[HN Gopher] Math Problems for children from 5 to 15 (2004) [pdf]
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Math Problems for children from 5 to 15 (2004) [pdf]
Author : sebg
Score : 325 points
Date : 2021-07-19 17:11 UTC (5 hours ago)
(HTM) web link (www.imaginary.org)
(TXT) w3m dump (www.imaginary.org)
| gnull wrote:
| For Russian-speaking readers here who may want to challenge their
| children, here's the (original?) open book in Russian:
| http://ilib.mccme.ru/pdf/VIA-taskbook.pdf
| coolspot wrote:
| I suspect Russian-speaking readers of HN mostly have kids who
| can't read/write Russian, unfortunately.
|
| Like my daughters, for example.
| gregsadetsky wrote:
| There are interesting Wikipedia articles on this topic:
| "Heritage language"
|
| https://en.wikipedia.org/wiki/Heritage_language
|
| https://en.wikipedia.org/wiki/Heritage_language_learning
| gizmondo wrote:
| How actively did you try to teach them to do that?
| amativos wrote:
| Thank you for that link! I can read Russian and that version is
| much clearer.
| anonymousDan wrote:
| What I would like is a book of projects/real world
| problems/applied maths relevant to kids from age 5 on that could
| be used to motivate them better than rote memorization.
| ordu wrote:
| The problem #13, mentioned in the introduction, is said to be
| really tough for academicians, but I'm not! Probably I'm just
| plain stupid.
| prvc wrote:
| He didn't specify the order (or/and script, if you prefer) in
| which the books were placed, so it's ambiguous.
| ordu wrote:
| Tomes of Pushkin have a natural order ascending from left to
| right. It may be a cultural thing, but it would be obvious
| for any Russian child 5 years old or older. No tricks here.
|
| But, yeah, even knowing about the natural order of Pushkin on
| the shelf, I also gave it a thought. I was wrong and just
| wasted my time. It is an easy problem, without any tricks.
| SamBam wrote:
| The same order a multi-volume set would be displayed in any
| bookstore or library in a left-to-right ordering country.
| syops wrote:
| One problem I give children aged 5 - 7 is the following.
|
| How old are you? (They answer X.)
|
| How many years did it take for you to become X years old?
|
| I've found that at 6 years old they start to relate their age
| with how many years it took to become that age. At 5 they usually
| can't make this connection.
| imvetri wrote:
| When child labour is illegal, Why shouldn't be child education.
|
| We are born with natural skills, mainstream education ruins
| originality.
| scotty79 wrote:
| Derivation of answer to the problem #16 here:
| https://datagenetics.com/blog/may32013/index.html
| xn wrote:
| Sunshine Math is a great set of math problems for grades K - 8. I
| couldn't find a publisher, but PDFs of scanned copies are
| available online.
| ksec wrote:
| On a related subject, here is a recent experience and I dont know
| how to deal with it.
|
| I have been helping my kids with their homework during the
| pandemic, I thought it would be easy since I got very good grade
| 25+ years ago. And then when I sat down doing it. I couldn't
| remember a thing. Not a _single_ thing. All of a sudden, apart
| from basic algebra, all of the maths were gone. Zip, Zero. I
| couldn 't remember how sin cos tan works any more. It was like a
| few years of memory in my brain went missing. For some people it
| may be funny and have a laugh about it. For me it was shocking,
| quite horrifying and depressing.
|
| I am thinking if I should relearn all those maths again. If so
| how do you go about it? Most of my friends aren't any good at
| maths so they thought not remembering any thing was not a
| problem.
|
| But for some strange reason all the basic for Physics, Chemistry
| and Biology were still there. At least half of it. It was just
| maths. I dont know if anyone else have similar experience.
| scotty79 wrote:
| If you don't use something you are at risk of not retaining it
| at all.
|
| About 10 years after I got my masters degree I browsed through
| some notes made during my studies. I was very surprised to find
| out that it's not that I don't remember some things, I didn't
| remember if I ever learned them.
|
| Not sure why Physics, Chemistry and Biology stuck with you. I'm
| sure I don't remember 90% of history, geography, literature and
| many, many things.
|
| What stuck for me are things that I was learning myself
| anyways. Math, physics, chemistry, a bit of biology. Same way I
| retained a bit of electronics even though school never
| attempted to teach me that. The rest went to hell and I don't
| regret a single thing forgotten from primary school and high
| school.
|
| Curriculum for such young humans is aimed at keeping little
| buggers from annoying their parent for x hours a day, not for
| usability and future retention.
|
| Kids don't even need decades to forget this stuff. I vividly
| remember coming back to school after summer break and knowing I
| forgot everything I learned last year and feeling safe because
| I'll most likely have no use for that information this year or
| later (except for math because it's the only thing in school
| that can be learned only on the foundation of simpler math that
| you need to learn earlier and retain).
| zeven7 wrote:
| I learned math way better as a math teacher than I did as a
| student because I had to figure out how to explain it - which
| meant I had to learn it first. Open up your child's math
| textbook and read the section they're working on, get to where
| you understand it yourself, then teach them. The textbooks do
| teach the material, and as an adult I found them to be easy to
| understand and sufficient explanations.
| teekert wrote:
| This, and it's hard work, no way around that.
| handrous wrote:
| I have a sneaking suspicion that there's something
| fundamentally wrong with how we approach math in school, given
| that:
|
| 1) It's presented as the most important thing in the world,
| pretty much, and
|
| 2) I've forgotten most of it past the first semester of algebra
| 1 in high school but that's mostly because... it wasn't
| important, at all, for me. And I think that's overwhelmingly
| the _typical_ experience.
|
| Honesty, I struggle to even talk fluently about early grade
| school math. "You can flip around the terms in a multiplication
| problem and the result's the same, because of the... uh...
| transitive property? Maybe? I think that's the name?"
|
| Meanwhile, aside from when I'm trying to help my kids with
| math, life goes on just fine.
| jacobsenscott wrote:
| Math is a skill, just like playing an instrument. Just like
| an instrument, if you don't practice regularly you lose the
| skill. People have no problem accepting this when it comes to
| a musical instrument, but for some some reason our schools
| seem to teach people that math doesn't require ongoing
| practice.
|
| As for being presented as "the most important thing" - well
| for students it is one of the most important things at that
| time in their lives because it opens so many career paths.
|
| But once you are out of school and on a career path that
| doesn't require math (or requires just certain subset of
| math) it really isn't important anymore.
|
| This is just like music. If you hope of become a professional
| musician mastering your instrument and music theory is pretty
| much the most important thing it the world for you. But if
| you end up becoming a programmer and don't play for 20 years
| - you can't pick it up and play without a lot of practice and
| catch up - and nobody is surprised by that.
|
| We need to teach math a little more like we teach music.
| hellotomyrars wrote:
| I find it very similar to primary education language classes.
| Unless you use it as an adult after school, you're not going
| to retain the knowledge for very long. And most people aren't
| going to be using either set of skills in their adult lives
| after school.
|
| I took several years of Latin in both high school and college
| but outside of those academic environments I never had cause
| to use it and while I remember a lot of aspects of it
| structurally, my Latin vocabulary is almost all gone. I have
| at times pulled out my old textbooks just to try and see what
| I can do, and I can certainly work through that material a
| lot faster than the first time around, but I'm still needing
| to start at a rudimentary level to get anywhere.
| analog31 wrote:
| Everybody says it's important, but for the wrong reasons.
| It's treated like a contest, to get "ahead," get high test
| scores, get into a desired college, and hopefully major in
| STEM. Then it can be safely forgotten.
|
| I know adults from the countries that are supposed to have
| wonderful math education (high test scores), and they forget
| their math too.
|
| I think the people who remain good at math in adulthood were
| the ones who developed a genuine interest in math as an end
| unto itself, and figured out a way to keep up with it after
| college.
| Isthatablackgsd wrote:
| I have a hard time to conceptualize mathematics because of
| the teaching methods and how they presents the information.
|
| 1) Math teachers loves to gave out their own shortcuts, I
| mean they will tell us to use it every chance they gets. Then
| in next mathematics level, they warned that method is old and
| shouldn't be using it at all. Then the new teacher taught
| their own shortcuts. This method made it difficult to solve
| problems because some of the formula wasn't taught how to
| properly solve without shortcuts. 2) "Why? How?", lots of
| mathematics teachers during my education times have struggled
| to give out the explanation of how it get to that answer and
| why it is that answer. Their response is simply just nodding
| and "That is how I taught, so it is the answer".
|
| It is hard for me to be able to solve mathematics because I
| can't conceptualize it well and struggled a lot without using
| technologies to help me. I do love math, I just can't enjoy
| math because of my past teachers have failed to educate me.
| And I failed myself.
| sobriquet9 wrote:
| If you can forget math, it means that you memorized it. I
| don't think one can ununderstand math.
|
| Oftentimes math is taught as a set of rules. Do these steps
| in order to get the answer. Works well to pass the test with
| minimum effort, does not help much long term.
| handrous wrote:
| It's definitely possible--common, even--to forget things
| you didn't learn by memorization.
| bentcorner wrote:
| I use math often, but most of the time it's basic math.
| Simple things like ratios when trying to calculate per-unit
| costs in a grocery store when two things are displayed with
| different units, or converting between Fahrenheit and
| Celsius. Basic multiplication for tip calculation.
|
| The most complex was when I used some trig to calculate the
| angle at which I had to wrap a square column with christmas
| lights to ensure I covered the column from top to bottom with
| a single string and no excess.
|
| For finance and stuff like that I don't even bother trying
| and just use calculators.
| walshemj wrote:
| Years ago I had to correct a Bridge design I was tasked
| with writing a program to draw out the complex curved
| shape.
|
| The engineer had used 2d instead of the 3d formulae :-)
| waynesonfire wrote:
| >The most complex was when I used some trig to calculate
| the angle at which I had to wrap a square column with
| christmas lights to ensure I covered the column from top to
| bottom with a single string and no excess.
|
| that doesn't seem trivial at all.. wonder how that's done.
| Someone wrote:
| The length _l_ of the Christmas lights is the hypothenuse
| of a rectangular triangle of height _h_ , the height of
| the column. So, if the slope angle is a, we have _sin(a)
| = h /l_, or _a = arcsin(h /l)_.
