MPM1D1 - Day 34 The Big Nickel

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.

MPM1D1 - Day 33 Volume & Hot Coffee

The focus today was on volume. I started with this brilliant.org problem.

What I really like about this problem is that there are no numbers. I sent groups to work on it at the board. Some groups struggled at first not knowing how to go about the problem without any numbers. One group just wanted to give a verbal explanation. Another group explained exactly what they had to do and told me they couldn't start because they didn't have any numbers. I asked if it mattered what 'the numbers' were. They realized it didn't and carried on. Some groups quickly realized that it didn't matter what the dimensions were so they picked a number. For whatever reason four seemed to be a common dimension for the length of the cube. When I asked groups why they chose four, some said because there were four balls across in image C. Another group said that they thought four might be easy to work with since the perimeter of a square of length four was the same as the area of a square of length four. I'm not sure what this had to do with this problem, but I was happy to hear someone recalling a discussion we had as a class earlier in the semester. I'm guessing that some groups had a peek at the work of others and used their numbers (though nobody gave that as a reason).

This problem took a long time to get through, partly because of the lack of numbers and possibly partly because it was a Monday. Some groups had a hard time focusing. Eventually all groups were working effectively and came up with a solution.

Next we moved onto Hot Coffee. I had students complete the first part of the problem solving framework that we use on their own (state the problem, give an estimate, what do you know, what do you need). I asked what information they needed and gave it to them then I sent them up to the boards to do the work in groups. They started finding the volume (in cubic feet), then converted to gallons, then used some information about the flow rate to determine how long the process would take. The problem was good in that it involved some volume, some proportional reasoning and also dealt with rates. I often forget to do Act 3 of these problems. I tend to have faith in the work students have done and I'm happy with that. What I forget is how much pride students get from seeing that their answer was correct. I showed Act 3 and there were some pretty happy faces.

Once they finished at the board I sent them to their seats to get everything on paper so I can see how they're doing. I then collected their work so that I can provide some feedback.

I was hoping at this point to do the Big Nickel but we only had about ten minutes left so I handed out a page of volume questions they could practice. We'll save the Big Nickel for tomorrow.