Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Calculate the area of compound shapes.
• Determine the surface area of rectangular prisms.
• Calculate the volume of rectangular prisms.
• Solve real-world problems using these skills.
• Use the correct units like cm², m², cm³, and m³.

Lesson summary

This week, we delve deeper into the exciting world of measurement, focusing on area, surface area, and volume. Understanding these concepts is crucial because they help us make sense of the space around us. Think about building a shack in Khayelitsha – you need to know how much material to buy (area and surface area) and how much space you have inside (volume). Farmers need to calculate field sizes and water tank capacities. Even baking a cake requires an understanding of volume! This topic equips you with practical skills for everyday life and future careers.

Lesson notes

2.1 Area: Compound Shapes Area is the amount of surface a two-dimensional shape covers. We've already looked at the area of simple shapes like rectangles and squares (Area of a rectangle = Length x Width, Area of a square = Side x Side). But what happens when we have shapes that aren't simple rectangles or squares? These are called compound shapes. To find the area of a compound shape, we need to decompose (break it down) into simpler shapes like rectangles and squares. Then, we find the area of each simple shape and add them together.

Example 1: Imagine a floor plan for a small spaza shop. It’s L-shaped. One section is 5m long and 3m wide. The other section is 2m long and 2m wide. What's the total floor area?

Step 1: Decompose the shape. We can divide the L-shape into two rectangles.

Step 2: Calculate the area of each rectangle.

Rectangle 1: Length = 5m, Width = 3m. Area = 5m x 3m = 15m 2 Rectangle 2: Length = 2m, Width = 2m. Area = 2m x 2m = 4m 2 Step 3: Add the areas together. Total Area = 15m 2 + 4m 2 = 19m 2 Therefore, the total floor area of the spaza shop is 19 square meters. 2.2 Surface Area: Rectangular Prisms Surface area is the total area of all the faces of a three-dimensional object. A rectangular prism is like a box – it has six faces, all of which are rectangles. Think of a corrugated cardboard box used for packing goods in a factory. To find the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them all together. Remember that a rectangular prism has three pairs of identical faces (the front and back, the top and bottom, and the two sides).

Formula: Surface Area = 2(lw) + 2(lh) + 2(wh) where l = length, w = width, and h = height Example 2: A builder is creating a concrete block that's a rectangular prism. It’s 30cm long, 20cm wide, and 10cm high. What's the total surface area of the block?

Step 1: Identify the dimensions: Length (l) = 30cm Width (w) = 20cm Height (h) = 10cm Step 2: Calculate the area of each pair of faces: Front and Back: Area = 2(l x h) = 2(30cm x 10cm) = 2(300cm 2 ) = 600cm 2 Top and Bottom: Area = 2(l x w) = 2(30cm x 20cm) = 2(600cm 2 ) = 1200cm 2 Sides: Area = 2(w x h) = 2(20cm x 10cm) = 2(200cm 2 ) = 400cm 2 Step 3: Add the areas together. Total Surface Area = 600cm 2 + 1200cm 2 + 400cm 2 = 2200cm 2 Therefore, the total surface area of the concrete block is 2200 square centimeters. 2.3 Volume: Rectangular Prisms Volume is the amount of space a three-dimensional object occupies. It tells us how much something can hold. Think about the volume of a water tank – it tells us how much water it can store. The volume of a rectangular prism is found by multiplying its length, width, and height.

Formula: Volume = Length x Width x Height (V = lwh)

Example 3: A community garden needs a new compost bin. They want to build a rectangular prism-shaped bin that is 1.5m long, 1m wide, and 0.8m high. How much compost can the bin hold?

Step 1: Identify the dimensions: Length (l) = 1.5m Width (w) = 1m Height (h) = 0.8m Step 2: Calculate the volume: Volume = l x w x h = 1.5m x 1m x 0.8m = 1.2m 3 Therefore, the compost bin can hold 1.2 cubic meters of compost. Guided Practice (With Solutions)

Question 1: A farmer wants to fence off a vegetable patch. The patch is shaped like a rectangle with a smaller rectangular section removed for a tool shed. The large rectangle is 8m long and 5m wide. The tool shed section is 2m long and 1m wide. What is the area of the vegetable patch that needs fencing?

Solution: Step 1: Calculate the area of the large rectangle: Area = Length x Width = 8m x 5m = 40m 2 Step 2: Calculate the area of the tool shed rectangle: Area = Length x Width = 2m x 1m = 2m 2 Step 3: Subtract the area of the tool shed from the area of the large rectangle: Vegetable Patch Area = 40m 2 - 2m 2 = 38m 2 Answer: The area of the vegetable patch that needs fencing is 38m 2 .

Question 2: A tuck shop is selling boxes of sweets. Each box is a rectangular prism with a length of 25cm, a width of 10cm, and a height of 5cm. How much cardboard is needed to make one box (i.e., what is the surface area)?

Solution: Step 1: Identify the dimensions: Length (l) = 25cm Width (w) = 10cm Height (h) = 5cm Step 2: Calculate the area of each pair of faces: Front and Back: Area = 2(l x h) = 2(25cm x 5cm) = 2(125cm 2 ) = 250cm 2 Top and Bottom: Area = 2(l x w) = 2(25cm x 10cm) = 2(250cm 2 ) = 500cm 2 Sides: Area = 2(w x h) = 2(10cm x 5cm) = 2(50cm 2 ) = 100cm 2 Step 3: Add the areas together. Total Surface Area = 250cm 2 + 500cm 2 + 100cm 2 = 850cm 2 Answer: 850 cm 2 of cardboard is needed.

Question 3: A bricklayer is building a small water feature. He uses a rectangular container that is 60cm long, 40cm wide, and 30cm high. How much water can the container hold (what is the volume)?