Lesson Notes By Weeks and Term v5 - Grade 7
Measurement: perimeter, area and volume (Grade 7) – Week 7 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Measurement: perimeter, area and volume (Grade 7) – Week 7 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 7
Term: 3rd Term
Week: 7
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This week, we'll be diving deep into the world of measurement, specifically focusing on perimeter, area, and volume. These aren't just abstract mathematical concepts; they are fundamental skills that are used daily in various aspects of our lives. From planning a vegetable garden to calculating the amount of paint needed for a room, understanding measurement is crucial. In South Africa, these skills are particularly important for everyday problem-solving, from managing resources to participating in construction or crafts. They form the basis for understanding spatial relationships and problem-solving in a variety of careers from construction and farming to design and architecture.
2.1 Perimeter: Perimeter is the total distance around the outside of a two-dimensional (2D) shape. Imagine walking around the edge of a field – the total distance you walk is the perimeter. To calculate perimeter, you simply add up the lengths of all the sides.
Square: A square has four equal sides. If the length of one side is s, then the perimeter is P = 4s.
Rectangle: A rectangle has two pairs of equal sides (length l and width w). The perimeter is P = 2l + 2w.
Triangle: Add the lengths of the three sides a, b, and c. So, P = a + b + c.
Composite shapes: Break the shape down into simpler shapes (squares, rectangles, triangles), find the lengths of all the outer sides and then add them up.
Example 1: Finding the perimeter of a rectangular garden A farmer in Limpopo wants to fence a rectangular garden that is 12 meters long and 8 meters wide. How much fencing does he need? Here, l = 12 m and w = 8 m. P = 2l + 2w = 2(12) + 2(8) = 24 + 16 = 40 meters. The farmer needs 40 meters of fencing. 2.2 Area: Area is the amount of surface a two-dimensional (2D) shape covers. Think of it as the amount of carpet needed to cover a floor. Area is measured in square units (e.g., cm², m²).
Square: Area, A = s² (where s is the length of a side).
Rectangle: Area, A = l x w (where l is the length and w is the width).
Triangle: Area, A = ½ x b x h (where b is the base and h is the perpendicular height). Remember the height must form a right angle with the base.
Composite Shapes: Divide the composite shape into simpler shapes. Find the area of each simpler shape, and add the areas together to find the total area.
Example 2: Calculating the area of a rectangular classroom floor A classroom in a school in Gauteng is 10 meters long and 7 meters wide. What is the area of the floor? Here, l = 10 m and w = 7 m. A = l x w = 10 x 7 = 70 m². The area of the classroom floor is 70 square meters.
Example 3: Finding the area of a triangular piece of land. A triangular piece of land has a base of 15 meters and a height of 8 meters. Calculate the area. A = ½ x b x h A = ½ x 15m x 8m A = ½ x 120 m² A = 60 m² 2.3 Volume: Volume is the amount of space a three-dimensional (3D) object occupies. Think of it as how much water a container can hold. Volume is measured in cubic units (e.g., cm³, m³).
Cube: A cube has all sides equal (side length s). The volume is V = s³.
Rectangular Prism/Cuboid: A rectangular prism has length l, width w, and height h. The volume is V = l x w x h.
Example 4: Calculating the volume of a water tank A rectangular water tank used for collecting rainwater is 2 meters long, 1.5 meters wide, and 1 meter high. How much water can it hold? Here, l = 2 m, w = 1.5 m, and h = 1 m. V = l x w x h = 2 x 1.5 x 1 = 3 m³. The water tank can hold 3 cubic meters of water. 2.4 Unit Conversions (Metric System): It's important to be able to convert between units.
Remember these key conversions: 1 meter (m) = 100 centimeters (cm) 1 centimeter (cm) = 10 millimeters (mm) 1 kilometer (km) = 1000 meters (m) 1 hectare (ha) = 10 000 m² To convert m² to cm², multiply by 100 x 100 = 10 000 To convert m³ to cm³, multiply by 100 x 100 x 100 = 1 000 000 Example 5: Converting Units. Convert 5 meters to centimeters. Since 1m = 100cm, then 5m = 5 x 100cm = 500cm Convert 2 m² to cm² 2m² = 2 x 100 x 100 cm² = 2 x 10 000cm² = 20 000 cm² Guided Practice (With Solutions)
Question 1: A square has a side length of 7 cm. Calculate its perimeter.
Solution: P = 4s = 4 x 7 = 28 cm.
Commentary: This question reinforces the basic formula for the perimeter of a square.
Question 2: A rectangle has a length of 15 cm and a width of 6 cm. Calculate its area.
Solution: A = l x w = 15 x 6 = 90 cm².
Commentary: This question assesses the understanding of the area of a rectangle. Make sure students include the correct units.
Question 3: Calculate the volume of a cube with a side length of 4 meters.
Solution: V = s³ = 4 x 4 x 4 = 64 m³.
Commentary: This tests the understanding of volume for a cube. Again, emphasize the importance of cubic units.
Question 4: A farmer wants to build a rectangular kraal for his goats. He has 50 meters of fencing. If the length of the kraal is 15 meters, what will be the width of the kraal?
Solution: Perimeter, P = 2l + 2w. We know P = 50 and l =
1
5. So, 50 = 2(15) + 2w -> 50 = 30 + 2w -> 20 = 2w -> w = 10 meters.
Commentary: This is a real-world application that involves solving for an unknown variable within the perimeter formula.
Question 5: Convert 3.5 m³ into cm³.
Solution: 1 m³ = 1 000 000 cm³, so 3.5 m³ = 3.5 x 1 000 000 cm³ = 3 500 000 cm³.
Commentary: Testing the unit conversion skills. Independent Practice (Questions Only) A triangle has sides of length 5 cm, 8 cm, and 10 cm. Find its perimeter. Calculate the area of a triangle with a base of 12cm and a perpendicular height of 7cm. A rectangular swimming pool is 8 meters long, 5 meters wide and 2 meters deep. How much water (in m³) is needed to fill the pool completely?