Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate perimeter of 2D shapes (squares, rectangles, triangles, circles).
• Calculate area of 2D shapes.
• Calculate volume of cubes and rectangular prisms.
• Solve problems in practical contexts.
• Convert between different units of measurement.

Lesson summary

Measurement is a fundamental skill that we use every day, whether we're figuring out how much fencing we need for a garden, calculating the space in a room, or determining how much water a container can hold. In South Africa, these skills are particularly important. For example, understanding area helps farmers plan their fields efficiently, while knowing volume is crucial for managing water resources, especially during droughts. Measuring accurately allows us to plan and build better, and it's a key part of many careers, from construction to catering. This week, we will focus on perimeter, area, and volume of various 2D and 3D shapes.

Lesson notes

Perimeter Perimeter is the total distance around the outside of a two-dimensional shape. To find the perimeter, we add up the lengths of all the sides.

Square: All sides are equal. If a side is 's', then Perimeter = 4s Rectangle: Two pairs of equal sides (length 'l' and breadth 'b'). Perimeter = 2l + 2b Triangle: Add the lengths of all three sides (a, b, c). Perimeter = a + b + c Circle: The perimeter of a circle is called the circumference (C). C = 2πr, where 'r' is the radius and π (pi) is approximately 3.14 or 22/

7. Example 1: Square A farmer wants to fence a square piece of land with sides of 25 meters. How much fencing does he need? Side (s) = 25 m Perimeter = 4s = 4 25 m = 100 m He needs 100 meters of fencing.

Example 2: Rectangle A classroom is 8 meters long and 6 meters wide. What is the perimeter of the classroom? Length (l) = 8 m Breadth (b) = 6 m Perimeter = 2l + 2b = (2 8 m) + (2 * 6 m) = 16 m + 12 m = 28 m The perimeter of the classroom is 28 meters.

Example 3: Triangle A triangular garden bed has sides of 3 meters, 4 meters, and 5 meters. What is the perimeter of the garden bed? Side a = 3 m, Side b = 4 m, Side c = 5 m Perimeter = a + b + c = 3 m + 4 m + 5 m = 12 m The perimeter of the garden bed is 12 meters.

Example 4: Circle (Circumference) A circular swimming pool has a radius of 7 meters. What is the circumference of the pool? (Use π = 22/7) Radius (r) = 7 m Circumference (C) = 2πr = 2 (22/7) * 7 m = 44 m The circumference of the pool is 44 meters. Area Area is the amount of surface a two-dimensional shape covers. It is measured in square units (e.g., cm², m², km²).

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

Rectangle: Area = l b, where 'l' is the length and 'b' is the breadth.

Triangle: Area = (1/2) b * h, where 'b' is the base and 'h' is the perpendicular height.

Circle: Area = πr², where 'r' is the radius and π (pi) is approximately 3.14 or 22/

7. Example 1: Square A square tile has a side length of 15 cm. What is its area? Side (s) = 15 cm Area = s² = 15 cm 15 cm = 225 cm² The area of the tile is 225 square centimeters.

Example 2: Rectangle A rectangular table is 2 meters long and 1 meter wide. What is its area? Length (l) = 2 m Breadth (b) = 1 m Area = l b = 2 m * 1 m = 2 m² The area of the table is 2 square meters.

Example 3: Triangle A triangular sail has a base of 4 meters and a height of 6 meters. What is its area? Base (b) = 4 m Height (h) = 6 m Area = (1/2) b h = (1/2) 4 m * 6 m = 12 m² The area of the sail is 12 square meters.

Example 4: Circle A circular garden has a radius of 5 meters. What is its area? (Use π = 3.14) Radius (r) = 5 m Area = πr² = 3.14 (5 m)² = 3.14 * 25 m² = 78.5 m² The area of the garden is 78.5 square meters. Volume Volume is the amount of space a three-dimensional object occupies. It is measured in cubic units (e.g., cm³, m³).

Cube: All sides are equal (side = s). Volume = s³ Rectangular Prism: Volume = l b * h, where 'l' is the length, 'b' is the breadth, and 'h' is the height.

Example 1: Cube A cube has a side length of 3 cm. What is its volume? Side (s) = 3 cm Volume = s³ = 3 cm 3 cm * 3 cm = 27 cm³ The volume of the cube is 27 cubic centimeters.

Example 2: Rectangular Prism A rectangular box is 5 cm long, 4 cm wide, and 2 cm high. What is its volume? Length (l) = 5 cm Breadth (b) = 4 cm Height (h) = 2 cm Volume = l b h = 5 cm 4 cm * 2 cm = 40 cm³ The volume of the box is 40 cubic centimeters. Unit Conversions It is often necessary to convert between different units of measurement.

Here are some common conversions: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 cm = 10 millimeters (mm)

Example: Convert 2.5 meters to centimeters. 5 m 100 cm/m = 250 cm Guided Practice (With Solutions)

Question 1: A rectangular garden is 12 meters long and 8 meters wide. What is its perimeter and area?

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

Commentary: This question reinforces the formulas for perimeter and area of a rectangle. It's important to remember to include the correct units (meters for perimeter, square meters for area).* Question 2: A circular tablecloth has a radius of 1.5 meters. What is its circumference and area? (Use π = 3.14)

Solution: Circumference: C = 2πr = 2 3.14 * 1.5 m = 9.42 m Area: A = πr² = 3.14 (1.5 m)² = 3.14 * 2.25 m² = 7.065 m²

Commentary: This question applies the formulas for circumference and area of a circle. Make sure to square the radius correctly when calculating the area.* Question 3: A cube-shaped storage container has a side length of 40 cm. What is its volume?

Solution: Volume: V = s³ = (40 cm)³ = 40 cm 40 cm * 40 cm = 64000 cm³

Commentary: This question tests the formula for the volume of a cube. Remembering that we need to multiply the side length by itself three times is essential.* Question 4: A rectangular swimming pool is 10 meters long, 5 meters wide, and 2 meters deep. How much water can it hold (what is its volume)?