## Thursday, May 9, 2013

### Boxing it up!

On the second (or third?) day of school my Precalc kids are tasked with making a box. I cut up different colors of card stock into various sizes and they have to determine how much to cut out of each corner to create an open box. (I wrote more about it here.)

It's a good reminder of a lot of function stuff - graphing, domain, max and min, zeros. And it gets them to start thinking out of the box. (Ha!)

Once they're done, I have them write up a sheet that I call the Summary Sheet. It has their original paper dimensions, the formula they used to find the optimum height (l x w x h) and their simplified version V(x) = 4x^3 + . . .

I keep it. I pitch the boxes. (Who has room for 70+ open paper boxes?!)

Today we were finally ready to follow up on the boxes. I gave them what I called the "Box Project Follow-Up"  (I know... what an imaginative title!)

I was out this morning because I had to take a little girl to the doctor, but I made it back for my 3rd precalc class. They tend to struggle a little more with ideas, so it was nice to be here.

The gist was to find the derivative of their volume formula (although we haven't named that the derivative yet, but we've talked about how it's the slope of the function when given a point x) and then set that equal to 0. (Why?  I'll ask tomorrow and see if anyone thought about that....)

Several kids wanted to try and factor the nasty quadratic that they ended up with, but most went straight to the quadratic formula. It works out so that of the two answers you get, one is too big (more than width/2) and one of them is the value that they cut out as their height.

It was fun to see the lightbulbs go on when the kids realized that the value they found from graphing in August is the same as the value they found using a limit in May!

We've learned so much since then. :)