Driving Them Nuts

I'm proud of my students. I'm proud of what we do in room 15. My classroom. My home away from home for the last 11 years. These bopping teenagers, sullen one minute bubbly the next, hormonal but invincible. They don't all love math like I do. (Not everyone loves college football, but we get along.)

What is happening in room 15 is the loud and proud math culture that we have set in place. We build it from day one — then we continue to do, say, and write stuff to sustain and strengthen the culture because we know our behaviors are our best evidence that this culture exists.

Here's one piece of that evidence:

Her frustration resulted in her loving the problem. Her last sentence is an enormous celebration of how much we honor the process of problem solving. Her classmates had their own reflections — short snippets of how they engaged in the problem.

They worked hard on the problem because it was driving them nuts. It's not unusual to hear kids blurt out, "This problem is making me crazy!" Or, "I won't be able to think about anything else until I get this!" Now, they've owned it. This isn't about a letter grade any more; and it certainly isn't about me.

This was the problem they'd worked on.

The Missing Area

A 10 by 16 rectangle is attached to a triangle as shown below. If the purple section is 24 square units, then what is the area of the yellow section of the rectangle?

John Golden, GeoGebra extraordinaire, created an animated gif of this problem.

Mike Lawler solved this problem using similar triangles.