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