Names: _______________________,_________________________,_________________________
The Native American Game of Sticks: An Introduction to Probability
Stick Design
Preparing the playing pieces
Search and Discuss: symmetry
A discussion of symmetry, tessellations and transformations will greatly help before designs
are made. With markers, decorate each popsicle stick on one side. Use a different decoration or color
for each stick. You might want to decorate the sticks with Native American symbols (See below). The
decorated side is called the face. Use the templates below to do a rough draft. Use a ruler to do a
final design on the face of the sticks.
Stick 1
Stick 2
Stick 3
Stick 4
Examples: (notice the symmetry)
Names: _______________________,_________________________,_________________________
The Native American Game of Sticks: An Introduction to Probability
Playing the Game
Playing the Game
Hold the sticks in one hand, and let them fall to the table. In taking turns play continues until
the first person reaches a tally of 50. Keep track of the score in the table below. The first person to
reach 50 wins.
Scoring
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All four up
Three up and one down
Two up and two down
One up and three down
All four down
Player 1
5 points
2 points
1 point
2 points
5 points
Search and Discuss: Combinations vs. Arrangements
Just from experience playing the game, about how
many different arrangements of the sticks did you see?
Describe some of the combinations.
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Player 2
Player 3
Names: _______________________,_________________________,_________________________
The Native American Game of Sticks: An Introduction to Probability
Theoretical Probability
Fill out the table at the right. Every box must be
filled.
Note: Make your work easier by using a pattern.
Some mathematicians use a “Tree Diagram” to
make sure all the possibilities are found. If time
allows, work on a separate sheet and draw the
tree.
Find the frequency of the combinations
All four up: _______
Three up and one down: _______
Two up and two down: _______
One up and three down: _______
All four down: _______
Search and Discuss: Theoretical Probability
Then find the theoretical probability of the
combinations below.
All four up: _______
Three up and one down: _______
Two up and two down: _______
One up and three down: _______
All four down: _______
TABLE A
Stick #1
Stick #2
Stick #3
Stick #4
Up
Up
Up
Up
Down
Up
Up
Up
U
D
U
U
Names: _______________________,_________________________,_________________________
The Native American Game of Sticks: An Introduction to Probability
Experimental Probability
Now, play the game and have a recorder keep a tally of all the outcomes occurring during a
game, using the following table.
Player 1
Player 2
Player 3
TABLE B
Outcome
Tally Marks
Frequency
All four up
Three up one
down
Two up and two
down
One up and
three down
All four down
Search and Discuss: Experimental Probability
Find the experimental probability of the following based on
the information gathered from Table B.
All four up: _______
Three up and one down: _______
Two up and two down: _______
One up and three down: _______
All four down: _______
Names: _______________________,_________________________,_________________________
The Native American Game of Sticks: An Introduction to Probability
What’s Fair?
Search and Discuss: Fairness in a game
1) Determine whether the game is fair using the above probabilities explain you’re reasoning for your
answer:
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2) Create your own fair system of scoring:
Scoring
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All four up
___ points

Three up and one down
___ points

Two up and two down
___ point

One up and three down
___ points

All four down
___ points
3) Justify the fairness of your scoring method for the Native American game of sticks. (Be ready to
defend and demonstrate your answer using a document camera)
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