Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve complex conversion problems (metric & imperial).
• Calculate areas and volumes of complex shapes.
• Interpret and use scale drawings and maps.
• Apply measurement to financial calculations (costing, VAT).
• Analyse measurement data from tables and graphs.

Lesson summary

This week, we delve deeper into the practical applications of measurement, focusing on more complex real-life scenarios. Measurement is crucial not just in academic settings, but also in everyday life, impacting decisions related to budgeting, construction, cooking, travel, and many other areas. Understanding measurement empowers you to make informed choices and solve problems effectively. In South Africa, these skills are particularly important for navigating economic challenges and contributing to community development through informed participation in projects and initiatives.

Lesson notes

2.1 Unit Conversions: Metric and Imperial Systems While South Africa primarily uses the metric system, understanding the imperial system is still important, especially when dealing with imported goods or historical data. Conversion factors allow us to move between these systems.

Common conversions include: 1 inch (in) = 2.54 centimetres (cm) 1 foot (ft) = 30.48 cm = 0.3048 metres (m) 1 yard (yd) = 0.9144 m 1 mile = 1.609 kilometres (km) 1 pound (lb) = 0.4536 kilograms (kg) 1 gallon (gal) = 3.785 litres (L)

Example 1: A container of paint imported from the US has a volume of 5 gallons. How many litres of paint are in the container?

Solution: 5 gallons 3.785 litres/gallon = 18.925 litres.

Therefore, the container holds approximately 18.93 litres. 2.2 Areas and Volumes of Complex Shapes Many real-world objects are not simple shapes like squares or cubes. We need to break them down into simpler components, calculate the area or volume of each, and then add them together.

Example 2: A farmer wants to build a kraal (livestock enclosure) with a rectangular section measuring 10m x 8m and a semi-circular section attached to one of the shorter sides. Calculate the total area of the kraal.

Solution: Area of the rectangular section: 10m 8m = 80 m² Radius of the semi-circular section: 8m / 2 = 4m Area of the semi-circular section: (1/2) π (4m)² ≈ (1/2) 3.14159 * 16 m² ≈ 25.13 m² Total area of the kraal: 80 m² + 25.13 m² = 105.13 m² Example 3: Calculate the volume of a cylindrical water tank with a diameter of 2m and a height of 3m. Then, convert this volume to litres.

Solution: Radius of the tank: 2m / 2 = 1m Volume of the cylinder: π (1m)² 3m ≈ 3.14159 1 m² * 3m ≈ 9.42 m³ Conversion to litres: 1 m³ = 1000 L Volume in litres: 9.42 m³ 1000 L/m³ = 9420 L 2.3 Scale Drawings and Maps Scale drawings and maps represent real-world objects or areas in a smaller, proportional size. The scale indicates the ratio between the drawing/map distance and the actual distance.

Example 4: A map has a scale of 1:50,

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0. Two towns are 7 cm apart on the map. What is the actual distance between the towns in kilometers?

Solution: Actual distance in cm: 7 cm 50,000 = 350,000 cm Conversion to meters: 350,000 cm / 100 cm/m = 3500 m Conversion to kilometers: 3500 m / 1000 m/km = 3.5 km 2.4 Measurement in Financial Calculations Measurement is often intertwined with financial decisions. Calculating the cost of materials requires understanding area, volume, and unit prices.

Example 5: A builder needs to tile a rectangular floor that measures 4m x 3m. Tiles cost R120 per square meter. Calculate the total cost of the tiles, including 15% VA

T. Solution: Area of the floor: 4m 3m = 12 m² Cost of tiles before VAT: 12 m² R120/m² = R1440 VAT amount: R1440 0.15 = R216 Total cost of tiles (including VAT): R1440 + R216 = R1656 2.5 Data Analysis and Interpretation Measurement data is frequently presented in tables, graphs, and charts. Being able to extract meaningful information from these representations is vital.

Example 6: A table shows the daily water consumption of a household in litres for a week. Analyze the data to determine the average daily water consumption. (Assume a table with daily water consumption is provided. The average is calculated by summing the daily consumptions and dividing by 7). Guided Practice (With Solutions)

Question 1: A recipe calls for 2 cups of milk. If 1 cup is approximately 250 ml, how many litres of milk are needed for the recipe?

Solution: Total ml needed: 2 cups 250 ml/cup = 500 ml Conversion to litres: 500 ml / 1000 ml/L = 0.5 L Answer: 0.5 litres of milk are needed.

Question 2: A rectangular garden is 8 meters long and 5 meters wide. A path 1 meter wide is built around the garden. Calculate the area of the path.

Solution: Dimensions of the garden with the path: (8 + 1 + 1)m x (5 + 1 + 1)m = 10m x 7m Area of the garden with the path: 10m 7m = 70 m² Area of the garden: 8m 5m = 40 m² Area of the path: 70 m² - 40 m² = 30 m² Answer: The area of the path is 30 m².

Question 3: A blueprint of a house is drawn to a scale of 1:

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0. On the blueprint, the living room is 6 cm long and 4 cm wide. What is the actual area of the living room in square meters?

Solution: Actual length: 6 cm 100 = 600 cm = 6 m Actual width: 4 cm 100 = 400 cm = 4 m Actual area: 6 m 4 m = 24 m² Answer: The actual area of the living room is 24 m². Independent Practice (Questions Only) Convert 3.5 miles to kilometers. A cylindrical storage tank has a radius of 1.5 meters and a height of 4 meters. Calculate its volume in cubic meters.

A map has a scale of 1:25,

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0. If two points are 12 cm apart on the map, what is the actual distance between them in kilometers? A rectangular swimming pool is 10m long, 5m wide and 2m deep. Calculate the volume of water (in litres) needed to fill the pool to 80% of its capacity. Carpet costs R85 per square meter. A room is 4.5m long and 3.8m wide. Calculate the total cost of carpeting the room, including 15% VAT.