It depends on the shape of the board. If it's a 2x4, and cutting off a section of it takes ten minutes, yes, the student's right.
But what if it's a square sheet of plywood? Cutting it half takes ten minutes. Then take one of those pieces (which are now rectangular) and cut it in half in the short way. That's half the distance, so it's only five minutes. Another five minutes to cut the other piece in half, and you have four pieces in twenty minutes.
Of course in the sheet-of-plywood scenario since the size of the pieces aren't specified, you could just lop a couple of corners off of the plywood and call it done in a couple of minutes.
But considering the illustration, I'm going to call this one a poorly worded question and either a dumb teacher or a teacher who's really over thinking it.
The question is not about how many boards, but how many cuts it takes to make that number of boards. 1 cut makes 2 pieces. 2 cuts make 3 pieces. End of story.
The teacher is guilty of bad reading comprehension when she copied the question from another source. The teacher obviously didn't come up with the question on her/his own.
Mel V., A sheet of plywood isn't a board. It clearly says a board.
The student is right because Marie makes one cut to divide the board into two pieces, taking 10 min. To make three pieces she will make two cuts, taking 20 min.
Actually, there is ONE more alternative and correct solution - but one without an answer.
Once the board is in two pieces, either piece can be cut, right?
But it doesn't talk about the option to make the next cut across the board. It COULD be down the length of the board - whose length is not known and whose cutting time - "at the same speed" - would also be unknown.
it'll take her 10 minutes to saw the second board. The question supplies the answer with no math work required at all. "if she works just as fast" indicates the next task takes the same amount of time as the first task. So the correct answer is 10.
if the question was "If she works just as HARD how long will it take her to saw another board into 3 pieces?" the answer would be 20 minutes for the two cuts to ge three pieces.
Given the information presented, the student is right. I'm not entirely sure the teacher is wrong, unless they were scoring this test without a corresponding answer sheet from whoever put together the test - and if that's the case, they're wrong and the teacher didn't catch it.
It's math, not an exercise in language, although tests do sometimes fall prey to semantics. It's a poorly worded question wrapped around a simple math problem. You could say the entire task takes the same amount of time and have Marie end up with 10 boards instead of two - and you see how applying language works against what the question's asking. No need to complicate things any further.
The teacher (or test writer) may have been overthinking it, but they aren't alone.
Ah, but the simple math problem is defined by the language with which it is described. Therefore an ambiguous question creates an equation with poorly defined variables. The answer to that equation will depend upon one's interpretation of those variables. Exercising proper use of language is ESSENTIAL in word problems.
I would politely disagree. The problem is NOT poorly worded. ONE cut will make two pieces out of one. To make three pieces, it ALWAYS takes two cuts. There is no ambiguity. It is not a matter of language. The teacher had a brain fart - or the teacher had never cut a board. It is a problem of either a stupid teacher or an ignorant teacher.
The math teacher is skimming the word problem for the numbers involved. The teacher isn't counting the cuts (which are not listed specifically) and that's the mistake. Number of cuts (C), can be one less than the number of resultant pieces (P): P-1=C critical thinking is important in mathematics, too!
According to the pattern that the teacher assumed (of which there was no basis on) it would take her five minutes to saw the board into one piece, which would be taking 5 minutes to reach the objective of doing nothing. So yea, wtf
It depends on the shape of the board. If it's a 2x4, and cutting off a section of it takes ten minutes, yes, the student's right.
ReplyDeleteBut what if it's a square sheet of plywood? Cutting it half takes ten minutes. Then take one of those pieces (which are now rectangular) and cut it in half in the short way. That's half the distance, so it's only five minutes. Another five minutes to cut the other piece in half, and you have four pieces in twenty minutes.
Of course in the sheet-of-plywood scenario since the size of the pieces aren't specified, you could just lop a couple of corners off of the plywood and call it done in a couple of minutes.
But considering the illustration, I'm going to call this one a poorly worded question and either a dumb teacher or a teacher who's really over thinking it.
So, you consider a "sheet" of plywood a board, not a sheet?
DeleteI perceive a teacher whose never gut a board into 2 OR 3 pieces.
The question is not about how many boards, but how many cuts it takes to make that number of boards. 1 cut makes 2 pieces. 2 cuts make 3 pieces. End of story.
DeleteThe teacher is guilty of bad reading comprehension when she copied the question from another source. The teacher obviously didn't come up with the question on her/his own.
If it takes Marie 10 minutes to cut a board in half, she shouldn't be thinking about a career as a carpenter.
ReplyDeleteMel V., A sheet of plywood isn't a board. It clearly says a board.
ReplyDeleteThe student is right because Marie makes one cut to divide the board into two pieces, taking 10 min. To make three pieces she will make two cuts, taking 20 min.
I am sure the reason we are seeing this is because the student called the teacher out on this. And then really wanted to rub the teacher's nose in it.
DeleteActually, there is ONE more alternative and correct solution - but one without an answer.
DeleteOnce the board is in two pieces, either piece can be cut, right?
But it doesn't talk about the option to make the next cut across the board. It COULD be down the length of the board - whose length is not known and whose cutting time - "at the same speed" - would also be unknown.
If for the second task, Marie uses the other side of the saw, the one with teeth, it will take thirty seconds.
ReplyDeleteit'll take her 10 minutes to saw the second board. The question supplies the answer with no math work required at all.
ReplyDelete"if she works just as fast" indicates the next task takes the same amount of time as the first task. So the correct answer is 10.
if the question was "If she works just as HARD how long will it take her to saw another board into 3 pieces?" the answer would be 20 minutes for the two cuts to ge three pieces.
Given the information presented, the student is right. I'm not entirely sure the teacher is wrong, unless they were scoring this test without a corresponding answer sheet from whoever put together the test - and if that's the case, they're wrong and the teacher didn't catch it.
ReplyDeleteIt's math, not an exercise in language, although tests do sometimes fall prey to semantics. It's a poorly worded question wrapped around a simple math problem. You could say the entire task takes the same amount of time and have Marie end up with 10 boards instead of two - and you see how applying language works against what the question's asking. No need to complicate things any further.
The teacher (or test writer) may have been overthinking it, but they aren't alone.
Ah, but the simple math problem is defined by the language with which it is described. Therefore an ambiguous question creates an equation with poorly defined variables. The answer to that equation will depend upon one's interpretation of those variables. Exercising proper use of language is ESSENTIAL in word problems.
DeleteI would politely disagree. The problem is NOT poorly worded. ONE cut will make two pieces out of one. To make three pieces, it ALWAYS takes two cuts. There is no ambiguity. It is not a matter of language. The teacher had a brain fart - or the teacher had never cut a board. It is a problem of either a stupid teacher or an ignorant teacher.
DeleteThe math teacher is skimming the word problem for the numbers involved. The teacher isn't counting the cuts (which are not listed specifically) and that's the mistake. Number of cuts (C), can be one less than the number of resultant pieces (P): P-1=C critical thinking is important in mathematics, too!
ReplyDeleteYes. Nice going.
DeleteAccording to the pattern that the teacher assumed (of which there was no basis on) it would take her five minutes to saw the board into one piece, which would be taking 5 minutes to reach the objective of doing nothing. So yea, wtf
ReplyDeleteROFL. Nice take on it!
DeleteCutting the board into one piece is hilarious...