Time Versus Money - A Probability Game

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Note: This activity involves two variables while most of my other probability posters involve a singe variable.

Starting in elementary schools, students are usually introduced to probability through experiments and definitions. As students mature intellectually, they are presented with probability concepts and methods of determining appropriate probabilities. However, few probability problems are assigned that require or expect students to make reasonable decisions based on probability values. Therefore, this activity can serve as a catalyst to engage students in reflective thought about probability values, how they might affect our lives, and how personal experiences dictate our reactions to them. In particular, this activity provides an enjoyable diversion from regular classroom presentations and assignments.

Use the 8.5" x 11" two-sided colored master to produce enough colored copies so that each pair of students has a copy. It is advisable to have the copies laminated for future use. Allow approximately 20 minutes for this activity, and stress to your students that the numbers on the perimeter of the poster are to be selected randomly. An additional 10 minutes should be sufficient to allow the students to complete the activity a second time if desired.

After the posters are handed out (one to each pair of students), read out loud the Background and Procedure listed below.

Background: Each year one student is identified as your school’s “Ultimate Warrior” for completing a challenging obstacle course in the quickest time. It is a grueling event that requires a combination of mental maturity and physical stamina for ten different obstacles.

Procedure: Carefully read the information given for each obstacle. Then select one of the two available options. Next, randomly select a number from the array of numbers that lie on the perimeter of the poster to determine the outcome of your choice. Then record the time elapsed for the obstacle. At the end of this activity, record the cumulative elapsed time to see if you were the fastest.

If students work in pairs, one of the students can move his/her finger either clockwise or counterclockwise over the perimeter of numbers until told by the other student to stop. The number closest to the student's finger is to be used to determine his/her outcome of that particular step. Then the students interchange roles so the second student can also randomly select a number to determine the outcome of the same step.

An alternative approach would be for the students to identify a number on the perimeter of the poster. The teacher then randomly selects a number (perhaps from 1 to 12) and then informs each student to move clockwise or counterclockwise that number of spaces to arrive at a new number, which is to be used for that step in the activity.

One of the unique characteristics of this poster is that the activity can be completed over and over again with unpredictable outcomes. Therefore, the activity could be repeated several times in a class period. To enhance student motivation, an “Ultimate Warrior” certificate is available by request through my email address: mnerbovig@gmail.com
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