Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate the perimeter of 2D shapes.
• Determine the area of 2D shapes.
• Calculate the volume of cubes and rectangular prisms.
• Convert between different metric units.
• Solve realistic word problems.

Lesson summary

This week, we delve into the exciting world of measurement, focusing on perimeter, area, and volume. These concepts are not just abstract mathematical ideas; they are crucial for understanding and interacting with the world around us. From calculating how much fencing we need for a garden to determining the amount of water a JoJo tank can hold during a drought, these skills are incredibly practical for everyday life in South Africa. Understanding measurement helps us make informed decisions, solve practical problems, and appreciate the spatial relationships that govern our environment.

Lesson notes

Perimeter: The perimeter is the total distance around the outside of a two-dimensional (2D) shape. Imagine walking along the edges of a field; the total distance you walk is the perimeter. To calculate the perimeter, you simply add up the lengths of all the sides of the shape.

Square: A square has four equal sides. If each side has a length of 's', then the perimeter (P) is: P = 4s Rectangle: A rectangle has two pairs of equal sides: length (l) and breadth (b).

The perimeter (P) is: P = 2l + 2b Triangle: A triangle has three sides. If the sides have lengths a, b, and c, then the perimeter (P) is: P = a + b + c Compound shapes: Compound shapes are made up of two or more basic shapes joined together. To find the perimeter, carefully add up the lengths of all the outer edges of the shape. Don't include any lengths that are inside the shape.

Example 1: Perimeter of a Vegetable Patch A farmer wants to fence a rectangular vegetable patch that is 8 meters long and 5 meters wide. How much fencing does he need?

Solution: This is a rectangle, so we use the formula P = 2l + 2b. P = (2 x 8) + (2 x 5) = 16 + 10 = 26 meters. The farmer needs 26 meters of fencing.

Area: The area is the amount of surface a two-dimensional (2D) shape covers. Think of it as the amount of paint you'd need to cover the entire shape. Area is always measured in square units (e.g., cm², m², km²).

Square: Area (A) = s² (side x side)

Rectangle: Area (A) = l x b (length x breadth)

Triangle: Area (A) = ½ x b x h (½ x base x height). The height is the perpendicular distance from the base to the opposite vertex (corner).

Example 2: Area of a Classroom Floor A classroom floor is 7 meters long and 6 meters wide. What is the area of the floor?

Solution: This is a rectangle, so we use the formula A = l x b. A = 7 x 6 = 42 m² The area of the classroom floor is 42 square meters.

Example 3: Area of a Triangular Garden A garden is in the shape of a triangle. The base of the triangle is 10 meters and the perpendicular height is 6 meters. What is the area of the garden?

Solution: This is a triangle, so we use the formula A = ½ x b x h. A = ½ x 10 x 6 = 30 m² The area of the triangular garden is 30 square meters.

Compound shapes: Divide the shape into simpler shapes (squares, rectangles, triangles), calculate the area of each, and then add the areas together.

Volume: Volume is the amount of space a three-dimensional (3D) object occupies. Imagine filling a container with water; the amount of water the container can hold is its volume. Volume is always measured in cubic units (e.g., cm³, m³).

Cube: A cube has all sides equal in length (s). Volume (V) = s³ (side x side x side)

Rectangular Prism: A rectangular prism has three dimensions: length (l), breadth (b), and height (h). Volume (V) = l x b x h Example 4: Volume of a JoJo Tank A JoJo tank is in the shape of a rectangular prism. It is 2 meters long, 1.5 meters wide, and 1 meter high. What is its volume?

Solution: This is a rectangular prism, so we use the formula V = l x b x h. V = 2 x 1.5 x 1 = 3 m³ The volume of the JoJo tank is 3 cubic meters.

Unit Conversions: In South Africa, we primarily use the metric system. It's important to be able to convert between different units.

Here are some common conversions: 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 m² = 10000 cm² (100 cm x 100 cm) 1 m³ = 1000000 cm³ (100 cm x 100 cm x 100 cm)

Example 5: Converting Units A rectangular room is 5m long and 4m wide. What is its area in cm²? First find area in m²: A = l x b = 5m x 4m = 20 m² Convert m² to cm²: 20 m² x 10000 cm²/m² = 200000 cm² The area of the room is 200,000 cm². Guided Practice (With Solutions)

Question 1: A square has a side length of 7 cm. What is its perimeter and area?

Solution: Perimeter: P = 4s = 4 x 7 cm = 28 cm. We multiply the side length by 4 because a square has 4 equal sides.

Area: A = s² = 7 cm x 7 cm = 49 cm². We square the side length to calculate the area.

Question 2: A rectangular garden is 12 meters long and 8 meters wide. What is its perimeter and area?

Solution: Perimeter: P = 2l + 2b = (2 x 12 m) + (2 x 8 m) = 24 m + 16 m = 40 m. We double the length and breadth and add them together.

Area: A = l x b = 12 m x 8 m = 96 m². We multiply length and breadth.

Question 3: A triangular flag has a base of 30 cm and a height of 20 cm. What is its area?

Solution: Area: A = ½ x b x h = ½ x 30 cm x 20 cm = 300 cm². We multiply half the base by the height.

Question 4: A rectangular box is 25 cm long, 10 cm wide, and 5 cm high. What is its volume?

Solution: Volume: V = l x b x h = 25 cm x 10 cm x 5 cm = 1250 cm³. We multiply length, breadth, and height together. Independent Practice (Questions Only) A rectangular field is 150 meters long and 85 meters wide. Calculate its perimeter. What is the area of a square with a side length of 11 cm? A triangular sail on a boat has a base of 4 meters and a height of 6 meters. What is the area of the sail?