I had each student write their answer on their whiteboard and then asked them all to hold them up. I chose one student to explain their reasoning to the class. They did it well. We continued.
They were liking this. They were talking to each other - about math! They were all engaged! We continued with a few more (I skipped some) and a tutorial popup showed us that you can drag the beam at the top to show the equation:
We were now starting to see the tie-in to algebra. We kept going (and I was hearing "Can we do this all period?") until this one stumped some students:
The "I quit!" quickly turned to "I can do this." after I asked about the 28 at the top. What did it mean? What did that mean for each side?
They could see the patterns in solving these and were keen to keep going. But I wanted to start making the connection to an algebraic representation stronger (side note: they did not feel this need at all).
(I was tempted to solve this by elimination, but that was not my goal for today and didn't want to lose them.)
We did one more before moving on.
I really like these puzzles and will include them in my warm-ups from the beginning next time. I think it will really help build up students' equation solving skills over the semester.
They each received this handout, which was created by Alanna Street (thanks, Alanna!). They zipped through the front but then I asked them to write algebraic solutions, too. It is hard to convince them to do this as they are really good at solving in their heads. As we worked through them together, they started to realize that they knew what to do. The hurdle here was writing it down.
They continued to work on the questions on the back side of the handout while I circulated and helped some get going. Those who finished early got to go to the Solve Me site (on their phones) and I showed them the higher levels (Puzzler & Master).
We finished off by tying this back to what we were doing yesterday. I decided that I didn't want to interrupt their work and collected new data for the red cups myself. We found the rate of change, starting value and equation to relate height to the number of cups. Then we worked on finding the number of cups that would give the same height - this is just what we had been practicing!
6 cups, same height : )