I’m not sure that my use of attend to precision is quite what SMP6 has in mind, but there was some interesting discussions in class yesterday.
As we ran out of time on a previous day, I had students jot down their measurements for their group’s cups on a post-it before they left.
And I had an issue with some of their information. Either their measuring was incorrect or their calculations were wrong. Didn’t matter which one really, I mean, it’s only math class. Right? Not like there is brain surgery going on or anything.
Most of the jibberish below will make no sense unless you were in class at that point in time. I wish I’d kept a clean copy of their information and created a new slide with each new comment made. The info is numbered with 1 through 7 if you can make that out in bottom corners of each box.
I simply stated I had an issue with some of their shared information and then gave them time to consider it. One by one students began pointing out some things they noticed or what the stack height should have been based on the initial measurements. If you can make out those expressions…
Then I actually stated, “Either some of your measuring was incorrect or you calculations were wrong. Doesn’t matter which one really, I mean, this is only math class. Right? Not like we’re doing brain surgery or anything.” Pause. “But what if you were really a box designer and your measurements and/or calculations were wrong? Do I fire you, or just give you a kind warning?” Pause. “Or let’s assign grades, since it is only math class, based on your preciseness. Who is the most wrong? Who is the most right? Who gets da da duh…the A?”
We looked at the amount each group missed their mark. Somewhere you’ll see a +3, +1, +1, +16, -0.8, ,+44. We guess group 6 mis-measured. But not sure what happened with group 7… Here’s where it became a little interesting…groups 3 and 4 appeared to be wrong by the same amount, but a student brought up… one group was off 1 cm from 15 cm and the other was off 1 cm from 18 cm. “What are you saying?” Group 3 has a bigger error than Group 4. Pause.
It was suggested we look at error compared to what the height should have been. And so we did. Group 7 caused some issue…can they be 290% wrong? Hmmmm. What do you think? What does that mean? One student said, they don’t get a second chance…they’re outta here.
Lastly, we took a look at error. One group submitted a rim measure of 1 cm when it should have actually been .6 cm. They were over .4 cm. Big deal, right? It’s a little less than half a pinky width. That’s not enough wasted material to get fired,right?
What if you had a stack of 10 cups? 50 cups? Not likely gonna get you fired.
But what about 500,000 cups? That’s 200,000 cm too much. CM are small, so not a big deal. Wait. 78,oooish inches, 6,561ish feet, 1.24ish miles. 1.24 miles of wasted material may get you fired.
Anyway, the size of the error is relative. It was a nice little discussion of how not being precise in our measurements may grow to an outlandish error is a larger context…outside of math class.