Subtraction is the one operation that every time it arises in class, throws one more thing for me to think about into the mix. I have two recent posts around decimal subtraction, here and here, and I continue to work with whole number subtraction through number talks.
Today, I only had time for two problems in the Number Talk due to testing 😦 The first problem was 400 – 349. I was most anticipating students would subtract 50 and add one back or add up from the 349 to the 400 (1+50) to arrive at the answer of 51. I was surprised when a student said he “subtracted 100 – 49 to get 51 and knew that would be the same answer because if you added 300 to both numbers it would give you the same problem, so the same answer.” This made me think of a distance model on a number line, but I completely missed that opportunity and moved into the next problem. Seeing what happened next, it may have either made one strategy more clear or completely caused us to miss out on the conversation that followed.
Problem #2: 400 – 274
The student, “M”, on the right subtracted to find the distance between 400 and 274, however did not explain it that way so it left many students wondering how she knew what to subtract. I had a student ask her if that was her second strategy because she seems to have subtracted the answer from the 400.
The student, “C”, on the left solved it the way the majority of the class did, removal in part with some compensation at the end. Before he started explaining, he prefaced with, “I did it pretty much like M.” When he finished, he realized it was not the same and was confused as to where “M” came out with the same answer. He even exclaimed that, ‘I think she got the answer by mistake.”
“M” knew exactly what she did, however, I didn’t let her explain yet because I wanted the rest of the class to think about it a bit more. I told her she would be able to explain it tomorrow after we chat a bit more with it. I had them all end the class with a journal entry (surprising, right?:) I asked them what they understood, saw happening in each, or were not too sure about. It is just the most beautiful thing to read the honesty and reflection in their writings.
Some students could see what was happening…(even though it seems some tables have the vocabulary a little mixed up:)
Some had a really interesting way of thinking about it…
Now, the question is, how to approach this tomorrow? I am thinking I would love three groups, one who subtracted in parts, one who found the distance by subtracting back to the minuend, and one group who adjusted the subtrahend and minuend to find the distance between. Have them create a context and representation that shows what they did (still working within the same problem they all have the same answer for) and do a share. I would like the share to go in the exact order of the groups I just listed above. Crossing my fingers I have time to talk some more math with them tomorrow, a silent classroom is probably more torture for me than them 🙂