Exploring probability: Part 2 of 2

This lesson will introduce students to the concept of fairness as it relates to probability following Part 1 of this lesson which introduces the concept and procedure for calculating probability. Both of these lessons use the resources of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop Interactivate Your Bored Math Students. Students will define fairness and determine if a game is fair.

A lesson plan for grade 6 Mathematics

By Wendy Korbusieski

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Related pages

• Exploring probability: Through teacher guidance, students will experiment with objects to generate probable outcomes to consider probability.
• Spin, toss, and roll!: Students will use hands-on experiments to find the probability that certain events will occur.
• Fair or unfair: Introduction to probability: This lesson introduces the idea of probability theory. Students will use everyday experiences and intuitive understanding to gain an understanding of probability.
  
  This lesson uses resources of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop-"Interactivate Your Bored Math Students."

Related topics

• Learn more about fairness, mathematics, and probability.

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Learning outcomes

Upon completion of this lesson, students will:

• have learned what it means for a game to be fair
• determine if a game is fair

Goals taken from: http://www.shodor.com

Teacher planning

Time required for lesson

45 minutes

Materials/resources

• Pencil
• Computer lab with access to the Internet for all students or groups of two
• Copies of Blank Data Chart
• Copies of Follow Up Questions or questions written out on overhead/board for students to copy

Technology resources

• Color monitor with access to the Internet for each student
• Calculators(optional)
• Projection capability for teacher’s computer
• Access to a printer and copier (for teacher use only)

Pre-activities

Students must be able to convert between fractions, decimals and percents and calculate single probability.

Activities

1. 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:
   

   If I bet you that we could play a game and that I could win every time, would you believe me?
   This game is a racing game in which we take turns rolling a six-sided die and advancing on the numbers that we each are assigned. I bet you I can assign us an equal quantity of numbers that we move on and no matter how many times we play I will always win.

2. Then tell them that the numbers that you assign yourself are 1, 2, 3, 4, 5, and 6, while the numbers you assign the person who takes you up on your bet are 7, 8, 9, 10, 11, and 12. (If you are only playing with one die then it is impossible to roll anything higher than a 6 so the person assigned 6 -12 will never move.)
3. As students,”Who thinks this game is fair?” Lead class in discussion on the found at the Shodor website
4. Have students use The Racing Game with One Die as an example of a game that is either fair or not. Make sure to adjust the settings on the game so that the race is only one step long. Since the game is used for illustration only, each student can play it individually, by groups of students, or by one person who broadcasts it for everybody else to see.
5. Have students discuss different ways that they can make the game fair and not fair.

Assessment

Have the students play The Racing Game with One Die. Each group of students can come up with their own way of randomly choosing which players move on which rolls.

See attached sample trial chart and blank chart. Ideally, students should be placed in two per group. Results should show trials for both fair and unfair games. The sample shows 3 fair and 3 unfair trial results. The teacher can decide how many trials to assign. Ask students to follow-up their investigations by answering the following questions:

1. In your own words define fairness as it relates to probability and
2. Explain how to determine if a game is fair.

Responses can be attached to or written on the bottom of their data sheet. See Grading rubric for this activity.

Supplemental information

Comments

Activities taken from http://www.shodor.com

If time allows or the teacher wishes to investigate further, the Racing Game can also be played with two dice at the following website http://www.shodor.org/interactivate/activities/racing/index.html