Intent

In this activity, students design their own simulations and are encouraged to think more deeply about the difference between “average over the long run” and “most likely to occur.”

Mathematics

The discussion of students’ simulations may bring forth the notion that as more experiments are conducted, the outcomes tend toward the theoretical probabilities. The activity also indirectly inquires about the expected value—preparing students to wrestle with the difference between “average over the long run” and “most likely to occur.”

Progression

This activity should be done individually, followed by a brief whole-class sharing and discussion of results. The activity is very similar to students’ work in One-and-One and sets the stage for developing methods to figure two-stage probabilities in The Theory of One-and-One.

Approximate Time

5 minutes for introduction

20 minutes for activity (at home)

10 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Materials

Grid paper (optional)

Doing the Activity

Tell students that they will be designing a simulation at home. You might encourage some brainstorming of materials they might use.

Discussing and Debriefing the Activity

Ask a few volunteers to report their results. Then ask, Was the average score you found also the most likely result? Although the majority of students should have found that Terry’s most common result was 0 or 2, most should also see that the average for 40 trials is quite close to 1.

Ask students how they could state the results for Question 4 in terms of expected value. They should see that the answer to Question 4 is an experimental estimate of Terry’s expected value for each one-and-one situation.

Key Questions

What results did you get?

Was the average score you found also the most likely result?

Can you state the results for Question 4 in terms of expected value?