I got this idea from Alex @AlexOverwijk in person and his blog Slam Dunk Math.
He spirals his curriculum and gets to work with the shirts for a few days. I knew my small class would not be interested for more than one day. But, I did have their attention today - at least the girls. They were working. The boys did not.
I brought in my t-shirts:
Before class they were asking questions, but I formalized it on the board with "What do you notice? What do you wonder?" Should have taken a better picture of their wonderings? How much did you spend? How long did it take you to get them all? Are they clean? Why do I have that many?
I answered the ones I could and then we focused on how many shirts. They looked at me like - we will just count. I said, no. They said, "We have to guess?" We do Estimation 180 every day so they knew that was coming. I handed out sticky notes and asked them to guess.
Then, I asked what the shape was. We are working on 3D shapes, surface area, and volume now. They first guessed pyramid but we got to it being a cone. I asked how they might measure that. They asked for string, scissors, and measuring tape which I provided and they got to work.
We haven't done the formula for a cone yet but I told them 3 cones would fit into a cylinder and we worked with the formula.
They found the circumference, then the diameter, and the radius. Then, we calculated the Volume. We got a really big number - now what? They were stuck. I told them I would give them a little pile of 8 shirts. "What we have to do all that measuring again?" Yes, now, you know the process.
They found the volume of the 8 and then were able to put it together and do big divided by little times 8! Yeah! That was a huge jump they successfully made.
A student bet me her life savings we would not calculate the exact answer. And, granted we didn't get exact, but we were only 3 away. We talked about why we were a little off.
The actual answer was: 65
Finally, I asked how much of the hallway the shirts would cover. I asked how this was different. They linked it to surface area. They got excited to work in the hallway. I gave them one to work with. We figured out how many tiles one t-shirt took up and made our prediction. We were off again because the shirts were different sizes, but they had fun.