Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret and analyze maps and plans.
• Use scales to calculate actual distances and dimensions.
• Apply these skills to solve real-world problems.
• Calculate costs for projects based on plans.
• Compare plans to find the most cost-effective option.

Lesson summary

This week, we delve into the vital skill of interpreting and using maps, plans, and other visual representations to make informed decisions. In South Africa, where access to resources and opportunities can vary greatly, the ability to understand and utilize these representations is crucial for navigating daily life, planning for the future, and participating effectively in society. Whether it's understanding transport routes, interpreting building plans, or comparing data presented in graphs, these skills empower you to make informed choices. This week specifically focuses on practical application of these skills in various scenarios.

Lesson notes

2.1 Understanding Maps and Scale A map is a visual representation of an area, whether it's a city, a country, or even the entire world. The scale of a map is the ratio that compares a distance on the map to the corresponding distance on the ground. This is crucial because it allows us to translate measurements taken on the map to real-world distances.

There are three main types of map scales: Verbal Scale: This expresses the relationship in words, such as "1 cm represents 1 kilometer." This is easy to understand but less precise.

Ratio Scale (Representative Fraction): This is written as a ratio, like 1:100,

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0. This means that 1 unit of measurement on the map represents 100,000 of the same units on the ground. For example, 1 cm on the map equals 100,000 cm (or 1 km) in reality. The units MUST be the same on both sides.

Linear Scale (Graphic Scale): This is a line divided into segments that represent specific distances on the ground. You can use a ruler or a piece of paper to measure distances on the map and then compare them to the linear scale to determine the actual distance.

Example 1: Converting Map Distance to Real Distance A map has a scale of 1:50,

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0. The distance between two towns on the map is 8 cm. What is the actual distance between the towns in kilometers?

Step 1: Understand the scale. 1 cm on the map = 50,000 cm in reality.

Step 2: Calculate the real distance in cm: 8 cm (map) 50,000 cm/cm (scale) = 400,000 cm Step 3: Convert cm to km: 400,000 cm / 100 cm/m / 1000 m/km = 4 km Therefore, the actual distance between the towns is 4 km.

Example 2: Using a Linear Scale Imagine a map with a linear scale where 1 segment of 2 cm represents 5 km. You measure a road on the map and it covers 3 segments of the linear scale. What is the actual length of the road?

Step 1: Determine the distance represented by one segment: 2 cm = 5 km Step 2: Calculate the total distance: 3 segments 5 km/segment = 15 km The actual length of the road is 15 km. 2.2 Interpreting Plans and Drawings Plans and drawings, such as building plans or furniture assembly diagrams, provide visual instructions for creating or understanding a structure or object.

They often include: Dimensions: Indicate the size of different parts of the object or structure. Look for units of measurement (mm, cm, m).

Scale: Similar to maps, plans often use a scale to represent the real size of the object.

Symbols and Legends: Explain what different lines, shapes, and colors represent in the plan. Examples include symbols for doors, windows, electrical outlets, or plumbing fixtures.

Elevations: Show the vertical view of the structure or object.

Floor Plans: Show a top-down view of the layout of a building or room.

Example 3: Interpreting a Building Plan A building plan for a rectangular room has a scale of 1:

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0. The length of the room on the plan is 10 cm and the width is 6 cm. Calculate the actual area of the room in square meters.

Step 1: Calculate the actual length: 10 cm 50 = 500 cm = 5 m Step 2: Calculate the actual width: 6 cm 50 = 300 cm = 3 m Step 3: Calculate the area: 5 m 3 m = 15 square meters The actual area of the room is 15 square meters. 2.3 Costing and Project Planning Many real-life decisions require costing and planning. This includes calculating material costs, labour costs and overall budgets.

Example 4: Project Planning You are planning to build a small rectangular garden in your backyard. The dimensions of the garden are 4m x 3m.

The costs are: Bricks = R200 per meter Soil = R50 per square meter Labour = R400 Calculate the total cost of this project.

Step 1: Calculate the perimeter to determine the meters of brick needed. Perimeter = (4m+3m) x 2 = 14m Step 2: Calculate the cost of the bricks 14m x R200/m = R2800 Step 3: Calculate the area to determine the meters of soil needed. Area = 4m x 3m = 12 square meters Step 4: Calculate the cost of the soil 12 square meters x R50 per square meter = R600 Step 5: Calculate the total cost R2800 + R600 + R400 = R3800 Why is understanding scale so important? Imagine you're using a map to plan a road trip from Johannesburg to Durban. If you misinterpret the scale, you might underestimate the distance and not allocate enough time or fuel for the journey. This could lead to significant delays and unexpected costs. Similarly, when working with building plans, accurately interpreting dimensions is crucial to ensure that structures are built according to specifications and that materials are ordered correctly. Failure to do so can result in costly errors and structural problems. Guided Practice (With Solutions)

Question 1: A map of Gauteng has a scale of 1:250,

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