Unfortunately due to a snow day last week, I was not able to watch this student complete this task. However, I was able to ask him a few question about how he did complete it. On this day, the students were to find the rule to the chart. This was a new concept that was first introduce at the beginning of the week. Most of the students seemed to catch onto this new topic quickly, however we had a few students struggle. I found this students had really interesting way of solving this problem.

In the photo there are four tables, that have an in side and an out side. Students were to analyze the in side and then look at the outside of the first column and see how many numbers the in is from the out. Students were then to look at the next column and see the number in the in is away form the number in the out. When students have figured out this pattern the would write it in the rule box. The students also had to place a + if the in box counted up to the number in the out box. For example, as shown in problem 1 the in box is 3 and the out box is 5 so the students would count up from 3 to 5 and find that the rule was 2. Since they counted up and not down they would put it as a plus. If the in box was counting down to the out box then the rule would be a negative. Students worked independently on problems 1-3 trying to find the rule by looking at the in and out chart. Once they finished with this they moved onto problem 4 which asked them to make their own.

From walking around the classroom and checking a variety of different students math workbook, I came to the conclusion that all of the students seemed to understand this new concept. I do not think this problem was super challenging for the students, it did require some high level thinking, but once they understood how to figure out the answer then it should have come easier.

Nathans approach to this problem informed me that he understands the task and is on track for a first grader in math. While working on this problem, Nathan told me that he thought it was easy. He said that all he did was look at the in box and then the out box and either counted up or down. Since the first one was 3 he said he counted up to 5. Nathan said this was his guess that it was 2 away. Then he would look at the second column and saw that the in and out were the same only 2 away. Thats how he knew the rule was going to be 2. Nathan's explanation of how he came up with this method of figuring out the problem was very good thinking.

If I were to advance Nathan's thinking I would give him a table that wasn't as simple as going up by 2's, or 10's, but something challenging like 12 or 9. I would also ask him to make another one of his own problems that was not going up by 1,2,5, or 10, cause those are pretty easy and he shows he understands them.