Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate perimeter of squares, rectangles, triangles, and composite shapes.
• Calculate area of squares, rectangles, triangles, and composite shapes.
• Calculate volume of cubes and rectangular prisms.
• Solve practical problems using these skills.
• Convert between different units of measurement.

Lesson summary

Measurement is a fundamental part of mathematics that helps us understand the world around us. In South Africa, measurement skills are crucial for everyday tasks, from buying groceries and building houses to managing land and conserving resources. Understanding perimeter, area, and volume allows us to accurately quantify spaces and objects, make informed decisions about resources, and solve practical problems in construction, agriculture, and many other fields. This week, we will delve into the concepts of perimeter, area and volume, focusing on common 2D shapes and 3D objects.

Lesson notes

Perimeter: The perimeter of a two-dimensional shape is the total distance around its boundary. It is measured in units of length (e.g., cm, m, km). Think of it as the length of fence needed to enclose a field.

Square: All sides are equal. If a side is 's', then Perimeter = 4s.

Rectangle: Opposite sides are equal. If length is 'l' and width is 'w', then Perimeter = 2l + 2w.

Triangle: The sum of the lengths of its three sides. If sides are 'a', 'b', and 'c', then Perimeter = a + b + c.

Composite Shapes: Break down the shape into simpler shapes (squares, rectangles, triangles) and add up the lengths of all the outer boundaries.

Area: The area of a two-dimensional shape is the amount of surface it covers. It is measured in square units (e.g., cm², m², km²). Imagine it as the amount of paint needed to cover a wall.

Square: Area = s², where 's' is the side length.

Rectangle: Area = l × w, where 'l' is the length and 'w' is the width.

Triangle: Area = (1/2) × b × h, where 'b' is the base and 'h' is the perpendicular height. The height must be perpendicular to the base.

Composite Shapes: Divide the shape into simpler shapes, calculate the area of each, and add them together.

Volume: The volume of a three-dimensional object is the amount of space it occupies. It is measured in cubic units (e.g., cm³, m³). Think of it as the amount of water a container can hold.

Cube: All sides are equal. Volume = s³, where 's' is the side length.

Rectangular Prism (Cuboid): Volume = l × w × h, where 'l' is the length, 'w' is the width, and 'h' is the height.

Worked example

Example 1 (Perimeter): Farmer Thabo wants to fence his rectangular field. The field is 25 meters long and 15 meters wide. How much fencing does he need?

Solution:

Perimeter of a rectangle = 2l + 2w

l = 25 meters, w = 15 meters

Perimeter = 2(25) + 2(15) = 50 + 30 = 80 meters

Farmer Thabo needs 80 meters of fencing.

Example 2 (Area): Maria wants to tile her kitchen floor, which is a rectangle 4 meters long and 3 meters wide. Each tile covers an area of 0.04 m². How many tiles does she need?

Solution:

Area of rectangle = l × w

l = 4 meters, w = 3 meters

Area = 4 × 3 = 12 m²

Number of tiles = Total area / Area per tile = 12 m² / 0.04 m² = 300 tiles

Maria needs 300 tiles.

Example 3 (Volume): Sipho is building a sandcastle using a bucket shaped like a rectangular prism. The bucket is 20 cm long, 15 cm wide, and 10 cm high. What is the volume of sand the bucket can hold?

Solution:

Volume of rectangular prism = l × w × h

l = 20 cm, w = 15 cm, h = 10 cm

Volume = 20 × 15 × 10 = 3000 cm³

The bucket can hold 3000 cm³ of sand.

Example 4 (Composite Shape - Area): Calculate the area of the L-shaped figure consisting of two rectangles. The first rectangle has a length of 8cm and width of 3cm. The second has a length of 5cm and a width of 2cm, and is attached to the end of the first to form an L shape.