Most of my more advanced students have worked their way through most of the first five tasks. I've had some interesting conversations with students-especially the more advanced ones.
One of the restrictions in the project is that cotton can take up no more than 80% of their land.
The inequality I was presented with this morning was: c
"So why is that your inequality?"
"Because I can't have more than 80% cotton, I need to multiply by .2"
"Because it has to be less than 80%."
"Alright. What's the maximum number of acres you can use for cotton?"
"700 times .8 which is 560. Oh, so I need to multiply by .8 and not .2."
"So what is that going to look like on your graph?"
"I go to 560 on the x axis and shade to the left."
"Are you using a number line or the coordinate plane?"
"Coordinate plane. I need to find a polygon to shade for all of my restrictions."
"If 560 is your maximum, what is the minimum?"
"Because if 80% is my maximum, 20% is my minimum."
"Step away from the math for a minute and tell me what is the minimum number of acres you can farm."
"So you're telling me that if you are a farmer, you can be required to farm a certain number of acres of a particular crop?"
"No, but if I am trying to maximize my profit, I wouldn't farm zero acres."
"Ah, but what was my question?"
"What is my minimum?"
"And what would that be?"
I find this type of exchange to be pretty common with my students. It's almost as if they are trying to live up to some sort of image of what a good math student looks like and often they check the common sense at the door. Kind of like the opposite of what Jason describes here.
I run into that same problem daily as well. "Stop making it so hard!" is what I usually end up saying in frustration. They get so used to "following directions" or using formulas that they don't think about the concepts they already know.
But, I think "we" are part of the problem here. On the one hand, we want them to "use common sense" in situations like these. On the other hand, when we ask them to prove that these two sides have the same length, they're not allowed to say, "Because it looks like it!"
The balance between "rigorous proofs" and "obviously!" is not always an easy one to strike, I think.
So true. I wonder if the teachers who teach the grades below us are having the same conversations about kids wanting their hands held.
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