Wednesday, January 25, 2012

This Logic Game Needs a Name

This is a game to give Geometry students practice evaluating the truth value of conjunction, disjunction and conditional statements.

This is what one game set looks like, for use by two students:


Each set has: 36 statement cards, 18 T/F cards, a cube with logic operations on it, and 4 negation chips. (All the cards are one-sided.)

The sides of the cube look like this:

I bought unfinished wooden cubes at a craft store and wrote on them with a Sharpie (hence the bleeding.) I'm sure someone clever will comment with a better way to make these. You could also just use regular 6-sided dice and provide a decoder (rolling a 1 or 2 means "or", etc), but I was in overachiever mode yesterday. 
The kids are very much beginners in the Logic unit, so we gradually dialed up on the cognitive load by playing two easier warm-up games before the real game. I also had them set their notes from yesterday out on their desk for reference.

Warmup Game 1: Easy Mode


1) Use only the True/False cards and the cube.

2) Distribute half the cards to each player.

3) The person whose birthday is next wins when the outcome is True. The other person wins when the outcome is False.

4) Game play is like “War.” On each turn, each player flips over one card, and the cube is rolled. The players work together to determine whether the resulting compound statement is True or False. The winner keeps both cards.

5) The game is over when time is up or one person gets all the cards.

So if this happened, "True" would win the round:



But if this happened, "False" would win the round:
 
 
We only played Game 1 for a couple minutes, because it's pretty lame. Not very challenging, no strategy, also the "True" player has an advantage, because more of the possible statements come out True. On to...
 
Warmup Game 2: Like Game 1 but Harder


1) Use only the Statement cards and the cube.

2) Shuffle and randomly distribute 10 cards to each player. I gave them a few minutes to look through them to familiarize themselves with what the statements looked like, and think about whether they were true or false.

3) The person whose birthday is next wins when the outcome is True. The other person wins when the outcome is False.

4) Game play is like “War.” On each turn, each player flips over one card, and the cube is rolled. The players work together to determine whether the resulting compound statement is True or False. The winner keeps both cards.

5) The game is over when time is up, or when one person gets all the cards.

6) VARIATION: Each player also gets two negation chips. A negation chip can be played at ANY TIME, but can only be used once and must be discarded after use.

So if this happened, False would win the round:



But if this happened, True would win the round:
 

But if the False player still has a negation chip, she could opt to throw it down, and take the round:
 

So that was all a warm up to familiarize ourselves with the materials, and remember the stuff we learned about yesterday. Still kind of lame because there's not really any strategy. Finally, we get to play the very fun...

The Real Game (which still needs a good name)


1) Each player gets: 10 Statement Cards, 5 True/False Cards and, 2 Negation Chips. You will be choosing cards to play on each turn, so it’s ok to look at all the cards in your hand. (You could deal out more or less cards if you want the game to take more or less time. This number was manageable for about a ten-minute game. Most groups were able to play two games.)
2) The goal is to get rid of all your cards by making statements that work.

3) Game play is turn-based. On your turn, you select three cards and place them in the field of play: two statement cards and a True/False card.

4) Then, roll the cube.

5) Both players should agree on whether the resulting compound statement works or not. If the statement works, you discard the three cards used in the turn, and go again. If the statement doesn’t work, you keep the cards in your hand, and lose your turn.

6) A negation chip can be played at any time. Even after the cube is rolled. However, once a negation chip is used, it must be discarded, whether the resulting statement worked or not.

7) The player that gets rid of all her cards first, wins.

So if a player selected these three cards, and rolled OR, the statement works:

They discard those three cards from their hand and take another turn.
 
But if a player selected these three cards, and rolled IF THEN, the statement does not work:
 

And they return the cards to their hand, and lose their turn.
 
HOWEVER, if they still have negation chips, they could play one now:
 

and now the statement works, so they can discard these cards and go again.
 
All the kids were engaged in playing for the whole period. Some of them asked "Can we play this again?" which blew my mind. I intended to do an exit assessment but didn't, so I'll give it to them at the beginning of class tomorrow and see what they retained. If I made new games, I would make the Statement Cards a different color from the T/F cards for easier sorting. It also needs an awesome, catchy name! But I haven't thought of anything worthy yet.
 
The final version owes a big debt to my colleague Dina Kushnir who talked through the game play with me, and came up with some of the basic mechanics. I'd also like to thank Maria Andersen for all her writing and insights about what makes a good math game - I don't think this would exist without her.

Here are some resources so you can make your own games. Enjoy!