Mathematical games interesting to both you and a five-year-old child | Hacker News Reader

Mathematical games interesting to both you and a five-year-old child

mathoverflow.net

749 pointslainon131 comments

I imagine that a good portion of HN's readership (and probably MathOverflow.com's) were intellectually gifted as children. Or at the very least, remember themselves that way.

I would therefore caution people on two things: (1) your personal memories of early childhood are often quite distorted, and (2) it's not fair to impose upon a child today the expectations that come from your own ego-distorted memory.

This post caught my attention because I happen to be the father of a 5-year old son, and I myself have been searching for interesting mental exercises to share with him.

It's been an exercise for me as much as for him, teaching me about patience and tempered expectations.

Five years is YOUNG. A generation ago, early childhood educators in the U.S. didn't even typically introduce reading until age six. We start reading in kindergarten now, but typical 5-year olds can generally be expected to recognize repetitive words and basic arithmetic concepts (e.g. 1 + 2 = 3). Even that is limited to short periods of study in each sitting.

Children may vary, but I believe that many of the suggestions on that MathOverflow.com page (as well as comments here about chess, etc) would be better suited for around 7-8 and up. I think it would be unrealistic to expect the majority of 5-year olds to handle much of this, and it would be a mistake to push too hard at that age.

> Five years is YOUNG. A generation ago, early childhood educators in the U.S. didn't even typically introduce reading until age six.

We used to start reading in 1st grade when I was a kid. That was 7 years old back then in my country. We learned letters and stuff in kindergarten, but reading was the main task of 1st grade.

My parents decided I was pretty smart so they tried to encourage me to learn how to read sooner than 7.

I vehemently opposed this idea and said that I'm not old enough yet to read and that they should leave me alone and that I will read when it's time to read. I was upset, I think, that people were pushing me to do things beyond my age and it seemed somehow like that was not what I want.

Somehow I was a fluent reader on the first day of 1st grade. I suspect I actually knew how to read before but refused to do it until I was the right age.

I'm not sure what my point was in sharing this story, but here we are.

I started learning to read around 4 and was reading pretty well before the end of kindergarten, basically because I had the expectation that I could. First grade had a few tracks, based on reading ability. Some wires got crossed, and I ended up in the remedial class. The teacher wouldn't let me go, and the principal supported the teacher. That year was hell.

I had a similar experience with remedial reading in 6th grade. When we were asked to bring in self-chosen reading material, I brought in "Complete Works of Shakespeare," as a protest. Turned out my reading level was measured at grade 12+, but despite being off their scale, rules gotta be rules!

I have the _exact_ same story. Parents thought I was reasonably smart so while the school starts teaching reading at 6 or 7 years old they tried to have me learn it earlier but I was extremely opposed to it since I didn't want to have nothing to do in school (and I thought that was all you'd learn there - which I guess is sort of true :^)

That and what it means to have "protection".

I think the bigger issue here is interest.

I sure as hell would never have enjoyed these games, except maybe Set, as a 5 year-old. My attention span was fit for assembling legos and catching lizards, and a few years later, I became interested in math and programming. Not because my parents foisted them upon me: math because math showed up in school, and I had questions that needed answering; programming because my dad was building a website, and I wanted one too. My siblings took very different paths as well that were similarly organic.

I agree, a lot of interest in math/programming starts up without a plan and without external pressure. Less when you are a child.

Interest/enjoyment is a factor, but I don't think it's the only factor that matters. Long term success also matters. Pardon my racist stereotype but Asian families are supposedly very strict on and focused towards education for their children, seemingly in spite of the enjoyment of the child. The results here are obvious, Asian adults are kicking every other race's ass in basically every metric of success you can name: lower criminality rates, higher education, higher incomes, lower divorce rate, lower single motherhood rate, etc. Now, I'm not suggesting that everyone must adopt the stereotyped child rearing practices of Asian families, but it's worth considering that enjoyment for the child need not be the only priority.

If you look at Nobel prizes, Turing awards, and Fields medals are not represented by Asians.

I think it's better to have fewer medals but have the majority of the population receive the above-mentioned benefits.

I'm certainly open to the idea of studying the early childhood development practices of the parents of those award winners. Individualized success seems like it is more likely to attributable to unique factors such as high IQ coupled with obsessive personality traits. That may not be as helpful as looking at the practices of success groups the size of entire cultures. Shooting star vs rising tide sort of thing.

I think you would find jewish people more represented there.

It's worth mentioning that Jewish people share most if not all of those same "benefits?" I mentioned for Asians: higher education, lower criminality, etc. So there's surely something there to look at.

It is really difficult to generalize but I see Jewish people less strict and giving more freedom to their children while valuing education. It seems there are multiple articles about the subject [1] mainly triggered by Amy Chua [2] bestseller. BTW I just discovered that her husband is Jewish and he has been interviewed here [3]. All this conversation is turning funny in unexpected ways.

