Expected Value

### Abstract

This lesson's activity and discussion 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

### Standards

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

Number and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• work flexibly with fractions, decimals, and percents to solve problems
Compute fluently and make reasonable estimates
• develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use
• develop and use strategies to estimate the results of rational-number computations and judge the reasonability of the results
Data Analysis and Probability

Understand and apply basic concepts of probability

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

### 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:

### Key Terms

This lesson introduces students to the following terms through the included discussions:

### Lesson Outline

1. Focus and Review

Remind students of what they 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 they will be doing and learning today.

• Lead a discussion on what the stock market is and 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 Follow-up

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.