Lesson Notes By Weeks and Term v5 - Grade 5
Measurement: perimeter, area and volume (Grade 5) – Week 4 focus
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Measurement: perimeter, area and volume (Grade 5) – Week 4 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 5
Term: 3rd Term
Week: 4
Theme: General lesson support
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Welcome, Grade 5 mathematicians! This week, we're diving into the world of measurement, focusing on perimeter, area, and volume. These skills aren't just about numbers; they're about understanding the world around us. Imagine you're helping your family build a vegetable garden, painting a wall in your house, or even figuring out how much juice will fit in a cool drink container – these all involve perimeter, area, and volume! Perimeter is the distance around a shape, like the fence around a soccer field. Area is the amount of space a flat surface covers, like the carpet on your bedroom floor. And volume is the amount of space a 3D object occupies, like the amount of water in a bucket.
Perimeter: The perimeter is the total distance around the outside of a two-dimensional shape. Think of it as walking around the edge of a field – the total distance you walk is the perimeter.
Rectangles: A rectangle has two pairs of equal sides (length and width). The formula for the perimeter of a rectangle is: Perimeter = 2 x (length + width) or P = 2(l + w)
Squares: A square has four equal sides. The formula for the perimeter of a square is: Perimeter = 4 x side or P = 4s Example 1: A rectangular vegetable patch is 5 meters long and 3 meters wide. What is the perimeter of the vegetable patch?
Solution: Identify the length and width: Length (l) = 5 meters, Width (w) = 3 meters Apply the formula: P = 2(l + w) = 2(5 + 3)
Calculate: P = 2(8) = 16 meters Answer: The perimeter of the vegetable patch is 16 meters.
Example 2: A square window has sides of 80 centimeters. What is the perimeter of the window?
Solution: Identify the side length: Side (s) = 80 centimeters Apply the formula: P = 4s = 4 x 80 Calculate: P = 320 centimeters Answer: The perimeter of the window is 320 centimeters.
Area: Area is the amount of space a two-dimensional shape covers. Think of it as the amount of carpet needed to cover your bedroom floor.
Rectangles: The formula for the area of a rectangle is: Area = length x width or A = l x w Squares: Since all sides of a square are equal, the formula for the area of a square is: Area = side x side or A = s x s = s² Example 3: A rectangular piece of cardboard is 12 centimeters long and 7 centimeters wide. What is the area of the cardboard?
Solution: Identify the length and width: Length (l) = 12 centimeters, Width (w) = 7 centimeters Apply the formula: A = l x w = 12 x 7 Calculate: A = 84 square centimeters (cm²)
Answer: The area of the cardboard is 84 square centimeters. Remember to use square units for area!
Example 4: A square tile has sides of 25 centimeters. What is the area of the tile?
Solution: Identify the side length: Side (s) = 25 centimeters Apply the formula: A = s² = 25 x 25 Calculate: A = 625 square centimeters (cm²)
Answer: The area of the tile is 625 square centimeters.
Volume: Volume is the amount of space a three-dimensional object occupies. Think of it as how much water a container can hold. We will focus on rectangular prisms (cuboids), which are like boxes.
Rectangular Prism (Cuboid): The formula for the volume of a rectangular prism is: Volume = length x width x height or V = l x w x h Example 5: A cool drink box is 20 centimeters long, 8 centimeters wide, and 15 centimeters high. What is the volume of the box?
Solution: Identify the length, width, and height: Length (l) = 20 centimeters, Width (w) = 8 centimeters, Height (h) = 15 centimeters Apply the formula: V = l x w x h = 20 x 8 x 15 Calculate: V = 2400 cubic centimeters (cm³)
Answer: The volume of the cool drink box is 2400 cubic centimeters. Remember to use cubic units for volume! Important
Note: Make sure all measurements are in the same units before you calculate perimeter, area, or volume. If one measurement is in meters and another is in centimeters, you'll need to convert one to match the other. Guided Practice (With Solutions)
Question 1: A rectangular school sports field is 80 meters long and 50 meters wide. What is the perimeter of the field?
Solution: Identify the length and width: Length (l) = 80 meters, Width (w) = 50 meters Apply the formula: P = 2(l + w) = 2(80 + 50)
Calculate: P = 2(130) = 260 meters Answer: The perimeter of the sports field is 260 meters.
Commentary: We used the formula for the perimeter of a rectangle because the field is rectangular. We added the length and width, then multiplied by
2. Question 2: A square table top has sides of 1.2 meters. What is the area of the table top?
Solution: Identify the side length: Side (s) = 1.2 meters Apply the formula: A = s² = 1.2 x 1.2 Calculate: A = 1.44 square meters (m²)
Answer: The area of the table top is 1.44 square meters.
Commentary: Since it's a square, we squared the side length. Remember the units are square meters because we are calculating area.
Question 3: A rectangular brick has a length of 22 centimeters, a width of 11 centimeters, and a height of 7 centimeters. What is the volume of the brick?
Solution: Identify the length, width, and height: Length (l) = 22 centimeters, Width (w) = 11 centimeters, Height (h) = 7 centimeters Apply the formula: V = l x w x h = 22 x 11 x 7 Calculate: V = 1694 cubic centimeters (cm³)
Answer: The volume of the brick is 1694 cubic centimeters.
Commentary: We multiplied the three dimensions to find the volume. The units are cubic centimeters.
Question 4: A square garden has a perimeter of 36 meters. What is the length of each side of the garden?
Solution: Recall the formula for perimeter of a square: P = 4s We know P = 36 meters, so: 36 = 4s Divide both sides by 4 to solve for s: s = 36 / 4 Calculate: s = 9 meters Answer: The length of each side of the garden is 9 meters.