I finally... FINALLY left a class feeling like it was great!
As I have been slowly building my thinking classroom in Algebra 1, I have learned so many things that haven't worked. What I've learned the most is really two things.
First, have a well thought out plan. One that includes how to launch a task and how to monitor the task.
Second, be ready to throw that plan out the window. I've done this a lot, usually because I've realize that my well thought out plan was not as well thought out as I envisioned.
I teach two sections of Algebra 1. I always feel bad for the first group because of how much I modify for the second group. Yesterday and today, I introduced my students to arithmetic sequences. We started by making tables for the following sequence of pictures...
So, students were asked to make a table to show the number of stars for each picture (picture #1, #2, etc.) We went up to picture #3 and I added the number 57 to the "picture #" column. Well, that was fun. Most groups were able to answer the question using the patterns they saw in the first few rows but I realized that they were using the number 57 to get their answer: (57*2)+1. So, I then asked them to determine the number of stars in picture 57 based on the number of stars in picture #1. Students were originally coming up with 3+2(57). After some discussion and questioning from me, we were all able to figure out that it was 3+2(56). Yeah!!
Then came the algebra. I added "n" to the picture # column. Audible gulps and sighs. But, off they went and off they succeeded!
We changed up the picture and I asked them to repeat the process and they were quickly able to come up with the appropriate rule.
Consolidation came next.
Fill in the blank: ______ + ______ (n-1)
Students came up with "first number" and "change" which I defined as a "common difference." So, off they went to answer thin-sliced problems to write the rule for the arithmetic sequence. At this point, they were simply writing the expression ___ + ____ (n-1). There was no equal sign. There were no subscripts. I eventually flipped it around and gave them the expression and they had to produce the sequence of numbers. Success!! Not only were they nailing it, they were claiming it was easy!
I did not use any vocabulary other than "common difference" and I didn't even emphasize it. Next class, the students will pick this up again and we will expand to add geometric sequences.
I'm keeping my fingers crossed for two solid (or semi-solid) BTC lessons in a row. That would be a record!
