Not as often as you might think, but every now and then someone in our office asks me for help on a homework problem for one of their kids. Today I got asked to help out on this question:

In case the picture isn’t clear, you have an isosceles trapezoid with sides of length 24, 3x + 2, x – 4, and x – 4 and you are asked to find x. Plug and chug through the math and you’ll find that x = 14, but there’s a problem. Plugging in x = 14 you find a trapezoid with sides 24, 44, 10, and 10, which only works if the configuration is a straight line (or if you want to save a little face for the problem writers, a degenerate trapezoid).

I don’t like this question at all and I have all kinds of sympathy for any student who is confused by it.

Of course, there have been many examples of other poor test / homework questions. Patrick Honner quickly pointed out a bad trapezoid question on the New York State 5th grade math exam:

Two of my favorite examples of homework / exam problem goof ups are (1) this geometry problem from V. I. Arnold on Tanya Khovanova’s blog:

A Vladimir Arnold problem on Tanya Khovanova’s blog

and (2) the Pyramid puzzle which we talked about at the end of this Family Math project:

Octahedrons Tetrahedrons and the Pyramid Puzzle

But, despite the occasional fun story this type of question annoys me on homework and makes my blood boil on standardized tests. Hopefully today’s example will be the last one I see, but I’m not counting on it π¦

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Ah, but you overlook the educational value of the math joke – I spent an hour trying to figure out what was wrong with this when I saw it on your twitter feed earlier today. Finally had to make an 88-cm-long string and mark it at the appropriate places – at which point I realized, oh, I see, so every straight line segment is a trapezoid in disguise… mrhonner’s examples are a gold mine in that respect.

(by the way, it was also instructive in terms of culture clash: the people I typically hang out with wouldn’t notice the “degeneracy” any more than I did – but they’d be outraged by use of Comic Sans font)

π