[1] https://www.google.com.ar/search?q=asian+mothers+vs+jewish+m...

[2] https://en.wikipedia.org/wiki/Amy_Chua

[3] http://www.telegraph.co.uk/men/relationships/fatherhood/1066...

https://en.wikipedia.org/wiki/List_of_Jewish_Nobel_laureates

I find it interesting to see almost no Sepharad on this list. And that the list exists at all.

>Nobel Prizes have been awarded to 887 individuals, of whom 195 were people of Jewish descent, although people of Jewish descent comprise less than 0.2% of the world's population.

Guessing it's due to upraising among Ashkenazi and strong networks effects.

Asian here, Indian to be precise. While I agree with you, I must point out the side effects. This obsession with grades and studies pushes lot of kids on a sort of rat race. There is immense pressure to succeed and success is typically narrowly defined like high grades and a secure job. I don't know the numbers in US, but in India this has caused a lot of rise in teenage and young adult suicides, it is not uncommon to here of suicides of kids studying for IITs due to pressure to perform. Another side-effect of this obsession with academic achievement has given rise to herd mentality where everyone is pushed to pursue similar career paths like engineering or medicine irrespective of a child's aptitude or interest. In India, especially this has led to a huge number of engineers who never wanted to be engineers. This has also meant that despite the aptitude lot of kids never got to pursue arts or pure sciences, in fact the popular perception of someone pursuing arts or pure sciences is that he or she could not make into engineering or medicine. Not to mention that this also discourages risk taking and entrepreneurship. Last thing I want to mention is that in Indian culture the idea of social perception is very strong, what will the society say tends to be a big factor in how decisions are made. This is one reason why despite sizeable population, India tends to be behind the world in pure science or in many sports. The mentality is changing a bit but not a lot and it is coming at a cost of many innocent lives.

> The results here are obvious, Asian adults are kicking every other race's ass in basically every metric of success you can name.

Perhaps you need to look at more than just metrics of success. South Korea has one of the highest suicide rates in the world, and a lot of this is due to societal pressures like exams and work. While China's done what everyone was skeptical about 20 years ago, it now recognises that there's a dire lack of the "innovative spirit" - which really is part and parcel of being "free spirit".

I do agree that we can't just pander to children's interests only. Still too young, and they need basic education as a foundation. But childhood is also the perfect time to explore as much as possible, and plant those seeds of interest. Go the "Asian" way if you want, but just bear that in mind to strike a fair balance.

I got into math because of programming, oddly enough. As a kid, what I really wanted to do was make games to show off to peers. And to do that I needed some mathematical building blocks first. Programming was a way to explore those things and then I ended up being more into that stuff than making RPG games to look cool to peers.

And by accident I transformed a normal interest (games and showing things off) into something that turned out to be useful and insightful to me later.

My mother-in-law was a kindergarten teacher many many years ago and she said it was typical to have to teach 5-6 year-olds the names of colors, shapes, and to identify letters. Then Sesame Street became widely available and the next generation of kids already knew everything they would normally teach.

Fascinating, I wouldn’t have expected that. I’m sure it depends on the family, too—my parents read with me from a young age, and I liked it, so I learned quickly.

In retrospect, 3 was a big year for me, haha. I remember going from not being able to read, to my parents finding out that I could read on my own (when they discovered me reading aloud the opening of Legend of Zelda for the NES) to reading proficiently by myself (thanks, Dr. Seuss!)

And at 4, I remember being very surprised when I went to kindergarten, and some of the kids made me read things for them because they couldn’t yet. I thought they must have been joking or making fun of me at first, but it turns out my parents are just great.

It's not just the parents. Some kids just don't take to it. My wife and I are both voracious readers, we read to our kids every day, and our 7-year-old is just not that into reading yet. On the other hand, her 4-year-old sister is picking it up great, and is only a few steps behind her sister. Each kid is different, and engaged parents are helpful, but necessarily everything.

Indeed, our 10 year old didn't start reading independently until she was almost 9, but now goes through a book a week. Our 4 year old and 6 year old are both at the point where they can read common words, and sound out simple phonetically spelled words (and we neglected reading enough to our 4 year old because we had 3 older kids we were dealing with), so the difference innate ability and interest have is huge.

Oh, definitely—I didn’t put enough emphasis on “and I liked it” as a factor.

My daughter was reading at ~18 months. Or something like reading. You be the judge: My wife took 3x5 cards and wrote words like "BUCKET" on them and put the card next to the bucket in the kitchen. All over the house on things. Then she'd go around with her and point out "Look at the bucket! That card says bucket. Look at the chair! That card says chair." Etc. Then she'd gather up the cards and put them on the floor face up in a grid and say "Now go find me bucket!" And she would find the card. Soon after that she was pronouncing words on billboards on her own. From there she started to pick out and read books from the library. It was awesome but of course it relied heavily on my wife's patience every day to do this.

