Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2011/08/29/test-yourself-math-aug-29-2011/
This problem is based on the government bailout of General Motors. How much would the U.S. government lose if they sold all their G.M. stock right now?
Wrapping up this gift was much more challenging than I expected.
But it got me thinking about how this could be an interesting project. Questions such as “What’s the smallest square piece of wrapping paper that could do the job?” or “What kind of rectangle would work best?” are compelling and easy to investigate. And maybe someone could make a triangle or trapezoid do the job efficiently. There’s a lot of room for creativity and exploration here.
The usual restrictions on tearing and cutting would apply, although relaxing those restrictions might create interesting problems, too.
It wasn’t easy, but I did pick up some unexpected ideas along the way. And the gift was well-received, too!
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2011/08/08/test-yourself-math-aug-8-2011/
This question is based on a rash of bee hive burglaries in the Western U.S. How much is a bee hive worth?
A favorite pastime of mine is offering impossible problems to students as extra credit, like asking them to find the smallest perfect square that has a remainder of 3 when divided by 4. I don’t tell them the problems are impossible, of course, as that would ruin the fun. Usually it engages and confuses them, and it makes them suspicious of me. That’s a win-win-win in my book.
So while discussing some three-dimensional geometry, I offered extra credit to anyone who could build a model of a Klein bottle. The Klein bottle is a hard-to-imagine surface that has neither an inside nor an outside; it’s like a bag that is sealed up, but somehow the bag is inverted in on itself. If you are familiar with the Mobius strip, the Klein bottle is basically a Mobius strip, one dimension up.
One reason that the Klein bottle is hard to visualize is that it can’t exist in three dimensions. It needs a fourth dimension in order to twist around on itself, kind of like the way the Mobius strip (which itself is two-dimensional) needs that third dimension to twist through before you tape it back together. So, I was pretty impressed with the student who made this:
Not bad at all, for someone who is dimensionally challenged. Here’s a nice representation for comparison, although it’s still a cheat: the Klein bottle really doesn’t intersect itself.
A nice example of student work!
My contribution to Pi Day Celebrations: a student-made necklace that encodes the first 80 or so digits of pi in beads!
Starting with the pendant as 3, the student carefully strung the beads in a circle (clockwise) according to the following mapping:
Thus, you can read off 3.14159265358, and so on. A truly thoughtful, creative, and inspired work! I think the student’s original inspiration might have been this other pi-themed necklace.
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