"How do you see this pattern growing?"
In some of the classes, this was a basic question for our warm up, but in a few others, it took on a deeper exploration, particularly in how students saw the pattern itself.
"In the 5th step, I had a line of 5 and put 4 more going up from the last one." (n + (n-1))
"I had a line of 4 on the bottom with a column of 5 on the end." ((n-1) + n)
"I had a row of 5 and a column of 5, then I took one off for where they overlap." (2n-1)
"I saw a line of 4 and a column of 4 with another block in the corner to connect them." (2(n-1) + 1)
I saw a 5x5 square with a 4x4 square taken out. (n^2 - (n-1)^2)
I really enjoyed taking whatever formula they developed for the number of blocks in the nth step and showing them that they were all the equivalent.
Each time we do an exercise like this, I make a conscious point to remind them that I'm looking for them to think about numbers in many ways. I want them to be able to manipulate numbers and figures into configurations that are most comfortable for them, provided they are valid methods.
The Math 7 students took an assessment today. It was supposed to be on Friday, but I didn't think they were ready. Then I was out with a sick child yesterday. I'm still not sure they were ready.
The quiz had 9 questions: 4 problems of "convert these decimals to fractions," 4 problems of "add or subtract these fractions" and 1 "here are the dimensions of a table. If I add a border, what are the new dimensions?"
A large portion of the students didn't finish the assessment in 40 minutes. I told them again that their not being able to finish in that time meant that they were not familiar or comfortable enough with the material. Several students after school to finish and, in 25 minutes, managed to complete 1 addition problem. I'm not really sure what's going on or how to address it. Much of what I see deals with lack of focus and concentration to the task at hand.
I also started one of my classes by telling them that, regardless of the election results, my expectations for behavior were unchanged. The good or bad behavior of adults is not an excuse for students to behave poorly.
I told them that there were strong emotions on all sides and, if they want to talk about any issues, I would be happy to do so.
I tried to give this talk with dispassion, but the students know how I feel and where I stand. They know I won't stand for incivility of any kind.