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 rationalnumber 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
Links to other standards.
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
 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.
 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.
 Teacher Input
Lead a class discussion using the Expected Value discussion that will formalize and develop the concepts introduced by the Stock Exchange activity.
 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.
 Independent Practice
Have groups of students experiment with the activity to generate discussion ideas to use during the closing discussion.
 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 Followup
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.
