Analyze This (Grade 6)

Master Teacher

April Ulmer

Time Allotment

90 –120 minutes

Overview

Fair and unfair games have to be analyzed based on their probabilities. If the probabilities of a game are equal for all outcomes, then the game is fair. If the probabilities of a game are not equal for all outcomes, then the game is not fair.

Through activities presented in this lesson, including video and Internet, students will be able to become more familiar with what makes a game fair or unfair and how to analyze those games based on probabilities.

Subject Matter

Math

Learning Objectives

Students will be able to:

• Find simple probabilities
• Analyze one and two stage events to determine fairness

South Carolina Standards

(These Standards are available online at http://www.myscschools.com/offices/cso/)

Grade 6, Data.IV.B.2: From a given sample space, determine and interpret the probability of an event.

Data.IV.D.1: Making a tree diagram or using models, determine the number of possible outcomes in two-stage events.

Media Components

Video

Cyberchase, Lesson “’R-Fair’ City”

Web site

Introduction to Probability Models

This page contains a dice simulation. Students are able to simulate rolling 1 die, 2 dice, 6 dice or 9 dice. The simulation students will be using for this activity is the rolling of 2 dice.

Materials

• Activity Sheet 1 for all students
• Transparency of Activity Sheet 1
• Activity Sheet 2
• Activity Sheet 3 for all students
• Transparency of Activity Sheet 3
• Activity Sheet 4 for all students.

Equipment

• Overhead Projector
• TV
• VCR
• AverKey

(Note to Teacher: You will need an AverKey if you plan to display the website to the entire class for interaction and discussion prior to the computer lab activity.)

Prep for Teachers

• Prior to teaching the lesson, bookmark the Web sites used in the lesson on each computer in your lab or classroom.
• Cue the video
• Make a transparency of Handouts 1, 3 and 4.
• When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Websites, or other multimedia elements.

Introductory Activity

Step 1: Place the transparency of Activity Sheet 1 “ROLL ‘EM AND TAKE THE SUM” on the overhead and direct student’s attention.

Step 2: Distribute a copy of Activity Sheet 1 to all students.

Step 3: Read through the game scenario and discuss the question, “Is this a fair game?”

Step 4: Have students complete blanks on the handout for notes and discussion purposes. Complete the handout on the overhead as students complete their sheets.

(Note to Teacher: The statements should read, “To determine if a game is fair, we must analyze the probabilities. The probabilities of each outcome of the game must be equal for the game to be fair.”)

Step 5: Read the directions for completing the table on the handout.

Step 6: Have students complete the table. Complete the table on the overhead (with the overhead off) while students are working. They will be able to check their answers when complete by comparing their work to your chart on the overhead.

(Note to Teacher: An answer sheet is included as Activity Sheet 2)

Step 7: When students are finished, turn the overhead on and let them compare their answers for the chart only.

Step 8: Discuss the chart and any questions students have.

Step 9: As a class, answer questions 1-6 on the handout, leading the class through discussion on each question. A point of discussion for question 6, “Is the game fair or unfair?” is that the probabilities must be equal for a sum that is even and for a sum that is odd.

Learning Activities

Step 1: Cue the video up to the beginning of the lesson where “R-Fair City” shows in the upper left corner of the screen. Prior to viewing the video provide the students with a Focus for Media Interaction. Explain to the class that they are going to watch a video that takes place at a “carnival” with lots of games. Tell them to look for facts to help them determine if the games are fair or unfair.

Step 2: PLAY video until the hat, with birds numbered 1-4 inside, is slid on the rope to the birdie. Madame Incognito says “If the answer is odd, you win the hat. If the answer is even you take the swim. It’s simple.

Step 3: STOP the video. Ask students if. Facilitate a class discussion on the question, “Is the game fair or unfair?” (Answer: The game is unfair as you’ll see below.)

Step 4: PLAY video until Madame Incognito says, “Eight, even number, you lose, bye, bye birdie.” Madame Incognito pulls the handle to drop Digit, the birdie, into the water. He lands in a cage and says, “A cage, a cage, let me out of here.”