It's amazing that you remember the emotions you experienced at the age of 3 and 4.

Memory is such a strange thing. I don’t remember many things from that time, but what I do is as if it happened yesterday.

I can feel the crooked wooden floorboards under my bony pajama-clad bottom, and the NES controller in my hands with its creaky plastic buttons, and the warmth of the summer afternoon sun, and the vibration of my boy soprano voice reading the text on the screen. I can smell the static of the Sharp CRT television, and my dad’s warm chamois shirt with (I now realise) maybe just a hint of weed on it. And I can hear him standing above me saying “You can read?”

This kind of thing is what makes me suspicious when I hear education experts say that N is too young to teach kids X. It's fine for each jurisdiction to have its own ideas about when to introduce particular topics, but they probably have very little info about how well things would have worked at a different rate or in a different order.

This all goes n-tupley when we consider any individual kid in. In that case you should just see what the kid can do and wants to do for yourself and not bother with what teachers think they are unready for.

I don't have much respect for the school system's standards for what age is appropriate to start teaching different subjects. Children in my family start reading around 3. I consider reading a power tool that bootstraps further learning. If I had waited until school to start learning, I would have been held back in my development for years.

Children have wildly different capabilities. I've seen quite a few who probably wouldn't be able to read at age three. As the father of two highly intelligent kids myself (according to a few unprompted remarks by a number of people), I don't see what the rush is either. Kids are kids, let them play! They can be serious the rest of their lives. If they are intelligent enough to read at three they'll be fine anyway....

It is because they have different capabilities that I don't respect the standard put forth by the school system.

If your kids can read at 3, then good. But the power-tool argument allows for flexibility.

I think I was a little slow, or at best normal in picking up reading as a kid. But for whatever reason, by about the age of 8 I was reading well ahead of the rest. So I never read The Cat in the Hat, but I read the The Hobbit long before most kids.

And I'm glad, because that second level is where the real power-tool lies. There's little point reading non-fiction at Cat in the Hat level. But there's plenty of facts available that are simpler to read than The Hobbit.

That isn't to say I didn't learn other stuff: my favorite childhood book was about science. But it had lots of pictures, and when fist got it, my parents read an explained it to me.

I was a precocious reader (<3yo), and I have a strong suspicion that kids who learn to read early read differently than those who learn "on schedule". I think early readers do something much more like code breaking, and I wonder if this affects second language acquisition or other skills. I don't necessarily think one style is preferable to the other, but I do think there is a potentially interesting difference.

I was very happy to read early, and I think it was advantageous for me, but I have not seen evidence that early reading in itself provides any lasting advantages on average. There may be a good deal of heterogeneity in the early-reading population.

"Code breaking." Interesting. I think I agree. I learned to read around 4 years old, and I did so by trying to follow along and predict words as my dad read to me. I can recall thinking "ok, there is a word coming up that looks like 'be'" and then verifying it was correct when he read it. I taught myself in that fashion. I can recall passing a road sign and reading "tippecanoe" aloud and surprising my parents shortly thereafter.

When we taught our own kids to read, I was surprised that this was not the way that they would learn to read. We ended up having good success with hooked on phonics with our first two and the last one did well with vast amounts of repetition and memorization of his favorite books.

Great observation. There is more pressure on kids than in the past. My daughter (1st grade now) was assigned homework every day in kindergarten (age 5), at a regular public school in the US, albeit a small amount and she didn't seem to be too bothered by it. These do seem possibly above a 5-year-old's level, and potentially a turn-off if they don't latch on quickly.

However, I'm actually impressed that the Math curriculum at schools today is much less narrowly arithmetical, and much in the vein of some of the puzzles mentioned here, in particular the "sets" game.

These games are good ideas, I will definitely try them, at the same time if the kid just isn't into it, no need to give up on them going to college. Let them try something else, or just go outside and play.

If anyone wants to try Set out with their kids, I made a free[0] Android version a while back. It's called Pipster[1] and it uses dog/cat/rabbit pictures instead of abstract shapes. "Beginner" difficulty is 3 dimensions (shape/color/number of stripes) which is much more appropriate for young children; "normal" and higher difficulties add color-of-stripes as the fourth dimension, which is equivalent to the normal Set game.

0: no ads or anything, this was a "teach myself android" project 1: https://play.google.com/store/apps/details?id=com.bogus.trio

Great job! Have been playing it all morning. Only request would be ability to change difficulty level. :)

Eh, I think it should unlock when you play enough but I have no idea how long that takes or if it even works anymore! Thanks tho!

