Pi Approximation Day

We celebrate Pi Approximation Day on 22nd July (22/7) because as a fraction this is an approximation to Pi. Celebrate Pi Approximation Day by finding other, more accurate, rational approximations to Pi using the continued fractions method.
Age groups relevant for by Key Stage:
KS4,
KS5
Possible duration of tasks:
Up to 30 mins,
30 mins - 1 hour

Curriculum Topics Covered

Manipulating fractions, Rounding and accuracy. 

More Information

The task sheet challenges students to find better rational approximations of Pi by using the method of continued fractions. 

The info sheet demonstrates how the continued fraction method works and shows how the first two rational approximations to Pi are found using this method. It is provided as information for teachers, to help them teach students the method for the task.

The task sheet also challenges students to re-write each continued fraction as one single fraction. As the continued fractions get more detailed, this gets quite tricky! Students need to be able to easily manipulate fractions.

In the video below Matt demonstrates this method of approximation and shows how it is also used to predict when solar eclipses will occur.

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