Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate the perimeter of 2D shapes (squares, rectangles, triangles).
• Calculate the area of 2D shapes (squares, rectangles, triangles).
• Calculate the volume of cubes and rectangular prisms.
• Apply the correct units for each measurement.
• Solve real-world problems involving these concepts.

Lesson summary

This week, we're diving into the fascinating world of measurement! We'll be focusing on perimeter, area, and volume – understanding what they are, how to calculate them, and why they're important in our everyday lives. Measurement is a fundamental skill that we use constantly, whether it's figuring out how much fencing we need for a garden, calculating how much paint to buy for a room, or determining how much water a tank can hold. In South Africa, these skills are especially important for things like planning agricultural spaces, designing buildings, and managing resources efficiently. Why is this important for South African learners?

Lesson notes

2.1 Perimeter: Definition: The perimeter is the total distance around the outside of a two-dimensional (2D) shape. It's like walking around the edge of a field – the total distance you walk is the perimeter.

Units: Perimeter is measured in units of length, such as millimeters (mm), centimeters (cm), meters (m), and kilometers (km). It is not measured in square units.

Calculating Perimeter: Square: Perimeter = 4 × side length (P = 4s)

Rectangle: Perimeter = 2 × (length + width) (P = 2(l + w))

Triangle: Perimeter = sum of the lengths of all three sides (P = a + b + c)

Compound Shapes: Add up the lengths of all the outer sides. Be careful to identify and include all the outer edges!

Example 1 (Rectangle): A farmer in Limpopo wants to fence a rectangular vegetable patch that is 8 meters long and 5 meters wide. How much fencing will they need?

Solution: Length (l) = 8 m Width (w) = 5 m Perimeter (P) = 2(l + w) = 2(8 m + 5 m) = 2(13 m) = 26 m The farmer needs 26 meters of fencing.

Example 2 (Triangle): A triangular garden bed has sides of length 3.5 m, 4.2 m, and 5 m. What is the perimeter of the garden bed?

Solution: Side a = 3.5 m Side b = 4.2 m Side c = 5 m Perimeter (P) = a + b + c = 3.5 m + 4.2 m + 5 m = 12.7 m The perimeter of the garden bed is 12.7 meters. 2.2 Area: Definition: Area is the amount of surface a two-dimensional (2D) shape covers. Imagine painting a wall – the area is how much wall you're painting.

Units: Area is measured in square units, such as square millimeters (mm²), square centimeters (cm²), square meters (m²), and square kilometers (km²).

Calculating Area: Square: Area = side length × side length (A = s²)

Rectangle: Area = length × width (A = l × w)

Triangle: Area = ½ × base × height (A = ½bh)

Important: The height must be perpendicular to the base.* Example 3 (Rectangle): A classroom floor is rectangular, with a length of 10 meters and a width of 7 meters. What is the area of the classroom floor?

Solution: Length (l) = 10 m Width (w) = 7 m Area (A) = l × w = 10 m × 7 m = 70 m² The area of the classroom floor is 70 square meters.

Example 4 (Triangle): A triangular sail on a small boat has a base of 2 meters and a height of 3 meters. What is the area of the sail?

Solution: Base (b) = 2 m Height (h) = 3 m Area (A) = ½ × b × h = ½ × 2 m × 3 m = 3 m² The area of the sail is 3 square meters. 2.3 Volume: Definition: Volume is the amount of space a three-dimensional (3D) object occupies. Think of filling a box with sand – the volume is how much sand the box can hold.

Units: Volume is measured in cubic units, such as cubic millimeters (mm³), cubic centimeters (cm³), cubic meters (m³), and liters (L). Note that 1 cm³ = 1 ml and 1000 cm³ = 1 L Calculating Volume: Cube: Volume = side length × side length × side length (V = s³)

Rectangular Prism (Cuboid): Volume = length × width × height (V = l × w × h)

Example 5 (Rectangular Prism): A JoJo tank for storing water is a rectangular prism with a length of 1.5 meters, a width of 1 meter, and a height of 2 meters. What is the volume of the tank?

Solution: Length (l) = 1.5 m Width (w) = 1 m Height (h) = 2 m Volume (V) = l × w × h = 1.5 m × 1 m × 2 m = 3 m³ The volume of the JoJo tank is 3 cubic meters.

We can also convert this to litres: 3 m³ = 3 x (100cm)³ = 3 x 1000000 cm³ = 3000000 cm³ = 3000000 ml = 3000L Example 6 (Cube): A sugar cube has sides that are 1cm long. What is the volume of the sugar cube?

Solution: Side (s) = 1 cm Volume (V) = s³ = 1 cm x 1 cm x 1 cm = 1 cm³ Guided Practice (With Solutions)

Question 1: A rectangular picture frame has a length of 30 cm and a width of 20 cm. Calculate the perimeter of the frame.

Solution: Length (l) = 30 cm Width (w) = 20 cm Perimeter (P) = 2(l + w) = 2(30 cm + 20 cm) = 2(50 cm) = 100 cm The perimeter of the frame is 100 cm.

Question 2: A triangular piece of land has a base of 12 meters and a height of 8 meters. What is the area of the land?

Solution: Base (b) = 12 m Height (h) = 8 m Area (A) = ½ × b × h = ½ × 12 m × 8 m = 48 m² The area of the land is 48 square meters.

Question 3: A rectangular box has a length of 40 cm, a width of 25 cm, and a height of 15 cm. What is the volume of the box?

Solution: Length (l) = 40 cm Width (w) = 25 cm Height (h) = 15 cm Volume (V) = l × w × h = 40 cm × 25 cm × 15 cm = 15000 cm³ The volume of the box is 15000 cubic centimeters.

Question 4: Calculate the perimeter of a square with sides of 7 cm.

Solution: Side (s) = 7 cm Perimeter (P) = 4 × s = 4 × 7 cm = 28 cm The perimeter of the square is 28cm.

Question 5: A rectangular swimming pool is 10m long and 5m wide. Calculate the area of the swimming pool.

Solution: Length (l) = 10 m Width (w) = 5 m Area (A) = l x w = 10 m x 5 m = 50 m² The area of the swimming pool is 50 square meters. Independent Practice (Questions Only) A rectangular garden is 12 meters long and 7 meters wide. What is the perimeter of the garden? What is the area of a square with sides of 9 cm? A triangular flag has a base of 60 cm and a height of 40 cm.