
Mathematical games interesting to both you and a five-year-old child - lainon
https://mathoverflow.net/questions/281447/mathematical-games-interesting-to-both-you-and-a-5-year-old-child
======
StevePerkins
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.

~~~
failrate
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.

~~~
akie
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....

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

------
ideonexus
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.

~~~
dunham
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.

~~~
kej
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.

------
eric_h
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).

~~~
Karrot_Kream
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.

~~~
eric_h
> 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 ;)

------
codeulike
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://itunes.apple.com/us/app/numplussed-number-puzzle-
maze/id1193295317?mt=8)

[https://play.google.com/store/apps/details?id=com.codeulike....](https://play.google.com/store/apps/details?id=com.codeulike.numplussed&hl=en_GB)

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)

------
Splines
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...

~~~
gjm11
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
Interesting game, thanks for sharing.

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

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

------
jotux
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...](https://www.amazon.com/gp/product/082186873X/ref=oh_aui_search_detailpage?ie=UTF8&psc=1)

~~~
sytelus
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
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
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_\(board_game\))

------
peterburkimsher
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
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?

------
indescions_2017
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
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
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.

------
krisives
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 :(

------
galeforcewinds
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.

------
tw1010
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?

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

------
appellation
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.

------
xydinesh
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...](https://www.amazon.com/SmartGames-SG-480-IQ-
Twist/dp/B004TGVNHA)

------
eru
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.)

------
agentultra
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.

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

------
sytelus
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.

------
tebruno99
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)

------
henrik_w
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...](https://henrikwarne.com/2011/09/30/set-probabilities-revisited/)

------
elihu
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)

------
guiltygatorade
[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.

------
spot
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.

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

------
jrimclean
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
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.

------
rmetzler
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.

------
satishf
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.

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

~~~
cableshaft
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.

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

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

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

------
alexfoo
Mancala

