Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate perimeter of 2D shapes in real-world scenarios.
• Calculate area of 2D shapes to solve practical problems.
• Calculate volume of 3D shapes to solve practical problems.
• Convert between different units of measurement.
• Solve multi-step problems involving perimeter, area, and volume.

Lesson summary

Measurement is a fundamental skill in mathematical literacy, impacting our daily lives in countless ways. From planning a garden to calculating the cost of building materials, understanding perimeter, area, and volume is crucial for informed decision-making. In a South African context, these skills are particularly relevant for activities like small-scale farming, home improvement projects, and understanding municipal services. This week, we focus on applying these concepts to practical situations and solving problems relevant to our everyday experiences.

Lesson notes

2.1 Perimeter: Perimeter is the total distance around the outside of a two-dimensional shape. It's like walking around the edges of a field – the total distance you walk is the perimeter.

Rectangle: Perimeter = 2 × (length + width) or P = 2(l + w)

Square: Perimeter = 4 × side length or P = 4s Triangle: Perimeter = sum of all three sides or P = a + b + c Circle: Perimeter is called the circumference. Circumference = π × diameter or C = πd, where π (pi) is approximately 3.

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2. Example 1: A farmer in Limpopo wants to fence a rectangular vegetable garden. The garden is 15 meters long and 8 meters wide. How much fencing does the farmer need?

Solution: Perimeter = 2(length + width) = 2(15m + 8m) = 2(23m) = 46 meters The farmer needs 46 meters of fencing. 2.2 Area: Area is the amount of space inside a two-dimensional shape. It's like measuring the amount of carpet needed to cover a floor.

Rectangle: Area = length × width or A = l × w Square: Area = side length × side length or A = s² Triangle: Area = ½ × base × height or A = ½bh Circle: Area = π × radius² or A = πr², where r is the radius (half the diameter).

Example 2: A homeowner in Gauteng wants to tile a rectangular bathroom floor. The floor is 3 meters long and 2 meters wide. Each tile is a square with a side length of 30 cm. How many tiles are needed?

Solution: First, convert everything to the same units.

Let's use centimeters: Floor length = 3 meters = 300 cm Floor width = 2 meters = 200 cm Area of the floor = length × width = 300 cm × 200 cm = 60000 cm² Area of one tile = side × side = 30 cm × 30 cm = 900 cm² Number of tiles needed = (Area of the floor) / (Area of one tile) = 60000 cm² / 900 cm² = 66.67 Since you can't buy a fraction of a tile, you need to round up to 67 tiles. 2.3 Volume: Volume is the amount of space inside a three-dimensional object. It's like measuring how much water a container can hold.

Rectangular Prism (Cuboid): Volume = length × width × height or V = lwh Cube: Volume = side length × side length × side length or V = s³ Cylinder: Volume = π × radius² × height or V = πr²h Cone: Volume = (1/3) × π × radius² × height or V = (1/3)πr²h Example 3: A community in the Eastern Cape wants to build a cylindrical water tank to store rainwater. The tank has a radius of 1.5 meters and a height of 3 meters. What is the volume of the tank in liters?

Solution: Volume = π × radius² × height = π × (1.5m)² × 3m ≈ 3.142 × 2.25m² × 3m ≈ 21.21 m³ Since 1 m³ = 1000 liters, the volume of the tank in liters is 21.21 m³ × 1000 liters/m³ = 21210 liters. 2.4 Unit Conversions: It is important to be comfortable converting between different units of measurement.

Here are some common conversions: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 liter (L) = 1000 milliliters (mL) 1 m³ = 1000 liters (L) Guided Practice (With Solutions)

Question 1: A gardener wants to build a rectangular flower bed with a length of 4 meters and a width of 2.5 meters. They want to put edging around the flower bed. How much edging will they need?

Solution: Perimeter = 2(length + width) = 2(4m + 2.5m) = 2(6.5m) = 13 meters The gardener needs 13 meters of edging. This question directly applies the perimeter formula for a rectangle. We calculated the perimeter by substituting the given length and width into the formula.

Question 2: A school is painting a wall in the shape of a triangle. The base of the triangle is 6 meters and the height is 3 meters. How much paint do they need if one liter of paint covers 4 square meters?

Solution: Area of the triangle = ½ × base × height = ½ × 6m × 3m = 9 m² Amount of paint needed = (Area of the wall) / (Coverage per liter) = 9 m² / 4 m²/liter = 2.25 liters They need 2.25 liters of paint. We first found the area of the triangular wall using the appropriate formula. Then, we divided the total area by the coverage of one liter of paint to determine the amount of paint needed.

Question 3: A municipality is building a cylindrical water tank with a diameter of 4 meters and a height of 5 meters. What is the volume of the tank in cubic meters?

Solution: Radius = diameter / 2 = 4m / 2 = 2m Volume = π × radius² × height = π × (2m)² × 5m ≈ 3.142 × 4m² × 5m ≈ 62.84 m³ The volume of the tank is approximately 62.84 cubic meters. This problem reinforces the application of the cylinder volume formula. Remember to calculate the radius from the diameter first. Independent Practice (Questions Only) A farmer wants to fence a square piece of land with a side length of 35 meters. How much fencing will they need? A rectangular room is 5 meters long and 4 meters wide. What is the area of the room? A circular swimming pool has a diameter of 8 meters. What is the area of the surface of the pool? A cylindrical storage container has a radius of 1 meter and a height of 2 meters. What is the volume of the container? A cone-shaped pile of sand has a radius of 2 meters and a height of 1.5 meters. What is the volume of the sand?