Today, I had one of those opening activities that was planned as a 10-minute math talk, turn into something much more than that. I am always excited when the students drive the conversation that way, however today, I felt at a bit of a loss for the “right” question in our discussion.
We started with an Estimation and Number Sense activity in Investigations in which I flip four digit cards that form a 2-digit by 2-digit multiplication problem. Students estimate a product, we discuss strategies and whether our actual answer will be more or less than our estimate and why. It always sounds so simple in the planning part.
I flipped cards for the problem 81 x 82. Thumbs went up right away (our symbol for having an answer and strategy in our Number Talks) and we got the initial estimate of 6,400 because 80 x 80 was 6,400. A few students explained and revoiced that our actual answer would be more than that because we rounded both numbers down. One student said she had the actual answer of 6,642 and proceeded to take us through the partial products she used. So far, so good. Then a student says he used the estimate to get an actual answer, but came up with 6,644. He said since he only used 80 x 80, he needed one more group of 82 and two more groups of 81, which gave him 82 + 162 = 244. He added that to the 6400 and arrived at 6644. This is our board:
Students are nodding their head in agreement but then start to wonder why it is not matching the answer when we found partial products. It is off by 2, so some students think it is a calculation mistake somewhere but soon realize it is all correct. I send them back to their journals because they want to know which is right and I am not telling them. We come back together in a couple minutes and everyone has 6,642, even the student who gave me the 6,644. So, I ask them, “Then why isn’t “Billy’s” strategy working?” because that is really the fun part :).
This is where I was at a loss for a good question. Everyone could prove to me why the answer they got was right, but I didn’t know what to ask them in that moment without completely giving them the solution path. It is SO hard to question students. I say it all of the time and today, no matter how prepared I was, I was at a loss for a good question. Don’t get me wrong we shared some great work…
I got a example of why it doesn’t work when you have another problem…
I got the student who gave me 6,644, trying to compare what he did to what he knows the answer should be…
But even after we went through our volume lesson and they left me for the day, I still am thinking about what I could have asked them to push their thinking. I was feeling, in that moment, that certain questions would have pushed quite a few students to disengage while at the same time, I was not wanting to let it go. They left not knowing why that was happening, which I am completely fine with, but I don’t want it to be a missed opportunity either. I am thinking that tomorrow I will try to connect it to an area model another student had used to solve it and see how that compares to the problems that “Billy” used to get 6644.
I am up for any and all suggestions as to how to pull this conversation together. What would you have asked in that moment? What would you follow it up with tomorrow?