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 real-world problems involving measurement.
• Understand the difference between perimeter, area, and volume.

Lesson summary

This week, we delve into the fascinating world of measurement, focusing on perimeter, area, and volume. Measurement is a crucial skill that we use daily, whether we're calculating how much fencing we need for a garden, figuring out how much paint to buy for a wall, or determining if a container can hold our favourite amahewu. It's especially relevant in South Africa, where understanding measurement is important for tasks like budgeting for household projects, calculating land sizes, and understanding construction plans. These skills contribute to financial literacy and problem-solving abilities crucial for everyday life and future careers.

Lesson notes

2.1 Perimeter Perimeter is the total distance around a two-dimensional shape. Imagine you are a security guard walking around the edge of a building – the total distance you walk is the perimeter of the building's base. We calculate perimeter by adding the lengths of all the sides of the shape. It's important to use the same unit of measurement for all sides before adding. For example, if some sides are in centimeters (cm) and others are in meters (m), convert everything to either cm or m before adding. Perimeter is always measured in units of length (e.g., cm, m, km).

Square: All four sides are equal. Perimeter = 4 x side length Rectangle: Two pairs of equal sides (length and breadth/width). Perimeter = 2 x (length + breadth)

Triangle: Add the lengths of all three sides.

Example 1: Finding the Perimeter of a rectangular garden Farmer Thando wants to build a fence around his rectangular vegetable garden. The garden is 12 meters long and 8 meters wide. How much fencing does he need?

Solution: The perimeter of a rectangle is given by the formula: P = 2 x (length + width) Length = 12 meters Width = 8 meters P = 2 x (12 m + 8 m) P = 2 x (20 m) P = 40 meters Therefore, Farmer Thando needs 40 meters of fencing.

Example 2: Finding the Perimeter of a Triangle A triangular piece of land has sides measuring 15m, 18m and 21m. What is the perimeter?

Solution: Perimeter = side1 + side2 + side3 Perimeter = 15m + 18m + 21m Perimeter = 54m 2.2 Area Area is the amount of surface a two-dimensional shape covers. Think of painting a wall - the area is the amount of paint you need to cover the entire wall surface. Area is always measured in square units (e.g., square centimeters (cm²), square meters (m²), square kilometers (km²)). Remember to always convert your measurements to the same unit before calculating the area.

Square: Area = side length x side length = (side length)² Rectangle: Area = length x breadth Triangle: Area = ½ x base x height (The height is the perpendicular distance from the base to the opposite vertex.)

Example 3: Calculating the Area of a Classroom Floor A classroom is 8 meters long and 6 meters wide. What is the area of the classroom floor?

Solution: Area of a rectangle = length x breadth Length = 8 meters Breadth = 6 meters Area = 8 m x 6 m Area = 48 m² The area of the classroom floor is 48 square meters.

Example 4: Calculating the Area of a Triangular sail. A triangular sail on a small boat has a base of 3m and a height of 4m. What is the area of the sail?

Solution: Area of a triangle = 1/2 x base x height Base = 3m Height = 4m Area = 1/2 x 3m x 4m Area = 6 m² 2.3 Volume Volume is the amount of space a three-dimensional object occupies. Think of filling a bottle with water – the volume is the amount of water the bottle can hold. Volume is always measured in cubic units (e.g., cubic centimeters (cm³), cubic meters (m³)). Just as with area and perimeter, make sure to convert measurements to the same unit before calculations.

Cube: All sides are equal. Volume = side length x side length x side length = (side length)³ Rectangular Prism (Cuboid): Volume = length x breadth x height Example 5: Calculating the Volume of a Fish Tank A rectangular fish tank is 60 cm long, 30 cm wide, and 40 cm high. What is the volume of the fish tank?

Solution: Volume of a rectangular prism = length x width x height Length = 60 cm Width = 30 cm Height = 40 cm Volume = 60 cm x 30 cm x 40 cm Volume = 72000 cm³ The volume of the fish tank is 72,000 cubic centimeters.

Example 6: Calculating the Volume of a Cube A cube has sides of length 5cm. What is the volume of the cube?

Solution: Volume of a cube = side length x side length x side length Volume = 5cm x 5cm x 5cm Volume = 125 cm³ 2.4 Relationship between Perimeter, Area and Volume Perimeter measures the distance around a 2D shape. Area measures the surface covered by a 2D shape. Volume measures the space occupied by a 3D object. They are related because they all involve measuring dimensions.

However, perimeter is a linear measurement (length), area is a two-dimensional measurement (length x width), and volume is a three-dimensional measurement (length x width x height). You can't directly convert between them because they measure different things. 2.5 Unit Conversions It's essential to be able to convert between units.

Here are some common conversions: 1 meter (m) = 100 centimeters (cm) 1 centimeter (cm) = 10 millimeters (mm) 1 kilometer (km) = 1000 meters (m) When working with area, remember to square the conversion factor.

For example: 1 m² = (100 cm)² = 10,000 cm² When working with volume, remember to cube the conversion factor.

For example: 1 m³ = (100 cm)³ = 1,000,000 cm³ Guided Practice (With Solutions)

Question 1: A square garden has a side length of 7 meters. What is the perimeter of the garden?