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.
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.