Another variation of set that recently came out. Pretty challenging and my 7 year old always wins. https://itunes.apple.com/us/app/zort-4/id1288184054?mt=8&ign...

The worst potential harm in exposing a child to stimulating problems too early is that he could fail to become immediately interested in them; the potential harm in failing to do so is that he will never fulfill his maximum potential.

No. The potential harm is experiencing failure, in the very field she feels strongly is precious and important to her beloved parents.

The potential harm is having a kid less eager to try new things because he's afraid of something.

I'd think "experiencing failure" is only a problem if a parent persistently tries to push something inappropriate. Otherwise it is just part of life and of growing up.

The (minor) failure is still a learning experience, just a moral rather than mathematical one.

"avip" nailed it already, better than I could.

I'm just replying to say that if your username is "pervycreeper", you might reconsider whether to weigh in on exposing a child to anything...

An interesting case is famous educator László Polgár, who believed that "geniuses are made, not born" and raised his three daughters to become very, very successful in chess with "two of them becoming the best and second best women chess players in the world" (Wikipedia). He did this especially by beginning to teach them, when they were very young - four years old. "Judit was able to defeat her father at chess when she was just five"

Wikipedia article: https://en.wikipedia.org/wiki/László_Polgár

Another discussion: http://slatestarcodex.com/2017/05/30/hungarian-education-iii...

> I imagine that a good portion of HN's readership (and probably MathOverflow.com's) were intellectually gifted as children. Or at the very least, remember themselves that way.

Not gifted. But definitely curious.

I've been writing little one-page javascript pages to introduce my four- and six-year-old to various mathematical concepts like cardinality, place-value, sets, factors, equivalency, etc, etc:

http://ideonexus.github.io/Explorable-Explanations/

The boys love some of them (others not-so-much). Based on this article, I'm getting lots of ideas for new ones to code. Most of the code is original, but I try to be careful to give credit to anyone whose code or ideas I build upon.

This is excellent. I've been meaning to do something similar for my five year old. As always the hard part is finding the time to get started. This will get us started.

(It was easier back when building this stuff was my day job! -- http://mw.concord.org/nextgen/)

For a slightly older audience, https://www.redblobgames.com/ has awesome interactive explanations.

(But I'd say you probably want to be at least around 12 years old and interested in programming games to seriously benefit from them.)

This is amazing! Thanks for bringing up this site.

I'm glad you like it! It's an awesome website. The tutorial as written describes the solution in Python, if memory serves right; but of course you can have a look at the source and see that the little animations are written in JavaScript. So it's a twofer.

And the kids might still like just clicking around, and seeing what happens. They might not understand the algorithms, but they can still see how opening a passage in a wall changes the optimal path that a baddy in a computer game might take to catch your character.

Awesome, thanks for sharing!

The "Dragon Box" game on iOS is a fascinating way of presenting "algebra" (isolating a variable in a linear equation). It starts with a very abstract presentation of the rules (using cards with monsters on them - gradually introducing the rules) and eventually subs in letters and numbers. I suspect it might also be useful for adults who've had anxiety and poor success with more formal approaches.

It's a progressive game, where you have to complete a puzzle to get access to the next one. One thing that was surprisingly effective at motivating my four year old boy (almost five) was that they change the appearance of a cartoon monster at the end of each puzzle (or every 2-3 puzzles). He kept wanting to do the next puzzle to see how it changed.

As a footnote to your comment, the Dragon Box game is available on Android as well, and there are actually a series of games for different age groups and different skills.

The ones I tested have really good content and work well on mobile. Our 5 year old has been begging us to play with "her phone," so I'll be sharing these with my partner. Thanks for sharing these, they're fantastic!

Thanks! I struggle to make them mobile-friendly since younger children have a hard time with using the mouse and touchscreens are much more accessible for them. I keep learning a lot of CSS on the way, but it's really not my specialty. I would love for someone with CSS skills to rework my mess.

The word families page is great! I'll have to sit my daughter down with it today.

I should probably bite the bullet and get comfortable enough with javascript to take your approach. Here are some pico-8 demos I made with similar ideas:

https://www.lexaloffle.com/bbs/?tid=3846

https://www.lexaloffle.com/bbs/?tid=3259

https://www.lexaloffle.com/bbs/?tid=3136

In the Factors Demo, could you change the degree when you paint the next star? Maybe even change the degree between the factors the same as the first one. I think that might look a little nicer.

I think I know what you mean. The factors are drawn as a tree, and the way things are drawn now, it's possible for the line segment drawn for a child to go partway along the line segment drawn for its parent. Do you mean that I should rotate the children slightly so that this sort of alignment doesn't happen?

