Lesson Plan A Game of Chance Stick Dice

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					Lesson Plan: A Game of Chance-Stick Dice
Concept:               Through the playing for a game of chance, originated from the Pomo
                       Indians of California, students will gain understanding of mathematics
                       in the area of probability and statistics.

Class level:           Algebra

Time:                  45-50 minutes

Activity:              Students will play a game called Stick Dice. This game will be followed
                       up with a discussion and worksheet.

Questions:             These questions should be asked before the playing of the stick dice
                       begin:

                          What combination of blank side-up and painted side-up do you
                           expect to show up the most?
                          Which combination do you expect the least?
                          Do you agree with the points values?

State Standards:       Minnesota State 7.4.3.3

                       Minnesota State 9.4.3.2

Materials:             6 tongue depressors or popsicle sticks (dice) for each group of 2; 12
                       toothpicks (counting sticks) for each group of 2; and markers

Prerequisite skills:   Students should have some background in the area of probability. This
                       activity will strengthen these skills.

Key Questions:         These questions should be asked during the playing of Stick Dice:

                          Which combination has come up most? Is this what you expected?
                          Does the game seem fair? If not, what could be done to make the
                           game fair?

Procedure:             Give the students the worksheet about Stick Dice. Tell the students
                       about the history of the Stick Dice. Discuss the game and how
                       probability is involved. Also figure out the various possibilities of the
                       outcomes and fill them in on the worksheet. Here is what the table
                       should look like:
           Possible Outcomes                      Number times you got outcome
           6 painted, 0 non-painted
           5 painted, 1 non-painted
           4 painted, 2 non-painted
           3 painted, 3 non-painted
           2 painted, 4 non-painted
           1 painted, 5 non-painted
           0 painted, 6 non-painted


                      Have them get in groups of 2. Each group should decorate one side of
                      their 6 popsicle sticks. They may then begin playing Stick dice. Have
                      the students play the game for approximately 25 minutes. After the
                      games have finished, discuss the different combinations, i.e. which
                      combinations were most common. When finished, give the students a
                      worksheet to figure the actual probabilities of the game.

Discussion:           You should discuss with the students the chance of each combination,
                      which combination is expected the most, and how the game is or is not
                      fair (i.e. the player going first has an advantage).

Follow-Up Activities: The students may play other similar games of chance. There are other
                      variations of the game, Stick Dice, you may introduce to the class. This
                      provides an opportunity to compare the variations of the games.

Assessment Plan:      Include a question on quiz or exam related the probability of a certain
                      stick combination.

Extension/Enrichment: How would the outcome of the game change if you added more sticks?
                  How would changing the points affect the outcome of the game? How
                  could you change the points to lengthen or shorten the game?

Additional Activities: Including other variations of Stick Dice from other origins.

Source:               http://mathcentral.uregina.ca?RR/database/RR.09.00/treptau1/game2.html

                      Carlson L. (1994). More Than Moccasins, Chicago I1: Chicago Review Press.
                                           Stick Dice
Origin:

Include table for students to keep track of tallies.
                                                               Name______________________

                                 Stick Dice Probabilities
Answer the following questions assuming you have six sticks with one side blank and one side
painted.

   1. What’s the probability of getting six blank side up?


   2. What’s the expected number of tosses until you get all blank side up?


   3. What’s the probability of getting six painted side up?


   4. What’s the expected number of tosses until you get all painted side up?


   5. What’s the probability of getting three painted and 3 blank side up?


   6. What’s the expected number tosses until you get 3 painted and 3 blank side up?


   7. What percent of the time are any toothpicks taken?


   8. Compare these answers to your results when you played Stick Dice by filling in the
      following table. (You can get the expected probabilities from 1, 3, and 5.)
                          Expected Probability    Actual Probability          Difference
        6 painted


          6 blank


    3 blank & 3 painted



   9. How would the game change if you had only 2 sticks?
   10. How would the game change if you had 10 sticks?



                           Stick Dice Probabilities Answers
Answer the following questions assuming you have six sticks with one side blank and one side
painted.

   1. What’s the probability of getting six blank side up?
                                             6
              1  1  1  1  1  1   1  1
                                      .015625
              2  2  2  2  2  2   2  64
   2. What’s the expected number of tosses until you get all blank side up?
               1
                    64
              1
                64
   3. What’s the probability of getting six painted side up?
                                             6
                1  1  1  1  1  1   1      1
                                            .015625
                2  2  2  2  2  2   2      64
   4. What’s the expected number of tosses until you get all painted side up?
                 1
                      64
                1
                  64
   5. What’s the probability of getting three painted and 3 blank side up?
                6  1   1 
                           3     3
                                            1   5
                     20 
                3 2                               .3125
                   2                 64 16
   6. What’s the expected number tosses until you get 3 painted and 3 blank side up?
                 1      16
                            3.2
                5        5
                 16
   7. What percent of the time are any toothpicks taken?
               .015625  .015625  .3125  .34375
   8. Compare these answers to your results when you played Stick Dice by filling in the
      following table. (You can get the expected probabilities from 1, 3, and 5.)
                              Expected Probability        Actual Probability  Difference
        6 painted                     .015625
          6 blank                     .015625
   3 blank & 3 painted                  .3125


   9. How would the game change if you had only 2 sticks?
           Points would always be given or exchanged.

   10. How would the game change if you had 10 sticks?
            Points would be given or exchanged less often.

				
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