Overview

This game is based on a Native American game of chance. Students compare what happened in their game (experimental probability) with what is supposed to happen (theoretical probability).

Objective

Students will be able to explain theoretical and experimental probability.

Standards Addressed

Mathematics — Data Analysis

Grade 4

Probability, Benchmark G

13. List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2 pair of shoes.

 

Grade 5

Probability, Benchmark J

10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment.

Probability, Benchmark K

11. Make predictions based on experimental and theoretical probabilities.

 

Grade 7

Probability, Benchmark I

07. Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.

 

Materials

• Four sticks (tongue depressors or Popsicle sticks) per player

• 12 game tokens per group of three or four students

• Colored markers or paint

Procedure

1. Have each student decorate one side of four sticks to show symmetry or Native American glyphs, which can be found at http://www.WesternReservePublicMedia.org/onestate/glyphs.htm.

2. If the sticks are tossed in the air, here are the possible outcomes:

One colored side and three plain sides

One plain side and three colored sides

Four colored sides

Four plain sides

Two plain and two colored sides

3. Students will determine how many points they will give for each possible outcome and write it down. There are many possible point totals.

4. Divide students into groups of three or four.

5. Twelve game tokens are placed in the center of the group. The first player drops the four colored sticks onto the table or tosses them in the air. He or she then takes the number of tokens from the pile that was assigned in step 3. If there are not enough tokens, the player can take the number earned from an opponent. This continues until one person has all of the tokens. That person is declared the winner.

6. Students should keep a record of the outcome of each of their turns.

7. Discuss with the students what point system they used and why. This could be done with a tree diagram and writing the sample space. If they have kept a record, you can have the students compare the experimental and theoretical probability. Answer: The fair scoring system is as follows: four alike equals eight points, two alike equals four points and three of a kind equals three points.

   

   NOTE: There are many variations of this game. One variation is to use six sticks and 10 game tokens. The scoring is as follows:

   1. If all six sticks land on the colored side, the player takes three tokens.

   2. If all six sticks land on the plain side, the player takes three tokens.

   3. If three are plain and three are colored, the player takes one token.

   4. If any other combination comes up, the player gets no tokens.

   Players can take tokens from each other when none are in the middle. The winner is the person who collects all the tokens. The probability for this game is more difficult to determine.

Evaluation

Made a frequency table showing their tosses.	5 points
Made a tree diagram.	5 points
Wrote the sample space.	5 points
Calculated the theoretical probability.	5 points
Made a fair scoring system.	5 points

 

There are many versions of this game online. One version can be found at http://educ.queensu.ca/~fmc/april2003/NativeAmericanGame.html.