That's a good idea. On the topic of place value, I've been wondering whether either of these concepts is suitable for entertaining youngish minds:

https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem (leads to a number representation)

https://oeis.org/wiki/Primorial_numeral_system (could be base for applet game: represent a number in this system)

Or, also https://oeis.org/wiki/Factorial_numeral_system

Ohhh... I like these. I was thinking of an interface for exploring binary algebra one and the Zeckendorf Theorem would fit right into it. I think getting kids to think in other systems expands their appreciation of math.

Oh, very nice.

I earned my first money programming little games which looked like the coordinate one.

I always dream about recreating something like this, but keep deferring it. I should kick myself in the butt and deliver.

Your "Pattern Blocks" game isn't working for me, or is it that I don't know how to use it??? I drag the shapes to the grid and none of them want to stay...

I tried that first too. You have to just click the shape, and it appears.

Looks interesting. You have a typo on the main page: "Mathmatics".

I like that the game Set is mentioned. I haven't played in a few years but I've always loved that game. The only problem with it is that for whatever reason some people are _significantly_ better at it than others (right off the bat; obviously you can get better with practice, playing with a group of relative noobs and having one of them drastically outshine the other can be frustrating for the other).

Set is awesome. And my 6 year old can crush me!

I'll have to give set a shot. My 3.5 year old (now 4) could consistently beat me and other adults at memory matching games. :)

I'm colourblind. I can sort-of distinguish the colours in set, because they still differ in some attributes like brightness, but it takes me much, much longer.

And of course some people are better at spatial stuff then other.

Well shit, color blindness would definitely make the game more difficult, but I bet a grayscale version of the game could actually be made to work.

> And of course some people are better at spatial stuff then other.

Of course. My remark was really that the starting skill level of players can differ so dramatically that some people will literally have no fun at all (because they can't possibly win).

I've never come up with a reasonable handicap system to make the game more fun for everyone.

Probably best to follow standard guidelines: Don't distinguish anything by color alone. Using color and a pattern within the color would work fine. Figuring out how to make that work with partial fills is another question...

Coloretto (https://boardgamegeek.com/boardgame/5782/coloretto) is really good at this.

For Set, it might not be enough to bridge the gap: being able to differentiate by colour and some pattern might still be faster for a player than relying on pattern alone? (But still better than the status quo.)

My vision ain't gray scale. I'm just red-green deficient.

A reasonable handicap system is to allow the better players to take set(s) only if they can take two at once (depending on difficulty, the sets may or may not share a card). Sounded scary at first, but works quite well actually.

Friend of mine was an ace at it, her handicap was to call "set" as normal but then wait three seconds - allowing others to chime in with "set" and grab it. If her set was still available after the three seconds (no one grabbed it or they grabbed a diff. one) then she got it.

I'm terrible at visualizing things and I lose almost every game I play. I've convinced my friends who are good at Set to play a variant based on natural numbers and operations in them, but turns out they're a lot worse at that and it's a lot less fun for them...

I think my point is that Set really lends itself to someone with strong visual abilities, and is much much harder for everyone else.

> I've convinced my friends who are good at Set to play a variant based on natural numbers and operations in them

I'm curious about this and would like to subscribe to your newsletter ;)

We like Set, too. We also play a similar game called Qwirkle (played by laying tiles in interlocking groups). Qwirkle is played in turns, so some of that pressure of not being fast enough is eliminated.

I play a game with the creative name "make 10" with my kids sometimes that was inspired by Set, except that you have to pick groups of cards that add to 10 (or other numbers, if they're too good at it). My daughter has to find groups of three cards and can use addition and subtraction, and my son just uses addition on groups of two cards. We use regular playing cards with only A-9 included.

Many years ago, when I was first starting a company with 2 other partners, we used to play a few games of Set every lunch. We did this for months, maybe even a year.

Needless to say, we got really good. After the initial learning curve of "getting" the rules, it becomes almost entirely a game of memory and recognition. You just remember sets, having seen them so often, that you can almost instantly spot them.

It loses a lot of its mathematical shine at this stage, of course, so I consider it less of a mathematical game.

I've written a game that's a mix of algebra and maze solving. I believe its pretty relevant to this question. There are easy levels but also it can get surprisingly complex even for small mazes. Its called Numplussed and its free on Android or iOS:

https://itunes.apple.com/us/app/numplussed-number-puzzle-maz...

https://play.google.com/store/apps/details?id=com.codeulike....

Example of a hard level:

https://twitter.com/codeulikegames/status/911725658929291264

some easier ones:

https://twitter.com/codeulikegames/status/890246328290332672

I'm not sure if this is serious or satire: https://mathoverflow.net/q/281475

I mean, it feels like satire, but who knows...

I think it might be a bit tongue-in-cheek, but when I look at the game as written, it actually sounds fun.

