Thanks again for this blog post, it was really helpful.

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.

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.