Behrman-Student Work Blog Wk 10

To introduce my unit about subtraction, I worked with students to break down numbers and use their knowledge of addition to aid in this transition. Some of my students challenged themselves and turned these single-digit problems into two, three, or four-digit numbers. However, this student's work shows that when he was breaking down numbers into two groups, he put zero in one of the "groups" on more than one occasion.

This reveals to me that this student does not understand conceptually that although he can write a zero in one of the boxes, in reality that means that that second group does not exist. I think a helpful next step for him would be to practice this type of activity again with bingo chips and a sheet of paper with three squares drawn on it (a larger version of the above worksheet's format). I would have this student show me the problems using bingo chips and have him put all the chips in the top box, then decide how many to move into one of the connected boxes, and then move the remaining chips into the other box. By explaining that both of the connected boxes need to have something in them in order break down the number, this student would be able to see that he can break a number down into zero and itself. Additionally, I would have him practice breaking down the same number in different ways so that he understand the existence of different possible combinations as a result of breaking down numbers.