Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Calculate perimeter of squares and rectangles.
• Calculate area of squares and rectangles.
• Find the volume of rectangular prisms by counting cubes.
• Solve word problems using perimeter, area, and volume.
• Know when to use perimeter, area, or volume.

Lesson summary

This week, we're diving into the exciting world of measurement! We'll be exploring perimeter, area, and volume, which are essential skills used every day, from figuring out how much fencing you need for a garden to determining how much water your Jojo tank can hold. In South Africa, understanding measurement helps us with things like planning community gardens, building homes, and even understanding the sizes of land areas. For example, imagine you are helping your family build a kraal for your goats – you need to know the perimeter to calculate how much fencing to buy, and the area to ensure enough grazing space.

Lesson notes

2.1 Perimeter: Perimeter is the total distance around the outside of a two-dimensional (2D) shape. Imagine walking all the way around a field – the total distance you walk is the perimeter. It's like putting a fence around the shape. We measure perimeter in units of length, like centimetres (cm), metres (m), kilometres (km), millimetres (mm)

Rectangle: A rectangle has two pairs of equal sides: length (l) and breadth (b). The formula for the perimeter of a rectangle is: Perimeter = 2 x (length + breadth) OR Perimeter = 2l + 2b OR Perimeter = length + breadth + length + breadth Square: A square has four equal sides. The formula for the perimeter of a square is: Perimeter = 4 x side (s) OR Perimeter = s + s + s + s Example 1: Rectangle A farmer wants to fence his vegetable patch, which is rectangular. The patch is 8 metres long and 5 metres wide. How much fencing does he need?

Solution: Perimeter = 2 x (length + breadth) Perimeter = 2 x (8m + 5m) Perimeter = 2 x 13m Perimeter = 26m He needs 26 metres of fencing.

Example 2: Square A soccer field is a square with sides of 90 meters each. How much running distance does a player cover when running around the field once?

Solution: Perimeter = 4 x side Perimeter = 4 x 90m Perimeter = 360m The player covers 360 meters. 2.2 Area: Area is the amount of space a two-dimensional (2D) shape covers. Imagine covering a floor with tiles – the area is the number of tiles needed. We measure area in square units, like square centimetres (cm²), square metres (m²), square kilometres (km²).

Rectangle: The formula for the area of a rectangle is: Area = length x breadth OR Area = l x b Square: The formula for the area of a square is: Area = side x side OR Area = s x s OR Area = s² Example 3: Rectangle A woman wants to tile her kitchen floor. The kitchen is 4 metres long and 3 metres wide. How many square metres of tiles does she need?

Solution: Area = length x breadth Area = 4m x 3m Area = 12m² She needs 12 square metres of tiles.

Example 4: Square A farmer plants mielies in a square plot of land that is 15 meters on each side. What is the area of the plot?

Solution: Area = side x side Area = 15m x 15m Area = 225m² The area of the plot is 225 square meters. 2.3 Volume: Volume is the amount of space a three-dimensional (3D) object occupies. Imagine filling a box with sugar – the volume is the amount of sugar the box can hold. We measure volume in cubic units, like cubic centimetres (cm³), cubic metres (m³). For Grade 5, we'll focus on rectangular prisms. A rectangular prism is like a box. To find the volume of a rectangular prism by packing and counting, imagine filling the box with small cubes, each with a side length of 1cm. The number of cubes needed to fill the box completely is the volume in cubic centimetres. Volume is also equal to length x breadth x height (l x b x h).

Example 5: Rectangular Prism A shoebox is 30 cm long, 20 cm wide, and 10 cm high. What is the volume of the shoebox?

Solution: Volume = length x breadth x height Volume = 30cm x 20cm x 10cm Volume = 6000cm³ The volume of the shoebox is 6000 cubic centimetres. We could fit 6000 cubes that are 1cm x 1cm x 1cm inside this box! Important

Note: It's crucial to use the same units of measurement when calculating perimeter, area, and volume. If the length is in metres and the breadth is in centimetres, you need to convert them to the same unit before you can calculate. Guided Practice (With Solutions)

Question 1: A classroom is 7 metres long and 6 metres wide. What is the perimeter of the classroom?

Solution: Perimeter = 2 x (length + breadth) Perimeter = 2 x (7m + 6m) Perimeter = 2 x 13m Perimeter = 26m The perimeter of the classroom is 26 metres. We used the formula for the perimeter of a rectangle.

Question 2: A farmer's field is a square with sides of 25 metres each. What is the area of the field?

Solution: Area = side x side Area = 25m x 25m Area = 625m² The area of the field is 625 square metres. Since it’s a square we used the appropriate formula.

Question 3: A rectangular container has a length of 4 cm, a breadth of 3 cm, and a height of 2 cm. What is its volume?

Solution: Volume = length x breadth x height Volume = 4cm x 3cm x 2cm Volume = 24cm³ The volume of the container is 24 cubic centimetres. This represents how many tiny 1cm x 1cm x 1cm cubes could fill the container.

Question 4: Granny wants to put a lace border around her rectangular table cloth which is 150 cm long and 100 cm wide. How much lace border will she need?

Solution: Perimeter = 2 x (length + breadth) Perimeter = 2 x (150cm + 100cm) Perimeter = 2 x 250cm Perimeter = 500cm She will need 500cm of lace border. Independent Practice (Questions Only) A garden is rectangular, with a length of 12 metres and a width of 8 metres. Calculate the perimeter of the garden. What is the area of a square tile with a side length of 30 cm? A box is 25 cm long, 15 cm wide, and 10 cm high. What is the volume of the box?

Reference guide

• for walls and fencing (perimeter). Imagine designing a RDP house – you need to calculate the area of each room to ensure it's functional and meets minimum space requirements.
• Farming and Agriculture: Farmers use area to determine the size of their fields and how much fertilizer or seeds they need. Perimeter helps them calculate the amount of fencing required to protect their crops or livestock. A farmer might calculate the area of a field to know how much maize to plant or the perimeter to build a fence around it.
• Packaging and Logistics: Volume is essential in the packaging industry to determine the size of boxes and containers needed for shipping goods. Companies use these calculations to optimize space and reduce transportation costs. Think of how many boxes of canned goods you can fit into a delivery truck – that's a volume problem! Even determining the correct size box to send goods to family living in another province is a volume-related calculation.
• Differentiation, Remediation and Extension
• Remediation (Supporting Struggling Learners):
• Visual Aids: Use concrete materials like blocks or square tiles to demonstrate perimeter, area, and volume. Let students physically measure and count. For perimeter, use string to represent the distance around shapes.