-I think the real game there might be inventing such graph for your oponent, so that you have a chance for a draw? :)-

Wow, finally finished reading the comment. This looks quite interesting and deep.

I'm voting for some combination of "honestly oblivious", "ha ha only serious", and "actually this isn't as bad as it sounds" over "satire". My 11-year-old daughter was recently introduced in a school mathematics lesson to a game in this family, which she enjoyed and eagerly asked me to play with her.

It wasn't described in those terms, though. Their class has been looking at factors and multiples, so the game was presented like this: you have the numbers from 1 to 100 written down; one player picks a number (constrained to be no bigger than 50 for reasons as an exercise for the reader) to start with; then each player picks a still-unused number that's either a factor or a multiple of the one before. So a game might go like this: 25, 5; 15, 3; 99, 33; 11, 22; 44, 4; 8, 16; 32, 96; 48, 24; 12, 6; 18, 9; 27, 81; 1, 97 and now the first player has no legal move and loses. (I do not claim that either player played well in that game; I just picked random legal moves.)

If this game sounds like fun to you or your child, you can find an implementation here: https://nrich.maths.org/5468 and you may also see how long a chain of factors-and/or-multiples you can construct (imagine both players are now cooperating to make the game last as long as possible).

Interesting game, thanks for sharing.

> Printing, or playing by means of some graphics software, seems safe.

emphasis mine

It's a math post on math website. The discussion is for mathematical adults, but the games described are fun for kids -- kids have been playing pencil and paper graph games for many decades

I don't think it feels like satire since it sounds like a fun game? I'm actually astonished that I never played a game in this family before.

This one is huge among the kids here in NE Seattle: https://en.m.wikipedia.org/wiki/Chopsticks_(hand_game)

The roll-over and splitting variations are standard here, which makes the game more interesting.

I've only ever seen it as a drinking game in Singapore.

Not strictly mathematical, and maybe not exactly 5 year old difficulty (some of these are HARD) but here goes:

https://www.chiark.greenend.org.uk/~sgtatham/puzzles/

There's an Android version of these puzzles and Linux packages (usually called "sgt-puzzles" or something similar). Apparently (I just found this out) they also work on the browser, which is pretty cool.

I gave these to the high school kids that I mentor Robotics for - they each seemed to find different puzzles that they liked, so I consider that a win. These are the same kids who had fun learning binary search as a way to always win "high-low" guessing games, so they were already interested in logic.

My personal favorite from Tatham's puzzles is Net - I have it on my phone, with 15x15 wrapping being a nice way to relax and spend some time.

I have doodled away many hours on Net and Pearl :-)

I bought this book last year and found it really interesting with respect to how children interact with math as their brain develops: Math from Three to Seven [1]. There are a lot of little experiments and games that teach kids basic concepts and show how specific reasoning develops. I'm looking forward to doing some of them with my son in a few years.

[1] https://www.amazon.com/gp/product/082186873X/ref=oh_aui_sear...

Book looks like out of print but PDF is here: http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf

I haven't heard of set yet, but I have a wooden board game with a quite similar premise. All pieces are laying around and two players take terms putting them on a 4x4 grid. The first player to finish a row with 4 pieces with the same feature (there are 5 with two variants each) wins. I am normally quite bad at board games, but I am winning this one nearly every time, as others always seem to overlook one feature.

I have this game too, it goes by the name Quarto.

https://en.wikipedia.org/wiki/Quarto_(board_game)

This is physics, not just maths, but the logic is interesting to all ages.

Why do you need a seatbelt in a car but not on a train?

The heavier mass of the train means the force to you is smaller, so you're less likely to get thrown as far forwards.

(I just explained this to my girlfriend when she asked on the train. Thanks, engineering degree.)

Alright.

Why can you see into a house through its windows at night while those inside only see their reflections in the windows. Why is this reversed during the day?

5 is tough. Although I suppose Terry Tao was working out proofs by then ;)

By 8-9, something like the Japanese city-building card game Machi Koro is great for learning about variance, expected value, and optimization.

A while ago Terence Tao posted a a problem from his son's Math Circle. It is in his own words "surprisingly difficult":

> Three farmers were selling chickens at the local market. One farmer had 10 chickens to sell, another had 16 chickens to sell, and the last had 26 chickens to sell. In order not to compete with each other, they agreed to all sell their chickens at the same price. But by lunchtime, they decided that sales were not going so well, and they all decided to lower their prices to the same lower price point. By the end of the day, they had sold all their chickens. It turned out that they all collected the same amount of money, $35, from the day's chicken sales. What was the price of the chickens before lunchtime and after lunchtime?

https://plus.google.com/+TerenceTao27/posts/CR1ZoNe9ojQ

EDIT: From what I found online, I believe Terry Tao's son was 10 at the time.

