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A “simple” 3rd grade problem

math.stackexchange.com

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Re: A “simple” 3rd grade problem

#31

Post by quacker »

bayesianhorse wrote: post #14

The problem at hand is "what are you supposed to do" vs the actual problem at hand. At first I had a difficulty seeing why 20 should be wrong, but then it dawned upon me: The teacher set out to create a word problem for a specific mathematic solution strategy. Students probably were inundated with this strategy for weeks before the test, so for them it is very clear what they were supposed to do.

Absolutely. The test was probably written by the person grading it to cover fraction/ratio problems. The question shown is a poor rewrite of something like, "If it takes 10 minutes to fill two buckets, how long does it take to fill three buckets?"

Re: A “simple” 3rd grade problem

#32

Post by wampey »

SilasX wrote: post #21
hmottestad wrote: post #8

Earlier quoted context omitted.

Can you explain why you think it has two correct interpretations? I obviously thought 15 min when I first read it and my brain didn't want to accept any other solution until I read the post below where it said 20 min and explained it as 2 pieces = 1 cut = 10 min, 3 pieces = 2 cuts = 20 min. And now I can't see why my first thought was correct. Did you come up with some good rationale as to why it should be 15 min or…

>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.

Re: A “simple” 3rd grade problem

#33

Post by hmottestad »

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: ------------- | | | | | | |-----------| | | | | -------------

Or you could say 11 minutes and do this:

  -------------
  |/          |
  |           |
  |-----------|
  |           |
  |           |
  -------------
Cut into two equal pieces and then cut off the corner :)

Re: A “simple” 3rd grade problem

#34

Post by downandout »

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

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.

Re: A “simple” 3rd grade problem

#35

Post by randlet »

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

It's only open for debate if you're being extremely pedantic. There is even an illustration demonstrating exactly what the cuts look like!

Yes, if you want to be very nit-picky the question is undefined, but this is a third grade math test and the only reasonable answer is 20min. The student was absolutely correct.

Re: A “simple” 3rd grade problem

#36

Post by downandout »

shurcooL wrote: post #25
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…

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.

Re: A “simple” 3rd grade problem

#37

Post by learc83 »

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

There is a picture of that illustrates the cut that is being made well enough to infer.

Some inferences have to be made, this is a human taking the test not a robot, and it's a 3rd grade test.

Even if the size of the pieces were specified, she could be cutting a different kind of wood or using a different saw or the humidity level could be different, but she's still "working just as fast".

3rd graders would be confused if you attempted to be completely unambiguous with this time of question.

Re: A “simple” 3rd grade problem

#38

Post by randlet »

Anybody talking about how this problem is ambiguous or under-specified are of course technically correct. By making that claim though, you are ignoring the context of the problem!

This is a 3rd grade math test that even includes an illustration of how the cuts are made! Within that context, the answer is unambiguously 20 minutes.

Re: A “simple” 3rd grade problem

#40

Post by hashmymustache »

s_kilk wrote: post #26
auctiontheory wrote: post #20

A friend of mine teaches school in rural North Carolina - here's what she tells me. Her school has to meet certain percentage-based "standards" - I forget the exact numbers, but let's say 75% is the cutoff. So now when Joey gets 5 answers right out of 10, the resulting 5/10 is defined as "75%." We're doomed.

Wait... How on earth do they justify redefining 50% as 75% ? (or whatever the actual numbers are)

sounded like teachers were scaling performance to meet standards instead of adjusting teaching quality
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