Probability and Fairness

Lesson Plan for Grades 4-7
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Everyday Math (2004)
Teacher Lesson Guide, pp. 104-109, 876-882
Student Reference, pp. 47, 58, 109, 119, 121-124
Math Journal, pp. 43-45, 410-413
Math Master, pp. 16, 168-169, 232, 367

Investigations/Scott Foresman (2006)
Between Never and Always (complete)
Data: Kids, Cats, and Ads (complete)

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Overview

In this Cyberchase activity, students are introduced to concepts of fairness in games based on the probability, or odds, of winning and losing a game of chance. This activity is motivated by a Cyberchase video segment in which the CyberSquad plays a fair game of chance called the Squares Game and one game created by Hacker.

Grade Level:

4-7

Suggested Time

1 hour

Media Resources

The Squares Game QuickTime Video
Hacker's Four-Zergen Game QuickTime Video

Materials

Four Zergens in a Hat handout
Assessment: Level A
Assessment: Level B
Answer Key

The Lesson

Part I: Learning Activity

1. Discuss the idea of a coin having a 50% probability of landing with its head up ("heads") and a 50% probability of landing with its head down ("tails"), if the coin is "fair."

2. Tell the students that they will watch a video segment in which the CyberSquad have to determine whether the "Squares" game is fair.

3. Show the The Squares Game QuickTime Video, and pause it after Lucky wins.

4. Discuss with the students whether they think the game is "fair."

5. Show the students the rest of the video segment in which the CyberSquad define "fair" as an "equal chance of winning" and analyze the chances as 3 out of 9 or 1 out of 3.

6. Distribute the Four Zergens in a Hat handout .

7. Introduce students to the "4 Zergens in a Hat" game using the handout.

8. Tell the students that they will next watch a video in which the CyberSquad analyze the game. Ask them to see if their analysis agrees with the CyberSquad's in the video segment.

9. Show the Hacker's Four-Zergen Game QuickTime Video .

10. Discuss different ideas. End by reinforcing the idea that the odds of winning are 1 out of 6 and the odds of losing are 5 out of 6.

Part II: Assessment

Assessment: Level A (proficiency): Students are asked to assess the fairness of a version of the Squares Game in which there is a 4 x 4 board, and different numbers of black and white squares.

Assessment: Level B (above proficiency): Students are asked to figure out the odds of winning a version of Hacker's game that uses 6 zergens instead of 4.