Monday, July 4, 2011

Linear War

So many things to write about to catch up... but it's been a while since I posted a game, so with an impending Math Teachers at Play at Math Mama Writes. The submission form seems to be wonky, so submit directly to Sue. Plus this kind of fits with U.S. Independece Day, as we have been known to fight a war or two.

This game is good already, but could be great. So if you have feedback, let me know, please! As is, it's probably best used as a review game, but I'll comment afterward about how it could be used as a framework for a unit.

Set up: Make your own deck: 11 lines. Each line should be drawn so that it passes through at least two points with integer coordinates, such as (-2,4) or (5,5).

Claim your deck! Mark each line card on the graph side with your insignia. Initials, emoticon, math symbol, etc. – your choice. Tip: make your cards NICE and personalized. Decorations and alterations that do not obscure the line or the math are not only permitted but encouraged.

War: 2-4 players. Each player needs a deck of 11 face down cards, shuffled or not – it’s up to you. Set aside any extras, make one more if you need it.

Players roll the die for the combat. (2nd roll and beyond, the winner of last battle rolls.) Flip over the top card of your deck and follow the combat rule. On a tie, flip over one more card to determine the winner of the battle. If more than two are playing, this is only on ties for best and only the people who are tied.

Play through the deck once. The winner is the player at the end with the most cards. Give cards back to the owner. Except for the Spoils of War.

Spoils of War: Out of the cards the winner captured, they take one card from the opponent’s deck to keep. Add your mark and cross out theirs. This may mean the loser needs to make a new card for their deck for the next game.

Example: The first roll is a 2. Least slope. -2 < 1

(The X and lemniscate are the players' personal marks.)

Math notes:
  • Use the cards for sorting activities before playing.
  • Have players keep track of hard to determine battles.
  • Discuss card design strategies.
  • What about undefined and zero slope lines?
  • What other combat rules could you have?
Handouts: as a Scribd file, and the graphs template. At the right is an image (larger when you click on it) that you could also print for the graphs.

Discussion: Ted, one of the excellent summer grad student/teachers, tried this cold as an end of year activity with a small group, and they struggled with it.  He felt like it had a lot of promise, but that the math requirements kept students from the game since they were rusty with it.

Trying this with teachers convinced me of it's potential, as it even uncovered math for them to discuss, and generated situations they had to think about. 

I could see this game being at the end of a linear unit, where students have been generating graphs as examples as they go through the topics, using them for activities like finding slope, sorting from least to greatest x-intercept, y-intercept and slope. Use them to construct tables or find equations.  Non-contextual, but strong on representation.  What do you think?

I'm trying hard not to use too many unlicensed images but this is too perfect. God bless you Bill Waterson, wherever you are.


  1. Great idea!
    I would play it like top-trumps rather than a dice roll, so that pupils are encouraged to think about the values of their graph, to choose a winning move.
    You could extend this by at some point adding extra cards with the equations of lines rather than their graph (Set-one would have the equations in standard y=mx+c form, Set-two would have equations in non-standard form).

  2. I love this! Thanks! Once we play it I'll give suggestions if we think of any.