Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret and use different map scales to calculate real-world distances.
• Calculate estimated travel times and costs for a journey.
• Use floor plans to calculate area and estimate material costs.
• Analyze charts and graphs for decision-making.
• Apply the concept of scale to models.

Lesson summary

This week, we delve into the crucial skill of interpreting and using maps, plans, and other representations to make informed decisions. In a country like South Africa, where spatial reasoning is vital for navigating diverse landscapes, understanding urban planning, and participating in economic activities, this skill is indispensable. From planning a road trip between Gauteng and the Western Cape to understanding the layout of a new shopping mall in Durban, the ability to extract and interpret information from visual representations empowers you to make sound judgments in various aspects of your life.

Lesson notes

2.1 Map Scales: A map scale shows the relationship between a distance on a map and the corresponding distance on the ground. It's how we translate a small representation into a real-world measurement.

Ratio Scale: Expressed as a ratio (e.g., 1:50,000). This means 1 unit on the map represents 50,000 units on the ground. If the unit is centimeters, then 1 cm on the map equals 50,000 cm (or 500 meters) in reality.

Word Scale: Expressed in words (e.g., "1 cm represents 1 kilometer"). This is a direct and easy-to-understand way to convey the scale.

Bar Scale (Graphic Scale): A visual representation of the scale, typically a line divided into segments that represent specific distances on the ground. This is useful because it remains accurate even if the map is photocopied or resized.

Example 1: Ratio Scale A map of Kruger National Park has a scale of 1:250,

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0. Two rest camps, Skukuza and Letaba, measure 15 cm apart on the map. What is the actual distance between them?

Explanation: The ratio 1:250,000 means 1 cm on the map equals 250,000 cm in reality. We need to convert the ground distance to kilometers for easier understanding.

Calculation: Real distance in cm: 15 cm 250,000 = 3,750,000 cm Real distance in meters: 3,750,000 cm / 100 = 37,500 m Real distance in kilometers: 37,500 m / 1000 = 37.5 km Answer: The actual distance between Skukuza and Letaba is 37.5 km.

Example 2: Word Scale A road map has a scale of "2 cm represents 5 km". If the distance between Johannesburg and Pretoria is 10 cm on the map, what is the actual distance?

Explanation: We know the relationship between map distance and real-world distance. We can set up a proportion to solve this.

Calculation: (2 cm / 5 km) = (10 cm / x km) 2x = 50 x = 25 km Answer: The actual distance between Johannesburg and Pretoria is 25 km. 2.2 Calculating Travel Time and Costs: This involves using map scales, speed limits, distances, fuel consumption rates, and other relevant information to estimate the duration and expense of a journey.

Example 3: Travel Time and Fuel Cost You're driving from Cape Town to Port Elizabeth, a distance of 760 km. Your car's fuel consumption is 8 liters per 100 km. The average speed you expect to travel is 100 km/h. Petrol costs R20 per liter. Calculate the estimated travel time and fuel cost.

Explanation: We need to calculate the total travel time based on distance and speed, then calculate the total fuel consumption and cost.

Calculation: Travel time: 760 km / 100 km/h = 7.6 hours Fuel consumption: (760 km / 100 km) 8 liters = 60.8 liters Fuel cost: 60.8 liters R20/liter = R1216 Answer: The estimated travel time is 7.6 hours, and the estimated fuel cost is R1216. 2.3 Interpreting Plans (Floor Plans, Building Plans): Plans provide a scaled representation of structures, allowing us to determine dimensions, areas, perimeters, and other properties.

Example 4: Area Calculation from a Floor Plan A rectangular room on a floor plan measures 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 in square meters?

Explanation: We need to find the actual length and width of the room using the scale, then calculate the area.

Calculation: Actual length: 5 cm 50 = 250 cm = 2.5 m Actual width: 4 cm 50 = 200 cm = 2.0 m Area: 2.5 m 2.0 m = 5 m² Answer: The actual area of the room is 5 m². 2.4 Other Visual Representations: Interpreting charts, graphs, tables, and diagrams is crucial for informed decision-making. For example, a graph showing traffic patterns can help you choose the best time to travel. A table listing the costs of different accommodation options can help you make a budget-friendly choice. 2.5 Application of Scale to 3D representations and Models: Scale models are used in architecture, engineering and other fields to represent real-world objects. The scale applies to all dimensions of the model. Guided Practice (With Solutions)

Question 1: A map uses a scale of 1:100,

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

Solution: Real distance in cm: 8 cm 100,000 = 800,000 cm Real distance in meters: 800,000 cm / 100 = 8,000 m Real distance in kilometers: 8,000 m / 1000 = 8 km Answer: The actual distance between the towns is 8 km.

Commentary: This question directly applies the concept of ratio scale. We multiplied the map distance by the scale factor and then converted the units to kilometers for a more practical understanding.

Question 2: A car travels 360 km. Its fuel consumption is 9 liters per 100 km. Petrol costs R18.50 per liter. What is the total cost of the petrol for the journey?

Solution: Fuel consumption: (360 km / 100 km) 9 liters = 32.4 liters Total cost: 32.4 liters R18.50/liter = R599.40 Answer: The total cost of the petrol is R599.

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0. Commentary: This question applies the concept of proportional reasoning to calculate total fuel consumption and cost based on given fuel efficiency and price.