Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate the perimeter of squares, rectangles, and triangles.
• Calculate the area of squares, rectangles, and triangles.
• Calculate the volume of cubes and cuboids.
• Solve real-world problems involving these measurements.

Lesson summary

Measurement is a fundamental skill in mathematics and in everyday life. Understanding perimeter, area, and volume allows us to calculate the size of objects and spaces. This is essential in various real-world scenarios, from planning a garden to estimating the amount of paint needed for a room or calculating the capacity of a storage container. In South Africa, this knowledge is crucial for everything from home improvements to understanding land sizes and even in specific industries like construction and agriculture. For example, knowing how to calculate area is essential for farmers planning crop yields, and volume calculations are crucial for builders working on concrete structures.

Lesson notes

Perimeter: The perimeter is the total distance around the outside of a two-dimensional shape. It's essentially the length you would travel if you walked around the entire shape. We measure perimeter in units of length, such as millimeters (mm), centimeters (cm), meters (m), or kilometers (km).

Rectangle: The perimeter of a rectangle is found by adding the lengths of all four sides. Since opposite sides of a rectangle are equal, we can use the formula: P = 2 (length + width) or P = 2l + 2w Square: A square is a special type of rectangle where all four sides are equal.

Therefore, the perimeter of a square is: P = 4 side or P = 4s Triangle: The perimeter of a triangle is found by adding the lengths of all three sides: P = side1 + side2 + side3 Area: Area is the amount of surface a two-dimensional shape covers. We measure area in square units, such as square millimeters (mm²), square centimeters (cm²), square meters (m²), or square kilometers (km²).

Rectangle: The area of a rectangle is found by multiplying its length and width: A = length width or A = l * w Square: The area of a square is found by squaring the length of one of its sides: A = side side or A = s² Triangle: The area of a triangle is found by multiplying half the base by the height. The height is the perpendicular distance from the base to the opposite vertex. A = 1/2 base height or A = 0.5 b * h Volume: Volume is the amount of space a three-dimensional object occupies. We measure volume in cubic units, such as cubic millimeters (mm³), cubic centimeters (cm³), cubic meters (m³). Sometimes we also use litres (L) where 1L = 1000cm³.

Cube: A cube is a three-dimensional shape where all six faces are squares. The volume of a cube is found by cubing the length of one of its sides: V = side side * side or V = s³ Cuboid: A cuboid (also called a rectangular prism) is a three-dimensional shape where all six faces are rectangles. The volume of a cuboid is found by multiplying its length, width, and height: V = length width height or V = l w * h

Worked example

Example 1: Perimeter of a rectangular garden

A gardener in Cape Town is planning a rectangular vegetable garden. The length of the garden is 5 meters, and the width is 3 meters. What is the perimeter of the garden?

Solution:

P = 2 (length + width)

P = 2 (5m + 3m)

P = 2 8m

P = 16m

Therefore, the perimeter of the garden is 16 meters. This means the gardener needs 16 meters of fencing to enclose the garden.

Example 2: Area of a square tile