I felt a great disturbance in the math as if a million minds applied themselves to a problem and were suddenly silenced. I fear something terrible has happened.
A “simple” 3rd grade problem
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Re: A “simple” 3rd grade problem
#72[deleted]
Re: A “simple” 3rd grade problem
#73Earlier quoted context omitted.
Answer: 1, 2 and 2 cuts.
If I cut myself shaving in two places with one motion of my razor, how many cuts have I made?
The answer to this question is open for debate. You see you didn't specify whether you cut all the way through resulting in two halves of a person with one cut on one of them. And which one!
Re: A “simple” 3rd grade problem
#74Earlier quoted context omitted.
It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007
Look at the image provided with the question. It shows a saw cutting the board in a way that leaves it unambiguous - the cutting time for that cut would be identical regardless of where each cut took place.
That's not a board...
Re: A “simple” 3rd grade problem
#75The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only…
While, given the picture presented the child's solution makes the most sense, there is another close scenario in which the teacher is correct[1]. So its not really "as simple as that." [1] http://math.stackexchange.com/a/380007
this is not a plausible scenario at all. if the quantity of work done is not equal at each step the question is impossible to answer which means that the teacher is nor right, just there is a possibility to be right. but then, every answer could be right, just adjust your cutting path according to the answer you would like to be correct.
Re: A “simple” 3rd grade problem
#76There are no assumptions about the size of pieces. I can do it it 2 secs. Just pinch 2 splinters of the board.
Re: A “simple” 3rd grade problem
#77The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only…
My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.
You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.
Re: A “simple” 3rd grade problem
#78Earlier quoted context omitted.
Answer: 1, 2 and 2 cuts.
If I cut myself shaving in two places with one motion of my razor, how many cuts have I made?
If you ask me to make these cuts with a chop saw (or mitre saw if you prefer) I am making 1, 2 and 2 cuts. Where one cut is defined as pulling the trigger on the saw arm and pressing the handle down.
Re: A “simple” 3rd grade problem
#79I would've arrived at the teacher's solution, but the question allows different interpretations and both answers are correct assuming different interpretations. The correct answer would be "I do not know, this problem is under-specified."
I disagree with your logic. As the corner-cut solution shows, there are only two sane answers. "20 minutes" where you have cuts across the plank or "any* amount of time whatsoever" where you allow any kind of cut.
There is no sufficiently logical way to get to any particular number other than 20; the shape of the plank does not allow you to cut across and make your cuts intersect like you might with a square board. There is no reason on this particular shape to prefer "15 minutes" over "14 minutes" or "25 minutes". It all gets lumped into "any amount of time whatsoever".
If "any amount of time whatsoever" was an acceptable answer it wouldn't make sense that a single cut takes 10 minutes, so we should discard that answer. This leaves only one candidate answer, 20 minutes.
*"any" would be limited by how long of a diagonal you can make but it would be hours
Re: A “simple” 3rd grade problem
#80The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only…
It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007
If it is ambiguous, there is no answer. There must be an answer. Therefore, it cannot be ambiguous.
The answer given is the only one it is possible to give. Therefore, it must be the correct one.
The context isn't so much "third grade" as it is "math test", and very, very few math tests allow "Question ill-formed as posed" as a valid answer. Maybe more should.