Spoiler: I got rambly here. If you're going to not read this, here's two quick takeaways: the four new games and James' start of a game/curriculum alignment.
I was delighted when James Cleveland asked if I'd do a Twitter Math Camp morning session (meaning three 2 hour sessions) on math games with him. He'd led a one hour session at TMC13, and Sebastian Speer led another at TMC14, but this would be the first one with time to really make new games.
The format seemed pretty natural and intuitive: look at some games together, introduce a few principles, and get making. Just in case, we each had some ideas for games in case people didn't have any urges, and James had a couple of neat statistics games ideas burning a hole in his pocket in particular. I had a mechanic; my family recently discovered Sushi Go, which has a simple and elegant drafting mechanic. There was also this Tug of War that I had been discussing with Nora Oswald based on a Daniel Solis idea.
The plan:
 Day 1  play good games and discuss.
 Day 2  start design.
 Day 3  playtest.
Day 1 Games
I brought Linear War , but we didn't actually play! I considered it for day 1 because I like how the students make the cards for the game (learning part one) and then play (learning part two) working on vocabulary, concept, quick recognition and computation. We did play: (in order of complexity)
 Product Game: Illuminations, handout (original & integers), post (decimal). My nominee for best math game ever. Comes at the content from multiple ways, amazing replay value due to the deep strategy, quick to learn, structure supports students in learning the content, adaptable... The only thing missing is context, but this would distract from it as a strategy game. Teachers thought of several different uses for this immediately.
 Quod Game/Metasquares (app not currently in US app store) All you need is a grid, and the strategy is deceptively deep. Subtle approach to content, though, as there is a great mathematical structure, but it's more about noticing it than learning it.
 Factor Draft, James' great game. Interesting in that you can parallel play or interact a lot. Really requires the mathematics that it concerns. Needs its own pieces manufactured, but they can be used for multiple purposes. Great example of development in balancing the pieces for interesting play. High cognitive load game, lots of challenge.
 Domain Ranger, post 1 and post 2. Norah's serious game. It's an intense strategy game, for which you need the math ideas of domain and range, and the ability to compare different graphs. Participants had awesome suggestions about this. Recognizing the difficulties in learning such a complex game, they thought about doing a 1dimensional board set up learning game. And also the great idea of doing a preset first game, Settlers of Catan style. I'll try to work one up the next chance I have to use the game.
Harvey Mudd had CHALK boards. Deja view. 
Day 2 Design
We started off this day with a look at Decimal Pickle, maybe my best game, with a focus on desing thinking, the mathematical goal, and how the mechanic works in the game. One of the most interesting parts about preparing with James was thinking about classic game mechanics are use of them in math games.
Classic Game

Math Game version: K7

816

Apples to Apples, Dixit
 
Blackjack
 
Connect 4/Tic tac toe

Exponent & factor block game
 
Guess Who
 
Racko
 
Rummy/Concentration
 
Taboo
 
Uno
 
War
 
Wits & Wagers

There's a lot of room for addition in there. I'd also like to hear your thoughts about what's missing. Even just writing this I got thinking of Farkle and Yahtzee. (King of Tokyo is an example of a tabletop game that uses that great Yahtzee mechanic. I have an upper el math game that's a direct
For design principles, I have this goofy list of 9 I use as a framework (adapted from Mark Rosewater of Magic fame). We emphasized just a few
1. Goal(s). Design starts with objectives. (Whole point of Day 1.)
4. Interaction.
5. Surprise.
6. CatchUp. As you start to playtest, these two are important to attend to for good design.
What's really promising from the prep for this day, though, is James' start of a spreadsheet for curriculum aligned games. Here's a Google spreadsheet version  open for editing. If you know of things to fill in, PLEASE DO. If you have a hole you especially want addressed, let us know on Twitter.
People got designing pretty quickly. We divided into 4 groups, working on statistics (James was in this group), Fraction operations, Arithmetic Sequences, and Unit Conversion. I floated amongst the groups. This was a bit of a breakthrough for me. I design mostly in isolation. But (like for most things) collaboration was energizing, powerful and fast. Between this part of day 2 and some wrap up on day 3, we finished four good games. 23 hours of work. My contributions floating were questions, connections with other game experiences, and the occasional idea.
Day 3 Playing
Also today, we took time to do some rule writing:
 Rules. For me this comes late; kind of a synthesis step as you think about how to communicate the game. It will often result in design revision, though.
People needed a little time to finish. We had a good Skype chat with Nora, who shared her experiences playtesting, took people's questions, then discussed some of their interesting feedback on Domain Ranger. Dave Chamberlain (participant) shared his published game of Team Up! which is a 412 common core review board game, and some of his process. Also what it took to get it in commercial finished form.
James gives a good write up of the statistics game, Fighting for the Center. Use playing cards, players build a data set that meets some goals (measures of central tendency) hidden from the other players. It's great at making players think about how changing a data point affects those measures. Lots of interaction, since you both are playing on the same data set, catch up is not an issue, and students will find more means and medians than they ever would in a homework set.
The fraction game is about addition and subtraction, modeled a bit on the Connect 4/Product Game framework. The board is really interesting, by asking for ranges, which really leads students to using representation (on the fraction cards we had). The teacher may want a way to get students to add precisely. I think there's some more playtesting to do here, too, as the placement of the various squares was more about coming up with them.
Honeycomb Madness, unit conversion game. This is a classic board game, and the closest to being a general review game. You start in the outer ring, and are trying to get to the inner ring by answering questions. The ring level serves as a kind of rubric, though, and might support some kind of awareness in students as to different levels of understanding of the material. There's a nice bit of randomness that's reminiscent of Trivial Pursuit. I liked that it is not the kind of game I might design; I think it might be quite popular with students, too.
Arithmetic Sequence Game. This one is right up my alley, though. Deck of playing cards. Deal three: starting value, common difference, step number. That determines a target. Each player is dealt 5 cards, and tries to get as close as possible. Then the idea that complete changes it: you bet on your play, 16 points. Closest gets the points everyone bet. 2nd closest gets their bet back. Wow. Plays great. I'll be trying this out, next algebra class for sure. I made a GeoGebra sketch to help with the calculation and to practice.
Thanks to James and all the participants. I feel like I learned a lot about collaborating in game design, and broadened my tastes a bit, too. This more than ever makes me want to get students designing games, so if you're in the area and wouldn't mind a mathematician in the room...
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