Wednesday, April 16, 2014

Dirty Triangles

I've been out for a couple of days--let's just say that I can think of better ways to drop 10 pounds--so, I'm in a really special frame of mind today.  While I was out, I left a few distance/rate/time problems for students to solve.  Upon my return, I was asking students about the problems and many students had similar responses.

S:  "This is easy, you just use the Dirt Triangle."

Me:  "The what?"

S:  "The Dirt Triangle."

Me:  "Hmm. I don't know what that is."

S:  "Look, Mr. Cox it's like this...

"...You cover up the one you're looking for and if the other two are next to each other, you multiply.  If one is above the other, you divide."

Me:  "Really? That's strange.  I never learned the Dirt Triangle. I learned...

The Turd Triangle

S1: "No, that won't work. That's not what he[1] told us."

S2: "He said it didn't matter how we wrote it."

Me: "So which is it; does one work or are they the same?  Make your case and be ready to defend it."

Helping students develop a turd detector one day at a time.

[1] Students picked up the triangle in another class.  They said that the formulas were given early on and explained.  However, many were still missing problems so the triangle was introduced.

Anonymous said...

First, welcome back and I hope you feel better. Second, if you are looking for the ten pounds you lost, I may have picked them up on accident...they didn't have a name and I always seem to collect what others loose.

In regards to the post, this is another great example where students learn the algorithm, but probably have very little understanding of the conceptual idea. I love the questioning you asked to go deeper with. I am curious what the kids will come up with.

I am wondering if you have already thought of this as an averaging process. I am thinking of a lab a middle school science teacher teaches regarding the turd triangle. Students measure a distance, and then time cars as they pass by the residential side of his school. One of the things they calculate with this is their average speed, and they act like they are cops and if the person deserves a ticket for speeding. It also helps the discussion grow into what the difference between a scalar and a vector, but that's another story.

Anonymous said...
This comment has been removed by the author.
Curmudgeon said...

Love the scenario. Do you mind if I put this (edited slightly) on http://matharguments180.blogspot.com/ on the 26th?

@MathCurmudgeon

David Cox said...

Jeremiah:
Thanks. Finally feeling better.

At first glance, some students said,"they're the same." But then we talked about how they could take numbers that they could deal with intuitively and tested them against both triangles. Only then did they realize that one actually worked.

I like the speeding idea; may have to borrow that one.

Curmudgeon
Sure, use it as you see fit.

alex said...

Great post.
http://www.nfomedia.com/profile?uid=rJgSbgJ

alex said...