How might you help students understand pi?

Many students can tell you that the numerical value of pi is  3.14… But do they understand what it actually means? Before I teach students what pi is, (for my Y5 higher achiever students), I give them an investigation to see if they can work it out for themselves.

Firstly, they need some back ground knowledge. I explain that the circumference of a circle is its perimeter or length. The distance from the centre of a circle to its edge is the radius and the distance from one side of the circle to the other is the diameter. Then I give students an investigation. I ask them to rule up a table in their books with the titles of the columns being:

Circle number    Radius   Diameter   Circumference

Then I give them a compass and ask them to draw circles of different sizes. After drawing circles, they number them, then measure and record the radius and diameter of each circle. To measure the circumference I give them a piece of string so that they can place it around the edge of the circle and then measure the length of the string using a ruler.

Once students have completed this for 5 to 6 circles, I ask them to see if they can find a relationship between the radius and the diameter. Guess what? They discover that the diameter is twice that of the radius, I didn’t have to tell them. Then, I ask them to find a relationship between the diameter and the circumference. They discover that the diameter, multiplied by 3 is about equal to the circumference. Little geniuses, they discover pi. This works with my Year 5 students!

Then of course you need to explain the word pi. Pi is the ratio of a circle’s circumference to its diameter. So, for any circle, dividing its circumference by its diameter will give you the exact number: 3.14159… or pi.

Once you’ve explained this to students, then show them a video of someone explaining the concept another way. I always try and give students 3 explanations of the same concept, explained by different people. A great online resources is . Below are two Math Antics videos which I use.

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