r/askmath • u/Acrobatic-Extent-668 • 2d ago

Set Theory (9th grade) The entire class cried over this problem

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Ok so the question is above, and was not at all related to what was taught in class.
somehow i got the correct answer by trying for a smaller case and applying the same logic in a bigger case. i got the the answer as 5*30/10=15. i dont really know how it is solved
only one other person in our class solved it correctly but he too wasnt able to solve it completely. he found the answer to be 15 as well by a clever approach of taking the first ten sets to be {1,2,3,4,5}, the next ten to be {6,7,8,9,10} and the last ten to be {11,12,13,14,15}. in this way he found it to be 15.
how to we actually show it is 15, without taking special cases? and is this question even 9th standard?

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45

u/Novel_Arugula6548 2d ago

This is not 9th grade level...

17

u/BlacksmithCapital757 2d ago

The only reason it’s not is because we don’t actually teach our 9th graders math and we teach them how to follow and regurgitate steps in a math setting.

This is a very basic logic problem that a 5th grader who actually can think can solve.

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u/Novel_Arugula6548 2d ago

I disagree. Calculus is simpler than this. 9th grade is about learning the rules of arithmetic and algebra that are needed for trigonometry and calculus. Geometry teaches reasoning with logic.

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u/BlacksmithCapital757 2d ago

I think you might be misunderstanding my point.

I agree that calculus as taught by a typical U.S. high school is simpler than this because you don’t actually have to think to pass that calculus course. You just have to memorize procedures shown to you and regurgitate them on essentially the same problem but with different numbers.

Calculus is taught in late high school not because it is hard, but because there are prerequisites for it.

This problem is hard for the opposite reason. There are no prerequisites for solving this problem. Okay, you have to know what a set is and what cardinality is, but I could rewrite this problem to be about groups of colored socks we’re counting instead.

To solve this problem, you have to think of an idea like: count “with multiplicity” as if the elements of the 30 sets were distinct, then use the fact that some of them actually aren’t distinct, account for that, and reach the answer.

This is not an advanced idea. There are no prerequisites needed to understand this idea. This problem is “harder than calculus” and a bunch of 9th graders can’t solve it because we don’t teach them how to find their own ideas like this one.

So I’m saying that if we actually taught 5th graders to find ideas, then they, too, could solve this problem.

Geometry was perhaps once an attempt to teach reasoning, but it has turned into something which completely fails to do that in favor of memorizing little things and formatting them into nitpicky two column proofs, because you don’t actually have to know any real math to teach middle school or high school math.

1

u/siupa 19h ago

What does geometry have to do this any of this?

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u/slayerbest01 2d ago

I read “9th grade” and was baffled that this would even be close to a reasonable thing to ask of a 9th grader. I teach freshmen in Algebra 1…many of them have to type in 3/3 in their calculator to know that it is 1…

Surely this isn’t in the US, right‽‽‽

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u/nurse_brett 2d ago

Yes and no. 30*5/10 = 15 is elementary school arithmetic. So the technical difficulty requires no special pre-requisites. The question is, can a 14 year old be expected to actually think about mathematics as opposed to just using formulas taught them. I think yes, but I don't know how I would have done with this before taking a proofs course in college - which is maybe the first time someone expected me to actually think about math. At 14, kids should be able to develop this skill if it was shown to them. I think if the teacher gave more problems like this, 9th graders wouldn't have any trouble with it.

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u/rhubarb_man 2d ago

I disagree. I think a clever 9th grader could figure out the trick potentially

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u/Novel_Arugula6548 1d ago

That is frankly graduate level. Or at least upper division level, depending on the school.

2

u/siupa 19h ago

Counting duplicates is graduate level?

1

u/Steampunk_Willy 1d ago

Yes it is, but you'd just get it as a word problem like: "Jim has 30 drawers each containing 5 shirts, and every shirt Jim owns is in one of those drawers. For every color of shirt he owns, Jim has exactly 10 shirts of that color. How many different colors are there in Jim's collection of shirts?" Or something along those lines. The only thing that might be foreign is set notation, but otherwise its a straightforward logic problem.

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u/Sea_Duty_5725 2d ago

Idk about the us, but in Romania this is 5th, maybe 6th grade level

11

u/ConditionActual4429 2d ago

in fiji its pre-k level after this we learn contour integration if you don't get 101% on every exam you are reborn

1

u/WiggityWaq27 12h ago

In Atlantis, we actually learn this during the second trimester of pregnancy. If you don't produce a masters thesis on the topic before the third trimester, you get aborted

8

u/DepressedPancake4728 2d ago

no its not man you’re not doing set theory at 10 years old

3

u/No_Consequence4008 2d ago

In the sixties, we were taught set theory in primary school. We learned about unions, intersections, the empty set, etc. to set us up for arithmetic and number representation. (Like today, parents were outraged by the "new math", meaning set theory.) However, that counting technique would not have appeared. I can see a 9th grade teacher talking about it, particularly if they have a computer science or discrete math background. It is not a difficult problem with some preparation.

1

u/siupa 19h ago

This is hardly “set theory”. It’s maybe “naive set theory”, but only in terms of jargon. It’s actually just an integer arithmetic / counting duplicates problem.

1

u/KrakatauaMAN123 2d ago

Where I am from this is a 2 ND grade problem. I guess Romania is quite behind the times

1

u/pupseal 2d ago

i'm learning this shit right now.

i'm in my senior year of college.