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 squares, rectangles, and triangles.
• Calculate volume of cubes and rectangular prisms.
• Solve practical problems.
• Convert between different units of measurement.

Lesson summary

This week, we delve into the fascinating world of measurement, focusing on perimeter, area, and volume. These concepts are fundamental to understanding the space around us and are used every day in various real-life scenarios, from calculating the amount of fencing needed for a garden to determining the space inside a room. In South Africa, understanding measurement is crucial for tasks like planning construction projects, estimating the amount of paint needed for a classroom, or calculating the water storage capacity of a JoJo tank. This week’s focus aims to build a strong foundation in these essential skills.

Lesson notes

2.1 Perimeter: Perimeter is the total distance around the outside of a two-dimensional (2D) shape. It's like walking along all the edges of a shape and measuring the total distance covered. The units for perimeter are always units of length (e.g., cm, m, km).

Square: All sides are equal in length. If the side length is 's', then Perimeter = 4 s Rectangle: Two pairs of sides are equal. If the length is 'l' and the width is 'w', then Perimeter = 2 (l + w)

Triangle: Sum of the lengths of all three sides. If the sides are 'a', 'b', and 'c', then Perimeter = a + b + c Composite Shapes: Divide the shape into simpler shapes (squares, rectangles, triangles) and find the perimeter of the whole shape by adding the lengths of all the outside sides. Remember not to include the lengths of any internal lines you use to divide the shape.

Example 1: A farmer in Limpopo wants to fence a rectangular vegetable patch. The length of the patch is 15 meters and the width is 8 meters. How much fencing does the farmer need?

Solution: The farmer needs to calculate the perimeter of the rectangular vegetable patch. Perimeter = 2 (length + width) Perimeter = 2 (15 m + 8 m) Perimeter = 2 (23 m) Perimeter = 46 m Therefore, the farmer needs 46 meters of fencing.

Example 2: A school needs to put reflective tape around a triangular road safety sign. The sides of the sign are 60 cm, 60 cm, and 40 cm. What length of reflective tape is required?

Solution: The school needs to calculate the perimeter of the triangular sign. Perimeter = sum of all sides. Perimeter = 60 cm + 60 cm + 40 cm Perimeter = 160 cm Therefore, the school needs 160 cm of reflective tape. 2.2 Area: Area is the amount of surface a two-dimensional (2D) shape covers. It's like measuring the space inside the shape. The units for area are always square units (e.g., cm², m², km²).

Square: Area = side side = s² Rectangle: Area = length width = l * w Triangle: Area = 1/2 base height = ½ b * h (where 'b' is the base and 'h' is the perpendicular height from the base to the opposite vertex)

Composite Shapes: Divide the shape into simpler shapes (squares, rectangles, triangles), calculate the area of each simple shape, and then add the areas together to find the total area.

Example 3: A painter needs to estimate how much paint is needed to paint a rectangular wall in a classroom. The wall is 5 meters long and 3 meters high. What is the area of the wall?

Solution: The painter needs to calculate the area of the rectangular wall. Area = length height Area = 5 m 3 m Area = 15 m² Therefore, the area of the wall is 15 square meters.

Example 4: A garden is in the shape of a right-angled triangle. The base is 4m and the height is 3m. What is the area available for planting?

Solution: The garden is a right-angled triangle, so we use the formula: Area = ½ base * height Area = ½ 4m * 3m Area = ½ 12 m² Area = 6 m² Therefore, the area available for planting is 6 square meters. 2.3 Volume: Volume is the amount of space a three-dimensional (3D) object occupies. It's like measuring the space inside the object. The units for volume are always cubic units (e.g., cm³, m³, km³).

Cube: All sides (length, width, and height) are equal. Volume = side side * side = s³ Rectangular Prism (Cuboid): Volume = length width height = l w * h Example 5: A JoJo tank is in the shape of a rectangular prism. It has a length of 2 meters, a width of 1.5 meters, and a height of 1 meter. What is the volume of water the tank can hold?

Solution: We need to calculate the volume of the rectangular prism (JoJo tank). Volume = length width * height Volume = 2 m 1.5 m * 1 m Volume = 3 m³ Therefore, the JoJo tank can hold 3 cubic meters of water. Note that 1 m³ = 1000 litres, so this tank can hold 3000 litres.

Example 6: A building block is a cube with each side measuring 5cm. What is the volume of the building block?

Solution: Volume = side side * side Volume = 5cm 5cm * 5cm Volume = 125 cm³ Therefore, the volume of the building block is 125 cubic centimetres. 2.4 Unit Conversion: It's essential to be able to convert between different units of measurement: Length: 1 m = 100 cm; 1 cm = 10 mm; 1 km = 1000 m Area: 1 m² = (100 cm)² = 10,000 cm²; 1 cm² = (10 mm)² = 100 mm² Volume: 1 m³ = (100 cm)³ = 1,000,000 cm³; 1 cm³ = (10 mm)³ = 1000 mm³ Example 7: Convert 2.5 m² to cm².

Solution: We know that 1 m² = 10,000 cm² Therefore, 2.5 m² = 2.5 10,000 cm² 2.5 m² = 25,000 cm² Guided Practice (With Solutions)

Question 1: Calculate the perimeter of a rectangle with a length of 12 cm and a width of 7 cm.

Solution: Perimeter = 2 (length + width) Perimeter = 2 (12 cm + 7 cm) Perimeter = 2 (19 cm) Perimeter = 38 cm

Commentary:* This question applies the formula for the perimeter of a rectangle. It emphasizes the addition of the length and width before multiplying by

2. Question 2: Calculate the area of a triangle with a base of 8 m and a height of 5 m.