Pi and Place Value

Monday morning. A cold 5 degrees C. I greet twenty year 8 students at the door. There are some smiles and lots of chatter about the weekend. I use my standard line: “Come in if you are intelligent and keen to do some Maths”.

Most file in, but a few jokers linger, pretending not to fall into either category. I call for attention when they are seated. The room quietens (thanks to months of building up a good working relationship with these great kids) but X and Y continue their banter.

I introduce today’s “Learning Intention” – What is Pi?

My lesson plan includes some video clips and then outside with string and chalk to “draw” some circles on the asphalt. The sun is now out and the day is starting to warm up. The students are enjoying a break from the four walls of the classroom and soon lots of yellow circles start to appear on the ground.

Students use their feet as measuring instruments. Each circle radius is recorded and doubled to make the diameter. Then carefully feet are placed end on end around the circumference.

Back in the classroom to calculate Circumference divided by Diameter. One boy proudly brings his book up to show me he has got pi equal to 3.16! I get student X to staple pi to 100 decimal places on the wall of the classroom.

I then ask the class to use their calculators to complete my prepared worksheet (shown below), which involves converting historical attempts at finding fractions equal or close to the value of pi.

To my surprise, even my best students have trouble with question 3: Which fraction is the best approximation for Pi?

Perhaps my next lesson should be on decimals and place value???????