How do you make the surface area of cylinders captivating? "Do more of what you love," rings in my ears. (thanks Christopher ) I had to stop looking for approval and go with what is important to me. I had just been through two social justice minded nights of Seder, so I had a lot on my mind. As I was looking around my classroom, I noticed how many students had cylindrical shaped vessels with them. I gathered them all up and put them on display. I had an agenda that was both mathematical and much broader. My underlying goal was to expand student thinking, get some critical evaluation going, and apply a simple notion to having a voice (and maybe sneak in some talk about branding, economics, and consumerism)
The first day I lead a conversation, it looked like this:
The conversation was loud, and active, and thoughtful. The students came up with cylinder-shaped right away. I loved getting thick into their vocabulary, "girth, coney, purpose, mass, volume, recyclable, durable." I got to give them a new word, "ergonomics," and we talked about product placement in movies and tv, why some were "coney" and some straight up and down (right), and I even got to sneak in some SJ with branding which led to tribes, acceptable tribes and not acceptable tribes. (reusable, that is my tribe, tree hugging dirt worshipers, Starbucks, that is my tribe, etc...(we are in the San Francisco Bay Area, so our sports are very tribal) 
I realized that I could include more students if the next day, (we are on a block schedule so I hadn't seen 2 of my 4 sets of Geometry kids yet) I started smaller. I was thinking YOU, WE, ME. 

The next day, I gathered up all the cylindrical vessels, and handed groups of 4 some large paper. I had them do a brain dump.  When the students figured out what we doing, MORE bottles came out of backpacks and book bags, including a glittery one! Their's looked like this:












I had them then get up, and move around to read what others had written. Back at their seats I gave them a few more minutes to be inspired. to write down anything they wanted to remember or add. 

This time, when I called them together, I asked each person to share something that their team wrote, something they heard, or something they saw. More voices, and a much more delighted me. It now felt more okay for me to ask the following questions:
1. What is the net of a right cylinder? (I love the surprise when students recognize the length of the rectangle part of the next is actually the circumference of the circle)
2. What is its surface area--I found a student's bottle, asked for the measurements of the diameter and height. 
3. What is the volume?
4. and most importantly, can you find another set of dimensions for the cylinder that has the same volume? 

We will see what I get on Tuesday and Wednesday. I am curious to know if the different set of classes will have more enthusiasm, more of their assignments completed, and/or more investment in the task.