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.

## Monday, October 23, 2017

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