Terry Tao seems to be forgetting some of his basic math as he spends most of time on super advanced stuff. He also has a post where he discovered the surprising fact that if you stay in your arrived airplane's seat until most people have exited, after the crowd clears you can walk off the plane more quickly.

Hi everyone I make a product called DnsLearning it turns the internet on and off based on progress made on supported sites.

We currently use PhantomJS to login to sites that don’t have API support, which is all of them except Khan Academy.

Are any of you guys who run these sites interested in setting up an OAuth API? We are glad to give some love and send users to sites that are improving.

Please respond or email me at kris@dnslearning.org

I feel bad posting anything like this on HN but it’s not often this space is on the front page and in general it’s not seen as a sexy enough subject :(

Measuring the world around you can be fun and humorous, especially when you are measuring with a peculiar reference object like a kid's shoe.

I find games of math with kids are most interesting when the adult is on a level playing field and doesn't "hold back" effort. In addition to measurement, games of sorting, spacial analysis, numismatics, and cultivating a favorite number can be fun.

In the 1970's, Hasbro made a game called "Something Fishy" which involved solving a spacial problem of fitting plastic sardines in to a tin can.

Many kids love to count money and learn about the different types of money, and calculate value. Be careful, as they may also be crafty enough to keep the money at the end of the game. The best ending is going to the store and letting them pay.

"The Book of Think: Or How to Solve a Problem Twice Your Size" may be a source of inspiration, as may "Brown Paper School book: Math for Smarty Pants".

Do you have a favorite number? Do you have a favorite shape? Did you know 7 is the scariest number?

I believe an early love of math often stems from a love of numbers, the thought that numbers are your friends. One great game to cultivate this friendliness is to simply go out in to the world and look for a complete set of numbers from 1..20 or so together. Numbers are all around.

I absolutely love the "prove me wrong" game. It reminds me of Nomic for some reason. Perhaps because both games are very language-based and have almost no rules (it's easy to "think outside the box" in both games). I've been searching for language-based games with a lot of room for creativity like that since forever, does anyone have any good suggestions for where to continue my search?

You could teach them chess variation known as minichess or halfchess. I have created a game halfchess.com for adults - but plan to add a learning mode for children in future.

I have given kids crash course on chess and it starts like this.

1. Ask them, how many squares are there on a board

2. Tell them about Pawns and make them play on a mini chess board with Pawns. Start with 3 pawns and slowly increase to 4,5,...,8.

3. Show them the knight. Some possible games with just knight are as follows:-

  a. Puzzles on how one knight can capture another knight placed in nearby squares.

  b. Play a game where one knight has to catch the other knight. The knight that is catching takes two steps every move, the running one takes one step.

  c. You can play above game with a dice and let two players battle just their knights. Even throw of dice gets 2 turns

And so on, introduce them to new pieces. You can tell them stories about each of the chess piece as you introduce them to it.

There are several mathematical concepts that you can teach children via chess - for example backtracking from a solution (when solving the puzzles with knights).

I find Arimaa is a fun and much easier game to learn the basics of. And you play it on a chessboard :)

Recently i've been trying to find an app like Duolingo but for math. Essentially, a way to practice bite sized pieces of mathematics to keep proficiency up.

Unfortunately the current selection of apps are fairly low quality and only allow very basic arithmetic. Any suggestions?

May just build it myself otherwise.

I've been playing IQ Twist with my 7 year old and 3 year old. It is fun for all of us.

https://www.amazon.com/SmartGames-SG-480-IQ-Twist/dp/B004TGV...

Kakerlakenpoker (https://boardgamegeek.com/boardgame/11971/cockroach-poker) is a game of pure bluffing that even small kids should fine enjoyable. The cute critters on the cards, like spiders and cockroaches, should help catch kids' interest.

The game itself is more about reading body language clues, but you can easily introduce a small amount of game theory mathematics in your deliberations.

(Ironically enough, Kakerlakenpoker has exactly the right structure for a drinking game. Lose a card: take a shot. Lose the round: finish the bottle.)

A surprising series of computer games that you might not even recognize are based on algebra (at first): http://dragonbox.com

I play games mostly of pattern recognition; repeating tiles, shape combinations (sets), etc. I mostly let the little ones drive and don't expect anymore than 20 minutes of focus.

What I'm paranoid about is the focus on literacy in schools and how formulaic and uninteresting maths can be. I'm hoping my kids won't be turned off of a beautiful subject just because they're taught in a rote manner to recall formulas and equations.

Bret Victor (of Apple fame) made Alligator Eggs which could be fun to play with a five year old. The game represents the untyped lambda calculus. You can download the PDF from Bret Victor's website.

http://worrydream.com/AlligatorEggs/

EDIT: Thinking about it, when I studied Petri nets at university someone showed me a Peri net board game.

https://boardgamegeek.com/boardgame/9727/play-net

Once you tell them that the game represents the untyped lambda calculus, you'll probably need to lock them in their rooms to get them to stop playing, I assume.

