## Tiny Games, mathematics edition?

So there’s a Kickstarter project closing today which has me wondering about mathematics potential.

Tiny Games: Hundreds of real-world games, inside your phone.

The concept here is to have games suited for different settings that can be described in only a few sentences.

Could one make an all-mathematics variant — mathematical scrimmages, so to speak? The only games I could think of offhand in the same spirit as Tiny Games were some Nim variants and Fizz-buzz.

1-2 Nim (for two players): Start with a row of coins. Alternate turns with your opponent. On your turn you can take either 1 or 2 of the coins. The person who takes the last coin wins.

Fizz-buzz (for a group): Players pick an order. The first player says the number “1”, and then the players count in turn. Numbers divisible by 3 should be replaced by “fizz”. Numbers divisible by 5 should be replaced by “buzz”. Numbers divisible by both should be replaced by “fizz-buzz”. Players who make a mistake are out. Last one in wins the game.

Anyone have some more?

EXTRA NOTE: One condition I’d add is the games need to work as games and not as glorified practice. “Challenge a friend to factor a quadratic you made” meets the “Tiny” but not the “Game” requirement.

EXTRA EXTRA NOTE: Dan Meyer asks “Aside from the counterexample that follows, what are the qualities that make Fizz-Buzz and Nim gamelike and not, say, exerciselike?” In both cases the games incidentally have some mathematics in them and are the sorts of games one might play even outside of a mathematics classroom. Even though Wikipedia claims Fizz-buzz was invented for children to “teach them about division” (?), my first encounter was from The World’s Best Party Games. (This still doesn’t totally answer the question, I know. A related question is: what is the difference between a puzzle and a math problem?)

### 16 Responses

1. Not yet an app user, I like the coffee cup better than the app they’re making. But I’m contemplating getting a smartphone and checking out math apps this summer. Maybe I’ll change my mind…

2. Agreed. Factor a quadratic is not a game. But find the equation of this polynomial pictured might work like a game for some. The visual makes it more intriguing to me, anyway.

3. That’s what made me think of it. Yesterday, I had my pre-calc class up front, looking at my laptop, analyzing the curve. We’re done with that unit, but it was great review.

4. Some of the Freeze Dried Games Pack games are of mathematical interest. Gomoku in particular swept through my group of peers when I was in middle school, and leads quickly to logical analysis of varying degrees of sophistication. (There may not be a common core standard you can point to, but there’s plenty of mathematical thinking going on.)

5. I think this is a really important post. This line just seems to be begging the question, though:

“One condition I’d add is the games need to work as games and not as glorified practice.”

Aside from the counterexample that follows, what are the qualities that make Fizz-Buzz and Nim gamelike and not, say, exerciselike?

• They have been played as games without any aforethought as to whether mathematics education is involved. (Fizz-buzz has been played as a drinking game, but I’ll leave the details to the imagination.)

(This still doesn’t totally answer the question, I know.)

• Is it an element of competition? “Factor my quadratic” isn’t a game, but “Who can factor this the fastest?” or “Can you factor these five quadratics faster than you factored the five we did yesterday?” might qualify.

It’s good to separate the concept of “game” from “fun”, also. It might be more fun to compete as teams, or individually. It might be fun to compete against others, or against yourself. I think fun will be partly subjective, and partly depends on the game and the group.

It’s definitely more fun (or should I say “engaging”?) when you have a legitimate chance at winning. In math games, having a legitimate chance might include that the game doesn’t have an undefeatable strategy or that the game is new to everyone and no one has discovered overwhelmingly strong strategies.

I’m seeing lots of games listed over on Dan’s blog, but I want to keep thinking about what defines game vs. practice (and I have a hunch that someone must have written about this already, somewhere). http://en.wikipedia.org/wiki/Game might be an approachable starting point for pondering, but I think their definition (“structured playing”) might be broader than what we’re talking about.

6. […] Dyer writes a very important post highlighting Tiny Games, a listing of games you can play quickly, almost anywhere, with only […]

7. Does 24 count? Or the 4 “4s” game? (How many numbers can you make using exactly four 4s?)

8. Our kids from China taught us a game: One person thinks of a number from 1 to 100, kids take turns guessing. Each time a kid guesses wrong, the person with the number uses the incorrect guess to set a new (and closer) higher or lower bound (this is where the admittedly low-level math comes in). The kid who guesses right gets a turtle drawn on their hand (I’ve never quite understood that part).

9. Trying to collect these and from Dan’s thread at http://bit.ly/TinyMathGames

10. […] Tiny Games, mathematics edition? […]

11. It’s funny that I play both these examples with my classes regularly (albeit, with some modifications). The kids love them, and we get into some really interesting discussions about strategy. The problem is, I only have one more, and I’ve been searching for similar games for a long time. I really like my variations though, so I’ll post them here before I go check out the collected resources.

1-2-Nim
I rename this and remove the resource requirement. You don’t need coins/matches/whatever. The first person starts the game by saying the number “21” and then the next person says either 1 number less or 2 numbers less, ie “20” or “19”. The goal is to make your opponent say (or skip) the number “1”. Works exactly the same, just removes a level of complication. It’s obviously a game of strategy between two people, but if we play it with 3, or 4 (or 20) people, it increases an element of chance. This is great for a discussion about luck-vs-skill in games. There are games that are all skill (Chess) there are games that are all luck (Chutes-and-ladders) and most games fall somewhere between these on a continuum. Where would you put football? Great conversation.

Fizz-Buzz
I call this Buzz-Zing but the rules are nearly the same. The numbers change, however. Great for late-primary and middle school kids for practising times-tables. The other main difference to what you’ve described is that you also say “Buzz” or “Zing” if the number has the base numbers as a digit.
EG, If the buzz number is 3 and the Zing number is 7, the sequence goes: 1, 2 Buzz, 3, 4, 5, Buzz, Zing, 8, Buzz, 10, 11, Buzz, Buzz, Zing, Buzz, 16, Zing, Buzz, 19, 20, Buzzing, etc.
Try adding a “Ga” number for extra difficulty (this is really tricky) but it allows you to call the game Buzzinga! (I hate Big Bang Theory but kids love a pop-culture reference.

Roman Goblin
My other new addition is only for primary and lower-middle for teaching different number systems. But, whether you’re teaching Roman Numerals or not, it’s a great game. I let the kids pick 5 random words and we substitute those for the roman digits I, V, X and L. The job is just to count upwards in turns.
eg, I = Cat, V = Pasta, X = Bowling, L = Flying
First student just says, “Cat” then the next has to say “Cat cat” then the next is “Cat cat cat” then “Cat Pasta” then “Pasta” then “Pasta Cat”, “Pasta Cat Cat”, “Pasta Cat Cat Cat”, “Cat Bowling” etc. The kids love it, and they love playing again trying to choose words that will result in funny outcomes.

Also works wonderfully as a drinking game where you substitute I, V, and X for swearwords.

12. […] Dyer launches a wonderful discussion in Tiny Games, mathematics edition? Dan Myer brings the project to everyone’s attention with Tiny Math Games. And John Golden […]