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

749 points by lainon 9y ago

pwaivers 9y ago
Wow this is a really cool question and even better answers!
mdturnerphys 9y ago
This one is huge among the kids here in NE Seattle: https://en.m.wikipedia.org/wiki/Chopsticks_(hand_game) https://en.m.wikipedia.org/wiki/Chopsticks_(hand_game) The roll-over and splitting variations are standard here, which makes the game more interesting.
- eru 9y ago
  I've only ever seen it as a drinking game in Singapore.
Splines 9y ago
I'm not sure if this is serious or satire: https://mathoverflow.net/q/281475 https://mathoverflow.net/q/281475 I mean, it feels like satire, but who knows...
- a-saleh 9y ago
  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.
- gjm11 9y ago
  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 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).
  - cableshaft 9y ago
    Interesting game, thanks for sharing.
- zokier 9y ago
  > Printing, or playing by means of some graphics software, seems safe. emphasis mine
- fjsolwmv 9y ago
  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
  - deleted 9y ago
    [deleted]
- mquander 9y ago
  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.
codeulike 9y ago
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-maze/id1193295317?mt=8 https://itunes.apple.com/us/app/numplussed-number-puzzle-maz... https://play.google.com/store/apps/details?id=com.codeulike.numplussed&hl=en_GB https://play.google.com/store/apps/details?id=com.codeulike.... Example of a hard level: https://twitter.com/codeulikegames/status/911725658929291264 https://twitter.com/codeulikegames/status/911725658929291264 some easier ones: https://twitter.com/codeulikegames/status/890246328290332672 https://twitter.com/codeulikegames/status/890246328290332672
jrimclean 9y ago
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.
- Jtsummers 9y ago
  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 https://boardgamegeek.com/boardgamecategory/1039/deduction More games of this form.
ideonexus 9y ago
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/ 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.
- r_klancer 9y ago
  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/ http://mw.concord.org/nextgen/)
- eru 9y ago
  For a slightly older audience, https://www.redblobgames.com/ 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.)
  - arvinsim 9y ago
    This is amazing! Thanks for bringing up this site.
    - eru 9y ago
      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.
disconnected 9y ago
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/ 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.
- msoucy 9y ago
  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.
  - zellyn 9y ago
    I have doodled away many hours on Net and Pearl :-)
eric_h 9y ago
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).
- dahart 9y ago
  Set is awesome. And my 6 year old can crush me!
  - tomhallett 9y ago
    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. :)
- eru 9y ago
  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.
  - eric_h 9y ago
    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.
    - jdmichal 9y ago
      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...
indescions_2017 9y ago
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.
- weinzierl 9y ago
  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 https://plus.google.com/+TerenceTao27/posts/CR1ZoNe9ojQ EDIT: From what I found online, I believe Terry Tao's son was 10 at the time.
  - fjsolwmv 9y ago
    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.
eru 9y ago
Kakerlakenpoker (https://boardgamegeek.com/boardgame/11971/cockroach-poker 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.)
jotux 9y ago
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_search_detailpage?ie=UTF8&psc=1 https://www.amazon.com/gp/product/082186873X/ref=oh_aui_sear...
- deleted 9y ago
  [deleted]
- sytelus 9y ago
  Book looks like out of print but PDF is here: http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf
Findus23 9y ago
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.
- alexbeloi 9y ago
  I have this game too, it goes by the name Quarto. https://en.wikipedia.org/wiki/Quarto_(board_game) https://en.wikipedia.org/wiki/Quarto_(board_game)
navalsaini 9y ago
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).
- Moru 9y ago
  I find Arimaa is a fun and much easier game to learn the basics of. And you play it on a chessboard :)
guiltygatorade 9y ago
https://en.wikipedia.org/wiki/24_Game 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.
StevePerkins 9y ago
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.
- Swizec 9y ago
  > 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.
  - khedoros1 9y ago
spot 9y ago
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.
weinzierl 9y ago
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/ 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 https://boardgamegeek.com/boardgame/9727/play-net
- onychomys 9y ago
  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.
  - weinzierl 9y ago
    I only realized after your comment that what I wrote was unintentionally funny. Rewrote my comment.
xydinesh 9y ago
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/B004TGVNHA https://www.amazon.com/SmartGames-SG-480-IQ-Twist/dp/B004TGV...
tw1010 9y ago
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?
rmetzler 9y ago
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.
agentultra 9y ago
A surprising series of computer games that you might not even recognize are based on algebra (at first): http://dragonbox.com 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.
ccvannorman 9y ago
If your child is 8+, I would recommend trying out my game, SuperMathWorld.com (or for ipad: Mathbreakers.com)
krisives 9y ago
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 :(
tebruno99 9y ago
I work for a company that makes Math games based on neuroscience research. https://www.mindresearch.org 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)
appellation 9y ago
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.
jonbarker 9y ago
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.
- ideonexus 9y ago
  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.
  - jonbarker 9y ago
    In Go we have 'pair go' where each side is a team conferring on the next best move. 'Pair chess' might encourage kids similarly.
- dorkwood 9y ago
  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.
satishf 9y ago
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.
alexfoo 9y ago
Mancala
peterburkimsher 9y ago
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.)
- mac01021 9y ago
  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?
elihu 9y ago
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/Ricochet_Robot
sturmeh 9y ago
The 5 year old can encode secrets using RSA with low primes using a calculator, and you can try decoding it with paper. :D
galeforcewinds 9y ago
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.
thirstysusrando 9y ago
Not to sound negative but I think games are inherently mathematical. Any creativity based on rules can be abstracted into some mathematical concept.
- cableshaft 9y ago
  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.
henrik_w 9y ago
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-revisited/ https://henrikwarne.com/2011/09/30/set-probabilities-revisit...
sytelus 9y ago
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.