I only realized after your comment that what I wrote was unintentionally funny. Rewrote my comment.

I am surprised no one has mentioned Monument Valley on iOS or Android. I played it a bit in front of 4 years old and they were instantly hooked. Of course, they will need bunch of hints and help to get through all the levels but it's almost an ideal logic puzzle game I have ever encountered. I also started playing tic-tac-toe where I lose randomly to keep things interesting :). It is surprisingly not easy to teach all rules of tic-tax-toe to (perhaps many) 4 year old. The trick was to show them I play it against computer on iPad for lots of games.

I work for a company that makes Math games based on neuroscience research. https://www.mindresearch.org

I find a lot of the games very interesting and founded more on actual learning (you're encouraged to make mistakes in this program). Turns out to learn you need to make mistakes and see why you were wrong, more than simply answer correctly.

(Product is currently in Flash but we are working very hard to move to HTML5)

I think Set is quite an interesting game, playable by adults and kids alike. I've written a blog post about the odds of not finding a set among the cads on the table. I'll link it here in case somebody is interested:

https://henrikwarne.com/2011/09/30/set-probabilities-revisit...

I haven't tried Ricochet Robots with children, but it seems like it's a simple enough game to understand. Some of the puzzles might be too hard, though -- I wonder if anyone has come up with alternate board layouts of varying difficulty?

https://en.wikipedia.org/wiki/Ricochet_Robot

https://en.wikipedia.org/wiki/24_Game

Maybe 5 is a bit young for all of multiplication and division (but you could include the face cards). The game is still playable without -- there would just be a lot of "welp we shuffle these back into the deck" situations.

I can't recommend go highly enough.

Not only are the rules simple enough for kids (mine are 5-9), but counting the score is directly mathematical (counting for the little ones, multiplication and addition for the older ones).

the key to go for kids is a small board. 9x9 to start, then 13x13. none of them has graduated to 19x19 yet.

I think the key to teaching chess is to gasp deliberately lose to the kid a few times. In my experience at the age of 5 I lost (in my recollection) about five times in a row and then lost interest, only to regain interest in my 30s. Not sour grapes at all, just food for thought.

I find this very important. I will find ways to turn competitive games into cooperative games just to keep my sons' interested in them. It works wondefully, and the increased engagement has a great payoff in seeing them get better at the games.

In Go we have 'pair go' where each side is a team conferring on the next best move. 'Pair chess' might encourage kids similarly.

I had the opposite experience as a kid. I'd lose to my father in Scrabble over and over, but I'd continue to play against him anyway. I think I just enjoyed playing a game that was meant for adults. As I got older, I started to win more and more, but for the first year or two I don't remember winning at all (although it's entirely possible I'm not remembering things correctly).

Still, I like to think losing at games as a child taught me to be focused less on the act of winning and more on the act of playing the game. It's a quality that very few people appear to have, even as adults.

Natural deduction for propositional logic? Simple rules, real math. There are lots of good problems of varying difficulty in Logic in Computer Science by Huth and Ryan.

Edit: Perhaps this doesn't qualify as a game per se, but I think it might be a fun activity to work through the proofs together.

I don't see why that wouldn't be a game. As a kid (maybe not at 5, closer to 10?) my parents were giving me puzzle books that included puzzles based on deductive reasoning.

Clue is based on this form of logic. Or that's how I played it at least.

https://boardgamegeek.com/boardgamecategory/1039/deduction

More games of this form.

Domino is one of the mathematical games, I play with my daughter. You have to make a chain of domino pieces which represent one of 28 possible combinations of two out of 0 to 6. She plays this very good.

She is a little bit too young yet for Backgammon and Chess, but I plan to play these with her.

I have been using ixl.com with my 5 year daughter. We have fun solving it together. She always clap when she reaches challenge zone and receives awards. Not really a game but fun way to learn basic Math. Very highly recommend it for kids.

Not to sound negative but I think games are inherently mathematical. Any creativity based on rules can be abstracted into some mathematical concept.

To some extent, they all are, yeah. If for no other reason than from a designer's perspective of "How many cards should I include? How many components are needed? Do I need to change this based on how many players? How long should the game last? How many turns/rounds/minutes? How to I model this to make sure the game is balanced?" etc. I design both board and video games, and these are questions I have to figure out the answers to for each and every game.

If your child is 8+, I would recommend trying out my game, SuperMathWorld.com (or for ipad: Mathbreakers.com)

Wow this is a really cool question and even better answers!

The 5 year old can encode secrets using RSA with low primes using a calculator, and you can try decoding it with paper. :D

Mancala

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