So this is supposed to be really simple, and it's taken from the following picture:

book image


It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will it take for her to saw another board into $3$ pieces?

I don't understand what's wrong with this question. I think the student answered the question wrong, yet my friend insists the student got the question right.

I feel like I'm missing something critical here. What am I getting wrong here?

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    $\begingroup$ This is simultaneously wonderful and sad. Wonderful for the student who was level-headed enough to answer this question correctly, and sad that this teacher's mistake could be representative of the quality of elementary school math education. $\endgroup$
    – Jared
    May 3, 2013 at 3:38
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    $\begingroup$ I took five minutes per cut. One cut yields two pieces. Two cuts yield three pieces. And so on..... $\endgroup$ May 3, 2013 at 4:40
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    $\begingroup$ I think the issue is that the language and image are incongruent. The question should have been "10 minutes to saw 2 pieces from a board" (2 cuts), then the teachers answer would be correct. As it is stated, it implies sawing a board in half (1 cut). $\endgroup$
    – Vijay
    May 3, 2013 at 5:23
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    $\begingroup$ The language and the image are in perfect agreement- the image shows two pieces resulting from a single cut. $\endgroup$
    – JayL
    May 3, 2013 at 8:01
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    $\begingroup$ By the way, originally this was posted as "Teacher Math Fail" at zerooutoffice: zerooutoffive.blogspot.com/2010/10/teacher-math-fail.html $\endgroup$
    – azimut
    May 6, 2013 at 20:21

32 Answers 32


You can cut the board in less than a second because assuming you can cut out 2 extremely small pieces of the board and if she works at the same rate this should take less than a second.


What's critical is the action at hand. The rate should not be of making pieces, but cuts. This is what's shifting the rate. A cut in 10 minutes mean 2 cuts in 20 minutes, which is necessary for 3 pieces.


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