|
| Soundness check: that doesn't have a solution if _h > l_.
| Looks good.
| waynesonfire wrote:
| does this assume the xmas tree is shaped like a column or
| a cone?
|
| edit: ah, i re-read the original problem and it does
| mention column. i thought it was a xmas tree that was
| being wrapped.
| Someone wrote:
| That would be harder, yes. Reading
| https://en.wikipedia.org/wiki/Conical_spiral#Slope, you
| want a logarithmic spiral (you need a constant angle to
| make the problem make sense)
|
| Luckily, arc length isn't too gnarly for those (same
| Wikipedia page), but you still have one equation with two
| variables.
|
| I would have to think hard about whether those give you a
| unique solution.
|
| I also doubt that spiral would give you uniform coverage
| of the cone (and that probably, is the real requirement,
| not constant angles), but again, I would have to do some
| thinking.
| philiplu wrote:
| Suppose you've got a 16 foot strand of lights and an 8
| foot column. If you unwrap the column in your mind, you
| can see you've got a right triangle with a hypotenuse of
| 16 and vertical leg of 8. What's the angle that the
| hypotenuse makes with the floor? It's the angle whose
| sine is opposite/hypotenuse = 8/16 = 1/2. That's 30
| degrees. So wrap the lights around the column at a 30
| degree angle and it'll be close (with a bit of slop
| thanks to rounding corners on the column).
| waynesonfire wrote:
| my xmas isn't shaped like a column, it's a cone.
|
| edit: ahh, the original question was for a column. i
| misread it and thought it was for a xmas tree.
| concreteblock wrote:
| If you unwrap a cone you get a circular sector. Similar
| idea.
| handrous wrote:
| Oh, yeah, to be clear I use math (well, I apply
| mathematical algorithms and formulas) many times a day. But
| the ROI for my time spent on formal math eduction peaks
| somewhere around 3rd grade and declines _fast_ after that.
| spaethnl wrote:
| I (genuinely) wonder how much that is attributable to
| having no actual use for other math, vs
|
| 1. not having been taught math early enough for it to be
| second nature
|
| 2. not having been taught useful every day applications
| of the math so as to keep practicing it
|
| I've also forgotten quite a bit of math, but I also
| frequently encounter scenarios where I acknowledge that
| having a better handle on it would be advantageous to
| myself or others. For example, a better understanding of
| statistics and probability would certainly help political
| discourse in our society.
| sethammons wrote:
| This is why math teaching pedagogy is important. I'm a fan of
| first principals and pattern finding for learning math (see
| Mathematician's Lament by Lockhart [0]).
|
| Most kids in the US are historically taught memorization
| tricks. You have a kid who can't recall if x^1 = 0 or 1 or if
| it was x^0 = 1 or 0. They can't _remember_ some fact like a
| needle in a haystack of thoughts. However, the student who
| understands that x^3 = x * x * x and x^2 = x * x, will quickly
| know that x^1 must be x, and if each step is "divide by x",
| then x^0 must be 1.
|
| I'm curious where the current math education trends will take
| us on this path, but I do like that they seem to focus more on
| understanding rather than rote memorization.
|
| For sin, cos, and tan, they are much more re-discoverable if
| you are familiar with the unit circle's basics.
|
| [0]:
| https://www.maa.org/sites/default/files/pdf/devlin/Lockharts...
| anyfoo wrote:
| Yes, but in my experience, it helps to _thoroughly
| understand_ (down to first principles if you want to), and
| then _memorize anyway_.
|
| I quickly figured out that even if I've deeply spent time
| with a subject, understanding every step and derivation of
| some equation, if I can just quickly pop up equations (and
| other facts) in my head to "look" at them, it not only helps
| with application, but also with further understanding.
|
| Being able to quickly recite the Taylor Series or an Inverse
| Fourier Transform in my head to apply in a problem beats
| stuff like "oh I remember understanding how it was derived,
| but I'd need to look it up", because all the details I
| otherwise once understood but did not bother memorizing might
| be important.
| avmich wrote:
| A person taught his son about sine and cosine. He himself got
| introduced to them as ratios of side lengths in a right
| triangle, but he didn't like the idea of changing definition
| when angles become more than 90 degrees, so he defined those
| functions as abscissa and ordinate of a point on a circle of
| unit radius, centered at origin.
|
| I think this is not perfect. Education is more of
| "progressing towards lesser and lesser lies", and changing
| definitions is an important part. The student might face it
| when he'll wonder about equation sin x = 2 , which will get
| to complex numbers.
|
| Similarly, here getting a one less power of x might
| correspond to "divide by x". But might sometimes not -
| choosing that it actually does correspond to "divide by x" is
| a choice. Often obvious, but sometimes not - which is seen in
| Gelfand's explanation of why "negative multiplied by negative
| makes positive", or similarly, why 0^0 is 1.
|
| Just saying that "x to one lesser power is the same divided
| by x" can also be seen as a convention (e.g. for some objects
| division can be not defined). And if it's a convention, not
| universal truth... then to somebody who's studying the
| subject this convention should be justified.
| threatofrain wrote:
| x0 is generally a matter of definition and not a fact
| reasonably accessed from deeper underlying fundamentals. It
| just so happens that the definition fits this story that you
| have for reasons of convenience. Also, you know, 00.
| mathattack wrote:
| I ran into this too. The process of relearning Math with my
| kids has made me much stronger than the first time around.
| eidelweissflow wrote:
| Same - I was a straight A student, loved solving math problems,
| but now I don't remember a thing. I think it's just how our
| brain works - it gets rid of knowledge that we don't use any
| longer. Muscle memory like swimming or riding bicycle stays,
| but seems like language and math skills don't retain unless
| they are being practiced.
| anyfoo wrote:
| I don't think so. The feeling described here is familiar to
| me with certain areas of maths, ones that I definitely knew
| and have then forgotten seemingly entirely, but when I had to
| get back into them it was nowhere near having to relearn
| them.
|
| It's true that you forget without regular usage, but it seems
| the "concept" sticks around, and all you need is some
| refresher to be able to access it again.
| wrycoder wrote:
| The information isn't erased - it's just that the retrieval
| synapses haven't been reinforced. It is relatively easy to
| do that.
| anyfoo wrote:
| Yes, and I believe that still existing but somewhat
| inaccessible information isn't just what was learned on
| the surface, but also includes the hard-earned intuition
| that was formed on the topic.
| tofuahdude wrote:
| Same issue/question. I was a pro until I stopped actively using
| it 10+ years ago and now, well, my math is embarrassing
| compared to teenage me.
|
| I'm pretty sure the only way to pull that knowledge back into
| "actively useable" would be to start studying a la college
| again. I imagine it'd be a lot easier since we would be
| revisiting it instead of learning for the first time.
|
| Hard to get excited about studying math relative to my other
| priorities :\
| tehnub wrote:
| If you look up the definitions of sin, arcsin, logarithms, etc,
| does it mostly come back to you? Or do you feel like you need
| to completely relearn? I'm wondering if in your case all you
| need is to take a little time for a math refresher.
| kccqzy wrote:
| Knowledge atrophy is real. I've even talked to math PhDs who
| have forgotten areas of math they have definitely learned and
| excelled at but hadn't been using actively.
|
| But I think your brain still subconsciously possesses knowledge
| of these supposed forgotten math skills. This is the reason why
| relearning these concepts will take way less time than learning
| them the first time. So I think just don't be afraid to relearn
| it.
| culebron21 wrote:
| sin/cos for me were quite common since I'm fond of geography
| and geometry. So, even though they weren't needed at all, I had
| areas to apply them.
|
| I never needed any math like log/exp at work, but somehow
| remembered it, probably because I used to do some fast
| estimations of things, for instance, "how big a pool of water
| you need to store energy to heat a house in winter", or "how
| fast will energy dissipate from the pool".
|
| And that was probably thanks our school physics teacher, who
| showed that such napkin calculations were easy.
| wly_cdgr wrote:
| Lots of good courses on Coursera and edX. Khan Academy is good
| too. I particularly recommend the A-level prep sequence from
| Imperial College London on edX
|
| But if you really want to maintain and maybe even further
| develop your math skills after getting back up to speed, I
| think the best long term strategy is to do personal creative
| and/or commercial projects in domains that interest you and
| that make heavy use of math. E.g. low level 3D graphics
| programming, etc
| anthomtb wrote:
| I have been working through the Art of Problem Solving Volume
| 1. I was a competent, though by no means excellent, maths
| student 20 years ago. AOPS was exactly the refresher needed to
| find those neurons again. Everything came back. However, had I
| jumped right into Trigonometry, I too would have been feeling
| like part of my mind was erased.
|
| The math will come back, but you need to sit down and give
| yourself a structured program and, most importantly, time to
| actually do some exercises.
| jedberg wrote:
| When I help kids with math homework I usually skim their
| textbook to see how they learned how to do it. This both
| refreshes my own memory and also makes sure that I am teaching
| it the same way they learned it (I can show them other methods
| after they master the way the teacher wants them to do it).
| sobriquet9 wrote:
| I had similar experience, but different outcome. I also had
| forgotten many formulas, but was able to derive everything from
| basic algebra. Quadratic formula, sine and cosine of sum of
| angles, derivatives, etc.
|
| Some of those things took much longer than necessary, but I
| made it a point to not look anything up on principle. How can I
| explain something if I can't do it myself?
| notenoughhorses wrote:
| I decided to start a CS undergrad degree 15 years after
| finishing my first undergrad degree.
|
| The university had a math placement test. I didn't remember
| almost at math, but spent about 3 weeks going through the
| placement test review materials for 30 min to an hour a day.
| Got almost perfect score on the placement test.
|
| I did retake calculus 1 and 2 by my own choice since I wanted
| to know it quite well, and much of that seemed completely
| unfamiliar.
|
| So it's much much easier to learn a topic the second time
| around even if it's forgotten. To get up to speed on it, you
| could use the placement test materials--collegeboard has some
| standard tests and materials to review for those tests, or your
| local university might have review materials for an in-house
| test.
|
| I will say, I completed calc 2 a year ago now, and I already
| feel it slipping away again due to disuse. Now I'm onto new
| math topics I never took the first time around, like linear
| algebra and higher levels of calculus.
| lordnacho wrote:
| This is like riding a bike isn't it? First few steps are a bit
| shaky but then you're back pretty soon.
