Shirts Volume and Surface Area

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.
Our answer:


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.