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A “simple” 3rd grade problem

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Re: A “simple” 3rd grade problem

#21

Post by SilasX »

hmottestad wrote: post #8
kaeluka wrote: post #7

I 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."

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 of the pieces into squares (which requires cutting along a line segment half as long).

Re: A “simple” 3rd grade problem

#22

Post by jay_m »

bbx wrote: post #4

It's more a logic question than a math one. The confusion spawns from the fact that the three numbers present in the question are 10, 2, and 3 (so the thought process would be 2 = 10 min so 1 = 5 min, thus 3 = 15 min). But 2 represents the final state, though requires only 1 action (cut). And the required answer (time spent) is related to the number of actions, not the final state. This reminds me of the water lily p…

That water lily problem is very neat, hadn't heard of it before.

Re: A “simple” 3rd grade problem

#23

Post by [deleted] »

redblacktree wrote: post #12
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…

If you were to cut off two pieces of the board from an unknown source, you'd require two cuts. Three pieces would require three cuts (with the rest remaining behind). I don't think the wording really allows for this interpretation, but that is the only way I could explain the alternative answer.

[deleted]

Re: A “simple” 3rd grade problem

#24

Post by utopkara »

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 must have learned something out of this.

Re: A “simple” 3rd grade problem

#25

Post by shurcooL »

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 tedious. It's easy to scrutinize a single highlighted problem that someone got wrong in hindsight, not realizing the person might've only dedicated 7 seconds to this problem out of 1000 others that were graded correctly.

I personally try to give them the benefit of doubt and assume best case scenario (but I also understand it might not be).

Re: A “simple” 3rd grade problem

#26

Post by s_kilk »

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)

Re: A “simple” 3rd grade problem

#27

Post by jrabone »

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

Re: A “simple” 3rd grade problem

#28

Post by yew »

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…

Some people are arguing about whether 'cut into two' might really mean 'cut two off'. So I think your answer makes three interpretations (and nicely demonstrates that you do indeed have to specify things like "cutting is abstract and all cuts are of the same length").

The problem does specify 'works as fast' without any regard for length, though. And it obviously isn't actually a geometry problem because it doesn't even specify any ratios or angles - you could just cut a corner off and be done in a few seconds!

Re: A “simple” 3rd grade problem

#29

Post by hmottestad »

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…

Like that:

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Re: A “simple” 3rd grade problem

#30

Post by randlet »

jamessb wrote: post #17
moioci wrote: post #6

Who was it that said the biggest problem in programming is concurrency and off by one errors?

Well, Phil Karlton said that "There are only two hard things in Computer Science: cache invalidation and naming things". Some people list off-by-one errors as the third hardest thing.

I think the joke is: "There are only two hard things in Computer Science; cache invalidation, naming things and off by one errors".
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