|
| Also keep in mind modern media has an explanation for
| everything online, there's not much below graduate level that
| isn't explained in several ways by several people.
| watwut wrote:
| I Googled what I forgot till I found text that was interesting
| to read, basically.
|
| For me, once I have found something to remind me, it all went
| back fast.
| drdec wrote:
| This story needs a nerd-snipe warning
| LeifCarrotson wrote:
| They're interesting to adults, too! Simple enough that it feels
| like you should be able to blurt out the answer, I'm more than
| twice the maximum recommended age and a professional engineer,
| but (at least for me) it takes some thought. The top recommended
| three:
|
| > 1. Masha was seven kopecks short to buy a first reading book,
| and Mishalacked one kopeck. They combined their money to buy one
| book to share, but even then they did not have enough. How much
| did the book cost?
|
| > 3. A brick weighs one pound and half the brick. How many pounds
| does the brick weigh?
|
| > 13. Two volumes of Pushkin, the first and the second, are side-
| by-side on a bookshelf. The pages of each volume are 2 cm thick,
| and the cover - front and back each - is 2 mm. A bookworm has
| gnawed through (perpendicular to the pages) from the first page
| of volume 1 to the last page of volume 2. How long is the
| bookworm's track?
|
| I do take objection to the answer to question 13 - the author
| seems particularly set on one way of loading the bookshelves as
| correct.
| culebron21 wrote:
| My answer to #1 is less than 8 kopecks, and Masha has less than
| one. There's a problem: nowadays kopecks are the minimal unit
| of currency. Either it means you have to think of the old
| Imperial money units (polushka, 1/4 of kopeck), or think of
| fractional amounts of money.
| desmosxxx wrote:
| Seems like Mishalacked isn't great at making deals.
| bencollier49 wrote:
| I assumed kopecks were pennies. If Misha needs one, and Masha
| doesn't have enough to give her one, than Masha must have
| none. So the answer follows from that.
| colinmhayes wrote:
| How can they combine their money if one of them doesn't
| have any?
| bencollier49 wrote:
| Communism?
| sethammons wrote:
| Ok. I literally laughed out loud.
| culebron21 wrote:
| But naturally, at first you assume the numbers are natural.
| :)
| throwaway744678 wrote:
| Well, yes, otherwise you'd have an infinite number of
| solutions.
| dahfizz wrote:
| > A brick weighs one pound and half the brick. How many pounds
| does the brick weigh?
|
| I am a native english speaker and am having a hard time parsing
| this one. The only sane interpretation I can think of is that
| one pound + half the brick = the whole brick.
|
| EDIT: I think the reason it is so confusing to me is because
| "and half the brick" sounds like (the start of) an independent
| thought. "A brick weighs one pound and half the brick was
| painted yellow".
|
| This version is much clearer, IMO: "A brick weighs one pound
| plus half a brick". Maybe there is a fear that wording the
| problems too clearly makes the solution obvious.
| idownvoted wrote:
| Interesting. There seem to be a lot of native speakers here
| that have problems with the grammar, while I - and assume
| many other non-native speakers - don't.
| wizzwizz4 wrote:
| Correct.
| [deleted]
| valbaca wrote:
| > side-by-side on a bookshelf
|
| Seems pretty explicit to me
| macintux wrote:
| Which volume is to the left? Thus the ambiguity.
| valbaca wrote:
| > A bookworm has gnawed through (perpendicular to the
| pages) from the first page of volume 1 to the last page of
| volume 2.
|
| How would a worm eat perpendicular to the pages and go from
| the first page of volume 1 to the last page of volume 2?
|
| It can only be vol1->vol2
| [deleted]
| thaumasiotes wrote:
| > How would a worm eat perpendicular to the pages and go
| from the first page of volume 1 to the last page of
| volume 2?
|
| Sorry, what is the question supposed to be? You're
| positing a contradiction between two facts:
|
| - The worm's path is perpendicular to the pages.
|
| - The worm's path begins at the first page of volume 1,
| and ends at the final page of volume 2.
|
| What's the contradiction?
| scratcheee wrote:
| The bookworm could have moved right to left from volume 1
| to volume 2. Assuming the spines are facing out, the
| books are right-way up, and volume 2 is on the left of
| volume 1, then the answer would be 44mm.
| SamBam wrote:
| While the answer _does_ assume that V1 is on the left,
| there 's no contradiction in your statement. If V2
| happened to be on the left, it would still be perfectly
| logical for "a worm eat perpendicular to the pages and go
| from the first page of volume 1 to the last page of
| volume 2." They would simply have to go through more
| pages.
| [deleted]
| scratcheee wrote:
| Assuming volume 1 is on the left and the books have their
| spine facing out.
|
| Reasonable assumptions, but relying on implicit knowledge
| nonetheless.
| bumbledraven wrote:
| Here's a way to use algebra to grind out the solution to #1
| with no particular insight needed.
|
| Assume that prices and the amount of kopeks a person has are
| both represented by nonnegative integers. Let A be Masha's
| kopeks, let I be Misha's kopeks, and let B be the price of the
| book. We are given the following:
|
| A = B - 7 (1)
|
| I = B - 1 (2)
|
| A + I < B (3)
|
| Substituting (1) and (2) into (3) yields
|
| B - 7 + B - 1 < B (4)
|
| This simplifies to
|
| B < 8 (5)
|
| B = 7 satisfies (5) and, from (1) and (2), implies that A = 0
| and I = 6, which together satisfy the givens (1), (2), and (3).
| So B = 7 is a solution. Furthermore, we cannot have B < 7 or
| else (1) would imply A < 0, contradicting the assumption that
| our variables are represented by nonnegative integers. So B = 7
| is the only solution.
| nostoc wrote:
| It's also quite easy to do intuitively.
|
| Since Misha is missing only one kopeck, had Masha owned any
| amount, the sum would have been enough to buy the book.
|
| Therefore, Misha doesn't have any money, and the price book
| is what Misha is missing : 7 kopecks.
| nbclark wrote:
| Couldn't the book cost 7.5k and one has 6.5 and the other
| has 0.5? Along those lines, isn't anything in the range of
| costing 7->8 (non-inclusive) acceptable (e.g. 0.9k and
| 6.9k)?
| bentcorner wrote:
| I was wondering the same thing but Kopecks are not
| currently subdivided.
|
| https://en.wikipedia.org/wiki/Kopek
| scotty79 wrote:
| These problems aren't current or modernized. There's no
| way a bottle with a cork in problem #2 costs 10 kopek.
|
| current 10 kopek is worth 0.0013$
|
| They probably come from time when 0.5 kopek was the
| smallest coin.
|
| #1 problem doesn't have single non-zero solution if the
| smallest coin has larger or smaller.
| Arnavion wrote:
| The second question's solution requires half-kopeks.
| bentcorner wrote:
| I came to the same conclusion the same way but it felt
| wrong due to the phrase "They combined their money to buy
| one book to share". Perhaps the phrase lost something in
| translation.
| bumbledraven wrote:
| That's a nice approach. (It's the same one given by
| bencollier earlier:
| https://news.ycombinator.com/item?id=27885681). I regard it
| as requiring a bit of insight, as opposed to my approach,
| which is more like grinding gears to reach a conclusion.
| lordnacho wrote:
| This is one of my main observations growing up with math:
| it's the moments of beauty and elegance that are the most
| exciting, but the grinding gears thing is also a
| necessity. They complement each other. For instance when
| you're just learning the basics there's a lot of these
| "wow what an insight" but over time you figure out that
| people have distilled it into a mechanical procedure,
| which also has some attraction to it. Something like
| quadratic equation turns the search for a pair of numbers
| that add up some one thing and multiply to another into a
| simple formula. You then use that mechanism to build ever
| more elaborate ones.
| colinmhayes wrote:
| The problem says they combine their money which implies Masha
| has more than 0 kopeks though.
| parsecs wrote:
| > They combined their money to buy one book to share, but
| even then they did not have enough.
|
| Is there some error here? I read it as "even then they did
| not have enough _individually_ "
|
| I used b-7+b-1=b to arrive at b=8... My math skills are
| pretty awful so I can't say if this even makes sense..
| BeFlatXIII wrote:
| These problems are worded to be deliberately confusing,
| especially #1. Is it a translation issue or are they worded
| because the math itself is too obvious once the wording has
| been deciphered?
| Negitivefrags wrote:
| What is your objection to question #13?
|
| I suppose the question doesn't mention that volume 1 is on the
| left and volume 2 is on the right but I guess that would be
| assumed by any speakers of left to right languages.
| frostirosti wrote:
| could also be the case that the two volumes are empty, ie
| have no pages
| [deleted]
| Jtsummers wrote:
| The problem statement gives us that there are 2cm of pages
| in each book. So they are not empty. The confusion is in
| which order the books would be on the shelf, and
| consequently which direction the bookworm would be moving
| and through what.
| valbaca wrote:
| what book has no pages? Also the problems states:
|
| > The pages of each volume are 2 cm thick
| thaumasiotes wrote:
| The pages would be less than 20mm thick in that case.
| maratc wrote:
| The point with this question is that if volume 1 is on the
| left and volume 2 is on the right, the first page of volume 1
| is facing right and the last page of volume 2 is facing left,
| so the only thing between them is the two covers. Hence, the
| answer is 4 mm.
| soperj wrote:
| It also assumes that the pages aren't facing out.
| thaumasiotes wrote:
| > I suppose the question doesn't mention that volume 1 is on
| the left and volume 2 is on the right but I guess that would
| be assumed by any speakers of left to right languages.
|
| The answer is supposed to be 4mm; the only way for that to
| work if volume 1 is on the left is for the bookworm to gnaw
| its way out of the book from v.1.p.1, cross the outside of
| the two books without gnawing anything until it reaches the
| back cover of volume 2, and then gnaw its way through that
| cover to reach the final page of volume 2.
|
| I don't think that's what the question has in mind. The point
| of being a bookworm is that you don't leave the book. So the
| answer would appear to require that volume 2 is shelved in
| front of volume 1. I don't know why that would be the case.
| SamBam wrote:
| This is incorrect. You seem to be making the same error as
| the author says the editors made in the footnote at the
| bottom.
|
| If volume 1 is on the left, and the worm goes from page 1
| of volume 1 to the last page of volume 2, it travels 4mm in
| a straight line.
