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:

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¦

One thought on “Math questions that make me groan”

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)

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