### Math teacher's error

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

The teacher marked this answer (20 minutes) wrong, and wrote down 15 minutes as the correct answer. Why is the teacher in error?

Ricochet said…
Because the girl will have to make a cut exactly the same as the first. Since we are not adding a second worker sawing at the same time, we will get no time benefit.

Wanna bet the math teacher has never sawn anything?
chihungchan said…

If everybody gets the same answer, it has to be right. Is it ? , with a follow-up in part 2 to find out what the answer will be within a given tolerance.
Jeff Thomas said…
The teacher mistakenly related time to pieces when in fact it is time related to cuts. If it takes 10 minutes for one cut (2 pieces), then it will take 20 minutes for two cuts (3 pieces). This is a great problem, one that can help teach problem solving skills. If the teacher had drawn a picture of the problem, the answer becomes obvious.
Su said…
The teacher is making the mistake of counting the *pieces* instead of counting the *cuts*.
Anonymous said…
This is an example of the "fencepost error" that plagues programmers.

More deeply, though, it is an example of how non-mathematical knowledge is crucial in word problems. The teacher made the same mistake many students make, she plugged the numbers mentioned in the problem into a convenient formula and called it good.

Teaching calculus to engineering students I was dumbfounded to see how many of them could not set up the equations for simple "tanks and pipes" problems. They simply had no notion of how water flows. It seems so basic I was at a loss for words how to begin to explain it.

There's no substitute for a well-labeled diagram when solving any problem.
Anna said…
Wait! There *is* a diagram on the page, demonstrating the single cut for two pieces. Oy.
David said…
The question is vague. It doesn't tell you anything about what the pieces should look like when you are done (equal size, etc).

If I cut a square board in half vertically, then cut one of the resulting pieces in half horizontally, it _will_ be 15 minutes, because the second cut will take half the time of the first cut.

Granted, the teacher was most likely NOT thinking about that, but it does illustrate problems are often not as clear cut (no pun, honest) as you might first think.
Anonymous said…
Is there a source for this picture? That is, it is real? Public, private, or home school? What book is illustrated?

thanks
jah
Maria Miller said…
Unfortunately I don't know the source, not even if it is real. I have seen the picture posted online in many places but no one has cited a source.
Anonymous said…
The only answer that makes sense is 20. If "20" is NOT the correct answer, then there is an infinite number of correct answers. There are too many unknowns. (1) We do not know the dimensions of the boards. (2) We do not know the manner / direction in which the pieces will be sawn. As someone said, the first cut could be in one direction and the second cut could be in another direction, at an angle to the first.

For example: If the board is perfectly square, and of the same width and thickness as the original board, then two perpendicular cuts would take 15 minutes, as the teacher said. But if the board is of a different length, it could take 11 minutes, 3,000 minutes, 2.7 minutes, or any number of minutes you would care to put down. All answers are correct. :)

If the board is a flat circle, with thickness the same as that of the original board and radius equal to half the width of the original board, then three cuts from equidistant points on the circumference to the center would result in three equal pieces and this would take 15 minutes... but the problem didn't exactly so stipulate, did it? Interesting.
Anonymous said…
If this paper is what I think it is. It looks like a Math Super Stars program that some Florida schools use as an extracurricular activity. Most of the time volunteers are used to score the papers and they may or may not the answer sheet that goes with it.
Anonymous said…
logic says it is 20
but if we look at it with a proportionally way it will be 15
the time needed will be ( 3 multiplying by 10 divided by 2 )

but i do not accept that way

logic is better even though it is wrong
Brian (Australia) said…
I am amazed anyone could come up with 15 minutes. You just have to picture the problem in your mind and the answer takes a fraction of a second to deduce. Obviously in questions like this you make many assumptions - like we're talking about a similar board, and we're making cuts across the board in the same direction (as shown in the picture)
Michelle said…
Yes, this is a real Math problem. It is taken from "Math Superstars" Program for Second Grade, Week 6. This is an enrichment program that is used in public schools in FL (and maybe elsewhere?). I pulled the worksheets to use in my homeschool as well. The program offers stars as rewards, and when the student amasses a set number of stars they get a physical reward such as a pencil, sticker, pizza party, etc.
Aly V said…
If you factor in the learning curve, the second cut could take less time. I would not have marked 20 minutes wrong but I might have considered 15 minutes if the student was able to support her reasoning.