|
| Page 1 of volume 1 and the last page of volume 2 will be
| right next to each other, if volume 1 is on the left.
| meristem wrote:
| Wow, this relies on both books being in the same
| orientation, with front cover to the right. It assumes a
| lot. For perspective, I for years kept books shelved
| upside down because that orientation was easier for me
| when reading spines.
| anyfoo wrote:
| German books have the orientation of the writing on the
| spine flipped. I don't like storing books upside down, so
| it makes a mess in my mixed English and German bookshelf.
| scotty79 wrote:
| There's a language-wide order in Germany of direction the
| of writing on the spines of a books?
|
| I just checked my bookshelf and my books go both ways.
| anyfoo wrote:
| Ah. I just checked, and while all the English ones seem
| to have a consistent orientation, the German ones indeed
| don't. Never noticed, huh...
| SamBam wrote:
| I guess it relies on the books being ordered and arranged
| the same way they'd be in every single bookstore and
| library in the world (in left-to-right ordering
| countries).
|
| But it's true, maybe this is too much to assume. Most of
| the time when I've seen this puzzle it's shown the book
| spines in an image to make it clear, and many people
| still can't get it. Then again, _that_ would rely on
| knowing whether it was using top-to-bottom or bottom-to-
| top book title orientation, so perhaps the only solution
| is for the author to spell out "the first page of volume
| 1 is next to the last page of volume 2."
| Jtsummers wrote:
| Diagram for the desired solution, on the shelf:
| V1 V2
|
| In that order you can see that the pages in each book are
| in this order: | V1 | V2 |
| +----------+----------+ |9876543210|9876543210|
|
| (0-indexing of the pages for fun, plus it fit better, also
| reminded me of annoying protocol specs that mix 0- and
| 1-based indices with different elements)
|
| The first page of V1 is the rightmost page (shelved) of
| Volume 1, and the last page of V2 is the leftmost page
| (shelved) of Volume 2. So the bookworm ends up going only
| through the covers. Having volumes shelved in order from
| left-to-right is conventional in left-to-right languages
| since that's the same direction we read, and you'd want to
| "read" through the titles to find the volume you wanted.
| sokoloff wrote:
| 1. Depends on whether kopecks are divisible into a smaller
| monetary unit or not. If they are divisible into 100 units, I
| believe the answer is "anywhere between 7.00 and 7.99 kopecks".
|
| (Problem #2 requires kopecks to be divisible.)
| [deleted]
| ekster wrote:
| A kopeck is like a cent (1/100th of a ruble).
| rjp0008 wrote:
| > (Problem #2 requires kopecks to be divisible.)
|
| Does it? Did I fail at problem 2? I got:
|
| Bottle + cork = 10
|
| Bottle = 9 _cork
|
| bottle/9 = cork
|
| 9(bottle + bottle/9) = 9(10)
|
| 9 bottle + bottle = 90
|
| 10 bottle = 90
|
| bottle = 9
|
| 9 = 9_cork
|
| 1 = cork
| sokoloff wrote:
| I read the second statement ("the bottle itself is 9
| kopecks more expensive than the cork.") as:
|
| Bottle = 9 + Cork
|
| Your statement (Bottle = 9 * Cork) would be "the bottle is
| 9 times as expensive as the cork".
|
| I solve it to:
|
| Bottle = 9.5 Kopecks.
|
| Cork = 0.5 Kopecks.
| valbaca wrote:
| They're not. It's like a penny. Sure you may have parts of
| cents like with gas, but for girls buying books, it's the
| lowest currency value.
| Symbiote wrote:
| Long ago, many currencies had more divisions than they do
| now.
|
| The penny of GBP came in quarter pennies (farthings) until
| 1950.
|
| Half US-cent coins were made until 1857.
| culebron21 wrote:
| Before 1917, they were divisible into 4 polushkas.
| haxiomic wrote:
| Works even if Kopecks are divisible: say the books value is
| 7.5, Mash must have 0.5 (7.5 - 7) and Misha 6.5 (7.5 - 1),
| however now when you combine them they sum to exactly 7.5 not
| less than, the only way to arrive at less than is if Masha
| has 0. So its always exactly 7
| [deleted]
| LeifCarrotson wrote:
| 6.5 plus 0.5 is 7.0, they don't add up to exactly 7.5.
| gabagool wrote:
| 6.5 + 0.5 is 7.0, not 7.5, so that should be valid.
|
| The book's cost can lie anywhere between [7, 8).
| haxiomic wrote:
| Right on the original typo, but still not convinced, I've
| rephrased to original to try to be clearer
| thaumasiotes wrote:
| > say the books value is 7.5, Mash must have 1.5 (7.5 -
| 7) and Misha 6.5 (7.5 - 1), however now when you combine
| them they sum to exactly 7.5 not less than
|
| There are several problems with this:
|
| - 7.5 - 7 is 0.5, not 1.5
|
| - 1.5 + 6.5 is 8, not 7.5
|
| - 0.5 + 6.5 is still less than 7.5
|
| The problem specifies that 2x - 8 < x. There is no way to
| constrain this to the specific solution x = 7. Everything
| would work fine if the book cost -2.6 kopecks.
| haxiomic wrote:
| Thank you :) I'm being very clueless today
| amativos wrote:
| I think part of the point of this brochure is to think about
| the problems intuitively in the context they are presented.
| So in the first problem it's just kids trying to buy their
| first book, it would be silly to think Masha had a fraction
| of a kopeck (assuming you understand what a kopeck is, I
| really think it should have been translated as cent) and that
| the answer could be in range [7, 8). This may be what he
| talks about when he says that many academics fail at these
| problems.
|
| Similarly, in problem #2 the cork indeed costs 0.5 kopecks
| but in this case we're just thinking about cost conceptually,
| not in terms of how much money a person actually has on hand.
| sokoloff wrote:
| Indeed, but it likewise seems intuitively reasonable to
| think that a book costs much more than 7 cents (or 7 times
| whatever the atomic unit of currency is) and likely more
| like 700 times the atomic unit.
| bowmessage wrote:
| > 12. A tide was in today at 12 noon. What time will it be in (at
| the same place) tomorrow?
|
| What is this, a maritime exam?
| maratc wrote:
| Considering the moon was at its highest today at 12:00, and
| will be at its highest again in ~29 days at 12:00, what time
| will the moon be at its highest tomorrow, which is 1/29 of its
| cycle?
|
| The question then turns into dividing 24 hours into 29 parts,
| or about 48 minutes per day, so 12:48.
|
| Bonus points (not in math) go to whoever knows that a tide can
| also come when the moon is at its lowest, or half that time, or
| 0:24 or so.
| simonebrunozzi wrote:
| At 1pm, considering that tides usually go with 6 hours and 15
| minutes increments?
|
| (I hope my memory is right, took the RYA exam a while ago)
| [deleted]
| SamBam wrote:
| But what's noon plus 12 hours 30 minutes?
| SamBam wrote:
| Yeah, this one doesn't have anything to do with math, does it?
|
| Off the top of my head, I'd guess that tides lose about an hour
| per day, so the tide would be in at 1:00 pm.
|
| Ah, I guess the point of this is that the next tide is half way
| between those two, and so would be just after midnight.
|
| But to know this, you'd have to know that the tide's cycle is
| slightly longer than the day's cycle.
| coldblues wrote:
| The problem here is that most people _won 't_ use most of the
| math knowledge they gain (and then lose) in school. But for
| programmers, it's different. Math can be fairly common in
| programming, especially depending on what field you're working
| with, and you wouldn't want to lose the knowledge you gained in
| school, but, unfortunately, most people will lose it.
|
| What I propose is a better way to find math knowledge. In
| contrast to programming, math problems are harder to find
| solutions for, and the information available is quite sparse and
| hard to find online, from my personal experiences.
|
| When I try to tackle programming problems, most of the time I
| won't memorize code snippets or algorithms, instead I'll have a
| mental link pointing to the name of the algorithm or the specific
| page, that I can search up, find, and then implement.
|
| This is the total opposite of what school tries to do. They try
| to force memorization, which should come naturally. A better way
| to do it is to let the students have the equations and the
| necessary information that they need, then they can fit the
| puzzle pieces together to solve the problem. We live in the age
| where everything is becoming more and more documented, and we're
| still forcing memorization on people.
| juanjmanfredi wrote:
| Anybody who has a credit card, mortgage, or retirement account
| needs to have a high-school level understanding of math.
| whimsicalism wrote:
| Disagree - or maybe I just don't know what high-school level
| is.
| allochthon wrote:
| Kind of going in the same direction, I wonder whether it would
| be good to have children start out learning math in the context
| of accomplishing concrete, real-world tasks that require
| mathematical problem solving, and then only gradually
| abstracting from this concrete starting point if an individual
| seems to have an aptitude for math.
|
| Example: learning statistics in the context of gathering
| information about the health of people in a village.
| walshemj wrote:
| Some of those are not even Grammatical
|
| "A brick weighs one pound and half the brick. How many pounds
| does the brick weigh?"
| France_is_bacon wrote:
| This whole thing does not make sense. Math is racist and this
| post should be deleted:
|
| This is actually a claim that is being made often these days: the
| sciences in general, and math in particular, are racist. The
| latest comes from Oregon:
|
| The Oregon Department of Education (ODE) recently encouraged
| teachers to register for training that encourages
| "ethnomathematics" and argues, among other things, that White
| supremacy manifests itself in the focus on finding the right
| answer.
|
| Part of the toolkit includes a list of ways "white supremacy
| culture" allegedly "infiltrates math classrooms." Those include
| "the focus is on getting the 'right' answer," students being
| "required to 'show their work,'" and other alleged
| manifestations.
|
| "The concept of mathematics being purely objective is
| unequivocally false, and teaching it is even much less so," the
| document for the "Equitable Math" toolkit reads. "Upholding the
| idea that there are always right and wrong answers perpetuate
| objectivity as well as fear of open conflict."
|
| ODE Communications Director Marc Siegel also defended the
| "Equitable Math" educational program.
|
| .
|
| The first sentence is mine. And I'm letting the sarcasm-impaired
| know that it actually is sarcasm on my side. The rest of it is
| real, though, I didn't write it.
| ZoomerCretin wrote:
| Can you not inject culture warfare where it doesn't belong?
