A quick flip to the quadratics section in each of the six textbooks lying around here I find at least one problem about finding the width of some border. The concrete around a pool, the walkway around a garden, the frame around a picture, the border around a rug. I present to you the collage.
I don’t know.
And because I don’t quite know what else to do, I come up with a lame lesson idea: make the kids create a frame around a picture given a specified amount of frame, this should drive them bonkers as they won’t be able to do it perfectly (not even close!), and then they’ll beg me to show them the math to make this task easier. They beg, I win.
I give them the goods. To each kid:
- any old picture, size 6 cm x 11 cm
- a white frame, 4 cm x 7 cm (but they get 4 of these because they’ll mess up!!)
My one-way conversation with them about the task. I do the talking:
Framing is very expensive. Even if you have the stupid 50%-off coupon, it still costs a lot. For example, last year I took my son’s art work that he’d done for his IB Art class to Aaron Brothers to get them framed. I wanted them matted also — you do know that matting is a fancy word for cardboard so they can charge you more, right? — anyway, guess how much the total was? Over four hundred dollars! Four-hundred-dollars-and-that’s-with-the-friggin’-coupon. I told the sales guy, “My son is not Picasso. His drawings are half crap. I don’t even want them, you can keep them.”
Just kidding. I didn’t say any of that to him. Even though I wanted to. So, your job today is to be a picture framer.
Show me which one is the picture… Good. Now, hold up the piece that is the frame… Good. Think of that piece of frame as gold. It’s expensive.
How come I gave you 4 frames?… That’s right, you’ll probably make mistakes, so you get 4 trials.
Your job is to cut your [expensive gold] frame into pieces — strips — that will go around your picture. You have to use the entire 4 cm x 7 cm piece with no leftovers.
But you don’t want to cut it into a million pieces either. Fewer cuts means fewer pieces to seal back together to form a frame. And it looks nicer.
Almost immediately, I hear:
Marissa: What do we do?
Me: I just… e x p l a i n e d…
Malainy: I’ll tell her, Mrs. Win. Okay, you cut up the picture to make it fit into…
Me: What?! Cut the picture?! People bring in their most precious picture to you to frame and you cut up their picture?!
Malainy: Oohh noo. Then I’m not sure what we’re doing.
Someone: Do the pieces have to be even?
Me: Have you ever seen a frame with different widths?
A Different Someone: I don’t get what we’re doing.
Me: Should I just speak Chinese to you guys from now on?
Yep. This is pretty much a verbatim snippet of what goes on in my last period today.
After lighting my hair on fire, they manage to work diligently.
Sure enough. About 15 minutes later they grow tired of the frame pieces. A few almost have it, but they know this is not good enough.
They speak up:
There must be a better way to do this!
I’m gonna be fired because I’m wasting all these gold frames and still not getting it right.
My pieces are thick and thin everywhere.
I always have this left over stupid piece!
And here comes the money:
Can you please show us the math for this?
Thank you to Christopher for sharing with me on Twitter his 3 trials:
Thank you to Mike Lawler for sharing this video of him working through this problem with his young son.