Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Interpret and use different types of scales.
• Apply scale to calculate real-world distances and areas.
• Use maps and plans to determine routes and estimate travel times.
• Construct basic scale drawings.
• Compare information on different maps and plans.

Lesson summary

This week, we delve into the practical applications of measurement focusing on scales, maps, and plans. These are fundamental skills that enable us to interpret and use information represented in scaled formats, crucial for navigating our environment, understanding spatial relationships, and making informed decisions in various aspects of life, from planning a road trip to understanding architectural drawings. In South Africa, with its diverse landscapes and varying levels of access to technology, the ability to interpret maps and plans is especially important for planning, resource management, and ensuring effective communication.

Lesson notes

2.1 Understanding Scale: Scale is the ratio between the distance on a map, plan, or model and the corresponding distance on the ground. It allows us to represent large areas or objects in a manageable size.

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

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0. This means that one unit of measurement on the map represents 50,000 of the same units in reality. If the unit is centimeters, then 1 cm on the map equals 50,000 cm in reality.

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

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 enlarged or reduced. 2.2 Converting between Scales: It's crucial to be able to convert between different types of scales.

For example: Converting Numerical Scale to Verbal Scale: If a numerical scale is 1:100,000, we can convert this to a verbal scale. Since 100,000 cm is equal to 1 km (because 100 cm = 1 m and 1000 m = 1 km), the verbal scale is "1 cm represents 1 km." Converting Verbal Scale to Numerical Scale: If a verbal scale is "2 cm represents 5 km," we need to express both measurements in the same units. 5 km is equal to 500,000 cm (because 1 km = 1000 m and 1 m = 100 cm).

Therefore, the numerical scale is 2:500,000, which can be simplified to 1:250,000. 2.3 Using Scale to Calculate Real-World Distances: Measure the distance on the map or plan using a ruler. Ensure you are using the correct units (e.g., cm, mm). Identify the scale of the map or plan. Apply the scale to convert the map distance to the real-world distance.

Example: On a map with a scale of 1:50,000, the distance between two towns measures 8 cm. What is the actual distance between the towns?

Solution: 1 cm on the map represents 50,000 cm in reality.

Therefore, 8 cm represents 8 50,000 cm = 400,000 cm.

Converting this to kilometers: 400,000 cm = 4,000 m = 4 km. The actual distance between the towns is 4 km. 2.4 Calculating Area Using Scale: When dealing with area, remember that the scale applies to both dimensions (length and width).

Therefore, you need to square the scale factor.

Example: A rectangular field measures 5 cm by 3 cm on a map with a scale of 1:10,

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0. What is the actual area of the field in square meters?

Solution:* First, find the real-world dimensions.

Length: 5 cm 10,000 = 50,000 cm = 500 m Width: 3 cm 10,000 = 30,000 cm = 300 m Area: Length Width = 500 m * 300 m = 150,000 square meters. 2.5 Interpreting Maps and Plans: Maps: Provide an overview of a geographical area, showing features such as roads, rivers, mountains, and towns. They use symbols and colors to represent different features (a legend or key explains these symbols).

Plans (Architectural Drawings): Detailed drawings of buildings or structures, showing dimensions, materials, and layout. They are used by architects, builders, and engineers. 2.6 Common Mistakes and How to Avoid Them: Incorrect Unit Conversions: Always double-check that you are using consistent units before performing calculations. Remember the relationships between cm, m, and km. Forgetting to Square the Scale Factor when Calculating Area: The scale applies to both dimensions, so you must square it.

Misinterpreting the Map Legend: Always refer to the map legend to understand the meaning of symbols and colors. Guided Practice (With Solutions)

Question 1: A road on a map measures 12 cm.

The map has a scale of 1:250,

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0. Calculate the actual length of the road in kilometers.

Solution:* 1 cm on the map represents 250,000 cm in reality. 12 cm on the map represents 12 250,000 cm = 3,000,000 cm Convert cm to km: 3,000,000 cm = 30,000 m = 30 km Therefore, the actual length of the road is 30 km.

Commentary:* This question requires a straightforward application of the scale factor. Emphasize the importance of unit conversion.

Question 2: A rectangular park measures 4 cm by 6 cm on a plan with a scale of 1 cm = 5 meters. What is the actual area of the park in square meters?

Solution:* Length: 4 cm 5 m/cm = 20 m Width: 6 cm 5 m/cm = 30 m Area = Length Width = 20 m * 30 m = 600 square meters.

Commentary:* This question reinforces the understanding of area calculation using scaled dimensions.

Question 3: The distance between Johannesburg and Durban is approximately 560 km. On a map, this distance is represented by 28 cm. Determine the scale of the map in the form 1:

X. Solution:* 28 cm on the map represents 560 km in reality.

Convert 560 km to cm: 560 km = 560,000 m = 56,000,000 cm The ratio is 28:56,000,

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0. Divide both sides by 28 to simplify: 1:2,000,000 Therefore, the scale of the map is 1:2,000,000.