| [deleted]
| repiret wrote:
| So that sounded rather incredible, so I did some fact checking.
|
| The Oregon Department of Education's February 2021 newsletter
| had a six sentence blurb about "A Pathway to Equitable Math
| Instruction". You can read it for yourself here [1], but I
| think its disingenuous to describe that as having "encouraged
| teachers to register for training". Oregon state's involvement
| appears to end there.
|
| You can look at the actual toolkit here: [2]. The connections
| it makes between white supremacy and math education strike me
| as strenuous, but the suggestions for removing the purported
| white supremacy strike me as generally good suggestions for
| improving math education. The quote about math not being purely
| objective struck a chord with me, but I wasn't able to find it
| in the course materials, only in the reporting about it. The
| complete quote about there not always being right and wrong
| answers is:
|
| "Upholding the idea that there are always right and wrong
| answers perpetuate objectivity as well as fear of open
| conflict. Some math problems may have more than one right
| answer and some may not have a solution at all, depending on
| the content and the context. And when the focus is only on
| getting the right answer, the complexity of the mathematical
| concepts and reasoning may be underdeveloped, missing
| opportunities for deep learning."
|
| which seems much more sensible that the cherry-picked excerpt.
| Continuing on this point, it says:
|
| "Of course, most math problems have correct answers, but
| sometimes there can be more than one way to interpret a
| problem, especially word problems, leading to more than one
| possible right answer.
|
| "And teaching math isn't just about solving specific problems.
| It's about helping students understand the deeper mathematical
| concepts so that they can apply them throughout their lives.
| Students can arrive at the right answer without grasping the
| bigger concept; or they can have an "aha" moment when they see
| why they got an answer wrong. Sometimes a wrong answer sheds
| more light than a right answer."
|
| [1]:
| https://content.govdelivery.com/accounts/ORED/bulletins/2bfb...
|
| [2]: https://equitablemath.org/wp-
| content/uploads/sites/2/2020/11...
| someelephant wrote:
| These people are entitled to their opinion. Pushing back is
| likely to make them stronger. Better to focus on the positives
| like finding the right answer brings a sense of accomplishment
| and showing one's work teaches the process of deduction. Those
| are some useful skills to learn with math while white supremacy
| culture can be learned about in other settings. We don't force
| people to do math in English class, it doesn't seem right to
| learn about white supremacy in math class.
| rdtsc wrote:
| > The hypotenuse of a right-angled triangle (in a standard
| American examination) is 10 inches, the altitude dropped onto it
| is 6 inches. Find the area of the triangle. American school
| students had been coping successfully with this problem over a
| decade. But then Russian school students arrived from Moscow, and
| none of them was able to solve it as had their American peers
| (giving 30 square inches as the answer). Why?
|
| That's a good one. I know the answer but won't reveal it since
| it's a fun one to discover yourself.
| cperciva wrote:
| Clearly the problem was too complex for the Russian students.
| cperciva wrote:
| Since this is being downvoted, maybe I should elaborate that
| it was _unreal_?
| scotty79 wrote:
| SPOILER:
|
| Well my answer but it's a correct one.
|
| .ts@t @Yt uo ,,@lbuairt Yons ou s,@r@Yt,, r@wsua ou saw @r@Yt
| @snao@q ti @^los t,uplnoo stu@pnts uaissn ss@nb I
|
| .lanb@ @ra s@bp@ r@Yto owt u@Yw s,tI .g tsoW ta @q plnoo ti uo
| p@ddorp @pntitla @Yt 0| @snu@todyY Ytiw u@Yt @lbuairt p@lbua-
| tYbir a s,ti jI
| [deleted]
| culebron21 wrote:
| Probably, I'm too proficient in English to see the problem.
|
| * guess #1: they read it as a Pythagoras triangle, with sides
| 10, 6 and 8, hence they answered 6 * 8 / 2 = 24.
|
| * guess #2: they could not make sense of "altitude dropped onto
| it".
|
| * they tried to convert units and forgot that for area, the
| coefficient is squared?
| thaumasiotes wrote:
| The problem is that right triangles have to obey a
| constraint. The angle opposite the hypotenuse is 90 degrees.
|
| Thus, once you've fixed the two endpoints of the hypotenuse,
| not all points are eligible to be the final point of the
| triangle. All other points in space can form a triangle with
| those two points, but it may not be a right triangle.
|
| If you interpret the hypotenuse as the diameter of a circle,
| all -- and only -- the points on the circle, except the
| hypotenuse's endpoints, will form a right triangle with the
| hypotenuse. If the diameter's length is, as specified in the
| problem, 10 inches, this tells us that the circle has radius
| 5 inches. This is the maximum distance between the hypotenuse
| and the third corner of the triangle. The problem tells us
| that the distance from the hypotenuse to the third corner is
| 6 inches, which is impossible.
| Koshkin wrote:
| > _which is impossible_
|
| Or, generally, is only possible in a non-Euclidean geometry
| (which the Russian students apparently did not know very
| well).
| rdtsc wrote:
| I doubt knowledge of non-Euclidian geometry expected in
| standardized tests like SAT or ACT, where supposedly this
| problem came from.
| Koshkin wrote:
| I think the whole story is a joke (not unlike the one
| about the "space pencil").
| chaosmachine wrote:
| Since none of the replies so far have it correct, here's a
| spoiler:
|
| https://math.stackexchange.com/questions/1594740/v-i-arnold-...
| rdtsc wrote:
| Fair enough. I was going to wait a bit longer to provide the
| hint. I do like that there are non-Euclidian answers.
| However, I doubt non-Euclidian geometry was expected on
| standardized tests tests in US, if the anecdote is to be
| believed that this came from say SAT or ACT.
| laszlokorte wrote:
| Funny in germany we learn the formular for just that:
|
| Area_triangle = Base_triangle * Height_triangle / 2
|
| /edit: fixed factor of two
| Someone wrote:
| That's either a nice example of hemibel thinking
| (http://libertycorner.blogspot.com/2004/07/hemibel-
| thinking.h...), of your memory going away, or of an extremely
| lousy education.
|
| (You are of by a factor of 2)
| satchlj wrote:
| I'm not sure sure if you made a mistake or if you are joking
| lordnacho wrote:
| The problem is exactly that the application of a formula
| requires some assumptions to be met, the first of which is
| logical consistency.
|
| Try to draw a triangle such as the one mentioned.
| hereforphone wrote:
| lol?
| blagie wrote:
| There's a funny story. Before PISA, Finland looked up to
| the German school system, which was clearly considered
| superior by both sides.
|
| When PISA came out in 2000, Finland was surprised to come
| out on top for Europe. Germany's performance in math was
| abysmal -- behind the US even. People started flocking to
| see what Finland did, and stopped looking up to Germany.
|
| https://nces.ed.gov/pubs2002/2002116.pdf
|
| The German school system has since gradually improved --
| it's no longer behind the US -- but it's far from world-
| leading.
| blagie wrote:
| Well, there's many possible answers. I'll give a few:
|
| - Russia doesn't have "inches"
|
| - The question has English terms like "hypotenuse"
|
| - The Russian students were younger
|
| - There were differences in conventions, e.g. which side is
| down. An altitude dropped onto the hypotenuse of a right
| triangle could be perpendicular, or either of the two other
| sides.
|
| - And so on...
|
| A lot of these problems are designed for a conversation rather
| than a solution.
| rdtsc wrote:
| Inches is not the issue. It could be any units. The joke
| about the American vs Russian students was a jab at the
| American students, not the Russian ones! Something about the
| Russian students seeing something that American student
| couldn't. I don't agree with the premise of course, just
| providing the extra info as a hint.
|
| I can believe, however, that this problem was on a
| standardized test in US at some point. This last sentence
| points to the answer a bit more too :)
| mhh__ wrote:
| https://en.m.wikipedia.org/wiki/Altitude_(triangle) for
| reference, I guessed what the issue was but wasn't familiar
| with the term altitude
| kccqzy wrote:
| Exactly. In grade school the formula being taught was "base
| times height over 2" but no one mentioned the term altitude.
| cycomanic wrote:
| On the subject of teaching math to kids I found two books quite
| fun (and my daughters have been enjoying them as well). 1.
| Moebius Noodles 2. Avoid hard work!
|
| Both of these take a playful approach to teach quite advanced
| mathematical concepts. What I particularly liked was a focus away
| from calculations and numbers.
|
| The argument given in one of the books is that starting to teach
| math by counting and then calculation is like only starting to
| read books after children learned the alphabet. Children are very
| capable to figure out more advanced maths concepts even without
| being able to calculate fluently yet.
| gnicholas wrote:
| Those books look cool, and it appears they are available for
| download on a name-your-price basis (literally says "Type the
| amount (from zero to infinity)"). What a generous and cool
| idea!
| marcodiego wrote:
| A paper with interesting problems for children:
| http://toomandre.com/travel/sweden05/WP-SWEDEN-NEW.pdf
| teekert wrote:
| I printed this, will try them all, then translate to my language
| and try with my kids. I love this stuff.
| [deleted]
| eevilspock wrote:
| A lot of comments complaining that many of the problems don't
| have definitive answers, e.g. #12 (tides) and #13 (bookworms).
|
| I think the point for some problems is not finding the answer so
| much as developing logical, analytic and critical thinking
| skills; to learn the value of looking at a problem from different
| perspectives and the necessity to sometimes think outside of the
| box; and to be able to find the holes and ambiguities -- sometime
| to even reject the question outright.
| Invictus0 wrote:
| > 12. A tide was in today at 12 noon. What time will it be in (at
| the same place) tomorrow?
|
| Am I a moron or is this a really bad problem?
| sethammons wrote:
| I agree - I don't see how this could be answered outside of
| guessing without outside information.
| yakshaving_jgt wrote:
| I had to look up the answer[0].
|
| > Due to the Moon's orbital prograde motion, it takes a
| particular point on the Earth (on average) 24 hours and 50.5
| minutes to rotate under the Moon, so the time between high
| lunar tides fluctuates between 12 and 13 hours, generally being
| 12 hours and 26 minutes. So, if the tide has affected the place
| at 6:00AM, then it would generally take around 12 hours and 26
| minutes for the place to be affected by Ebb i.e 6:00 AM+12
| hrs+26 mins=6:26 PM.