749 points by lainon 9y ago

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

This one is huge among the kids here in NE Seattle: https://en.m.wikipedia.org/wiki/Chopsticks_(hand_game) https://en.m.wikipedia.org/wiki/Chopsticks_(hand_game) The roll-over and splitting variations are standard here, which makes the game more interesting.

eru 9y ago
I've only ever seen it as a drinking game in Singapore.

Splines 9y ago

I'm not sure if this is serious or satire: https://mathoverflow.net/q/281475 https://mathoverflow.net/q/281475 I mean, it feels like satire, but who knows...

a-saleh 9y ago
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.
gjm11 9y ago
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 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).
- cableshaft 9y ago
  Interesting game, thanks for sharing.
zokier 9y ago
> Printing, or playing by means of some graphics software, seems safe. emphasis mine
fjsolwmv 9y ago
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
- deleted 9y ago
  [deleted]
mquander 9y ago
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.

codeulike 9y ago

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-maze/id1193295317?mt=8 https://itunes.apple.com/us/app/numplussed-number-puzzle-maz... https://play.google.com/store/apps/details?id=com.codeulike.numplussed&hl=en_GB https://play.google.com/store/apps/details?id=com.codeulike.... Example of a hard level: https://twitter.com/codeulikegames/status/911725658929291264 https://twitter.com/codeulikegames/status/911725658929291264 some easier ones: https://twitter.com/codeulikegames/status/890246328290332672 https://twitter.com/codeulikegames/status/890246328290332672

jrimclean 9y ago

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.

Jtsummers 9y ago
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 https://boardgamegeek.com/boardgamecategory/1039/deduction More games of this form.

ideonexus 9y ago

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/ 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.

r_klancer 9y ago
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/ http://mw.concord.org/nextgen/)
eru 9y ago
For a slightly older audience, https://www.redblobgames.com/ 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.)
- arvinsim 9y ago
  This is amazing! Thanks for bringing up this site.
  - eru 9y ago
    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.

disconnected 9y ago

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/ 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.

msoucy 9y ago
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.
- zellyn 9y ago
  I have doodled away many hours on Net and Pearl :-)

eric_h 9y ago

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).

dahart 9y ago
Set is awesome. And my 6 year old can crush me!
- tomhallett 9y ago
  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. :)
eru 9y ago
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.
- eric_h 9y ago
  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.
  - jdmichal 9y ago
    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...

indescions_2017 9y ago

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.

weinzierl 9y ago
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 https://plus.google.com/+TerenceTao27/posts/CR1ZoNe9ojQ EDIT: From what I found online, I believe Terry Tao's son was 10 at the time.
- fjsolwmv 9y ago
  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.

eru 9y ago

Kakerlakenpoker (https://boardgamegeek.com/boardgame/11971/cockroach-poker 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.)

jotux 9y ago

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_search_detailpage?ie=UTF8&psc=1 https://www.amazon.com/gp/product/082186873X/ref=oh_aui_sear...

deleted 9y ago
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sytelus 9y ago
Book looks like out of print but PDF is here: http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf

Findus23 9y ago

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.

alexbeloi 9y ago
I have this game too, it goes by the name Quarto. https://en.wikipedia.org/wiki/Quarto_(board_game) https://en.wikipedia.org/wiki/Quarto_(board_game)

navalsaini 9y ago

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).

Moru 9y ago
I find Arimaa is a fun and much easier game to learn the basics of. And you play it on a chessboard :)

guiltygatorade 9y ago

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

StevePerkins 9y ago

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.

Swizec 9y ago
> 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.
- khedoros1 9y ago

spot 9y ago

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.

weinzierl 9y ago

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

onychomys 9y ago
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.
- weinzierl 9y ago
  I only realized after your comment that what I wrote was unintentionally funny. Rewrote my comment.

xydinesh 9y ago

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/B004TGVNHA https://www.amazon.com/SmartGames-SG-480-IQ-Twist/dp/B004TGV...

tw1010 9y ago

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?

rmetzler 9y ago

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.

agentultra 9y ago

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

ccvannorman 9y ago

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

krisives 9y ago

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 :(

tebruno99 9y ago

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

appellation 9y ago

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.

jonbarker 9y ago

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.

ideonexus 9y ago
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.
- jonbarker 9y ago
  In Go we have 'pair go' where each side is a team conferring on the next best move. 'Pair chess' might encourage kids similarly.
dorkwood 9y ago
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.

satishf 9y ago

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.

alexfoo 9y ago

Mancala

peterburkimsher 9y ago

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.)

mac01021 9y ago
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?

elihu 9y ago

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/Ricochet_Robot

sturmeh 9y ago

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

galeforcewinds 9y ago

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.

thirstysusrando 9y ago

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

cableshaft 9y ago
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.

henrik_w 9y ago

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

sytelus 9y ago

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.