My Geometry students came to me with several major weaknesses. One of those is that they have a REALLY hard time with patterns. Since patterns show up on the state test, it is an area that I need to spend some time on with them, but because we a vocational school, I have these cherubs for only 90 of the 180 days.
Here is where Fawn Nguyen's Visual Patterns website has come to my rescue. I thought that working with visual patterns would be a good segue into working with number patterns. I put one of these each week into their warm ups. I choose a pattern by clicking on several until I find one that intrigues me! Usually I cut and paste into a SmartBoard Notebook page, but this one I just duplicated by drawing the shapes.
(I love using Stage 0 as the first stage, because it lends so well to "What did we start with at the very beginning? or at time 0? or before we worked any hours?")
Having worked with this group, I knew that just figuring out how many figures were in Stage 43 would be challenging for a few, which is why I asked the first question.
I covered up the 2nd two questions with the shade option on Smartboard, and asked them to take out their warm up books and write their responses to "Stage ?" and the first question. Some got right to it, some did "scrunchy face". I told them I expected everyone to have something written down and that Mr. G (student teacher) and I would be around just to peek.
And then I shut up.
We wandered and peeked, but said nothing. It was crazy hard.
When we were sure everyone had something down (even if it was just to name "Stage ?") we had kids respond.
Kiddo 1: I noticed that the Stage number was one less than the number of objects.
Kiddo 2: Yeah: the Stage number was always one less than the number of hexagons. But you could also say that the number of hexagons was one more than the stage number. (Wowzer! Yes, he got to pick from the candy tin for using such excellent polygon vocabulary!)
Kiddo 3: (and this one made me practically weep with joy because he is one of my MOST struggling students AND because it is NOT something I noticed!) I noticed that the Stage number is the same as the number of shared sides.
Kiddo 4: Oh! I noticed that too, but I thought it was wrong. (This, too, made me nearly weep for all the opposite reasons, but I told her that when you notice something, you absolutely, positively CANNOT be wrong because it is what YOU noticed!)
Next, I pulled the shade down a bit and asked them to find the perimeter for "Stage 0 - Stage ?".
And then I shut up.
Which was impossibly hard because I noticed a new way to find the perimeter! I actually went to the board to write some sort of leading question, when I put my hand over my mouth and slunk away. My student teacher gave me a puzzled look. "I am shutting up, " I whispered.
When everyone had something down, I pulled the shade all the way down and asked them to find a rule for what they had just done. Lots of them had already done that, without being asked! Whoo hoo!
But still I shut up.
And gave everyone some more think time.
And, wow, was it worth it!
I asked her what the 4 and the 6 represented. "I don't really know. I just played around with numbers until it worked for finding the perimeter of every stage."
At this point we really needed to wrap up the warm up time and I was pretty pleased that everyone had done SOMEthing with this problem. But THEN, one young man said, "Uh, I did something different."
And it was SO fantastic, that I need to share it with all of you:
Enlarge this picture and take a REALLY good look at it all. This kid was on fire!!!!!
The words in green are my handwriting: I wrote as he explained his thought process to the rest of the class when we asked him questions.
When he was done, I bowed to him!
I wanted to weep. He saw what I had seen. And I almost stole his thunder, which would have been SUCH a tragedy. Instead, he had his moment in the spotlight. He helped 13 other kids see this pattern in a really unique way, and did it using language that the kids really understood. It was amazing.
And all because I have finally learned to ---------------------shut up.