We started with two volume questions as a warm-up. I wanted to see how groups did with questions that didn't have any diagrams.

Overall, they did quite well. All groups found the volume of the cone and the sphere. A couple of groups forgot to divide the volume of the sphere by two by as I asked them to explain what they did, they all got it straightened out.

I was expecting most of the groups to get tripped up with the slant height in Problem 2 but only about half did. Again, a bit of prodding on my part led to students realizing that they needed to use the Pythagorean Theorem to find the height.

We moved onto the Big Nickel. We started by finding the volume of the big nickel. I was surprised at how long this took. Many students were desparate for a formula for the volume of a dodecagon. When I told them they didn't need it, many seemed quite stumped. After pondering the problem and comparing to their list of formulas many realized that they could break the nickle into twelve triangular prisms. One group chose square based pyramids at first but when I asked if they could show me a square based pyramid they realized that they were on the wrong track.

Once the groups calculated the volume of the big nickel they found the volume of an actual nickel and determined how many nickels would fit inside the big nickel. Some students moved on from there to find out how much that would cost. We were pretty much out of time so I gave them this handout to practice. It has a bit of surface area on it, which we haven't done, but I think they will be able to figure it out.

I was a little shocked at how long things seemed to take today. I'm not sure why things took so long. I was a little under the weather so I wonder if my lack of energy led to a lack of energy for my students. We'll see how it goes tomorrow.

Through the work that we did today I have come to the conclusion that many students don't seem to know the definition of a prism. I'll have to address this tomorrow.

## Wednesday, October 25, 2017

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