Abstract

An activity and a discussion of this lesson introduce and develop the idea of expected value. The discussion helps students investigate the definition and formula of expected value.

Objectives

Upon completion of this lesson, students will:

• have learned about expected value
• have been introduced to the concept of varying payoffs
• have used a computer simulation of a "real world" example where expected value is used

Activities

• Stock Exchange
• Crazy Choices Game

Standards

The activities and discussions in this lesson address the following Standards:

Probability and Data Analysis

• Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

• Use conjectures to formulate new questions and plan new studies to answer them.

Other standards addressed in this lesson include:

• Work flexibly with fractions, decimals, and percents to solve problems develop and use strategies to estimate the results of rational-number calculations and judge the reasonableness of the results.

• Develop and use strategies to estimate the results of rational-number calculations and judge the reasonableness of the results.

Key Terms

• expected value
• probability
• average expected payoff

Student Prerequisites

• Arithmetic: Students must be able to:
  • Calculate with decimals
  • Interpret data in decimal form
• Technological: Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• access to a browser
• pencil and paper
• Stock Exchange Worksheet

Lesson Outline

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Ask students to recall what probability is.

   • Ask the class if they know what the stock market is or ask if any students own stock. Briefly discuss the stock market.

2. Objectives

   Let the students know what it is they will be doing and learning today.

   • Lead from the discussion on what the stock market is to why someone would risk their money to purchase stock. Discuss this in terms of probability.

   • Ask such questions as, "Why would someone choose to purchase stock from one company rather than another?" This will lead into a discussion of expected value.

3. Teacher Input

   Lead a class discussion using the Expected Value discussion that will formalize and develop the concepts introduced by the Stock Exchange activity.

4. Guided Practice

   Describe the Stock Exchange activity which introduces the idea of varying payoffs, bringing probability and payoffs together and developing the concept of expected value.

5. Independent Practice

   Have groups of students experiment with the activity to generate discussion ideas to use during the closing discussion.

6. Closure

   Lead a class discussion using the Expected Value discussion that will formalize and develop the concepts introduced by the Stock Exchange activity.

Alternate Outlines

This lesson can be rearranged in several ways.

• Introduce the discussion before having students work with the Stock Exchange activity.
• Or use the material in the discussion to prepare a "live" discussion.

Suggested Extensions

After this discussion and activity, the students will have learned about expected value and payoff. At this point, if students still have questions about probability, choose some activities and discussions from earlier lessons that may have been omitted and use them to reinforce what students already know. If needed, refer to the Crazy Choices Game and draw comparisons with the Stock Exchange activity for students.