Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Convert distances using ratio, word, and bar scales.
• Interpret symbols and legends on South African maps.
• Calculate area and perimeter from scaled plans.
• Apply scale to solve real-world problems.
• Understand the limitations of maps and plans.

Lesson summary

This week, we delve into the world of scale, maps, and plans – tools crucial for navigating our environment, understanding spatial relationships, and making informed decisions. In South Africa, where inequalities in access to resources and information persist, the ability to interpret maps and plans is particularly vital. From understanding land ownership disputes rooted in historical mapping inaccuracies to planning efficient transport routes in sprawling townships, this knowledge empowers individuals and communities. We'll explore how scales are used to represent real-world distances and areas on smaller formats like maps and architectural blueprints.

Lesson notes

What is Scale? Scale is the ratio that represents the relationship between a distance on a map or plan and the corresponding distance on the ground. It indicates how much the real world has been reduced (or occasionally enlarged) to fit on a piece of paper or a screen. Understanding scale is crucial for accurately interpreting maps and plans.

Types of Scales: Ratio Scale (Representative Fraction): This is expressed as a ratio, for example, 1:50,

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0. This means that 1 unit of measurement on the map represents 50,000 of the same units on the ground. So, 1 cm on the map represents 50,000 cm (or 500 meters) in reality.

Word Statement Scale: This expresses the scale in words, such as "1 cm represents 1 kilometer." This is straightforward and easy to understand.

Bar Scale (Graphic Scale): This is a visual representation of the scale using a line divided into segments, each representing a specific distance on the ground. It allows for quick estimations of distances directly on the map. The bar scale is especially useful because it remains accurate even if the map is enlarged or reduced. Converting Between Map and Real-World Distances: The key to working with scales is understanding proportional relationships.

We use the following formula: Real-world distance = Map distance x Scale factor Where the scale factor is derived from the scale.

Example 1: Using a Ratio Scale A map has a scale of 1:25,

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0. Two towns are 8 cm apart on the map. What is the actual distance between the towns?

Scale: 1:25,000 Map distance: 8 cm Scale factor: 25,000 Real-world distance: 8 cm x 25,000 = 200,000 cm Now, convert cm to km (since km is a more practical unit for distance between towns): 200,000 cm = 200,000 / 100 cm/m / 1000 m/km = 2 km Therefore, the actual distance between the towns is 2 kilometers.

Example 2: Using a Word Statement Scale A plan of a house uses the scale "1 cm represents 50 cm." A wall on the plan measures 15 cm. How long is the actual wall?

Scale: 1 cm represents 50 cm Map distance: 15 cm Real-world distance: 15 cm x 50 = 750 cm Convert cm to meters: 750 cm / 100 cm/m = 7.5 meters The actual wall is 7.5 meters long.

Example 3: Using a Bar Scale Imagine a map with a bar scale. The bar scale shows a line segment of 2 cm representing 1 km. If two points on the map are covered by 6cm on that line segment (bar scale), what is the real distance between them? Given the Bar scale, 2cm = 1km Divide both sides by 2 to get: 1cm = 0.5km Thus, 6cm 0.5km/cm = 3km Interpreting Map Symbols and Legends: Maps use symbols to represent various features like roads, rivers, buildings, schools, and landmarks. The legend (or key) explains what each symbol represents. It's essential to consult the legend to correctly interpret the information presented on the map. South African maps often use symbols specific to the local context, such as symbols for informal settlements, taxi ranks, and specific types of vegetation. Calculating Area and Perimeter from Scaled Plans: When working with architectural plans or property maps, you often need to calculate areas and perimeters. First, use the scale to convert the measurements on the plan to actual dimensions. Then, apply the appropriate formulas for area and perimeter based on the shape (e.g., rectangle, triangle, circle).

Example 4: Calculating Area from a Plan A rectangular room is shown on a house plan with dimensions 5 cm by 4 cm.

The scale of the plan is 1:

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0. What is the actual area of the room?

Plan dimensions: 5 cm x 4 cm Scale: 1:100 Actual length: 5 cm x 100 = 500 cm = 5 meters Actual width: 4 cm x 100 = 400 cm = 4 meters Area: 5 meters x 4 meters = 20 square meters The actual area of the room is 20 square meters.

Accuracy and Limitations: It is crucial to understand that maps are representations of reality and, therefore, have inherent limitations. Factors like map projection, simplification of features, and the age of the map can affect its accuracy. Always consider the scale and the source of the map when interpreting information. Remember also that digitisation can result in errors, so check for consistency and plausibility. Guided Practice (With Solutions)

Question 1: A map of Gauteng has a scale of 1:500,

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0. The distance between Johannesburg and Pretoria on the map is 10 cm. What is the actual distance between the two cities in kilometers?

Solution: Scale: 1:500,000 Map distance: 10 cm Scale factor: 500,000 Real-world distance: 10 cm x 500,000 = 5,000,000 cm Convert cm to km: 5,000,000 cm / 100 cm/m / 1000 m/km = 50 km The actual distance between Johannesburg and Pretoria is 50 kilometers.

Question 2: An architectural plan uses the scale "2 cm represents 1 meter." A living room on the plan is 8 cm long and 6 cm wide. What are the actual dimensions of the living room in meters, and what is its area?