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A “simple” 3rd grade problem

math.stackexchange.com

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Re: A “simple” 3rd grade problem

#151

Post by shrikant »

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.

Surely I can't be the only one who wondered if the posts were of non-negligible thickness!

Re: A “simple” 3rd grade problem

#152

Post by GuiA »

katbyte wrote: post #81
GuiA wrote: post #70

Earlier quoted context omitted.

It's called grading on a curve, and it's (imo, unfortunately) very common in undergraduate courses in the US :)

it was used by many of my math & science classes here in canada, and i'm unsure why it is a problem? The prof would make the test very hard so the average was around 50-70 and then use a curve to get grades.

Curve grading is just conceptually silly. If a test does indeed cover the material, then answering correctly half of it should lead to a 50%, no more, no less.

If curve grading is required because the test doesn't properly assess what the students have been working on, that means the test was bad in the first place.

Re: A “simple” 3rd grade problem

#153

Post by GuiA »

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…

Thanks for a great, well-researched comment :)

Re: A “simple” 3rd grade problem

#154

Post by shrikant »

dfc wrote: post #116
rmrfrmrf wrote: post #114

Earlier quoted context omitted.

Unless you have some kind of vice holding that piece of wood together, you're making 3 cuts.

As I stated downthread: If you ask me to make these cuts I am plugging in my 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. Your "vice" will be my left hand pushing the wood against the fence and towards the stop block. Do you do a lot of woodworking?

For anyone else initially as confused as I was, dfc is saying that after the first cut, they would stack the resulting two pieces for the 2nd cut with the chop saw.

Re: A “simple” 3rd grade problem

#155

Post by sillysaurus »

waps wrote: post #143
Periodic wrote: post #120

Earlier quoted context omitted.

When I did my undergraduate degree in physics I think one of the best things I learned early on was estimation skills. I was used to doing things precisely and finding the tricks. Our professors made jokes about things just needing to be right to "within an order of magnitude", and it wasn't for two years that I internalized that. When you deal with the real world there are always a lot of errors and uncertainty in m…

I remember this from my first university physics class. We would derive a movement equation for a cannonball, to find the optimal angle to shoot a cannon for maximum travel. Everybody knew the answer of course, but we'd always just used the formula. This time we'd start with the obvious integration equation, movement + attraction between 2 point masses, integrate over flight time, and find the point where it crosses…

You may enjoy Feynman's excellent talk "The Relation of Mathematics and Physics": http://www.youtube.com/watch?v=kd0xTfdt6qw#t=1m05s

Re: A “simple” 3rd grade problem

#156

Post by noonespecial »

This seems like a simple matter of too many authors. The spec called for a question of the form "it takes x minutes to do two things, how many does it take to do three?", the copywriter remembered vaguely some brain-teaser question from his pre-SAT prep book and wrote the text of that already having the answer chosen as x + x/2, and then the layout guy picked a nice saw cutting wood from his clipart CD.

Add it all up and it only takes third grade math to know it equals fail.

Re: A “simple” 3rd grade problem

#157

Post by reeses »

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

Yet another reason Lisp > Python!

[1]> (+ (/ 12 13) (/ 7 8))

187/104

Re: A “simple” 3rd grade problem

#158

Post by reeses »

dfc wrote: post #44
wampey wrote: post #32

Earlier quoted context omitted.

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.

I read 2x2 and thought,"that's not a board!" and wondered why s/he was cutting it lengthwise to get 1x2.

If it was dressed, that 1 might be very small indeed.

Re: A “simple” 3rd grade problem

#159

Post by blei »

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…

Just curious: which aspects of this elementary math education would you say could be taught by automated high-quality means, such as the combination of interactive games and questions that many people are working on right now? I assume that video lectures would not be effective at that age.

Re: A “simple” 3rd grade problem

#160

Post by bigiain »

Periodic wrote: post #120
SiVal wrote: post #117

Earlier quoted context omitted.

I use the heuristic that many of us here probably use, consciously or not, after our years of experience with math problems: if it's a math problem, as opposed to problem in some other domain that ends up requiring math (science, accounting, carpentry, etc.), there will be some degree of artifice in the problem. Somehow, the numbers will just happen to end up being integers or perfect squares or exact multiples or wh…

When I did my undergraduate degree in physics I think one of the best things I learned early on was estimation skills. I was used to doing things precisely and finding the tricks. Our professors made jokes about things just needing to be right to "within an order of magnitude", and it wasn't for two years that I internalized that. When you deal with the real world there are always a lot of errors and uncertainty in m…

This is something I find tremendously useful in programming, but at the same time find a lot of other developers amazed when it's used.

I don't care if the dataset in memory is 553MB or 632MB - what I really need to know is whether it's "a few tens of MB", "a few hundreds of MB", or a "a few thousand MB".

I don't care if the API server can service 7321 simultaneous requests or 6578 - I just need to know if its "a few hundred", "a few thousand", or "a few tens of thousands".

You can solve an enormous number of engineering and architecture problems with a reliable order-of-magnitude estimate - at the very least you can quickly exclude solutions that are vastly under (or over) provisioned for the problem you're trying to solve.

A good order-of-magnitude estimate is also a great error check for a more detailed calculation, if my quick estimate said "5000-ish plus or minus 50%", and your calculation says "24,152", one of us has got something wrong.

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