Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate distances and travel times using map scales.
• Interpret floor plans to find area, perimeter, and estimate costs.
• Make decisions using tables, charts, and graphs.
• Apply scale to building plans to find actual measurements.
• Understand elevation on topographical maps.

Lesson summary

This week, we delve into the vital skill of interpreting and using maps, plans, and other representations to make informed decisions. In our daily lives, we constantly encounter visual representations of information – from road maps guiding us to a new location to floor plans helping us visualize a home renovation. Understanding how to extract meaningful information from these representations is crucial for navigating our environment, managing finances, and making sound judgments in various situations.

Lesson notes

2.1 Understanding Maps and Scales A map is a visual representation of an area, whether it's a small town, a province, or the entire world. Maps use symbols, colors, and lines to represent real-world features like roads, rivers, buildings, and terrain. The scale of a map is the ratio between a distance on the map and the corresponding distance on the ground. Understanding the scale is crucial for accurate distance measurement and route planning. Scales are typically represented in three ways: Verbal Scale: Expresses the scale in words, e.g., "1 cm represents 1 km".

Representative Fraction (RF): A ratio that expresses the relationship between map distance and ground distance as a fraction, e.g., 1:100,

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0. This means 1 unit on the map represents 100,000 of the same units on the ground.

Graphical Scale (Scale Bar): A line or bar drawn on the map that is divided into segments representing specific distances on the ground. This is especially useful because it remains accurate even if the map is enlarged or reduced.

Example 1: A map has a scale of 1:50,

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0. What distance on the ground is represented by 5 cm on the map?

Explanation: The scale 1:50,000 means that 1 cm on the map represents 50,000 cm on the ground.

Calculation: 5 cm on the map represents 5 cm 50,000 = 250,000 cm on the ground.

Convert cm to km: 250,000 cm = 2500 m = 2.5 km Answer: 5 cm on the map represents 2.5 km on the ground. 2.2 Using Floor Plans A floor plan is a scaled diagram of a room or building viewed from above. It shows the arrangement of walls, doors, windows, and furniture. Floor plans are essential for architects, builders, and homeowners for planning renovations, furniture placement, and estimating costs.

When working with floor plans: Pay attention to the scale: Just like maps, floor plans have a scale that relates the dimensions on the plan to the actual dimensions of the building.

Identify symbols: Floor plans use standard symbols to represent different elements, such as doors, windows, appliances, and electrical outlets. A legend usually accompanies the plan to explain these symbols.

Calculate area and perimeter: You can use the dimensions on the floor plan and the scale to calculate the actual area and perimeter of rooms or the entire building.

Example 2: A rectangular room on a floor plan measures 4 cm by 3 cm.

The scale of the floor plan is 1:

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0. Calculate the actual dimensions of the room: Length: 4 cm 100 = 400 cm = 4 m Width: 3 cm 100 = 300 cm = 3 m Calculate the area of the room: Area = Length Width = 4 m * 3 m = 12 m² Calculate the perimeter of the room: Perimeter = 2 (Length + Width) = 2 * (4 m + 3 m) = 14 m 2.3 Interpreting Tables, Charts, and Graphs Tables, charts, and graphs are used to present data in a concise and visual way. These representations are commonly used to compare options, show trends, and make predictions. In the context of maps and plans, these representations can be used to compare transport costs, analyze building material prices, or track construction progress.

Example 3: A table shows the costs of different modes of transportation from Johannesburg to Durban: | Mode of Transport | Cost | Travel Time | | ----------------- | --------- | ----------- | | Bus | R350 | 7 hours | | Train | R500 | 12 hours | | Car (Petrol) | R700 | 6 hours | | Airplane | R1200 | 1 hour | Analysis: The bus is the cheapest option, but it has a long travel time. The train is more expensive than the bus but takes even longer. The car offers a good balance between cost and travel time, but it depends on the fuel efficiency of the car. The airplane is the most expensive option but offers the fastest travel time.

Decision: The best mode of transportation depends on your priorities. If you are on a tight budget, the bus is the best option. If you value time, the airplane is the best option. 2.4 Topographical Maps Topographical maps show the shape and elevation of the land using contour lines. Contour lines are lines that connect points of equal elevation. The closer the contour lines are to each other, the steeper the terrain. Topographical maps are used by hikers, engineers, and planners to understand the terrain and plan routes or construction projects.

Example 4: Two contour lines on a topographical map are very close together. What does this indicate about the terrain?

Explanation: Closely spaced contour lines indicate a steep slope. The closer the lines, the steeper the slope. Widely spaced contour lines indicate a gentle slope. Guided Practice (With Solutions)

Question 1: A map of Gauteng has a scale of 1:250,

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0. The distance between Johannesburg and Pretoria on the map is 20 cm. What is the actual distance between the two cities in kilometers?

Solution: Scale: 1:250,000 Map Distance: 20 cm Ground Distance: 20 cm 250,000 = 5,000,000 cm Convert cm to km: 5,000,000 cm = 50,000 m = 50 km Answer: The actual distance between Johannesburg and Pretoria is 50 km.