Friday, December 12, 2014

Polynomial Pirates Game - Operations with Monomials

The Need:

 I created the game Polynomial Pirates because I realized there was a need for students to focus on the difference with certain polynomial operations.  For instance, students were confusing (x+x) with (x*x).  I could 'reason' with them until I was blue in the face and nothing changed.  Then I realized that I needed to come up with a game.

The Story:

You are one of four pirate captains searching for a sunken treasure. Not only are you competing against the other pirates to get to the treasure before they do, you will need to defeat the fire-breathing treasure-guarding sea monster first.  Battling other pirates and surviving the open seas will prove to be too difficult for the weak of heart; only the strongest will be victorious.

The Materials:

You will need 8 dice with these 6 monomials written on them; x, 2x, 3x, y, 2y, 3y.
A plate will be helpful because the players will roll the dice then pass them to the next player.
Frugal Options: Put stickers on dice you already own.

At least 2 sets of polyhedral 7 set dice will be needed.  These will be needed when your pirates either battle each other or the sea monster.
Frugal Option:  Use a random number generator.

Players use two forms of currency; coins and gems.  Pirates use these to buy and upgrade the cannons and shields for their ships.
Frugal Option:  Print out paper coins and gems.  Or use pennies and buttons or whatever you have lying around.

You will also need something to represent the treasure chest.  I was fortunate enough to find this lying around my house.  
Frugal Option:  Print a paper 2-D treasure chest.

Here are the pawns that I use.  They are stickers placed on bottle caps.  
Frugal Option:  Use any ol' pawns you have lying around from other games.  Or even different color bottle caps.

(Seriously, why is this sideways?  It's right-side-up in iPhoto.) 

To keep track of how many cannons and shields and their respective levels, players will need the cannon/shield cards and 6 paperclips per player.  I glued the player cards to large index cards.  On the front are the shield and cannon indicators.  On the back of the index cards are the rewards for winning.

In this game the game cards make up the board.  When you add, subtract, multiply for divide any two of the 6 monomials used in this game (x, 2x, 3x, y, 2y, 3y) there are 52 unique outcomes if I did my math correctly.  I bought a deck of pirate cards, printed my cards on sticker paper, and then stuck them to the playing cards.

Frugal Option:  print the cards and glue to index cards.

(Again, not sure why this is sideways)

Game Play:

Set up your "game board" like this.  It's a 5 by 5 array with the middle card missing.

Place the treasure chest in that middle spot.

Each player starts their pawn in a corner.

Each player is given a player card, 5 coins, and 5 gems to start the game.  

Suppose that the monkey is the first player.  He will roll all 8 dice on to the plate.  Looking at the cards adjacent to him, he can either move to xy or 3xy.  The monkey can use two or more dice to create any adjacent statement.

The monkey decides to use 2y, y, 3x, and 2x to create xy.  (2y - y)*(3x-2x) = xy
The monkey moves to that card and does what it says.  In this case it reads, "Buy a cannon 4 coins, or collect 2 coins, or collect 2 gems".  Once he is finished with his turn, he passes the plate to the next player.  

*Once a player moves his pawn and uses a card, that card is put on the bottom of the card pile and the top card is put in that spot.

Now it's pirate girl's turn.  Her options are x-2y or 2.  Looking at the remaining dice, I can't find a way for her to create either of those statements (remaining dice:  2x, 2x, 3y, 3y).  She will have to pay one gem to re-roll all 8 dice.  If she is unable to create either of those statements again she can pay another gem to re-roll or pass to the next person.  Note - re-rolls are free if there are three or less dice on the plate.


In order for players to battle each other they need to be on the same space.  The person who was on the space first is the defender, the player who lands on the space second is the attacker.  

In this case the pirate girl is the defender and uses her shields and the monkey is the attacker and uses his cannons.  At this point in the game the pirate girls has 2 shields; one level 8 shield and one level 6 shield.  So, she uses an 8-sided die and a 6 sided die, rolls both, and adds them together.  Her total is 4.  The monkey has two cannons; one level 8 cannon and one level 4.  So he uses an 8-sided die and a 4-sided die and adds those together.  His sum is 7.  
The monkey won 7 to 4 and wins by 3. 


Turn a player card over to see his reward.  Since he won by 3 he can take a combination of 2 gems or coins from the pirate girl.  Since the pirate girl lost she teleports back to her starting corner while the monkey can stay on that spot.  The pirate girl may not collect what is on that corner card.

If there is a tie, the defender is the winner.  He would collect nothing but the other player would need to go back to his starting corner.  
If the losing player in a battle does not have enough coins or gems to pay out, they are required to lose levels with their shields and/or cannons to equal the number of coins/gems they were to pay out. If things are dire enough, they may lose cannons and shields.  

Winning the Game:

In order to win the game, the sea monster must be defeated.  The sea monster is a level 20 fire-breather, meaning he uses a 20-sided die.  

To attack the monster, a player must be adjacent to the monster.  Please note that players may attack the monster individually.  In the photo below, the players have teamed up to attack the monster.  

Attacking the monster is different from players attacking each other.  
To attack the monster, the player will roll their cannon dice and find their sum., then roll the monster's 20-sided dice.  If the player has a higher sum than the monster, he wins the game and the treasure.  However, if he does not have a higher sum there is a second part to this.  Then the player rolls his shield dice and the monster rolls his 20-sided die again.  If the monster has a higher number, the player must forfeit the corresponding loot and return to his starting corner.  If the player successfully defends himself, he only moves to his starting corner.  

Cooperative play:  Attacking the monster is the same.  Each pirate would roll their cannon/shield dice and add them all together.  The only difference would be the amount of loot lost is paid by each player attacking.

Other Stuff:

Players can trade in coins and gems for half the amount.  For instance; a player can trade in 2 gems for 1 coin or 2 coins for 1 gem.  

Players may form alliances and freely give loot to other players.  

Next Steps:

I am in the process of creating pre- and post-tests in order to determine if the game is even worth it.  Stayed tuned for that information.

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