Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret different types of maps and plans.
• Calculate distances and travel times using map scales.
• Analyze floor plans to determine area, perimeter, and costs.
• Use graphs and tables to compare information.
• Apply scale to solve real-world problems.

Lesson summary

This week, we delve into the crucial skill of interpreting and using maps, plans, and other representations to make informed decisions. In South Africa, understanding these representations is essential for navigating our diverse landscapes, participating in community planning, and managing personal finances. Imagine trying to plan a road trip from Cape Town to Durban without a map, or understanding building plans for a RDP housing project in your community. These representations empower us to understand spatial relationships, visualize data, and ultimately make better decisions. This topic is also directly relevant to Paper 2 of your final Mathematical Literacy exam.

Lesson notes

2.1 Maps and Map Scales: Maps are representations of geographic areas, typically drawn on a flat surface. Understanding map scales is crucial for determining actual distances between locations. A map scale expresses the ratio between a distance on the map and the corresponding distance on the ground.

Ratio Scale: Expresses the scale as a ratio, e.g., 1:50,

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0. This means 1 cm on the map represents 50,000 cm (or 500 meters, or 0.5 km) on the ground.

Representative Fraction (RF): Another way to express a ratio scale, e.g., 1/50,

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0. It's the same as the ratio scale, just written as a fraction.

Statement Scale: States the scale in words, e.g., "1 cm represents 1 km." Linear Scale (Graphic Scale): A line drawn on the map representing a specific distance on the ground. You can use a ruler to measure distances on the map and then compare them to the linear scale to determine the actual distance.

Example 1: A map has a scale of 1:100,

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0. Two towns are 5 cm apart on the map. What is the actual distance between the towns in kilometers?

Solution: 1 cm on the map = 100,000 cm on the ground 5 cm on the map = 5 100,000 cm on the ground = 500,000 cm Convert cm to km: 500,000 cm / 100 cm/m / 1000 m/km = 5 km Answer: The actual distance between the towns is 5 km. 2.2 Plans (Floor Plans and Site Plans): Plans are scaled diagrams that show the layout of a building (floor plan) or a piece of land (site plan). Floor plans indicate the arrangement of rooms, doors, windows, and other features within a building. Site plans show the boundaries of a property, the location of buildings, and other relevant features like driveways, gardens, and utilities.

Example 2: A floor plan uses a scale of 1:

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0. A room measures 4 cm by 3 cm on the plan. What are the actual dimensions of the room in meters, and what is the area of the room?

Solution: Length: 4 cm on the plan = 4 50 cm = 200 cm = 2 meters Width: 3 cm on the plan = 3 50 cm = 150 cm = 1.5 meters Area: Length Width = 2 meters * 1.5 meters = 3 square meters Answer: The room is 2 meters by 1.5 meters, and its area is 3 square meters. 2.3 Other Representations (Graphs and Tables): Graphs and tables are visual representations of data that allow for easy comparison and analysis.

Bar Graphs: Used to compare different categories.

Pie Charts: Used to show the proportion of different categories that make up a whole.

Tables: Used to organize data in rows and columns.

Example 3: A table shows the monthly electricity consumption of a household for the past year. Analyze the table to identify the months with the highest and lowest consumption, and calculate the average monthly consumption. This can inform decisions on energy-saving measures. (Assume the table data is provided within the exercise). 2.4 Travel Time Calculations: Travel time can be estimated using the formula: Time = Distance / Speed Remember to use consistent units (e.g., distance in kilometers, speed in kilometers per hour, time in hours).

Example 4: You are planning a road trip from Johannesburg to Durban. The distance is approximately 560 km. You estimate an average speed of 100 km/h. How long will the trip take?

Solution: Time = 560 km / 100 km/h = 5.6 hours Convert 0.6 hours to minutes: 0.6 hours 60 minutes/hour = 36 minutes Answer: The trip will take approximately 5 hours and 36 minutes. Guided Practice (With Solutions)

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

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0. The distance between two points on the map is 8 cm. Calculate the actual distance between the two points in kilometers.

Solution: 1 cm on the map = 250,000 cm on the ground 8 cm on the map = 8 250,000 cm on the ground = 2,000,000 cm Convert cm to km: 2,000,000 cm / 100 cm/m / 1000 m/km = 20 km Answer: The actual distance is 20 km.

Question 2: A floor plan uses a scale of 1:

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0. A rectangular living room measures 6 cm by 4 cm on the plan. Calculate the perimeter of the living room in meters.

Solution: Length: 6 cm on the plan = 6 100 cm = 600 cm = 6 meters Width: 4 cm on the plan = 4 100 cm = 400 cm = 4 meters Perimeter = 2 (Length + Width) = 2 (6 meters + 4 meters) = 2 10 meters = 20 meters Answer: The perimeter of the living room is 20 meters.

Question 3: You are traveling from Pretoria to Polokwane. The distance is 320 km. You travel at an average speed of 80 km/h for the first 2 hours, and then at an average speed of 60 km/h for the remainder of the journey. Calculate the total travel time.

Solution: Distance covered in the first 2 hours: 2 hours 80 km/h = 160 km Remaining distance: 320 km - 160 km = 160 km Time taken to cover the remaining distance: 160 km / 60 km/h = 2.67 hours Convert 0.67 hours to minutes: 0.67 hours 60 minutes/hour = 40 minutes Total travel time: 2 hours + 2.67 hours = 4 hours and 40 minutes Answer: The total travel time is 4 hours and 40 minutes. Independent Practice (Questions Only)

Question 1: A map has a scale of 1 cm : 25 km. Two cities are 4.5 cm apart on the map. What is the actual distance between the cities?