## Thursday, February 08, 2007

### 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.

mrsfoster said...

Hi, I really want to use this as a group activity for a review of factoring, but, I really don't get the puzzle solution! Can you explain it to me? I see the words "Do 5 PUSH UPS", but, it's in no order and there are a lot of additional letters. Is that suppose to be correct?

Thanks,

Michelle Venable-Foster

Dan Greene said...

It's in order if you read it left to right, bottom to top. It says "Do 5 pushups get a sweet treat". I realized later that this was a bit more confusing than I originally intended. But I didn't want it to be so clear, because I thought students would just try to assemble the puzzle based on the letters. When I make these puzzles now, I write numbers on the front only, and then at then end they have to convert the numbers to letters, and this seems to work out better. You could do that for this puzzle - just print out the problems only, make up a message that has 24 characters, and write numbers on it before copying.

See this post for a better description, and files you can actually download and edit.

mrsfoster said...

Thank you so much for explaining your message! You have no idea how long I tried to read that! I will be using it now! Thanks again.

Michelle

Dan Greene said...

No problem. I also updated this post so that the file can be downloaded directly in pdf or word form (I wrote this post originally before I started storing my stuff at box.net). I hope your students enjoy it.

I would also suggest making an answer mat for them to work with, where you photocopy a blank grid, but fill in two or three of the pieces to give them something to start with.

Jean said...

Enjoyed working on the puzzle and will definitely give it to my students to work on. Thanks. I am now inspired to come with something similar to use in my calculus class!
Jean

Jean said...

Thanks. This is a great activity. I plan on having my students work on it. You have also inspired me to come up with a similar puzzle for my calculus students.
Thanks Again

Jean said...

Enjoyed working on the puzzle and will definitely give it to my students to work on. Thanks. I am now inspired to come with something similar to use in my calculus class!
Jean