Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret information from different maps.
• Calculate distances and travel times using map scales.
• Use floor plans to calculate area, perimeter, and costs.
• Analyze graphs and charts to make decisions.
• Apply ratio and proportion in scaled drawings.

Lesson summary

Maps, plans, and other representations are crucial tools for navigating our world, making informed decisions, and understanding spatial relationships. In South Africa, these skills are particularly relevant given our diverse landscapes, urban planning challenges, and the need for effective resource management. Understanding how to interpret and use these representations empowers individuals to participate more effectively in community development, personal financial planning, and many other aspects of daily life.

Lesson notes

2. 1. Understanding Maps A map is a visual representation of an area, usually on a flat surface. Maps use symbols and colors to represent different features like roads, rivers, buildings, and terrain.

Map Scale: The map scale is the ratio between a distance on the map and the corresponding distance on the ground.

It can be expressed in several ways: Verbal Scale: A statement like "1 cm represents 1 km." Representative Fraction (RF): A ratio like 1:100,

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0. This means 1 unit on the map represents 100,000 units on the ground (the units must be the same).

Graphic Scale (Bar Scale): A line on the map divided into segments that represent specific distances on the ground.

Types of Maps: Road Maps: Show roads, highways, cities, and other points of interest for navigation.

Topographic Maps: Show elevation using contour lines, providing information about the terrain.

Thematic Maps: Focus on a specific theme, such as population density, rainfall distribution, or land use.

Municipal Maps (Zoning Maps): Show property boundaries, zoning regulations (e.g., residential, commercial, industrial), and infrastructure.

Example 1: Using Map Scale to Calculate Distance A road map has a scale of 1:50,

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0. The distance between two towns on the map is 8 cm. What is the actual distance between the towns in kilometers?

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

Actual distance in cm: 8 cm * 50,000 = 400,000 cm Convert cm to km: 400,000 cm / 100 (cm/m) / 1000 (m/km) = 4 km Therefore, the actual distance between the towns is 4 km.

Example 2: Estimating Travel Time Using the same map and distance from Example 1 (4 km), estimate the travel time if the speed limit is 60 km/h.

Solution: Time = Distance / Speed Time = 4 km / 60 km/h = 0.0667 hours Convert hours to minutes: 0.0667 hours * 60 minutes/hour = 4 minutes (approximately) Therefore, the estimated travel time is approximately 4 minutes. 2.

2. Interpreting Plans and Diagrams Plans and diagrams are scaled representations of objects or spaces. Common examples include floor plans, building blueprints, and technical drawings.

Floor Plans: Show the layout of a building, including walls, doors, windows, and fixtures.

Scale Drawings: Uses a scale to accurately represent the dimensions of an object on a smaller surface.

Example 3: Calculating Area from a Floor Plan A rectangular room on a floor plan measures 5 cm by 4 cm.

The scale of the floor plan is 1:

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0. What is the actual area of the room in square meters?

Solution: Convert map dimensions to actual dimensions: Length: 5 cm 100 = 500 cm = 5 m Width: 4 cm 100 = 400 cm = 4 m Calculate the area: Area = Length Width = 5 m 4 m = 20 square meters.

Therefore, the actual area of the room is 20 square meters.

Example 4: Cost Estimation from a Floor Plan A builder needs to lay tiles in the room from Example

3. The tiles cost R150 per square meter. What will be the total cost of the tiles?

Solution: Total cost = Area * Cost per square meter. Total Cost = 20 m 2 * R150/m 2 = R3000 Therefore the total cost of the tiles will be R3000. 2.

3. Analyzing Other Representations Graphs, tables, and charts are used to present data visually and make comparisons.

Bar Graphs: Compare quantities across different categories.

Pie Charts: Show proportions of a whole.

Line Graphs: Show trends over time.

Tables: Organize data in rows and columns for easy comparison.

Example 5: Interpreting a Bar Graph A bar graph shows the monthly water consumption of a household over six months. The bars represent the following water usage (in kiloliters): Jan (15), Feb (18), Mar (20), Apr (16), May (14), Jun (12). What was the highest water consumption, and in which month did it occur? What was the lowest water consumption, and in which month did it occur?

Solution: Highest consumption: 20 kiloliters in March.

Lowest consumption: 12 kiloliters in June. Guided Practice (With Solutions)

Question 1: A map has a scale of 1:25,

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0. Two landmarks are 6 cm apart on the map. What is the actual distance between them in meters?

Solution: Multiply the map distance by the scale factor: 6 cm * 25,000 = 150,000 cm Convert centimeters to meters: 150,000 cm / 100 cm/m = 1500 m Answer: The actual distance is 1500 meters.

Question 2: A rectangular garden measures 8 meters by 5 meters. You want to create a scale drawing of the garden using a scale of 1 cm = 1 meter. What should be the dimensions of the garden on your drawing?

Solution: Since 1 cm represents 1 meter, the dimensions on the drawing will be: Length: 8 meters = 8 cm Width: 5 meters = 5 cm Answer: The dimensions of the garden on the drawing should be 8 cm by 5 cm.

Question 3: A pie chart shows the distribution of a household's monthly expenses. Rent accounts for 40%, food accounts for 25%, transportation accounts for 15%, and other expenses account for 20%. If the total monthly income is R10,000, how much is spent on rent?