The Pythagorean Leash

One of the most important things I think that I can train kids to do in geometry class is to draw pictures. Any time they come across a word problem, they need to be able to translate it into a picture because 90% of the time, word problems aren't that challenging if you can get the picture right. Furthermore, translating word situation into a mathematical model/equation is a skill that will be legitimately useful for them long after they've left school (just ask the history teacher who came to me the other day trying to figure out how many points his final exam should be worth).

I'm also a huge fan or word problems because I love writing ones that will elicit awesome drawings. I get a sad when I have to write ones like "Point A is the midpoint of BC and angle JKL is bisected by ray KM and WU is the perpendicular bisector of XY such that WU is the altitude of triangle WXY..." because those pictures just end up being shapes with a lot of letters on them. The good problems are ones like I put on a recent quiz. The gist is that Julian/Karla (obviously I always use student names and weirdly, the kids--even in high school--still LOVE it) is walking his/her pet spider/pig and I give dimensions about the height that Julian/Karla is holding the leash and how far the pet is in front of its owner. It's just a simple pythagorean theorem problem, but the pictures are the good part.

The pig in this first one looks so happy and carefree. Maybe because he is out for a lovely walk instead of taking a geometry quiz.

 

My favorite part of this one is that the pig is explaining all of the answer. I wonder whether the speech bubble was planned in advance or a last-minute add-on. Either way, brilliant.

 

Here, I can't figure out if this student named the pig because (1) she had too much time left and got bored, (2) she was killing time trying to figure out the problem, (3) she really needed to have a name for the pig in order to make the problem feel accessible, or (4) she knows more details about Karla's pets than the rest of us do (this student is one of Karla's good friends).

 

Not to judge students' artistic skills, but this is the least pig-like pig I saw on anyone's paper.

 

I think I have really gotten through to this student when I've stressed the importance of labeling everything you know about a picture. I'm so glad he labeled everything because I definitely would not have known which was the spider and which was Julian.

 

This is my favorite picture out of any of them. In case you can't tell (sorry, I took these with my camera phone as I was grading them), the spider-walker's t-shirt says, "Hi! I'm Julian."

 

And I'll conclude with a kid whose math skills are doing fine (he got the problem right, at least), but who could use a little work on his reading comprehension.