|
| Seems like a pretty tough question for a child?
|
| [0]: https://www.toppr.com/ask/en-my/question/if-a-place-is-
| affec...
| baldeagle wrote:
| I assume that these are meant to be universally understood. If
| the tests were given in fishing villages, it may have been a
| much easier premise since much of their world is defined by the
| tides.
| kangnkodos wrote:
| #18 is impossible. This margin is too small to provide the proof.
| eevilspock wrote:
| blueplanet200's proof can fit in a sentence or two. So sounds
| like you came up with an entirely different strategy. I'm
| curious what it is (doesn't matter if it's not as elegant).
| blueplanet200 wrote:
| spoiler for how to prove it:
|
| think of colors of chessboard (black/white alternating) and
| what colors a domino piece will always cover.
| SamBam wrote:
| Nice.
|
| I was confused by the L-shaped shading in the top-right
| corner of the diagram, though.
| waynesonfire wrote:
| > 3. A brick weighs one pound and half the brick. How many pounds
| does the brick weigh?
|
| huh? Good luck 5 year old. This is how you get kids to hate math.
| blagie wrote:
| No. This is how you get kids to love math, if you do it right.
|
| There's an American theory that math problems should be doable,
| that kids should score 90+% if they're doing well, and that
| struggle makes people hate things.
|
| That's contradicted in American sports, where coaches push
| people really hard, boot camps, frat hazing, and cult
| indoctrination.
|
| There's an Eastern European theory that math problems should be
| hard, interesting, involve struggle, and often too difficult to
| solve.
|
| On the whole, Eastern Europeans seem to do better for turning
| out kids who love math.
| Glavnokoman wrote:
| Exactly. If the problem does not involve the "Aha! moment"
| the kids won't love it. And there's no way to have both
| "Aha!" and 90+% scores.
| BeFlatXIII wrote:
| But the actual math in these is fairly trivial. The entire
| challenge is in deciphering the wording.
| culebron21 wrote:
| I actually got to hate math in grade 3 with such problems.
| Nobody explained to me that I could just write down an
| equasion, at least my father (physicist) could not. And all I
| saw in the magazines were cryptic answers like "it's plain
| obvious that for Jose-Rammstein conjuncture, x = 10"
|
| I also met the problem #9 at an interview, and was asked to
| write the solution in pseudocode, as a kind of fizz-buzz
| test. (A peasant must take a wolf, a goat and a cabbage
| across a river in a boat. However the boat is so small that
| he is able to take only one of the three on board with him.
| How should he transport all three across the river? The wolf
| cannot be left alone with the goat, and the goat cannot be
| left alone with the cabbage.)
| doovd wrote:
| I would not blame the problems here, but rather the lack of
| support.
| senko wrote:
| > This is how you get kids to love math, if you do it right.
|
| No. This is how you encourage kids who already love math. If
| they're not interested (yet), this is an awesome way to turn
| them off.
|
| If you do it right, you'll incorporate these into everyday
| life (walk down the street, see something that you can turn
| into a similar problem, then pose that to the kid).
|
| Source: loved these as a kid[1], now parent who wants to
| encourage a healthy sense of wonder in math/sciences.
|
| [1] Here's one for you I loved back in the day: A hen and a
| half lay an egg and a half in a day and a half. How many eggs
| do six hens lay in six days?
| HarryHirsch wrote:
| The point is this: you hand out problems that the kids can
| solve after some struggle with the problem to give them
| confidence that they can solve the problems that come their
| way. That's actually a concept in German pedagogy.
|
| The American way is to drill the kids with an algorithm and
| then hand them 20 more problems that are solved with the
| same algorithm, no insight required.
| blueplanet200 wrote:
| > This is how you get kids to love math, if you do it
| right.
|
| ...
|
| >If you do it right, you'll incorporate these into everyday
| life (walk down the street, see something that you can turn
| into a similar problem, then pose that to the kid).
|
| So you agree, this is how to get kids to love math IF you
| do it right?
| [deleted]
| vharuck wrote:
| This particular word problem is a clever one that can be sold
| a with different mental models (variable in an equation,
| imagining a brick being split, and probably other ways I
| haven't thought of). But it's a dumb problem with no
| reasonable analogy to real life. Who weighs things in
| comparison to a fraction of themselves plus a basic weight
| unit? I wonder if the problem is confusing not because of the
| wording, but because people rely on inferred context to
| understand language. This context is asinine, so people might
| think, "Clearly, that cannot be the intended meaning. I must
| have misread it."
| Jare wrote:
| "One Pound and Half the Brick" means one pound is the other
| half. It's interesting to visually explain it to kids so they
| start to see that "fraction" (half) doesn't have to mean "weird
| number".
| skyde wrote:
| 2 pounds ? brick_weight = 1 _pounds + 0.5_ brick_weight
| threatofrain wrote:
| > 12. A tide was in today at 12 noon. What time will it be in
| (at the same place) tomorrow?
|
| These problems seem so poorly organized and motivated, I don't
| understand the curation in putting them together in one
| document, especially one that goes from ages 5 to 15.
|
| Math problems shouldn't feel like random problems where you
| have to squint really hard or be really clever to see the
| connection to life. They should build with deliberateness into
| a worldview or a recognized skillset that a child can later
| translate into life wins.
| haunter wrote:
| Very classic problem but yeah maybe a bit overkill for 5 year
| olds
|
| http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/Sei...
| SamBam wrote:
| That uses the wording "plus half _a_ brick " instead of "plus
| half _the_ brick. " I think the "a brick" wording could be a
| little clearer for kids.
| jayrwren wrote:
| I can't even read this as english.
|
| I feel these "problems" are more about poor grammar than they
| are math.
| mhh__ wrote:
| I could parse it fine but if I were writing this I would
| include more redundancy e.g. "weighs one pound and half the
| weight of the [maybe use our to suggest to the reader it's
| the same one] brick".
|
| The well drilled student would be able to parse both but
| anyone who can struggle with getting the words into their
| head in the right order like me could struggle.
| valbaca wrote:
| Exactly. It would read better as "The weight of a brick is
| equal to one pound plus the weight of half an equivalent
| brick"
|
| i.e. x = 1 + x/2
| SamBam wrote:
| Replacing "the brick" with "a brick," I always thought the
| question was fine:
|
| > A brick weighs one pound and half a brick.
|
| I could easily imagine a brick being balanced by a one pound
| weight and a half brick on the other side, and the answer was
| easy.
|
| I agree that "half _the_ brick " is trickier wording.
| scotty79 wrote:
| The problem might have be created when bricks were hand
| made and there was no assumption that different bricks have
| same weight. So it was important to stress that it weighs 1
| pound and half of itself.
| satchlj wrote:
| in this case, the line between grammar and math is fuzzy -
| english (or russian) and mathematical symbols are two
| different languages here which are each capable of describing
| the same thing.
|
| the challenge is to do the necessary translation and
| rearrangement
| agentultra wrote:
| Another interesting book in this vein if these problems tickle
| your fancy: https://www.amazon.ca/Math-Three-Seven-Mathematical-
| Preschoo...
|
| Working on math problems together with your kids is a fun way to
| learn how they think and reason. It has led me to have a deeper
| emotional connection with my kids as I learn what they struggle
| with in school. I have slowly learned that some times framing the
| problem a certain way helps them to grasp what is being taught
| better than brute-forcing them through exercises and homework.
| orange_puff wrote:
| I wonder if #27 is supposed to be proven without Fermat's Little
| Theorem. (The question is if p is an odd prime, then 2^{p-1} = pk
| + 1 for some integer k). Since p does not divide k, it follows
| from Fermat's Little Theorem that p | (2^{p-1} - 1).
| gnicholas wrote:
| I'm looking at the first question and wondering:
|
| * What is the intended path the student is supposed to go through
| to figure this out? Guess and check? Some thing more specific?
|
| * What would you say is the generalizable lesson for the student?
| How does solving this problem, which is an edge case, help you
| think about other problems in the future?
| freshdonut wrote:
| Damn I am dumb
| brightball wrote:
| I try to make math fun in my house. A couple of things I've found
| that work:
|
| 1. Anytime there's a "guess how many are in the jar" contest, I
| get my kids to use the appropriate formula for volume to see if
| they can guess the right answer. They usually get really close.
|
| 2. Show them how math helps them win at games. Monopoly is great
| for this where you can calculate the ROI for different properties
| on the board, how many houses are ideal, etc. you can go further
| with likelihood of landing on certain properties too.
|
| It works. The hardest thing about math motivation as a kid is
| "where will I use this?"
|
| Moneyball (movie) is a good one too.
| ffffwe3rq352y3 wrote:
| Moneyball is one of my favorite movies!
| handrous wrote:
| > It works. The hardest thing about math motivation as a kid is
| "where will I use this?"
|
| I struggle to motivate myself to brush up on or move farther in
| math as an adult, for similar reasons.
|
| Some recreational math is kinda fun, but mostly worthless
| except as a pastime.
| anyfoo wrote:
| Just pick up (analog) electronics as a hobby, and it becomes
| relevant and necessary like nothing else. Add some light
| signal processing, and now you understand why you had those
| Algebra I and II courses in university.
| SeanLuke wrote:
| First question:
|
| > 1. Masha was seven kopecks short to buy a first reading book,
| and Misha lacked one kopeck. They combined their money to buy one
| book to share, but even then they did not have enough. How much
| did the book cost?
|
| My goodness, that's an impressive 5 year old.
| noisy_boy wrote:
| Clearly you have not seen primary school math questions in
| Singapore's curriculum.
| natpalmer1776 wrote:
| Honestly this confused me at first read through. If I'm
| understanding it right, the book costs 7?
| SeanLuke wrote:
| I figured it did.
| LeifCarrotson wrote:
| I figured the same, but that's a curious definition for
| "combined their money". That means that Masha has no money,
| and Misha has six kopecks, so they combined 0 + 6 and are
| still short of 7. If the price was eight kopecks, they'd have
| one and seven each, and would have exactly enough. If it cost
| nine kopecks, they'd have 2 and 8, and would have more than
| enough.
|
| Eventually I concluded that the price must be between 7 and 8
| kopecks, however, a kopeck is a fraction of a ruble, and
| Google tells me the exchange rate is currently something like
| 76 rubles per USD, and a kopeck is 1/100th of a ruble, so a
| tiny fraction of a penny, which is itself nearly worthless.
