It's always fantastic when students surprise me and ask questions that I wouldn't imagine them asking, or when they come up with an idea that takes our lessons in a completely different direction. This was never more evident than when one of my students asked me the following question this week...'would it work with Pi sir?'
Let me set the context, it was one of my set 5 year 8 classes and we were looking at solving simple linear equations. Now, in order to attempt to approach the topic I decided to only look at a 'function machine' approach and leave the balancing method for later on once they had grasped the concept of solving equations, and indeed letters standing for unknown numbers. So, to provide a link into this I asked my class to, on mini-whiteboards, think of a number...and then form a number of steps to which the answer would always come out as 5.
I gave the class plenty of time to work out each step of the process and wrote the instructions on the board. After I had finished writing the instructions, and verbally giving them to the class to work out on their whiteboards, I took the class' answers. Not all of them got the answer 5 and so I started with these students. I put up their starting numbers next to the instructions on the board and asked them for their workings at each stage, correcting where necessary and then getting the intended answer of 5. I did this with each student (only 10 in my set 5 classes) and then that's where the question arrived...'would it work with Pi sir?'
I believe I was visibly taken back by the question as were my 2 TAs, nonetheless I said yes, yes it would! But, before doing so we had a massive discussion about what Pi was, that it was an irrational number (what that meant), it was the ratio between the circumference and diameter of a circle (what both the circumference and diameter of a circle were), showed the class my year 9 top sets' Pi-ems (see previous post), and then wrote the symbol for and first few decimal places of Pi on the board. I then set about proving that the method worked for Pi too and asked the students for the 'expressions' at each stage of the process, and we did indeed arrive at the answer...5!
Here's a pic of the board that I took in class there and then...