A GAME OF CHANCE
Grades 4-6

The purpose of this lesson is to explore the theory of probability. Through cooperative group activities and interactive video technique, students will examine the use of probability in everyday situations.

Math Talk: Take A Chance Exploring Probability (#101)

Students will be able to:

• Judge whether an event is influenced by the theory of probability and if there are other influencing factors such as luck or skill.
• Use the theory of probability by creating a "fair" spinner game in a cooperative learning environment.
• Relate probability theory to events that occur in everyday life situations.

• pencil
• paper
• markers or colored pencils
• poster board
• T-fasteners

Begin by giving students a "math message". This focuses students' thought patterns toward numbers and mathematical concepts.

Have this problem on the chalkboard for the students to solve:
Friends shared a pepperoni pizza which consisted of 20 pieces total. Sue and Carla ate 3 pieces each, John and Meg only ate 2 pieces each and Bev and Earl ate 5 pieces each. What fraction of the pizza did each pair of friends eat and was there any pizza left over?

Answers (in lowest terms):
Sue and Carla: 6/20 or 3/10
John and Meg: 4/20 or 1/5
Bev and Earl: 10/20 or 1/2
No pizza left over.

Assess students' previous knowledge by asking if they have heard of the term probability, odds, or chances before today's lesson.

Review the definition of probability as:

The measurement of how likely it is that an event will occur.

(Put the definition on the chalkboard for reference.)

Pose examples using well-known games such as card games or chess. Ask students: Do you think these games use chance/probability or are there other influencing factors? (Include examples that use a combination of variables such as football.)

Explain differences between the example games that use chance, skill, luck, and a combination of factors. Emphasize chance. Encourage students to come up with examples of their own.

Ask the class to reiterate the definition of probability.

To give students a specific responsibility while viewing, tell them that they are going to be watching a video about probability. Ask them to decide whether the following games use chance, luck or skill, and if they think the games are fair or not.

PLAY
video beginning at On The Midway. Encourage students to examine the carnival game carefully. Focus their attention on whether the game uses chance, luck or skill, and if they think the game is fair or not.

PAUSE
after the carnival barker has described the game.

Ask students if they think the game is fair, why or why not.

RESUME
tape.

PAUSE
after the game is over.

Reiterate to students why the game was unfair. Discuss with them strategies for making the spinner game fair. Motivate students by telling them that their chances are good that they will be making a fair spinner game of their own later on in the lesson.

RESUME
at But Who's Talking. Challenge students to decide for themselves if they think the contestants are making the right choices and why.

PAUSE
after the directions on how to play the game.

Review the directions with the students. Make sure they understand odd/even numbers.

RESUME
tape.

PAUSE
after the game and before the bonus spin; announcers come back and pose the question, "What should Word and Name do with their replacement spin?"

Discuss the results of the game and have the students decide what they think the contestants should do with the replacement spin.

RESUME
tape.

PAUSE
after the contestants have made their choice about what to do with their replacement spin.

Ask students who they think has the best chance for winning and why.

RESUME
to find out whose predictions worked out to be correct.

PAUSE
tape.

Review with students and have them keep in mind during the video that the odds for tossing either a head or a tail is 1/2.

RESUME
at Square One Challenge.

PAUSE
after the question, "Which is more likely on my next flip, heads or tails?"

Ask students to predict the correct answer to the question.

RESUME
tape.

PAUSE
after Cynthia and Chris give their input.

Ask students who they think is correct and did they change their initial prediction.

RESUME
tape.

PAUSE
after the game.

Discuss the conclusion to the game reiterating the probability for tossing either a head or tail is 1/2.

RESUME
through the coin toss until the end of the tape.

Students will use artistic and mathematical talents to create a "fair" spinner game in a cooperative learning atmosphere. The game must contain a spinner that is divided up equally, making the odds of landing on any of the spaces the same. The game must also contain a written summary of rules. The subject of the game is strictly decided by the group. Each group is given poster board, construction paper, markers or colored pencils, scissors, (adventurous teachers might allow paint), and T-fasteners.

Encourage students to brainstorm ideas for their game in groups before starting the project. Each group member is given a specific responsibility, such as facilitator, artist, writer, presenter, etc. After completing the task, groups can either play their own creations or other groups' creations.

In groups of 3 or 4, students will write and give an oral presentation about a current event or situation that uses the theory of probability. Students are to describe the event/situation in detail and how the theory of probability influences the event/situation. It also must be written in an oral report format to present to the class (visual aids are a plus). Some example events include: weather reports, elections, picking the winning lottery numbers, winning at a video game, etc. Students are encouraged to use several research sources, including the newspaper (such as USA Today), computers, television, magazines, human contacts, various agencies, etc. Ample time needs to be given for students to complete their research and presentations. A minimum of 3 class periods is suggested.

1
Social Studies:
Research a state lottery program and invite a lottery official to discuss with the class the role probability plays in selected lotto games.

2
Geography:
Study weather predictions and the role meteorologists play in farming, air transportation, and the economy.

3
Health:
As presented in actuary tables, discuss the role probability plays in making healthy dietary choices.

Master Teacher: Kristin Bordenkircher