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A “simple” 3rd grade problem

math.stackexchange.com

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Re: A “simple” 3rd grade problem

#41

Post by quacker »

jrabone wrote: post #27
downandout wrote: post #15

The 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

In reality, it probably was not open for debate. This is third grade math, remember. The student probably spent the last three problems working similar questions covering ratios/fractions. And the student probably spent at least a few weeks of school working similar types of problems on homework. After so long taking these types of classes and tests, if a student answers a question without using knowledge gained from the class and gets the question wrong, well...what did they expect?

(Not saying I like it, but it's the way it is many places.)

Re: A “simple” 3rd grade problem

#42

Post by dfc »

utopkara wrote: post #24

This is a classical question I ask to children (and I was asked as a child too). It was/is fun, because it is easier to answer if you haven't yet started arithmetic, or if you can manage to step outside the pressure of this new thing that you are being taught at school. How many cuts do you need to make in order to split a board into 2? How about 3? How about 4? In this case, the teacher has failed. But, everybody mu…

Answer: 1, 2 and 2 cuts.

Re: A “simple” 3rd grade problem

#43

Post by dhimes »

downandout wrote: post #15

The 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.

Re: A “simple” 3rd grade problem

#44

Post by dfc »

wampey wrote: post #32
SilasX wrote: post #21

Earlier quoted context omitted.

>Can you explain why you think it has two correct interpretations? Because it depends on whether you 1) require that the N pieces be congruent and 2) what counts as a cut. I think the textbook answer is based on assuming 1) no, and 2) cutting along a line segment at least as long as a side. Alternately, what counts as a "board" and a "cut". Then you get the answer by assuming you cut a square board in half, then one…

I agree with you here. If a board is 2 x 2 and you cut it in half, you have 2 1x2 pieces. That took 10 minutes. If you cut one of those 1x2 pieces in half you could have 2 1x1 pieces of board, and one 1x2 piece of board, thus 3 pieces. The first cut took 10 minutes, the 2nd cut, being half the size of the original took 5 minutes, thus 15 minutes.

Lumber has three dimensions.

Re: A “simple” 3rd grade problem

#47

Post by DanBC »

downandout wrote: post #36
shurcooL wrote: post #25

Earlier quoted context omitted.

You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very ted…

True, but I think that maybe 1/3 or more of the students would have answered this correctly. At some point during the grading process, you would think the teacher would begin to wonder why all of these students would have answered such a seemingly simple question "incorrectly" and take a second look.

...because 'trick' questions are (at least, were) part of math. The justification is to make sure people read, and understand, the question.

Re: A “simple” 3rd grade problem

#48

Post by dhimes »

dfc wrote: post #42
utopkara wrote: post #24

This is a classical question I ask to children (and I was asked as a child too). It was/is fun, because it is easier to answer if you haven't yet started arithmetic, or if you can manage to step outside the pressure of this new thing that you are being taught at school. How many cuts do you need to make in order to split a board into 2? How about 3? How about 4? In this case, the teacher has failed. But, everybody mu…

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?

Re: A “simple” 3rd grade problem

#49

Post by josephg »

hmottestad wrote: post #29
SilasX wrote: post #21

Earlier quoted context omitted.

>Can you explain why you think it has two correct interpretations? Because it depends on whether you 1) require that the N pieces be congruent and 2) what counts as a cut. I think the textbook answer is based on assuming 1) no, and 2) cutting along a line segment at least as long as a side. Alternately, what counts as a "board" and a "cut". Then you get the answer by assuming you cut a square board in half, then one…

Like that: ------------- | | | | | | |-----------| | | | | -------------

There's a picture next to the question of a saw cutting a straight thin plank. Its very unlikely that this interpretation of the question was intended.
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