Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate real-world distances using a scale.
• Determine the scale of a map or plan.
• Interpret different types of scales: ratio, bar, and statement.
• Use maps to estimate area and perimeter.
• Apply scale skills to interpret floor plans.

Lesson summary

Maps and plans are essential tools that help us navigate and understand the world around us. In South Africa, where spatial inequalities and diverse landscapes are prevalent, the ability to interpret and utilize maps and plans is crucial for informed decision-making, problem-solving, and active citizenship. This topic, focusing on scale, maps, and plans, will equip you with the skills to analyze spatial information, understand distances, and make accurate estimations. Whether you are planning a road trip, designing a garden, or understanding urban development, these skills are invaluable.

Lesson notes

2.1 Understanding Scale: Scale represents the relationship between a distance on a map or plan and the corresponding distance on the ground in the real world. It's crucial for accurately translating measurements from a scaled representation to actual dimensions.

There are three main types of scales: Ratio Scale: Expressed as a ratio (e.g., 1:50000). This means that 1 unit on the map represents 50000 units in the real world. The units must be the same on both sides of the ratio.

Statement Scale (Verbal Scale): Expressed in words (e.g., 1 cm represents 1 km). This is a straightforward way to understand the relationship between the map distance and the real-world distance.

Bar Scale (Graphical Scale): A visual representation of the scale, usually a line divided into segments that represent specific distances on the ground. This is particularly useful because it remains accurate even if the map or plan is enlarged or reduced. 2.2 Converting Between Scale Types: It's essential to be able to convert between different types of scales.

Here's how: Ratio to Statement: If the ratio scale is 1:100000, it means 1 cm on the map represents 100000 cm in reality. To convert this to kilometers, divide by 100000 (to get meters) and then by 1000 (to get kilometers): 100000 cm / 100000 = 1 meter; 1 meter / 1000 = 0.001 km. So, 1 cm represents 1 km.

Statement to Ratio: If the statement scale is 1 cm represents 5 km, convert the real-world distance (5 km) to the same unit as the map distance (cm): 5 km 100000 cm/km = 500000 cm.

Therefore, the ratio scale is 1:500000. 2.3 Calculating Real-World Distances: To calculate the real-world distance using a map distance and scale, follow these steps: Identify the scale of the map or plan. Measure the distance on the map or plan between the two points of interest. Use the scale to convert the map distance to the real-world distance.

Example 1 (Ratio Scale): A map has a scale of 1:

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0. The distance between Johannesburg and Pretoria on the map is 20 cm. What is the actual distance between the two cities?

Scale: 1:250000 Map Distance: 20 cm Calculation: 20 cm 250000 = 5000000 cm Conversion to km: 5000000 cm / 100000 cm/km = 50 km Therefore, the actual distance between Johannesburg and Pretoria is 50 km.

Example 2 (Statement Scale): A floor plan has a scale of 1 cm represents 0.5 meters. The length of a room on the plan is 8 cm. What is the actual length of the room?

Scale: 1 cm represents 0.5 meters Map Distance: 8 cm Calculation: 8 cm 0.5 meters/cm = 4 meters Therefore, the actual length of the room is 4 meters. 2.4 Determining the Scale: To determine the scale of a map or plan, you need to know the distance on the map and the corresponding real-world distance.

Example 3: The distance between Durban and Pietermaritzburg is 80 km. On a map, this distance is represented by 4 cm. What is the scale of the map?

Convert the real-world distance to cm: 80 km * 100000 cm/km = 8000000 cm. The scale is the ratio of the map distance to the real-world distance: 4 cm : 8000000 cm. Simplify the ratio by dividing both sides by 4: 1:

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0. Therefore, the scale of the map is 1:2000000. 2.5 Interpreting Floor Plans and Building Plans: Floor plans and building plans use scale drawings to represent the layout and dimensions of buildings. Understanding the symbols, abbreviations, and dimensions on these plans is essential for construction, renovation, and interior design.

Pay attention to: Walls and partitions: Represented by thicker lines.

Doors and windows: Shown with specific symbols indicating their type and direction of opening.

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

Materials: Sometimes indicated with hatching or abbreviations.

Scale: Clearly stated on the plan.

Example 4: A building plan shows a kitchen with dimensions 4.5m x 3m.

The scale of the plan is 1:

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0. What are the dimensions of the kitchen on the plan?

Real-world dimensions: 4.5m x 3m Scale: 1:50 Conversion to cm: 4.5 m = 450 cm; 3 m = 300 cm Calculation for plan dimensions: 450 cm / 50 = 9 cm; 300 cm / 50 = 6 cm Therefore, the dimensions of the kitchen on the plan are 9 cm x 6 cm. Guided Practice (With Solutions)

Question 1: A map of the Kruger National Park has a scale of 1:

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0. The distance between two rest camps, Skukuza and Letaba, measures 12 cm on the map. Calculate the actual distance between the rest camps in kilometers.

Solution: Scale: 1:1500000 Map Distance: 12 cm Calculation: 12 cm * 1500000 = 18000000 cm Conversion to km: 18000000 cm / 100000 cm/km = 180 km Answer: The actual distance between Skukuza and Letaba is 180 km.

Commentary: This question applies the basic principle of using a ratio scale to find the real-world distance. Remember to convert the final answer to kilometers for ease of understanding.

Question 2: A municipal park is 250 meters long. On a plan, its length is shown as 5 cm. Determine the scale of the plan. Express your answer as a ratio scale.