I am exhausted and it is getting late, but I have to write this post tonight. I wish I had been able to write it immediately after class, because I was having quite an adrenaline rush after our patty paper exploration. I prepped the materials for class early this morning, knowing that every second spent in dealing with logistics would geometrically cost minutes of refocusing in class. As I was counting out sheets of patty paper and clipping them into stacks for each group, I remembered the wonderful document camera I was given by iPevo last fall. I don’t use it often because of my peripatetic schedule, but I knew that it would be a huge support for this lesson, making it much easier for the students to create the transformations if they could actually see what I was doing with the patty paper because they have never worked with this material before. I had enough time before classes began to install the drivers and test the document camera, so the stage was appropriately set.
When the students walked into the room, I had this wonderful photograph displayed on the board, courtesy of a tweet yesterday by Dan Meyer. The bulb in our SmartBoard is getting a little dim, so the lights were out. Following @ddmeyer’s instructions, I said nothing while the students began to question, argue, and debate. We took a vote before we began to discuss which calculator was displaying the correct answer – the class was evenly split. First we retraced the path of calculation of each calculator, and the corresponding order of operations that was being observed. And here was the most worthwhile part of the activity – just as Tina (@crstn85) decries in Nix the Tricks, the majority of the students swore that multiplication had higher priority as an operation than division. When I explained to them that the operations were evenly matched, and were to be performed in the order they appeared in any expression, they were skeptical. (I think they believed me in the end.) And then Jerrin, a rough and tough senior who secretly enjoys math, asked, “So if you were using that calculator on a test, and it gave you the wrong answer, you would lose points?”, which led to a conversation about when and how we should be using calculators. Truth be told, I don’t know why the calculator on the left is displaying the wrong answer, and how something like that could be prevented. I’d love to know.
We moved on to the transformations exploration. The students were intrigued and impressed by the document camera, and even more by my ability to write upside down. We talked about why patty paper was such a wonderful tool for exploring, how it enabled copying, tracing and measuring distance and right angles. Caroline, completely pre-empting part of the activity, pointed out that we could fold the paper and trace a figure, and create a reflection. She grinned every time I referred to her ‘instruction’ during class.
I walked through translations and rotations using the patty paper, demonstrating with the document camera and giving the students time to practice them in their groups (they had written instructions from Michael Serra’s Patty Paper Geometry as well). There was a lot of quiet talking during the activity, but I also heard a lot of patty paper rustling – a sure sign that they were working their way through the exercises, and helping each other to do it.
As I’ve said before, it is a large class with surprisingly good attendance (if not punctuality). Keeping a distractable group of kids focused while sitting in a corner in the dark with only a document camera and some tracing paper felt like a huge feat; I felt as if I had taken an aerobic class when the bell rang. But here’s my pre-assessment evidence that the activity was meaningful to the students: as we were winding down, I gave them some instructions for re-assembling the room at the end of the period. I told them that the patty paper they had used was theirs to keep, and in the event that they didn’t want it, I asked them to make sure it ended up in the trash by the door.
Guess what? When the class left, the wastebasket was empty. I hope there is some patty paper up on some refrigerator doors tonight!