Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate real-world distances using a map's scale.
• Determine map distances from real-world distances.
• Interpret different types of maps and their features.
• Determine direction and compass bearings.
• Use a map's key or legend to understand symbols.

Lesson summary

This week, we delve deeper into Maps, plans and other representations of the physical world. This topic is crucial because it empowers you to understand and navigate your surroundings, make informed decisions about spatial arrangements, and interpret information presented visually. In a country like South Africa, where spatial inequalities persist and access to resources varies greatly depending on location, understanding maps and plans allows you to advocate for yourself and your community effectively. Whether you're planning a trip, understanding a construction project in your neighbourhood, or even interpreting election maps, these skills are essential.

Lesson notes

2.1 Understanding Scale The scale of a map or plan is the ratio of a distance on the map to the corresponding distance on the ground. It allows us to represent large areas in a manageable size.

There are three main types of scales: Numerical Scale (Ratio Scale): This is expressed as a ratio, e.g., 1:50,

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0. This means that 1 unit of measurement on the map represents 50,000 of the same units on the ground. For instance, 1 cm on the map represents 50,000 cm (or 500 meters, or 0.5 km) on the ground.

Verbal Scale (Statement Scale): This expresses the relationship in words, e.g., "1 cm represents 1 kilometre." This is straightforward to understand but less versatile for calculations.

Bar Scale (Graphical Scale): This is a visual representation of the scale, usually a line divided into segments representing specific distances on the ground. It is particularly useful because it remains accurate even if the map is enlarged or reduced.

Example 1: Using a Numerical Scale A map has a scale of 1:25,

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0. Two towns, Thokoza and Katlehong, are 8 cm apart on the map. What is the actual distance between the towns?

Step 1: Understand the scale: 1 cm on the map = 25,000 cm on the ground.

Step 2: Calculate the real-world distance in cm: 8 cm (map) 25,000 cm/cm = 200,000 cm Step 3: Convert to a more practical unit (km): 200,000 cm / 100 cm/m = 2,000 m. Then, 2,000 m / 1000 m/km = 2 km Therefore, the actual distance between Thokoza and Katlehong is 2 km.

Example 2: Using a Verbal Scale A map states "1 cm represents 5 km." Two landmarks are 3.5 cm apart on the map. What is the actual distance between them?

Step 1: Understand the scale: 1 cm on the map = 5 km on the ground.

Step 2: Calculate the real-world distance: 3.5 cm (map) 5 km/cm = 17.5 km Therefore, the actual distance between the landmarks is 17.5 km.

Example 3: Using a Bar Scale Imagine a map has a bar scale where a 2 cm line represents 10 km. On the map, a road measures 6 cm using a ruler along its curvy path. Estimate the real distance of the road.

Step 1: Determine the ratio from the bar scale: 2 cm = 10 km.

Step 2: Find out how many "2 cm segments" fit into the road's length: 6cm / 2cm = 3 segments Step 3: Calculate the total distance: 3 segments 10 km/segment = 30 km Therefore, the road is approximately 30 km long. 2.2 Types of Maps and Plans Different maps serve different purposes: Road Maps: Primarily show roads, highways, and points of interest for navigation. Often include distances between towns.

Topographic Maps: Show elevation changes using contour lines. Useful for hiking, camping, and understanding the terrain.

Floor Plans: Architectural drawings showing the layout of a building, including rooms, doors, windows, and fixtures.

Thematic Maps: Display specific data related to a geographical area, such as population density, rainfall, or economic activity. An example could be a map showing the percentage of households in different municipalities with access to piped water.

Street Maps: Detailed maps showing streets, buildings and other features in a town or city. These are useful for finding addresses.

Interpreting Symbols and Legends (Keys): Maps use symbols to represent real-world features. The legend or key explains what each symbol represents. For example, a blue line might represent a river, a small airplane might represent an airport, and a star might represent the capital city. Always refer to the legend to accurately interpret the information on a map. 2.3 Direction and Compass Bearings Cardinal Directions: North, South, East, and West.

Intercardinal Directions: Northeast, Southeast, Northwest, and Southwest.

Compass Bearings: Expressed in degrees, measured clockwise from North (0°). For example, East is 90°, South is 180°, and West is 270°.

Using a Compass Rose: Most maps have a compass rose (or north arrow) indicating the direction of North. This helps you determine the direction of other features on the map relative to each other.

Example 4: Determining Direction On a map, Durban is located south-east of Johannesburg. This means that to travel from Johannesburg to Durban, you would generally need to travel in a south-easterly direction. Guided Practice (With Solutions)

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

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0. Two cities are 4.5 cm apart on the map. What is the actual distance between the cities in kilometers?

Solution: Step 1: Understand the scale: 1 cm on the map = 100,000 cm on the ground.

Step 2: Calculate the real-world distance in cm: 4.5 cm 100,000 cm/cm = 450,000 cm Step 3: Convert to kilometers: 450,000 cm / 100 cm/m = 4,500 m. Then, 4,500 m / 1000 m/km = 4.5 km Answer: The actual distance between the cities is 4.5 km.

Question 2: A road is 15 km long. On a map with a scale of 1 cm = 2.5 km, how long would the road be represented on the map in centimeters?

Solution: Step 1: Understand the scale: 1 cm on the map = 2.5 km on the ground.