 (since there are 100,000 cm in a kilometer): 100,000 cm / 100,000 = 1 km. So, the statement scale is "1 cm represents 1 kilometer".
Statement Scale to Ratio Scale: If the statement scale is "2 cm represents 1 km", we need to express this as a ratio where both sides have the same units.
Convert 1 km to centimeters: 1 km = 100,000 cm. So the statement becomes "2 cm represents 100,000 cm". To get the ratio scale, simplify by dividing both sides by 2: 1 cm represents 50,000 cm.
The ratio scale is 1:50,000. 2.3 Calculating Real-World Distances and Areas: To calculate real-world distances from a map: Measure the distance on the map using a ruler. Ensure you're using the correct units (cm, mm, etc.). Identify the scale of the map. Use the scale to calculate the real-world distance.
If the scale is 1:50,000 and you measure 5 cm on the map, then the real-world distance is 5 cm * 50,000 = 250,000 cm.
Convert to kilometers: 250,000 cm / 100,000 = 2.5 km.
To calculate real-world areas from a plan: Calculate the area on the plan. For example, if it's a rectangular room, measure the length and width on the plan and multiply them. Identify the scale of the plan. Square the scale factor.
If the scale is 1:100, the area scale factor is (100)^2 = 10,
0
0
0. Multiply the area on the plan by the area scale factor to get the real-world area. If the area on the plan is 20 cm 2 , then the real-world area is 20 cm 2 * 10,000 = 200,000 cm 2 . Convert to meters 2 (divide by 10,000): 200,000 cm 2 / 10,000 = 20 m 2 . 2.4 Interpreting Map Symbols and Legends: Maps use symbols and legends (or keys) to represent different features. A legend explains what each symbol on the map represents (e.g., a blue line might represent a river, a brown contour line might represent an elevation change). Learning to read a map legend is crucial for understanding the information presented on the map. In South Africa, it's particularly important to recognize symbols for roads, railways, rivers, dams, and different types of terrain.