Most students learn about Circles in Grade 5 or Grade 6 and this is how we usually introduce this topic to them.
We draw a circle, show them the center and radius and then we give them the formula for circumference and area.
Then, we tell them that π is 22/7 or 3.14
I feel that this is quite a boring introduction to such an interesting Mathematical Concept of Pi (π).
I want my students to be amazed by the beauty of Math. I want them to be curious about this subject. My job is not just to ‘teach’, my job is to create the desire for learning .
Let me introduce the Circle with this brief experiment :
- Draw a circle using the compass.
- Take a piece of string and place it along the circle, exactly once around the circle. Now measure the length of this string. This length is called the circumference of the circle.
- Next, measure the diameter of the circle ( length from any point on the circle passing through its center to another point on the opposite side )
If you divide the circumference of the circle by the diameter, you will get approximately 3.14, no matter what size circle you draw!
A larger circle will have a larger circumference and a larger diameter, but the ratio will always be the same. Go ahead and draw a few circles of various sizes and repeat this experiment. See it for yourself!
Yes, all circles are similar!
Doesn’t it sound exciting to you?
Take a look around you to appreciate this property of circle.
The ratio of ‘circumference to diameter’ of the Singapore Flyer is the same as the ratio of ‘circumference to diameter’ of your dinner plate. And this ratio is Pi (π) !!
Interesting, isn’t it ?
All circles are similar, and “the ratio of circumference to diameter” produces the same value regardless of their sizes. This value is called π (Pi).
Pi (π) has a long and interesting history! We can have a separate article on the history of Pi (π). In this article, I am just trying to introduce Pi in an interesting manner to grade 5 students. We will focus on Circumference and Area of circle – how does Pi (π) fit into these formulas.
Circumference / Diameter = π
C/D = π
C = π x D
C = 2 * π * Radius
Let us utilize our understanding of Area of a Rectangle to build the concept of Area of a Circle.
Let’s take a circle
Let’s make 4 equal parts and arrange it like this
Let’s make 8 equal parts and arrange it like this
Let’s make 16 equal parts and arrange it like this
Do you see that it is taking the shape of rectangle ? (If you feel the need to see more partitions before agreeing to this, check out the picture at the end of this article.)
Area of rectangle = length * width
If you observe closely, length of this rectangle is nothing but half of the circumference of the circle. ( I had outlined the circumference of the circle with a black marker to make it easy to follow )
length = 1/2 * 2 * π * radius = π * radius
Width = radius
Area of circle = Area of the transformed rectangle = π * radius * radius
Let’s make Maths Simple & Visual together @Maths2Art with Priya Asthana !
Education should ignite curiosity, encourage creativity and nurture intuition.