| Wikipedia says that hyperinflation in early Soviet Russia,
| inflation during the cold war, the 1998 redenomination of one
| new RUB ruble to 1000 RUR old rubles, and subsequent
| inflation in Russia all combine to mean that one kopeck in
| the early 90s is worth about 40,000 times less than one
| kopeck today. Similarly, my American son is sometimes
| confused why Mom and Dad pay for stuff at stores with dollar
| bills, but also have pennies, nickels, and dimes. Morris the
| Moose can buy a lemon drop for a penny, why does a small pack
| of lemon drops cost two dollars at the store?
|
| The last time you could subdivide a kopeck in half into a
| denga was around the 1917 revolution, so if the book cost 7
| kopecks and one denga, Masha could have one denga and Misha
| could have 6 kopecks and one denga, and they could combine to
| get 7 kopecks but not have enough.
|
| The true answer is that if Masha and Misha have been
| collecting old kopecks forgotten between the couch cushions
| in their piggybanks, they'll be better off melting the coins
| for scrap metal, because they're not keeping up with
| inflation. You can barely buy a piece of paper for a ruble,
| much less a kopeck. Except the dengas, if they're in good
| condition, they should sell those to rare coin collectors for
| on the order of 100,000 kopecks, which is an awfully large
| number for a five-year-old to be dealing with.
| scotty79 wrote:
| > kopeck in half into a denga was around the 1917
| revolution
|
| Really? I think I had 1/4 kopek coin somewhere when I was a
| kid (old foreign coin). I don't think it was this old.
| AlanYx wrote:
| I wonder if there's an issue in translation. How could they
| "combine" their money if Masha had nothing to begin with? But
| if we assume quantities of money can be non-integers, then the
| problem is underconstrained.
| karamanolev wrote:
| Kopeck - "It is usually the smallest denomination within a
| currency system."
|
| I presume they used kopecks for a purpose and not rubles,
| dollars or another unit that can be subdivided. That forces
| the integerness of the amounts and thus the presence of a
| solution.
| Arnavion wrote:
| The solution to the second question requires half-kopeks.
| karamanolev wrote:
| I looked at that problem after posting my original and
| was utterly confused. Would you trust yourself with an
| answer involving half-pennies? Seems like an error. As
| others pointed out, in #1, unless the kopecks are
| integer, the answer is underconstrained. #2 requires non-
| integer kopecks.
| [deleted]
| [deleted]
| watertom wrote:
| The problem is that the girls can't afford to buy a book
| singularly.
|
| Masha needs 7 kopecks to buy 1 book
|
| "Misha lacked one", which means to me as an native English
| speaker that Misha needed just one more Kopeck in order to
| purchase 1 book.
|
| When it's revealed that when they pool their money that they
| don't have enough to purchase just 1 book, I realized that
| the translation is faulty and stopped looking at the rest of
| the problems.
| bla3 wrote:
| Hint: It's much easier if you don't know linear algebra.
| skyde wrote:
| Can someone help me with this question. I tried wolframalpha
| but the question seem to make no sense.
|
| https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3...
| skyde wrote:
| Got it: cost is 7
|
| https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3.
| ..
| corpMaverick wrote:
| Please don't spoil it for the rest of us. @dang
| Arnavion wrote:
| Knowing the answer is 7 isn't a spoiler. The point is to
| work it out. You'd have to click the URL and see the WA
| input to be spoiled about that.
| 09asdf0asdf wrote:
| You can constrain the result to whole numbers by adding "y
| mod 1 = 0" as an additional constraint.
|
| https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%
| 3...
| waynesonfire wrote:
| neat trick, thanks.
| valbaca wrote:
| Yeah, this was confusing b/c to "be short" does imply that you
| have _some_ money, otherwise you 're 100% short of buying
| anything!
| rcoumet wrote:
| > Vasya has 2 sisters more than he has brothers. How many
| daughters more than sons do Vasya's parents have?
|
| In a world of gender and pronouns fluidity, does this even have
| an answer ?
| dang wrote:
| " _Eschew flamebait. Avoid unrelated controversies and generic
| tangents._ "
|
| https://news.ycombinator.com/newsguidelines.html
| jMyles wrote:
| Although I adore this guideline, I do want to step in to
| defend this comment.
|
| I think that many parents are trying to teach kids in this
| age range to take a wider view of the possibilities of family
| shapes and gender identities, and a question of this wording
| does indeed confound that.
| jMyles wrote:
| It is also nuclear-presumptive: it presumes that Vasya's
| parents have only daughters and sons with each other.
| culebron21 wrote:
| Curiously, Vasya (short for Vasiliy) can be a short form of
| girl's name Vasilisa (though it's rare).
|
| I can't recall any mention of divorce apart from school
| Literature course when I was in school in the 90s (most of
| material was inherited from the Soviet times).
|
| Knowing how Soviet editorial policies worked, I'm assured the
| editors considered mentioning divorces or non-married parents
| as seeding wrong attitudes and thus inappropriate for kids.
| [deleted]
| lhorie wrote:
| Curious to see comments quipping that some of the math problems
| geared towards young kids are too hard. I'd recommend taking a
| look at Singapore Math[0] to get an idea of what kids in those
| age ranges are actually _capable_ of doing, provided that adults
| shed preconceptions that children ought to be "sheltered from
| hard scary stuff", and instead encourage them.
|
| There are also great math-oriented games these days (I had some
| good success w/ prodigygame.com[1]).
|
| My youngest daughter is 6 and can solve simple multiplication and
| division problems. Sometimes she even surprises me. Some time
| ago, we were introducing ourselves to a new neighbor and the
| convo went somewhat along these lines:
|
| - my son: how old is your dog?
|
| - neighbor: she's 8
|
| - son: she's so small, is she a puppy?
|
| - neighbor: oh no, she's grown up. 1 dog year is about 7 human
| years, so-
|
| - daughter [interrupting]: oh wow, so then she is 56!
|
| The other day, she came to me beaming to explain how she had just
| solved 38/2 (by doing 40/2, 2/2 and subtracting the results).
| Gotta say it's a joy to see a kid that enjoys math.
|
| [0] https://www.singaporemath.com/
|
| [1] https://www.prodigygame.com/main-en/
| dxbydt wrote:
| Singapore Math & Prodigy are good recommendations. I'd also add
| IXL, Beast Academy, AOPS & RSM to the mix.
|
| Our public school here in Indiana was training middle schoolers
| for the Math Bowl statewide competition. I spoke to one of the
| teachers at the school and volunteered to help. She handed me a
| bunch of math problems. I quickly hacked up a web app to help
| the students train. Imagine my shock & surprise when a month
| later, our humble public school team took home the first
| prize[1], in a tournament that had some 300+ schools, many of
| which had private coaches. Congressmen from Indianapolis drove
| down to our little town to hand over the trophy & plaques!
|
| Since then, I do a weekly zoom session with those middle
| schoolers, sort of a Summer Math program. We work through AMC
| 8/10 problems & finish up with a friendly competition on the
| web app so I can track their progress.
|
| I believe competition math can be a lot of fun if taught well.
|
| [1] https://twitter.com/Hoosier47906/status/1400221783173775369
| Koshkin wrote:
| > _1 dog year is about 7 human years_
|
| This is the average; the correspondence is not linear...
| inamiyar wrote:
| Probably true, but the point was that the daughter was
| capable of quick multiplication, the age of the dog
| was..decidedly a minor detail.
| whimsicalism wrote:
| Classic HN
| MontyCarloHall wrote:
| Parent comment belongs in the hall of fame right next to
| the classic "Dropbox is trivial--it's just an FTP server
| under version control":
|
| https://news.ycombinator.com/item?id=8863
| ThePadawan wrote:
| I see your "classic HN" and counter with a "I'm one of
| today's lucky 10000!".
|
| I was taught the 7 years rule as a kid and only learned as
| an adult that it's an average, not true for all dog breeds.
| msrenee wrote:
| It's also not really true for young dogs. A 1-year-old
| dog of most breeds is reproductively mature, whereas a
| 7-year-old human is not.
| halgir wrote:
| > I'd recommend taking a look at Singapore Math[0] to get an
| idea of what kids in those age ranges are actually capable of
| doing, provided that adults shed preconceptions that children
| ought to be "sheltered from hard scary stuff", and instead
| encourage them.
|
| So much this. I've managed to make learning fun for my three
| year old son. All too often we turn some daily scenario into a
| fun exercise and a well-meaning family member will exclaim "he
| can't possibly know that!". I assume they intend to shield him
| from the inevitable failure they believe I'm setting him up for
| by asking these questions, but he usually figures it out. And
| when he doesn't, he still gets a kick out of understanding it
| when we go through it together.
|
| I repeatedly ask them to not make these comments. The more
| often he hears them say these things, the more liable he is to
| start believing them himself and say "I can't figure this out
| because I'm only x years old".
|
| I believe that if kids were allowed to be challenged and excel
| at the things they show an interest in and predisposition to,
| the scholastic standard would be much higher. Instead of adults
| deciding what children of certain ages are "supposed to" be
| able to do and not to do.
|
| My biggest fear at the moment is for his excitement at learning
| being crushed when he starts school.
| thebiss wrote:
| My personal experience is very very different, and is why I
| "quip these are too hard."
|
| I explain below, but since Singapore was mentioned, I need to
| ask a cultural question first:
|
| What do parents and teachers from outside the US do when a
| child DOESN'T understand math? How is math taught so that kids
| don't end up crying, getting sick, or hating themselves when
| faced with math problems? Or is there selection bias: it does
| happen, but "those kids" are left behind, and never seen by the
| rest of the world?
|
| My personal experience with kids and math:
|
| I'm in the US, and have one child who repeatedly could not
| complete math work during school, and would bawl and protest
| how stupid they were when given math homework at home.
| Completing it would take hours. Far behind, they could not
| multiply at age 8 or do fractions at 11. Tutors couldn't cover
| in an hour what other students finish in 10 minutes. Yet
| doctors indicated there's no learning disability.
|
| So this leads to my perspective: a prodigious child may
| certainly be capable of these and enjoy the challenge. But for
| some others, this may succeed in making them feel worse about
| themselves, because it's yet another example math they don't
| understand.
