Discovery of Pi

Year 8 (MKY) were given the task of creating a perfect circle and then had to measure the diameter and the circumference of the circle as accurately as possible. The class was split into groups. Each group was given string and a trundle wheel to create and measure the circle. No other instructions for creating the circle were given.

Students struggled initially with the idea of how to create a perfect circle. One of the strategies was for the group to stand in a circle holding the string and then to try and pull the string outwards and create the circle in this way. The students soon realised this was not efficient as they were getting more of a hexagon or octagon.

With a bit more brainstorming, students realised they had to measure a fixed length of string and then have a student hold one piece of the string in a central fixed position. Another student would hold the other end of the string and walk around the student whose position was fixed, keeping the string taught. This path was mapped out and the students were able to create a more accurate circle.

Each group created their circle and the radius, diameter and circumference were recorded. The results were then taken back to the classroom for analysis. The class results were placed on the board. Students were then asked to use their results to create the ratio of circumference by diameter. Each groups result was noted. Students were then asked to evaluate the number Pi on their calculator and compare this answer to their ratio result. The group with the best result had a percentage error of approximately 1.9 % working on 3 decimal places.

The students came to the realisation through class discussion that a number of different circles with different dimensions for the diameter and circumference had been created and almost all of the ratios of circumference divided by diameter gave a very similar result of approximately 3.14.

Students were then able to use this knowledge in subsequent lessons in order to calculate the circumference and areas of circles using the irrational number. In doing this activity students were able to demystify the concept of Pi and realise the importance of this number.

Congratulations 8MKY on the completion of this activity.

Mark Vorster
Maths Learning Leader