Step 5: STOP the video.

Step 6: Place transparency of Activity Sheet 3, “Madame Incognito’s Game” on the overhead and direct student’s attention.

Step 7: Distribute a copy of Activity Sheet 3 to all students.

Step 8: Read the game scenario to the students. This is the question you discussed in step 3.

Step 9: Generate the possible combinations from a class discussion. The possible combinations are 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4.

Step 10: Have students complete the chart with the products of the combinations and then decide if the product is even or odd.

Step 11: Complete the overhead transparency as students complete their handouts.

(Note to Teacher:

1-2, product: 2, even

1-3, product 3, odd

1-4, product 4, even

2-3, product 6, even

2-4, product 8, even

3-4, product 12, even)

Step 12: Give students time to answer questions 1-6 on Handout #3, “Madame Incognito’s Game.”

Step 13: Discuss answers to questions 1-6.

(Note to Teacher:

1. 5

2. 1

3. 6

4.
5.
6. unfair, because probabilities are not the same for even and odd

Step 14: Explain to the students that they are going to watch the video again. Provide them with a Focus for Media Interaction by telling them to watch for the scene where they are going to flip the coin to see if the cab ride is free or not. PLAY the video until after the taxi arrives and Lucky says, “Tell you what, I’ll flip you for the ride. Heads you win, you get a free ride. Tails you wash my cab.”

Step 15: STOP the video.

Step 16: Discuss with students whether this game is fair or unfair. The game is fair since both heads and tails are equally likely to occur on a regular coin.

Step 17: P: Tell the class that the next game involves starfish, cows, and airplanes. Give them a Focus for Media Interaction by saying: “Watch very closely. We are going to determine if this game is fair or unfair.” PLAY the video until the scene with the 9 squares (3 starfish, 3 cows, 3 airplanes) when the girl says, “Lucky won again, are you sure you’re on our side?” The boy says, “Yeah, how do we know it’s fair?” Then they do a rap song, “To be sure if it’s fair, look at the game, everyone’s chance of winning must be the same.”

Step 18: STOP the video.

Step 19: Facilitate a class discussion on whether or not the square tile (starfish, cow, and airplane) game is fair. The game is fair as the video will explain.

Step 20: PLAY the video until the end of the segment when digit says, “Probability, very, very high.”

Step 21: Tell the students they will now play a game based on what they learned about the products of two dice being even or odd. The game will help reinforce the products and fair and unfair games. You are now ready for the Culminating Activity.

Culminating Activity

Explain to the students that they are now going to play a game on the computer. Give them a Focus for Media Interaction telling them they are to determine which game is fair and which game is unfair. They are going to roll dice and use their sums and their products. If the sum or product is even then player one wins. If the sum or product is odd then player two wins.

Go to the website: Introduction to Probability Models

Ask students to scroll down using the right arrow until the green, gray and blue boxes show on the bottom.

Under “# Rolls” highlight the radio button 1. Under “# Dice” highlight the radio button 2.

Click on the “Roll‘em” button to get the first combination of 2 dice. Students should make the first entry on their charts in Handout #4 (“Roll the Dice Simulation”) with this combination. Write the combination in the cell under the column labeled “Roll.” Students should follow the directions on the handout to complete it.

Assessment

As the students are working on the Culminating Activity, walk around to observe how well they are doing, asking them questions about their work. The Assessment for the activity is teacher observation of the Culminating Activity and the paragraph they are writing. Activity Sheet 4 will be turned in as a graded assignment.

Cross-Curricular Extensions

Social Studies: Research games from a specific time period such as Colonial times.

Language Arts: Write a story about the life of a carnival worker.

Art: Design a slogan for a game.

Community Connections

• The State Fair: Conduct a math fair to simulate games at the state fair.
• Have a speaker from the state fair come and talk about how the games are chosen and what the chances are of winning some of them.

Student Materials

• paper
• pencils
• Activity Sheet 1 (PDF)
• Activity Sheet 2 (PDF)
• Activity Sheet 3 (PDF)
• Activity Sheet 4 (PDF)