Zenoferox has a very hands-on way to teach his students a math problem: suppose you have a rectangular piece of paper, a*b centimeters on the side. You cut out four x*x squares at each corner, and fold the margins you get to get a box with one face missing. How do you choose x to maximize the value of the box?

For the exact answer in terms of a and b, ask Dr. Math. What I’m thinking of is more about teaching methods for maximum/minimum problems.

The creative exercises, like the box problem or the window problem (maximize the area of a window shaped like a semicircle sitting on a rectangle, given a perimeter a), are a good way of applying principles already learned. I still think the best way to teach the differentiation rule for maximum/minimum problems is to start with a rectangle of a given perimeter and ask to maximize its area. In that case there are enough alternative formulas to help create the intuition that the area is maximized when the rectangle is a square.

This entry was posted on Monday, December 25th, 2006 at 2:38 am and is filed under Academics, Mathematics. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

This is, to a large extent, a free space. I don't delete comments unless they're spam, viruses, impersonations, etc. Shameless blog-whoring doesn't count as spam, because that would just be hypocritical.