Rolling the Dice: Check the difference between the theory and the practice Karim Noura Master of Education KN, Oct 2008

The Difference Game* Each player begins with 18 chips and a game board Players start by placing their chips in the numbered columns on their game boards (in any arrangement). Players take turns rolling the dice. The result of each roll is the difference between the number of dots on top of the two dice. Each player who has a chip in the column corresponding to the result of the roll removes one chip from that column. The first player to remove all of the chips from his or her game board is the winner.

1. Play the Difference Game in groups of two or more (a)Before starting, find a way to record the initial set-up of your game board have someone record the result of each roll (you'll refer to both of these in part (b)). (b)In the space provided, record the initial set-up of each of the players at your table and who won. xxxx xxxxxxx xxxxxxx xxx xxxx xxxxxx xxxxxx 

2.Did the results of the game give you any new ideas about how you should place the game pieces to start the game? Play the Difference Game, again to see if you're right. Again, record the starting positions of you and your tablemates, as well as who wins. 3.What have you noticed about the frequency of different results (dice differences)? Talk it over with those at your table. Which difference seems to occur most? Which occurs least? Are there any possible differences that haven't come up, yet?

4. Roll your two dice twenty times, recording the differences in the table provided. When you're done, combine the data from everyone at your table and create a bar graph to share with the other groups. 5. According to the data from the class, what is the experimental probability of rolling each of the possible differences?

5. Now, work with your tablemates to determine the theoretical probability of rolling each of the possible differences. Be ready to share your results, and the methods you used, with the whole group.

Theoretical and Experimental frequencies (two-dice differences with 36 rolls) Theoretical frequencyExperimental frequencies

What about sums? What are the theoretical probabilities of each possible two-dice sum?

What about sums? What are the theoretical probabilities of each possible two-dice sum? Rolling two Dice

Theoretical and Experimental frequencies (two-dice sums with 36 rolls) Theoretical frequencyExperimental frequencies