OK so someone in first period got up to sharpen his pencil and it was taking WAY too long. I gave him a pen. I guess I was just glad that they were actually taking notes (or drawing – but in some way using their brains). I have my prep 2nd period of the day, and I started to think about pencil sharpening. I got 2 boxes of unsharpened pencils, and went to town. 10 turns for the first one to be just about perfect. I stopped to lok after each turn, because I wanted to see the ideal number. Then I turned 10 times really fast, to see if speed of rotation changed anything. They looked just about identical. I turned it slowly 10 times. Triplets! I changed up as many variables as I could – speed, how hard I pushed, how hard my grip was on the pencil…10 turns seemed to be ideal. Okay – so then I started each class by telling them that they could not be at the pencil sharpener for any more than 10 turns of the handle, because I’ve experimentally shown that 10 turns is ideal to take an unsharpened stick to a writing utensil worth of Algebra. (read that like “Build me an army worth of Mordor!) Then I asked – I tested 2 boxes of pencils, how many times did I turn it? Most of them were figuring it out. I loved it! Hidden algebra. Next period I switched it up, I told them I turned it 240 times – how many pencils did I sharpen? Then I said, I have 24 pencils sharpened, how many turns? I have 19 here, but I gave some away. If my total number of turns was 240, how many pencils did I give away?! Two-step equations were being solved within seconds – in their heads. I explained to them that I no longer want to hear “I don’t know how to do this!” because almost every single student of mine showed me that they could. Groans – but that’s OK, I did get the point across. Math can describe everything.
Also – it took 100 turns to basically whiddle the pencil down to nothing. And! I did every positive integer multiple of 10 from 0 to 100. When I lined them up, I had virtually a straight line. I think I smell “using equations to predict.” In some other class, they take a pencil and turn it a certain number of times, and write that number down. I measure the pencil and use my linear regression equation to guess how many times. Or, they tell me how many times they turned it, and I use it to guess what my measurement will be. Equivalent equations. I don’t want to overdo the pencils though, so the second part will probably come later this year. I don’t know exactly what I hope to get out of this exercise, but I did get a video of me sharpening pencils for the better part of 10 minutes during my prep period. Word.
**Update – just 3 minutes after I published I realized this was one of my longer posts. It was sort of a train-of-thought post, so I apologize if some of the things came out in a non-coherent way. However maybe, I should wait a couple of hours to think things over before I post after school – if I internalize the day in my brain, maybe I won’t have to think as much about what I write. Looks like it’s time for another experiment of some kind.