Perplexing Polynomials

This has been a very busy and productive week. Maybe that explains why I haven't been able to post recently...

I just came back from an event at Villa Montalvo, a beautiful place in the mountains around Los Gatos where they host artists in residence. A group of poet/actors called headRush was in residence there and helped a group of our students create a one-act play. It developed from short skits to a larger play, and tonight they performed for their families and for the Montalvo guests on a real stage with lights and sounds. They were extremely nervous but did an excellent job, and there were many misty eyes in the house :)

I had a couple of good lessons this week in Algebra 2. On Tuesday, I taught them about u-substitution and how it can be used to convert expressions into quadratic form. I think this is a good thing to get used to, so these kinds of substitutions won't be as much of a mystery when they get to trig and calculus. Then, I handed out a factoring flow chart that I made. I'm not sure yet how effetive it will be, but now, whenever a student tells me that they don't know what to do next, I tell them to show me where they are on the flow chart. They groan, then open their binder and pull it out. They look at it, and then suddenly know what to do next, without me saying a word. It's magic!

Today, I spent a long time making a puzzle for them to solve, but it was worth it, as it was one of the best lessons I've had in a long time. I was inspired by my recent obsession with Perplex City to create this review activity. I made a 6 x 4 grid, where each square had various equations and/or solutions along the edges, and a letter on the back. The students needed to solve the equations and match them with the solutions in order to assemble the puzzle. Then, they had to turn over the pieces to see the message that was formed. When they responded to the message, they won the prize. Here is an image of the finished puzzle, which I also posted on ILoveMath.

Here is the puzzle in word and pdf form.



I gave students the cut out puzzle pieces, and all I told them was that they needed to figure out how to put the puzzle together, and that I'd know when they were done based on their actions. Most of the students were really confused at first, and wanted me to tell them exactly what to do. But I persisted in not telling them, and after a few minutes, they all figured out how the puzzle worked. I think this was a good move on my part, because the small success of figuring out what to do helped them get more excited about actually doing it.

I gave the students an hour to work on this puzzle (I wasn't sure if it was going to be too much or too little time). When there were 20 minutes left, most of the groups had some clusters of pieces assembled, but no more. I was worried that no one would complete it, but with 10 minutes to go, the first team got all the pieces together. They turned over the pieces and stared at the message for a while. The way they put it together, it was backwards and upside down, and it took them a couple of minutes to understand it. But then a lightbulb went on for them, and the four boys dove to the floor and cranked out their 5 pushups. The rest of the class (who had not yet read the message) looked at them like they were crazy. Another group was about to be finished, but one of the girls puffed in frustration (by accident) and all of their papers went flying. She was mortified; I need to think about laminating these for weight in the future. Then, two more groups got it, and 8 more kids jumped to the floor to do their pushups. A couple landed on top of each other. The prize was a lovely box of valentine chocolate cards that said, "You won my heart!". Of course, there were chocolate Kisses for all as consolation prizes. It was a lot of fun, and I hope someone else can use this activity and enjoy it too.

Tomorrow: polynomial long division! Hmm... I don't think it will be quite as fun, but not every class can be pushups and Kisses, I guess.