Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Solve complex problems involving area, perimeter, volume, and capacity.
• Convert between different units of measurement (metric and imperial).
• Apply scale and proportion to maps and blueprints.
• Estimate measurements and judge the reasonableness of answers.
• Interpret measurement data from tables, graphs, and diagrams.

Lesson summary

This week, we delve into complex applications of measurement, building on your prior knowledge of basic measurement concepts from previous grades. Measurement isn't just about finding lengths or volumes; it's a critical skill used in various real-world scenarios, from planning a community garden to understanding national infrastructure projects. In the South African context, these skills are essential for informed citizenship, entrepreneurship, and participation in the workforce. We'll be tackling problems that require you to combine multiple measurement skills and apply them in practical, relevant situations.

Lesson notes

This week centers around applying your existing measurement knowledge in more challenging and realistic scenarios.

Let's break down some key areas: 2.1 Combining Measurements: Many real-world problems require combining multiple types of measurements. For example, calculating the total cost of tiling a room requires knowing the area of the room, the cost per square meter of the tiles, and potentially the perimeter for edge finishing.

Example 1: Tiling a Kitchen A homeowner in Soweto wants to tile their kitchen floor, which is 4.5 meters long and 3 meters wide. The tiles they like cost R120 per square meter. They also want to install skirting boards around the perimeter, costing R35 per meter. Calculate the total cost of tiling the kitchen.

Step 1: Calculate the Area: Area = Length x Width Area = 4.5m x 3m = 13.5 m² Step 2: Calculate the Cost of the Tiles: Cost of tiles = Area x Price per m² Cost of tiles = 13.5 m² x R120/m² = R1620 Step 3: Calculate the Perimeter: Perimeter = 2 x (Length + Width) Perimeter = 2 x (4.5m + 3m) = 15m Step 4: Calculate the Cost of the Skirting Boards: Cost of skirting boards = Perimeter x Price per meter Cost of skirting boards = 15m x R35/m = R525 Step 5: Calculate the Total Cost: Total Cost = Cost of tiles + Cost of skirting boards Total Cost = R1620 + R525 = R2145 Therefore, the total cost of tiling the kitchen is R2145. 2.2 Unit Conversions: It's crucial to be comfortable converting between different units. This is especially relevant in South Africa due to its history and the ongoing use of both metric and imperial units in some contexts. We may need to convert liters to milliliters, meters to centimeters, or even kilograms to pounds (although less common).

Remember the following key conversions: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 liter (L) = 1000 milliliters (mL)

Example 2: Importing Fabric A seamstress in Durban imports fabric from the UK. A roll of fabric is advertised as 50 yards long. She needs to order enough fabric to make 60 dresses, and each dress requires 1.5 meters of fabric. Should she buy one roll?

Step 1: Convert yards to meters: 1 yard ≈ 0.9144 meters 50 yards ≈ 50 x 0.9144 meters = 45.72 meters Step 2: Calculate the total fabric needed: Total fabric = Number of dresses x Fabric per dress Total fabric = 60 dresses x 1.5 meters/dress = 90 meters Step 3: Compare the fabric needed to the fabric available: She needs 90 meters of fabric, but the roll only provides 45.72 meters.

Conclusion: No, she should not buy only one roll. She needs at least two rolls. 2.3 Scale and Proportion: Maps, blueprints, and models are all examples of scaled representations. Understanding scale allows us to calculate real-world dimensions from these representations.

A scale of 1:100 means that 1 unit on the map or blueprint represents 100 units in reality.

Example 3: Building a Model House An architecture student in Cape Town is building a scale model of a house. The house is 12 meters long and 8 meters wide.

She is using a scale of 1:

5

0. What are the dimensions of the model?

Step 1: Convert real-world dimensions to centimeters: Length of house = 12m = 1200 cm Width of house = 8m = 800 cm Step 2: Apply the scale: Model Length = Real Length / Scale factor Model Length = 1200 cm / 50 = 24 cm Model Width = Real Width / Scale factor Model Width = 800 cm / 50 = 16 cm Therefore, the model house will be 24 cm long and 16 cm wide. 2.4 Estimation and Reasonableness: Always estimate before calculating and check if your final answer seems reasonable. For instance, if you're calculating the volume of a room, and you get an answer of 500 cubic meters, ask yourself if that seems realistic for a normal-sized room.

Example 4: Estimating Paint You want to paint your lounge. The room is roughly 4 meters long, 3 meters wide, and 2.5 meters high. A 5-liter can of paint covers approximately 60 square meters. Estimate how many cans of paint you will need.

Step 1: Estimate the surface area to be painted: We'll ignore windows and doors for this rough estimate. Two walls are 4m x 2.5m = 10 m² each (20m²) Two walls are 3m x 2.5m = 7.5 m² each (15m²) Total wall area ≈ 20 m² + 15 m² = 35 m² We often need two coats of paint, so 35 m² x 2 = 70 m² to be painted.

Step 2: Calculate the number of paint cans: Number of cans ≈ Total area / Area covered by one can Number of cans ≈ 70 m² / 60 m² per can ≈ 1.17 cans Reasonableness: Since you can't buy 0.17 of a can, you would need to buy 2 cans of paint. This is a reasonable estimate for painting a small lounge. Guided Practice (With Solutions)

Question 1: A farmer in Limpopo has a rectangular field that is 150 meters long and 80 meters wide. He wants to fence the field. Fencing costs R45 per meter. What will be the total cost of the fence?