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.