Friday, January 2, 2015

Rolling Thrones: An Exponent Dice Game

How about a game to get the new year started right?  It seems that every time I ask my colleagues what topics their students struggle with and would like a game for, they mention the laws of exponents.  I've been rolling the idea of a game around in my head for a long time and decided to finally sit down and get serious about it.

Please note that this game has not been play tested yet.  If you play this game at all I would love your feedback.

Game Objective:

To reinforce the laws of exponents.


  • 3 6-sided dice for each team. 

  • 1 20-sided die for you.
You will need to print the net and select the D20.  Hold the paper up to a window so you can write in the spaces on the back.  Write the integers -9 to 9, and "re-roll".  Cut out, fold, and tape together so that your numbers are facing out.

  • Lots of Blank dice 
I'm not sure of how many because of the whole play-testing thing.  If I had to guess I would say 3 for each team.  I would use my blank dice, cover them with clear tape so the students can write on them, and then I can take the tape off at the end of class.

Set Up:

Divide your class into smallish teams of 3-4.  You need to find a balance here.  If the teams are too big, some students will do nothing.  But if there are too many teams, the game may be frustrating to play.

Give each team 3 6-sided regular dice.

Write the team names on the board and keep score underneath.

Game Play:

Roll your 20-sided die and write x to that power on the board.  For instance, if you roll a -5, write x^-5 on the board.  This is the target for this round.

Each team rolls the dice they have and try to create an expression that will equal the target.  The numbers that they rolled are used as exponents for the base x.

Suppose Team A rolls 4, 4, and 5.  They could create the expression (x^4) / (x^4 * x^5) and this would be equivalent to x^-5.  Since that team used 3 dice to create their expression they receive 3 points.

Suppose Team B rolls 1, 2, and 6.  They could create the expression (x^1)/(x^6) and receive 2 points.

Suppose Team C rolls 2, 3, and 5.  They could create the expression (x^5) ^ (2-3) and receive 2 points.

Suppose Team D rolls 1, 1, and 2.  They are unable to think of a way to create the expression x^-5 and receive 0 points.

Buying Stuff:

With the points they are accumulating the students are able to buy things.

For 1 point (and this needs to be play-tested) a team can purchase a re-roll of their own dice.

For the number of dice they currently have, they can buy a blank die for that many points.  In other words, if a team has 3 dice they can purchase a blank die for 3 points.  If a team has 4 dice, they can purchase a blank die for 4 points, etc.  I hope this is making sense.
Once they have their blank die, they can write any positive or negative numbers they wish.  They must do this before the next round begins.

Helping Other Teams:

I love when my students help each other.  So to add some cooperation in with the competition, teams are able to help other teams.  If a team is struggling to find an expression that is equivalent, another team may help.  If they are successful in finding an expression, the two teams split the points.  Yes, split the points even if it's an odd amount.  The decimals will be good for them.

Winning the Game:

I imaging this game ending when a team reaches a certain amount of points.  If I had to guess I would say 20-30 points.


You could play for a certain amount of time and the team with the most points wins.


To have multiple winners, you could set a goal for the class.  Every team that reaches ____ points is a winner.

What Could Go Wrong and Possible Solutions:

Possible Problem 1:  What if students cheat?  What if they change what was rolled?

Possible Solution 1:  Have one student from each group come to the front of the room, roll their dice, write the numbers on the board, you roll the D20 and write the target on the board, and the students work at their seats on their expression.

Possible Problem 2:  What if students are unable to create an expression with the three initial dice?

Possible Solution 2:  Start each team with 2 points, so they can purchase re-rolls.  If this doesn't work, each team could start with 4 dice instead of 3.

Possible Problem 3:  What if a group takes too long to create an expression?

Possible Solution 3:  Set a time limit of say, 60 seconds, to create and write the expression on the board.  This time includes any re-rolls.  If a team needs more time, they can purchase 30 seconds for a point.  Each teacher will need to adjust time limits according to their students' abilities.
For creating expression for other teams:  If a team does not have an expression after the time limit, the other teams have 30 seconds to create one and write it on their spot on the board.

Possible Problem 4:  What if one student is doing all of the work?

Possible Solution 4:  Have students in the groups take turns rolling the dice.  The student who rolls  is the student who writes the group's expression on the board before time is up.  This way, if one student is doing all of the work, at least the others seeing and writing it too.

Possible Problem 5:  What if students write 0 on their purchased dice?

Possible Solution 5:  My initial thought was that students shouldn't be allowed to write a 0 on a die because it would be too easy for them to earn a lot of points.  Let's say that a team buys a die and writes 0 on all 6 sides.  Then let's say the target is x^4.  That team rolls 0, 3, 4, and 6.  They could create the expression x^4 * (x^3 *x^6)^0.  And there is an easy 4 points.  I like that the students could have the option to discover this, but not have it available every single round.  So, here's the new rule. When students are writing the 6 numbers of a new die they must be 6 unique integers.

Possible Problem 6: What if a group is able to create more than one equivalent expression?

Possible Solution 6:  Yay!  Isn't this what we want?  This isn't a problem, this is something to celebrate and reward.  If a group is able to create more than one expression that is equivalent to the target they can and should do so.  However, a die cannot be used more than once.
For example:  Target is x^6 and a team rolls 2, 2, 3, and 4.  They could create (x^2)^3 and x^2 * x^4. That's 4 points.

Possible Problem 7:  What if a group comes up with an expression that is not equivalent to the target?

Possible Solution 7: My initial thought is that there should be a penalty, perhaps a deduction of points.  But the more I think about it, I would rather the groups just get no points.  I want this to be a learning experience, I don't want the students to be afraid to try something for fear of losing points.

Possible Problem 8:  What if the students aren't learning the laws of exponents through this game?

Possible Solution 8:  Create and pre- and post-test to determine if this game is getting the job done.  I created one that you could use on  #soc14351941

What About a Story?

I believe this game would work well enough without a story, but stories are always fun and more memorable.  

When I started to think about a title for this game, "Rolling Stones" popped into my head.  A simple rhyme with stones gave me "Rolling Thrones" and I have a story.  Each group is controlling a character that desperately wants to become King while he is currently a peasant.  He must work his way through the ranks to become royalty.  

As the teams earn points, their characters becomes more powerful within the kingdom according to the following chart: 

1-5 points --> peasant

6 - 10 points --> Knight

11 - 15 points --> Count

16 - 20 points --> Duke

21+ points --> King

You may have to adjust point values based on the length of your class and the skills of your students. 

Because teams are able to purchase things with their points, their character may go down a rank.  

When a team's character becomes king, that team wins.  I'm picturing Burger King crowns in my future.  


  1. This is AWESOME, Nora! Can't wait to play test it for you at the beginning of the new semester in Algebra IB. I'll let you know how it goes!

    1. Thanks Mark! I'm hoping to play-test this week with my College Prep Algebra 1 classes. I'll post an update.