On Sep 2, 2013, at 2:25 AM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> I was agreeing with your first paragraph. I agree that I have to go to the board and teach the content, proving that the Pythagorean theorem is correct and that the law of sines is correct. You may be surprised to learn that just because I teach it some of the students don't learn it... :-)
True, I don't expect all students to get it. I am not sure how that leads to doing activities that forgo the math altogether. What do the students that get it do during this time? Keep their mouths shut? But I am still mystified that in all the years of posting here you have never posted about the "content", yet you state "Yeah, sure, I teach all the content." What I see in these activities is evading "teaching the content". In an actual class, whether it be algebra or geometry after algebra, the "popcorn picker" problem would be nothing more than a word problem, maybe accompanied by a figure, and solvable by a student, using algebra, in a few minutes.
But that is not how it is presented by Dan because Dan clearly is not presenting this activity in the context of algebra.
If this was an actual algebra class, this would have been the end of it.
2. Write down a guess.
Guess? Guessing isn't algebra. Guessing isn't even mathematics.
3. What information would be useful to know here?
This sounds very much like asking the students to guess again. Maybe if question 2 wasn't there, this might be a sincere question.
4. Can a rectangular piece of paper give you the same amount of popcorn no matter which way you make the cylinder? Prove your answer.
After the student answers question 1 (algebraically) this question is moot.
5. How many different ways could you design a new cylinder to double you popcorn. Which would require the least paper?
This is guessing again.
6. Is there a way to get more popcorn using the exact same amount of paper? How can you get the most popcorn using the same amount of paper?
Not only does this activity not include a lick of "teaching" algebra, it evades algebra, because had the properly prepared student established the algebraic relationship between the dimensions of the paper and the volume of the cylinder, all of these questions, except the first one, are moot.
Richard, why must "regular" students suffer this fate?