Friday, July 17, 2015

Tug of War - Evaluating Expressions Game

@mathhombre pointed me in the direction of this interesting Tug of War game.  Click here.  I was playing around with the idea to make it more mathy, and here is what I came up with.

I thought trading cards would be fun and each card looks something like this:

Each card would have a function in the top left corner.  The game could start with linear functions, and then mix in cards with other functions.

In the top right is the suit.  The suits would be a letter (A, B, or C) and a color (Orange, Blue, or Green).

In the middle is the character.  He/she is wearing a shirt that indicates what makes them stronger for the tug of war battle.  This character is looking for Bs.  (If he was wearing a blue shirt, then he is looking for blue suits)

The arrows indicated in which direction the character can get his strength.

Each player places up to 9 characters in a 3x3 array.  (Just like in the Daniel Solis' post above).

Let's suppose that this card is placed on the bottom left of your 3x3 array.  I wrote in the suits for some other cards.

Since this character is looking for B in the indicated directions (up and right), we count the Bs in those directions.  There is 1 B to the right and 3 Bs up, for a total of 4.  This means that the value of x for this card is 4.  Determine f(4), to get the strength of this character.  f(x) = 3x + 2, f(4) = 14.

The players do this for each of their 9 cards to determine their strength.  Then, they determine the strength of their 3 characters in each column.  If their 3 characters are stronger than their opponent's 3 characters, they win that Tug of War. 

Some Thoughts

Playing this game requires a lot of book-keeping.  I have a strong feeling that all this computation will take the players out of FLOW if they even get there.  Also, there is little feedback for the players as to who is winning throughout the game (unless they are doing the problems the whole time or the game was digital).  At the end of the game the players would complete the 9 math problems and then determine the winner.  

I like Daniel's mechanic of each player taking a card from the deck, placing it face down on the 3x3 array, and then both revealing their card at the same time.

What if this were a 4 player game?  Tug of war up-and-down, side-to-side, and 2 diagonal wars????

The characters could be people in the school.  The Superintendent might have 4 arrows for strength, and maybe even a higher coefficient of x.  Next most powerful would be the Principal, etc.

What if the students earned their own set of cards?  and could trade them with each other???

What if the suits were classifications of triangles rather than letters and colors?  The suits are classified by angle (right, acute, or obtuse) and by side length (scalene, isosceles, or equilateral).

However, I think this game is worth a shot.  Hopefully, I remember this idea come September and play a few rounds with the students.  Hmm...maybe they could even make their own cards with some constraints.


  1. So interesting. I like the function evaluation idea in here, and how that uses the rows and columns. I agree with the book-keeping. Better than anything I came up with for this. I kept imagining cards as monomials, but didn't have a good mechanic for evaluating.

    What if each player just had three character cards and placed them in the beginning, then used suits & values of cards played into the grid to evaluate? The functions could even be things like 2*Hearts+3*Spades+2.(Introduce new functions as the year goes on.) I'll try it out when I get a chance.

    1. I like your idea about the functions being 2*Hearts + ...

      And what if the students use standard playing cards? Hearts go in one direction, diamonds in another, etc. The number of the card does something else. I didn't think this all through.

  2. Not sure what you mean by direction... oh, like tugging towards a border? What if the flag on the rope had twonotches to either side. If you get it off, you win that tug. _ _ F _ _.

    Set up: choose captains and place in grid, separate lines, but rows is up to you They see their line and row for evaluating. Each player plays a card, and the flags are moved according to current strength. (I think I have Word in the Street in mind... would love a math version.)

    Hmm... I think I need to try and add pictures.

  3. I love this idea for a game, I've made some cards for play testing. Here is a link to my blog post about it: The post is pretty simple right now, but I plan to add some to it after playtesting this evening. I'd love your thoughts as well!