## Think of a Number

I love to create math games almost as much as I love to play them.

My favorite professional project was leading the development of Calculation Nation. And my favorite game on the site is neXtu, though other games on the site may promote more sophisticated mathematical thinking.

I have many reasons to love my wife, not least of which is her creation of the game Dollar Nim. While I can’t take credit for the rules, I will take credit for its analysis and its popularization. (What do you call a wife who makes up a game that gets you a publication credit? A keeper!)

Recently, I’ve been frustrated by the lack of games for teaching algebra. I’ll give props to the good folks at Dragonbox, which uses a game environment to teach algebra. But I’m not yet convinced that it leads to deep algebraic understanding; even they admit “to transfer to pencil and paper, children must be explained how to rewrite equations line by line.” They also claim that “in-house preliminary tests indicate a very high level of transfer to pencil and paper,” but that’s the fox watching the henhouse.

So I’ve been thinking about games I can play with my sons that will allow them to engage in algebraic thinking. But I don’t want them to know they’re engaging in algebraic thinking. I have two criteria for all math games:

• The game mechanics depend on mathematics. The math is not tangential to the game; it is the game.
• Kids don’t realize (or at least they don’t care) that it’s a math game, because it’s fun.

It pains me to write that second criterion, because math is fun. But I know not everyone shares that opinion. So I do my best to disguise any math learning in the game and then, when they least expect it — BOOM! — I drop the bomb and show them what they’ve learned.

So here’s a game I recently devised.

• Player A chooses a number.
• Player B chooses two operations for Player A to perform on the number.
• Player A performs those operations and then tells the result to Player B.
• Player B then tries to identify Player A’s number.

These rules leave something to be desired, since Player B could simply ask A to “multiply by 1” and then “add 0,” in which case finding A’s number would involve no work whatsoever. To be a stickler, an additional rule could impose that either addition or subtraction can be used exactly once and that no operation can involve either 0 or 1. In a middle school classroom, I suppose I would state such a rule explicitly; for playing this game with my seven-year-old sons, I opted not to.

We played this game three times on the car ride to school yesterday. One game went like this:

• I thought of a number (14).
• Alex asked me to multiply by 3.
• I told them the result: 51.

Eli then guessed that my number was 16. He had subtracted 3, then divided by 3.

“No!” said Alex. “You added 3 first, so you need to subtract 9.”

“But he multiplied by 3, so if you subtract first, you have to subtract 3 × 3.”

Eli then realized that my number was 14.

He thought for a second. “Oh,” he said. “I should have divided by 3 first, then subtracted.”

Wow, I thought. This is going even better than I hoped.

Though they didn’t use the proper terminology, the boys had a great discussion about “undoing” operations by performing inverse operations in reverse order. In 10 minutes, they taught themselves how to solve a two-step equation:

3x + 3 = 51

Grace Kelemanik once said that she knew she was being effective when she didn’t have to say a word. She’d watch from the back of the room as students carried the conversation and guided one another to correct mathematical thinking.

I will never claim to be half the educator that Grace Kelemanik is. But yesterday morning, I was pretty darn effective.

I’d love to hear about math games you’ve played with kids, whether you invented them or not.

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• 1. goldenoj  |  August 16, 2014 at 11:15 am

I share your suspicions of Dragonbox. Also didn’t know your connection with CalculationNation, which is an awesome resource. So, thanks!

I love to make games as well. This page has mine plus links to others in the #MTBoS. http://mathhombre.blogspot.com/p/games.html

• 2. venneblock  |  August 21, 2014 at 10:57 am

Glad you like Calculation Nation. I loved working on that project.

Thanks for the link to your games. You can bet my sons and I will be playing some of them soon!

• 3. Joshua  |  October 1, 2014 at 11:46 am

My older two have had a lot of fun with your “guess” the number game. We started without explicit rules against adding 0 or multiplying by 1 and it was amusing to see their grins when they identified those strategies. After doing it a couple times, though, they stopped on their own because they realized it wasn’t fun that way.

I’ve taken two approaches: try to find games that fit certain math concepts or take existing games and enjoy the embedded math. Generally we have more success (more fun, deeper engagement) with the latter.

BTW, really enjoy Nextu! if that is typical of the stuff on calculation nation. . . then I’m not going to get any sleep for the next several weeks b/c I’ll be up all the time playing.

• 4. venneblock  |  October 2, 2014 at 5:46 pm

Glad you and your kids like the game, Joshua! And I agree with you — much better to pull the math out of a good game than trying to find a game that fits the math. The latter is what many publishers and commercial curriculum producers tend to do… often with mixed (or poor) results.

I think neXtu is the best game on Calculation Nation, but I hope you like the others, too. Ker-Splash is my second favorite, but it’s the chess of Calculation Nation — it takes a while to learn the rules, but once you know them, it’s a great game!

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