Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Calculate the cost of painting a house.
• Determine the most cost-effective travel option.
• Analyse municipal water bills.
• Compare packaging options based on volume and cost.

Lesson summary

This week, we delve into the practical applications of measurement, focusing on scenarios that require more than just simple formulas. We'll explore complex, real-life situations relevant to South African learners, enabling you to make informed decisions and solve problems effectively. This is crucial because understanding measurement allows you to budget for home improvements, calculate travel expenses, interpret municipal bills, and make informed consumer choices, all vital skills for independent living and participation in the South African economy. We are focusing on scenarios involving multiple calculations, different units, and decision-making based on measured values.

Lesson notes

This week focuses on applying measurement principles to complex, real-world problems. We'll build upon your existing knowledge of area, volume, perimeter, and cost calculations.

Here's a breakdown of key concepts: 2.1 Calculating Area: Understanding Different Shapes: We need to be comfortable calculating the area of rectangles, squares, triangles, and circles.

Remember the formulas: Rectangle: Area = length × width Square: Area = side × side Triangle: Area = ½ × base × height Circle: Area = π × radius² (where π ≈ 3.142)

Compound Shapes: Real-life often presents shapes that are combinations of basic shapes. To find the area of a compound shape, divide it into simpler shapes, calculate the area of each, and then add them together.

Surface Area: The surface area of a 3D object is the total area of all its faces. For a rectangular prism (like a box), the surface area is 2(lw + lh + wh), where l = length, w = width, and h = height. 2.2 Calculating Volume: Understanding Different Solids: We'll deal with rectangular prisms, cubes, cylinders, and potentially spheres.

Remember the formulas: Rectangular Prism: Volume = length × width × height Cube: Volume = side³ Cylinder: Volume = π × radius² × height Sphere: Volume = (4/3) × π × radius³ 2.3 Unit Conversions: Importance of Consistency: Always ensure that all measurements are in the same units before performing calculations.

Common Conversions: Know these conversions well: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 liter (L) = 1000 milliliters (mL) 1 liter (L) = 1000 cubic centimeters (cm³) 2.4 Cost Calculations: Unit Cost: The cost per unit of a product (e.g., Rands per liter).

Total Cost: Unit Cost × Number of Units Percentage Calculations: Useful for calculating discounts, VAT (Value Added Tax), and markups.

Remember: Percentage = (Part / Whole) × 100 2.5 Municipal Bills: Understanding Tariffs: Municipalities charge different rates for water and electricity consumption based on usage. Higher consumption often means higher tariffs (stepped tariffs).

Fixed Charges: Some bills include fixed monthly charges regardless of consumption.

Calculating Consumption: Consumption is the difference between the current meter reading and the previous meter reading. 2.6 Fuel Consumption: Liters per 100km (L/100km): A common way to express fuel consumption. A lower number indicates better fuel efficiency.

Calculating Fuel Cost: (Distance / 100) × Fuel Consumption (L/100km) × Price per Liter

Worked example

Example 1: Painting a Room

A rectangular room is 4m long, 3m wide, and 2.5m high. You want to paint the walls. There is a door (0.8m wide and 2m high) and a window (1.5m wide and 1.2m high). One liter of paint covers 10m². Paint costs R120 per liter. Calculate the total cost of the paint needed.

Step 1: Calculate the area of the walls:

Perimeter of the room = 2(4m + 3m) = 14m

Total wall area = 14m × 2.5m = 35m²

Step 2: Calculate the area of the door and window:

Door area = 0.8m × 2m = 1.6m²

Window area = 1.5m × 1.2m = 1.8m²

Step 3: Calculate the paintable area:

Paintable area = 35m² - 1.6m² - 1.8m² = 31.6m²

Step 4: Calculate the amount of paint needed:

Paint needed = 31.6m² / 10m²/liter = 3.16 liters. Since you can't buy fractions of a liter, you need to buy 4 liters.

Step 5: Calculate the total cost:

Total cost = 4 liters × R120/liter = R480

Example 2: Travel Costs

You are driving from Johannesburg to Durban, a distance of 560km. Your car's fuel consumption is 8L/100km. Fuel costs R22/liter. There are R150 toll fees along the route. Calculate the total cost of the journey.

Step 1: Calculate the amount of fuel needed:

Fuel needed = (560km / 100km) × 8L = 44.8L

Step 2: Calculate the fuel cost:

Fuel cost = 44.8L × R22/L = R985.60

Step 3: Calculate the total cost:

Total cost = R985.60 + R150 = R1135.60