| hellbannedguy wrote:
| Go over the basics with him again, and again. I bet the
| teachers rushed him through fractions/percentages.
|
| I was taught math, and was a C student through high school. I
| relearned everything I didn't know in high school, in one
| semester at a community college.
|
| In math, you know the answer, or you don't understand how to
| get there. Math should be pass/fail. It's different than the
| other subjects.
|
| I don't believe most of my grade/middle school American
| teachers (mine) truely understood what they were teaching.
| sobriquet9 wrote:
| You may not believe it, but parents outside the US do not do
| anything special when a child doesn't understand math.
|
| This seems to be uniquely American problem. Somehow in the US
| it's culturally acceptable and even normal to be bad at math.
| Elsewhere it's just another subject. You study it and get
| better. The expectation is that everyone in a normal school
| (not special needs) can learn the standard math curriculum.
| quickthrower2 wrote:
| Bad at math is OK (and being too good at math means you are
| weird) attitude is (maybe was?) very prevalent in UK.
| lhorie wrote:
| My wife frequents chinese parent forums, and according to
| parents there, study time in a lot of households involve
| children staring at the ceiling and parents yelling... a lot.
| The thing, though, is I never hear about the situation
| improving by yelling more.
|
| My older son had trouble concentrating in the beginning
| (still does to some extent).
|
| I'd say _starting off_ with overly challenging material is
| probably going to be counterproductive if you 're also
| simultaneously trying to establish a routine. My daughter
| started with "draw 5 beans" sort of exercises, and seeing her
| older brother comply with a routine it was much easier to get
| her to finish her studies in a timely fashion.
|
| "Helping" too much can also be counter productive. The kid
| may end up expecting you to be there all the time, when
| really, half of the point is to develop some self
| sufficiency.
|
| The feedback cycle structure may also be messed up. It may be
| that the kid is stuck in a vicious cycle of negative feedback
| (e.g. "Damn about time you finished your math! Why'd take it
| so long!"). WRT the anecdotes above, I doubt yelling more
| will yield different results.
|
| For my kids, math oriented games provided a very different
| feedback cycle structure than study time (getting answers
| correct is literally gamified to look like rewards), and this
| is motivation enough for them to furiously scribble
| calculations on top of doodles they had carefully colored
| previously. It also provided a different dynamic where we can
| casually praise them about their in-game progress, rather
| than being a strictly a "boring school conversation". Another
| example: we started to do Monopoly game nights as a pretext
| to sneak in math into playtime and my son got quite into
| making sure people got the correct amount of change from the
| bank. IMHO, incorporating more positivity (real, appropriate
| positivity) into daily life is important.
|
| Another more subtle and difficult to address problem is
| general outlook on education. I've heard, for example, my
| kid's teacher say things to the effect of "oof, it's monday",
| as if school is a chore. I've also noticed north american
| media also tends to portray education negatively (e.g. the
| nerd stereotype, ferris bueller-like tropes, etc). This is
| very very different from east asian culture, where the
| general default is that education is very important. I don't
| know how to fix this, other than try not to engage in
| negative behavior yourself.
| halgir wrote:
| I appreciate this point. But I don't think it's about setting
| extremely high standards across the board and leaving those
| who can't keep up behind.
|
| For me it's about losing the mindset that children of certain
| ages are incapable of doing certain things and deliberately
| holding them back (with nothing but the best intentions I'm
| sure).
|
| I have a friend who is a published poet and prosaic genius.
| But she literally cannot solve 2x=4. I'm not being
| hyperbolic.
|
| Pushing her in math as a child would probably have been
| catastrophic for her emotional well being. But limiting her
| in other skill sets (like literature) would be equally
| catastrophic in terms of wasted potential (and the well being
| that comes with excelling at something you care about).
| not_jd_salinger wrote:
| > I'm in the US, and have one child who repeatedly could not
| complete math work during school, and would bawl and protest
| how stupid they were when given math homework at home.
|
| My experience in the US is that the vast majority of math
| teachers, especially in primary school, don't understand math
| in the slightest and are abysmal at teaching math outside of
| rote memorization.
|
| I knew a child that was learning about negative numbers and
| understood the role of primes in building the number line in
| 1st/2nd grade. They were learning from pure interest, but
| were excited by what negative numbers were about conceptually
| and found primes fascinating. These are the foundations of
| real mathematical thinking.
|
| Seeing the student was advanced the school put the kid in a
| 4th grade math classes but then complained that the child
| didn't know the multiplication tables. Understanding
| multiplication tables is literally memorization, this child
| had never been given the task of memorizing them so couldn't
| possibly have memorized them. Memorizing tables says
| literally nothing about mathematical proficiency, whereas
| gaining the intuition that "subtracting a negative number is
| the same as adding it" requires mathematical reasoning. The
| teacher was unable to see this because they themselves had no
| notion that understanding things like inverse function in
| math are important tools for reasoning. The child was removed
| from that math class, and quickly started to see mathematics
| in school as uninteresting.
|
| This is just one example, but I've ran across plenty of
| curious students where a math professor would be impressed
| but a 4th grade teacher would find them falling behind. My
| experience working with adults has been that most adults who
| think they are bad math, are more often than not ones that
| are getting caught up on issues with math that are good
| issues to have if you understand what's going on. People with
| a solid mathematical intuition will be confused by the rote
| mechanical explanations regurgitated by most elementary
| school teachers.
|
| There are far more teachers that struggle at teaching math
| than students that struggle with learning it, but it's far
| easier to blame students. It's no wonder that many students
| grow to hate math in the US, because it feels they are being
| unfairly punished and they are.
|
| You can't completely blame teachers either since the pay and
| respect teachers get in the US means that anyone who can do
| basic math will find a much better paying and rewarding job
| else where. In many Asian countries teachers are respected,
| and there is a possibility that you can attract people that
| understand the subject well enough to teach it.
| [deleted]
| ransom1538 wrote:
| These seem pretty challenging for a 5 year old. I am pretty
| sure if I was interviewing senior engineers this would stump
| them - and I would get walk outs:
| https://i.imgur.com/lRfEQOs.png (from his book).
| Someone wrote:
| The search tree for that isn't very wide. At every step,
| there are at most 6 things you can do: fill vessel A/B from
| the tap, empty vessel A/B in the sink, fill up vessel A/B
| from vessel B/A.
|
| That sounds bad, but most of them return you to earlier
| states.
|
| 'Drawing' a transition graph until you hit a solution in your
| head can be done in less than a minute. On paper, it
| shouldn't take more than 2.
| teekert wrote:
| Guess they didn't watch Die Hard ;) [0]
|
| [0]: https://youtu.be/2vdF6NASMiE
| HarryHirsch wrote:
| You'd get walkouts? Any person with normal intelligence and
| average facility with math realizes within 3 minutes that
| (2*3)-5 = 1.
|
| People who have trouble with that problem have no guts.
| thereare5lights wrote:
| This requires realizing that you can stop pouring. It isn't
| as in your face obvious as you're making it out to be.
| Arnavion wrote:
| random1538 didn't say what kind of engineers they were
| hiring, but if it was software engineers I'd be confused by
| it too. I know the solution to the problem, but only
| because I've seen it before and thus know the method to
| solve it.
|
| If they were hiring cooks / chemists / anyone that is
| expected to have experience with measuring liquid volumes,
| it might make sense to assume they have the experience
| needed to solve this problem.
| harperlee wrote:
| Sure, but the actual document states that
|
| The book is addressed to school and university students,
| teachers, parents - to everybody who considers the thinking
| culture an essential part of the personality development.
|
| Not sure where the 5yold number came from.
| loonster wrote:
| Which singaporemath? There are several.
| lhorie wrote:
| We bought the Intensive Practice series[0], and paced study
| time at a couple of pages a day (which takes about 20-30
| mins), semi-supervised (i.e. kids mostly work on their own,
| but if they don't understand something, we help clarify). It
| does take some hand holding at the beginning though.
|
| [0] https://shop.singaporemath.com/index.php/product-
| category/su...
| loonster wrote:
| Interesting. So was this a supplement to math learned at
| school or was it the primary math?
|
| I was expecting you to name dimensions or one if the other
| programs they offer.
| gnicholas wrote:
| Yeah, would be interested to see an example other than the
| link provided, which seems to be to purchase workbooks. Are
| there any good free resources (or free to try/evaluate)
| online?
|
| I heard about Singaporean math a while ago and looked up some
| youtube videos. It seemed like they showed clever ways to
| solve highly stylized problems, but nothing that would
| actually ever come up in the real world. To be fair, I only
| watched 3 videos, but they were all from different channels,
| so I assumed they were a decent sample of what Singaporean
| math is about.
| SilasX wrote:
| I agree with your general point, but if you want to give math
| problems that inspire creative, rigorous thought, you need to
| make them very clear, with as little ambiguity and assumed
| knowledge as possible. These problems don't do that. Examples:
|
| Kopecks being indivisible, there being only one book at a
| specific price in the first problem, books being on a shelf in
| a specific order (13).
|
| >>A brick weighs one pound and half the brick. How many pounds
| does the brick weigh?
|
| As a native speaker, that doesn't even make sense, and I don't
| know a natural way to express it that doesn't do most of the
| work of the problem. (Another comment indicates it means "a
| brick's weight is equal to half of a brick plus one pound".)
| grouphugs wrote:
| we're doin' math alright
|
| one by one
|
| two by two
|
| then (tree n) by (tree n)
| domino24 wrote:
| Is there an answer list anywhere? It seems to me that some of
| these questions could have multiple answers depending on how you
| interprt the question. I know it is more about the thought
| exercise, but on some it would be nice to have the correct answer
| in order to learn how to find the solution.
| SamBam wrote:
| I only worked through the first 13, but none of them seemed to
| me to have multiple solutions (with the exception of whether
| you can have less than one kopeck, which the author would
| assume the readers knew you couldn't).
| kangnkodos wrote:
| #18 does not have any answer. It's impossible to cover the
| squares as requested.
| thaumasiotes wrote:
| What do you mean? You just provided the answer. It's
| unique.
| thaumasiotes wrote:
| > I only worked through the first 13
|
| > (with the exception of whether you can have less than one
| kopeck, which the author would assume the readers knew you
| couldn't)
|
| You did notice that the cork in the second problem costs half
| a kopeck?
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