Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate perimeter of 2D shapes.
• Calculate area of 2D shapes.
• Calculate volume of cubes and rectangular prisms.
• Solve practical problems using these skills.
• Convert between different metric units.

Lesson summary

This week, we delve into the fascinating world of measurement, focusing on perimeter, area, and volume. Understanding these concepts is crucial because they are woven into our daily lives. From calculating the amount of fencing needed for a garden to figuring out how much paint to buy for a room, or even estimating how much water a JoJo tank can hold during a drought, measurement skills are essential for practical problem-solving. In the South African context, where resources are often scarce, accurate measurement is vital for efficient resource management and planning.

Lesson notes

Perimeter Perimeter is the total distance around the outside of a two-dimensional (2D) shape. Think of it as walking around the edges of a field or a building – the total distance you walk is the perimeter. We measure perimeter in units of length like millimetres (mm), centimetres (cm), metres (m), or kilometres (km).

Square: All four sides are equal. If one side is 's', the perimeter is P = 4s Rectangle: Two pairs of equal sides (length 'l' and breadth 'b'). The perimeter is P = 2l + 2b Triangle: The sum of all three sides (a, b, and c). The perimeter is P = a + b + c Composite Shapes: Add up the lengths of all the outside edges. Be careful not to include any internal lines.

Example 1: A farmer wants to fence a rectangular field that is 50m long and 30m wide. How much fencing does he need?

Solution: The perimeter is P = 2l + 2b = 2(50m) + 2(30m) = 100m + 60m = 160m. The farmer needs 160m of fencing. We use the formula for the perimeter of a rectangle, understanding that the length and breadth represent the dimensions of the field.

Example 2: A square tile has sides of 15cm. What is its perimeter?

Solution: The perimeter is P = 4s = 4(15cm) = 60cm. We apply the formula for the perimeter of a square, recognizing that all sides are equal.

Example 3: A composite shape is made up of a rectangle (length 8cm, breadth 3cm) with a square (side 3cm) attached to one of its longer sides. What is its perimeter?

Solution: First, sketch the shape. The outside edges are 8cm + 3cm + 3cm + 3cm + (8cm - 3cm) + 3cm = 8cm + 3cm + 3cm + 3cm + 5cm + 3cm = 25cm. Important

Note: The side of the square that touches the rectangle is not part of the perimeter of the combined shape. We subtract the side of the square from the longer side of the rectangle that it is attached to. Area Area is the amount of surface a two-dimensional (2D) shape covers. Think of it as the amount of carpet needed to cover a floor. We measure area in square units, such as square millimetres (mm²), square centimetres (cm²), square metres (m²), or square kilometres (km²).

Square: Area = side x side = s² Rectangle: Area = length x breadth = l x b Triangle: Area = 1/2 x base x perpendicular height = 1/2 x b x h Composite Shapes: Divide the shape into simpler shapes, calculate the area of each part, and then add the areas together.

Example 4: A classroom floor is rectangular, 8m long and 6m wide. What is the area of the floor?

Solution: Area = l x b = 8m x 6m = 48m². The area of the floor is 48 square meters.

Example 5: A triangular garden bed has a base of 4m and a height of 2.5m. What is its area?

Solution: Area = 1/2 x b x h = 1/2 x 4m x 2.5m = 5m². The area of the garden bed is 5 square meters. We use the formula, ensuring we use the perpendicular height, not the length of a sloping side.

Example 6: A wall consists of a rectangle (3m x 4m) topped by a triangle (base 3m, height 1m). What is the total area of the wall?

Solution: Rectangle Area = 3m x 4m = 12m². Triangle Area = 1/2 x 3m x 1m = 1.5m². Total Area = 12m² + 1.5m² = 13.5m². Volume Volume is the amount of space a three-dimensional (3D) object occupies. Think of it as the amount of water that can fit inside a container. We measure volume in cubic units, such as cubic millimetres (mm³), cubic centimetres (cm³), cubic metres (m³).

Cube: All sides are equal. Volume = side x side x side = s³ Rectangular Prism (cuboid): Volume = length x breadth x height = l x b x h Example 7: A box is 5cm long, 3cm wide and 2cm high. What is its volume?

Solution: Volume = l x b x h = 5cm x 3cm x 2cm = 30cm³. The volume of the box is 30 cubic centimetres.

Example 8: A cubic container has sides of 4m. What is its volume?

Solution: Volume = s³ = 4m x 4m x 4m = 64m³. The volume of the container is 64 cubic meters. Conversions Important conversions for length: 1 cm = 10 mm 1 m = 100 cm 1 km = 1000 m When converting area, remember that you are squaring the conversion factor: 1 cm² = 10 mm x 10 mm = 100 mm² 1 m² = 100 cm x 100 cm = 10,000 cm² When converting volume, you are cubing the conversion factor: 1 cm³ = 10 mm x 10 mm x 10 mm = 1000 mm³ 1 m³ = 100 cm x 100 cm x 100 cm = 1,000,000 cm³ Example 9: Convert 5 m² to cm² Solution: 5 m² = 5 x (100 cm x 100 cm) = 5 x 10,000 cm² = 50,000 cm² Guided Practice (With Solutions)

Question 1: A rectangular garden is 12m long and 8m wide. Calculate its perimeter and area.

Solution: Perimeter: P = 2l + 2b = 2(12m) + 2(8m) = 24m + 16m = 40m Area: A = l x b = 12m x 8m = 96m²

Commentary:* We used the standard formulas for the perimeter and area of a rectangle.

Remember the units: meters for perimeter and square meters for area.

Question 2: A triangle has a base of 6cm and a height of 4cm. Calculate its area.

Solution: Area: A = 1/2 x b x h = 1/2 x 6cm x 4cm = 12cm²

Commentary: It’s important to use the perpendicular height of the triangle in the area formula.

Question 3: A cubic box has sides of 30cm. What is its volume? Express your answer in cubic metres.