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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!


  1. This game is awesome. I really like the negation aspect, and how it teaches the kids to understand logical symbols without some memorization quiz.

    Maybe a paint pen would be less likely to bleed? Or you could prime the cubes, but that would be a PITA.

    As for a name, how about Logical Line Dances? Logic Wars?

  2. So in your example of the real game, when you decide which cards to play, before you roll the die, do you also have to decide in which order you're going to play them? So, if you got the if then, could you decide to swap the order and say: 3-4>0 if/then 3sqrt(8)=sqrt(72) true (I think that would be true because any if false then whatever is a true statement)?

  3. Once you place the cards, you keep them in the same order. No changing the order after the die is rolled.

    (You're correct... if F then T is a true statement, but if T then F is a false statement.)

  4. Logic Wars is good. Random Truth?

    Cool stuff. Makes me wish I taught logic.

  5. It looks great.

    My first thought was the School House Rock 'Conjunction Junction'- but maybe that's too narrow.
    Is what you have here a 'propositional calculus'? Would 'Props' be a name that might appeal to your peeps?
    - D

  6. I quite like "Props." I'd say that's the current front runner.

  7. I'd call this "Negation" - the trick is know when or what to negate your play (or maybe your opponents). You could scale it through math/science/lit classes (you just make different cards). I'd be interested in an elementary school version of this.

  8. I like "Props" too! My own, less exciting suggestion: "Boole Rummy."

    Playing the game, have you noticed anything in the way of strategy? I can't see any obvious ways to improve one's chances... but I'm terrible at ordinary card games too. ;)

  9. I like this. It has me thinking of applying it to algebra where the cube is >, >=, =, etc. and using equations where the students need to solve for x, and make the comparison based on the value of x.

    As for the name - I like Negation.

  10. Please tell me you will still have the internet in Argentina after you move there.

    - Elizabeth (aka @cheesemonkeysf on Twitter)

  11. Kate - so I found this blog post a year ago, and have been saving it until I finally had a class to play with. I have prepared all the materials (which was fun), gone over the rules a whole bunch of times for clarity, and am ready to go. I was walking through the game with my student teacher, and he pointed out 2 things. First, in the Real Game, you get 5 T/F cards. Did you count which of each you got? Would it be unfair if one player got 3 Ts and 2 Fs and the other got 2 Ts and 3 Fs? Also, what about the turn where a player might put out 2 true statements and a T - they would surely win the round. Is this where strategy comes in - not using up all your Ts at once? (I'm actually playing this with the Geometry class I did the Stealing Second project with; they need things SUPER clear.) I'm excited to roll those conditional dice! - Wendy M

  12. Hey Wendy! I'm jealous of you! And, mad props for remembering to use something a year later. I'm also jealous of your organization skills.

    I hadn't thought about the relative numbers of T's and F's. Maybe the hand you are dealt is just part of the game? Like, you know, something like poker -- you could get a good hand or a crappy hand. Or maybe you want to level the playing field by specifying that each opponent gets the same numbers of T's and F's.

    I agree that 2 true statements and a T is an obvious winner. But what's obvious to us might takes kids a little while to figure out. And then, yeah, if you use up your trues and T's, you might make your life harder later. So I'd call that part of the strategy.


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