Lesson Notes By Weeks and Term v5 - Grade 12

Maps, plans and other representations for decision-making – Week 8 focus

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Subject: Mathematical Literacy

Class: Grade 12

Term: 2nd Term

Week: 8

Theme: General lesson support

Lesson Video

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Performance objectives

Lesson summary

This week, we delve into the crucial skill of interpreting and using maps, plans, and other visual representations to make informed decisions. In South Africa, this skill is essential for navigating our diverse landscapes, understanding urban planning challenges, and making responsible choices related to travel, housing, and resource management. From using street maps in unfamiliar cities to understanding floor plans when renting accommodation, these skills are applicable to various aspects of daily life. Misinterpreting maps or plans can lead to costly mistakes, wasted time, or even dangerous situations.

Lesson notes

2.1 Understanding Maps Maps are visual representations of an area, typically on a flat surface. Different types of maps serve different purposes.

Street Maps: Show roads, streets, landmarks, and points of interest within a city or town. Useful for navigating urban areas.

Route Maps: Show the best routes between two or more locations, often highlighting highways and major roads. Useful for long-distance travel.

Topographical Maps: Show the elevation and shape of the land using contour lines. Useful for hikers, engineers, and environmental planners.

Key elements of a map: Title: Describes the area represented by the map.

Scale: Shows the relationship between the distance on the map and the corresponding distance on the ground. Expressed as a ratio (e.g., 1:50,000), a statement (e.g., 1 cm represents 500 m), or a graphic scale (a bar that represents a specific distance).

Legend (Key): Explains the symbols and colours used on the map.

North Arrow: Indicates the direction of north.

Grid References: A system of lines used to locate specific points on the map (e.g., using latitude and longitude or a coordinate system). 2.2 Understanding Plans Plans are diagrams that show the layout or design of something, such as a building, a room, or a seating arrangement.

Building Plans (Floor Plans): Show the arrangement of rooms, walls, doors, and windows in a building. Used by architects, builders, and homeowners.

Seating Plans: Show the arrangement of seats in a theatre, stadium, or other venue. Used for assigning seats.

Key elements of a plan: Title: Describes what the plan represents.

Scale: Shows the relationship between the dimensions on the plan and the actual dimensions.

Dimensions: Indicate the length, width, and height of features.

Symbols: Represent different features, such as doors, windows, and furniture. 2.3 Using Map Scales The map scale is crucial for calculating real-world distances.

Ratio Scale: 1:50,000 means 1 unit on the map represents 50,000 units on the ground. If 1 cm on the map represents 50,000 cm on the ground, then 1 cm represents 500 meters (since 50,000 cm = 500 m).

Statement Scale: "1 cm represents 1 km" is a direct statement of the relationship.

Graphic Scale: Measure the length of the bar on the map and use it to determine the corresponding distance on the ground.

Example 1: Calculating distance using a ratio scale A map has a scale of 1:100,

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0. The distance between Johannesburg and Pretoria on the map is 5 cm. What is the actual distance between the two cities?

Solution: 1 cm on the map represents 100,000 cm on the ground. 100,000 cm = 1000 meters = 1 km.

Therefore, 1 cm represents 1 km. 5 cm on the map represents 5 1 km = 5 km. The actual distance between Johannesburg and Pretoria is 50 km.

Example 2: Calculating travel time using distance and speed You are driving from Cape Town to Durban, a distance of approximately 1600 km. You plan to drive at an average speed of 80 km/h. How long will the trip take?

Solution: Time = Distance / Speed Time = 1600 km / 80 km/h Time = 20 hours Example 3: Using grid references A map uses a grid system with numbered rows and columns. A landmark is located at grid reference E

4. Explain how to find this landmark on the map.

Solution: Locate column E on the map. Locate row 4 on the map. The landmark is located at the intersection of column E and row 4. 2.4 Analyzing Plans for Decision-Making When choosing between different options (e.g., apartments to rent), plans can provide valuable information for comparison.

Size: The floor plan will show the dimensions of each room, allowing you to calculate the total area of the apartment.

Layout: The floor plan will show the arrangement of rooms, which can affect the flow of traffic and the functionality of the space.

Features: The floor plan will indicate the location of doors, windows, closets, and other features.

Orientation: The plan may indicate the direction the building faces, affecting natural light and heating/cooling.

Example 4: Comparing apartment floor plans You are choosing between two apartments. Apartment A has a total area of 60 square meters and is located on the ground floor. Apartment B has a total area of 55 square meters and is located on the second floor. Apartment A has a larger balcony, while apartment B has a better view. Which apartment is a better choice depends on your personal priorities. If space is your primary concern, Apartment A may be the better choice. If security and a view are important to you, Apartment B may be more suitable. Guided Practice (With Solutions)

Question 1: 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 in kilometers?

Solution: 1 cm on the map represents 25,000 cm on the ground. 25,000 cm = 250 meters = 0.25 km.

Therefore, 1 cm represents 0.25 km. 8 cm on the map represents 8 0.25 km = 2 km. The actual distance between the towns is 2 km.