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A “simple” 3rd grade problem

math.stackexchange.com

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Re: A “simple” 3rd grade problem

#131

Post by jasomill »

keithpeter wrote: post #68
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…

Yes. This is the '10 posts, nine spaces' problem. Here is another version: A fence is made using 15 posts spaced equally along a straight line. There are 3m between each post. What is the distance between the first and last post? When I'm teaching this kind of thing, we go out and walk around the building site opposite with a few 15m measuring tapes. The physical walking out and measuring helps.

So does considering simpler cases of two posts (3), three posts (3 + 3), and four posts (3 + 3 + 3), then discovering the pattern (3(n - 1)).

Re: A “simple” 3rd grade problem

#132

Post by superuser2 »

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.

>Her school has to meet certain percentage-based "standards"

I went to a top-5 public high school in my state. "Standards" are so ridiculously low it's hilarious. I'm pretty sure you could still exceed the state standard for 12th grade reading with the reading level most of us (upper middle class, white, college-educated parents, high property taxes) had in 5th grade. Meeting standards certainly didn't mean you were even remotely qualified to go to college, and is orders of magnitude below the aptitude required to get into good colleges. So when I hear about districts where just reaching the standards is a stretch, it's shocking just how enormous the gulf in education quality in this country really is.

IMO this is a great argument to stop controlling schools at such a hyper-local level. There's no good reason for K12 education to vary geographically. The education that the professional world will expect of a kid in Chicago is the same as what it will expect from a kid in small-town Alabama or rural North Carolina. Why do we accept the argument that K12 education should be up to the community? Why is preparing workers for a global economy considered a local problem?

Because it's disgusting just how better-prepared I am than the children in your friend's school district. I didn't earn parents who can afford to live in an expensive community, I didn't earn the ability to take AP classes from talented teachers, I didn't earn a calculus teacher who refuses the school-provided textbooks in favor of illicit PDFs from a curriculum being drafted by one of her colleagues, I didn't earn a veteran teacher and former DuPont research scientist to get me a 5 in AP Chem. All our STEM AP programs get 4s and 5s save for a small handful of slackers; the teachers calm us down when we're getting nervous by reminding us that we're being graded on a curve alongside kids from the middle of nowhere. The opportunties we had that other communities don't is just staggering.

Re: A “simple” 3rd grade problem

#134

Post by jimmahoney »

tokenadult wrote: post #97

I read all the comments on the math.stackexchange.com submission and all the comments here before starting to type this reply. There are a lot of issues here, and I will try to add the perspective of a mathematics teacher. The reason I can gain paying clients for my mathematics lessons even though I have no degree in mathematics and no degree in teaching is that I can produce results that many elementary school teach…

In terms of your fraction problem, given that this is HackerNews I'm surprised that no one claimed that the answer should be zero. :)

  $ python
  >>> 12/13 + 7/8
  0

Re: A “simple” 3rd grade problem

#135

Post by pjungwir »

dos1 wrote: post #106
sillysaurus wrote: post #101

Earlier quoted context omitted.

It seems likely that no one taught those students how to think about math. I.e. teaching students the steps to solve a math problem is not teaching them how to think about the problem. I instantly knew 12/13 + 7/8 was ~2 because I visualize two pie charts in my head, both of which are mostly full. This is in contrast to the other way to solve the problem, converting the fractions to a common denominator and then divi…

It's always interesting to hear how people go about solving math problems. You mention a pie chart visualization and then the much more labor intensive (but maybe "correct"?) method. I used a third way, which was thinking that 13/13 would be one, so 12/13 is pretty close, so that's ~1. And 8/8 would be 1, so 7/8 is pretty close and also ~1. 1 + 1 = 2 :) I imagine there are myriad other ways people approach estimation…

As I read the question, I was prepared to work it out the hard way, and when I got to the part about not choosing the exact answer but only the closest, I was really dismayed because I thought I'd also have to work out how close each choice was to the actual value. Then I saw the possible answers and I thought, "Oh, 2."

Re: A “simple” 3rd grade problem

#136

Post by alok-g »

downandout wrote: post #102
Total_Meltdown wrote: post #98

Earlier quoted context omitted.

It is open for debate. The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes. It's a bad question. Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considerin…

As someone said below, it's only open for debate if you want to be pedantic. The Dr. Sheldon Cooper's among us may debate it, but it's pretty obvious what the question was looking for. There is even an illustration showing the cut, which would take an identical amount of time.

The question says "board" while the illustration shows more of a rod. I deduce the question to be at least one of inconsistent or incomplete.

Re: A “simple” 3rd grade problem

#137

Post by alok-g »

jay_m wrote: post #22
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.

My teacher used to give me this example when I was a kid: You see one matchstick with one eye. How many will you see with two eyes? :-)

Here's another one that used to confuse high school students in my class: You look at a 10 degrees angle with a lens of 3X magnification. How much would the angle look like? :-)

Re: A “simple” 3rd grade problem

#138

Post by pbreit »

wissler wrote: post #133
pbreit wrote: post #54

Only on HN would you find people trying to make the case that the question is ambiguous. What is the matter with you people?

I wish this kind of problem were only limited to HN...

You sorta wish or hope that the intelligence here is a tick higher.

Re: A “simple” 3rd grade problem

#139

Post by alok-g »

randlet wrote: post #38

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.

Some kids are smarter than others in a given grade, and would spot the ambiguities nevertheless. This used to be a problem I consistently faced in both school and college.

Re: A “simple” 3rd grade problem

#140

Post by mrdmnd »

jimmahoney wrote: post #134
tokenadult wrote: post #97

I read all the comments on the math.stackexchange.com submission and all the comments here before starting to type this reply. There are a lot of issues here, and I will try to add the perspective of a mathematics teacher. The reason I can gain paying clients for my mathematics lessons even though I have no degree in mathematics and no degree in teaching is that I can produce results that many elementary school teach…

In terms of your fraction problem, given that this is HackerNews I'm surprised that no one claimed that the answer should be zero. :) $ python >>> 12/13 + 7/8 0

You must not be using python 3, then.
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