 |
 |
 |
 |
|||||||
 |
||||||||||
|
||||||||||
|
TIME ALLOTMENT: Three 50-minute classes. OVERVIEW: SUBJECT MATTER: Mathematics LEARNING
OBJECTIVES: STANDARDS: Louisiana Mathematics
Frameworks: MEDIA COMPONENT: Web sites: http://www.geocities.com/thesciencefiles/rollthe/dice.html Per Every Two Students: Per Group (of four students): Per Teacher: Per Group: PREP FOR TEACHERS:
Prior to teaching this lesson: 1. Bookmark the Web sites: http://www.pbskids.org/cyberchase/games/probability/index.html and http://www.geocities.com/thesciencefiles/rollthe/dice.html 2. Obtain a copy of the Cyberchase episode: R Fair City. 3. View the episode R Fair City. Preparation for the hands-on component of the lesson: 1. Make copies of the student activity sheets: Coin Toss Recording Sheet, Roll One Number Cube recording sheet, Frequency Table, 2. Prepare chart paper for class graphs for the following activities: Coin Toss graph, Doggie Get a Bone graph, and Roll Two Number Cubes graph. 3. Make copies of the Doggie Get a Bone game board (You may want to laminate the game boards for future use.) 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, Web sites, or other multimedia elements. INTRODUCTORY ACTIVITY: Step 1: To introduce the lesson topic to students, show students a coin. Point out to students that each coin has two sides … one side marked with a head and one side marked with a tail. Show students each side of the coin and allow them to identify “heads” and “tails”. Step 2: Ask students to name the
possible outcomes that can occur when a coin is tossed. Introduce
the term “outcomes” to the students. Students
should identify heads or tails as the possible outcomes.
Ask Step 3: Tell students that they are going to conduct a coin toss experiment to find out if there is a fair chance of heads or tails occurring when a coin is tossed. Allow each student to make and record a prediction about the outcome of the experiment. Step 4: Divide students into pairs and provide each pair with a coin and a recording sheet. Instruct students to toss their coins 10 times and record the results. Discuss the results. Questions to include in the discussion: “Did your results match your predictions? If not, why do you think this occurred? Compare your results to another group’s results. Were your findings the same?” Step 5: Instruct students to toss their coins 20 times and record the results. Discuss the results. Using the class coin toss graph, allow students to record their results. Ask students, “What do you think will happen if we tossed our coins MORE than 30 times? Do you think the results will show a 50/50 chance or close to a 50/50 chance of heads or tails occurring when the coin is tossed? Why or why not?” Step 6: Use the class computer with PC/TV adapter, a projector, or allow students to work in small groups to log on to http://www.pbskids.org/cyberchase/games/probability/index.html. Students will use the virtual coin toss to simulate the tossing of a coin. NOTE: This website doesn’t allow students to see the coin being tossed. Students enter a number to tell how many tosses they want to the computer to perform. The results are generated automatically and the results are displayed. Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them to toss the virtual coin 1,000 times and analyze the results. Ask students to complete a journal entry that answers the following question: “Do you believe that there is a 50/50 chance of heads or tails occurring when a coin is tossed? Why or Why not? Use evidence from the class results and the virtual coin toss to defend your answer.” Allow students to share the journal entries. Students should determine that the more times a coin is tossed the results come closer to showing a 50/50 chance of heads or tails occurring when a coin is tossed. LEARNING ACTIVITIES: Step 1: Review the discussion from the previous day’s lesson. Use a class chart to record the students’ findings/conclusions. Step 2: Show students a number cube or dot cube and ask students to identify the possible outcomes that can occur when a number cube is rolled. Students should identify the possible outcomes as the numbers from 1 to 6. Allow students to use their experiences from the previous day to describe the probability of each number occurring. Students should record all predictions in their math journals. Ask students to determine if one number has a better chance of occurring than another when a number cube is rolled. Step 3: Divide students into pairs and allow each group to roll a number cube 30 times and record the results. “Check your group’s results with your prediction.” Step 4: Allow students to place their data on a class graph. Compile, graph, and analyze the class results. Step 5: Show students two number cubes and tell students that they are going to explore the possible outcomes that can occur when two number cubes are rolled. Roll two number cubes and ask students to add the two numbers together to get the sum. Tell students, “You are going to conduct an experiment to find out what sum(s) occur most often when two number cubes are rolled and the sums are recorded. We will play a game that will help us with our experiment.” Step 6: Place the transparency of the Doggie Get a Bone game board on the overhead projector. Explain the rules of the game to the students.
Play one game as a class using the transparency as the class game board. Place one chip on each dog. Roll two number cubes and select a student to calculate the sum. Advance the chip one space for the dog with the number that corresponds to the sum rolled. Keep playing until there is a winner. Using the prepared class graph, record the results to show which dog won the first game. Step 7: Allow students to work in pairs. Provide each pair with a copy of the Doggie Get a Bone game board and two number cubes. Each pair should play the game one time and record their findings on a frequency table and on the class graph. Allow students to play the game two more times to collect more data. Students should record their results on their frequency tables and on the class graph. Use the class graph to discuss the results. Possible questions to pose to students: “Is it possible to get a sum of 1?” “What is the smallest sum you can get?” What is the greatest sum you can get?” “Which dog won most often?” “Which dog was second place? Third place?” “If you roll the cubes again, which sum are you most likely to get? least likely to get? Why?” “Have you observed any patterns?” “Using the results of this game, what predictions can you make about the sum(s) that occur most often when two number cubes are rolled?” Instruct students to record their predictions in their math journals. Tell students that they will have the opportunity to use a Web site that allows you to roll two number cubes many times to collect more data on this experiment. Step 8: Use the class computer with pc/TV adapter, projector, or allow students to work in small groups to log on to http://ww.geocities.com/thesciencefiles/rollthe/dice.html. Students will “roll” the virtual number cubes and record the sums that occur. Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them to “roll” the number cubes 50 times and record the results with tally marks. Ask students, “Do the results support your prediction? If yes, tell how. If no, tell how. Can you make any conclusions about the sum(s) that occur most often when two number cubes are rolled? Use evidence from the class graph and the virtual number cubes to support your conclusion.” Allow students to record their findings in their math journals. Step 9: Assist students in making a class frequency table that shows the possible sums and the number of ways to get each sum. See example included with this packet. Allow students to express the probability of each sum occurring when two number cubes are rolled. (Students could express probabilities as fractions. For example the probability of the sum 3 occurring when two number cubes are rolled is 2/36 or 2 chances out of 36 possible outcomes.
Step 1: Using the class graphs, student journal entries, and frequency tables review student findings about probability. You may find it helpful to record student findings on chart paper. Step 2: Ask students if they know how to determine if a game gives everyone a fair chance. Student answers may vary. Step 3: Insert Cyberchase episode, R Fair City into your VCR. Provide your students with a FOCUS FOR MEDIA INTERACTION. Ask students to watch the video segment and note the method the kids and Lucky used to determine whether or not they would pay her for their cab ride. START the tape at the segment where the kids enter R-Fair City. PAUSE the tape after the kids get into the cab. Check for comprehension. (Students should state that Lucky used a coin toss to decide if the kids will pay for the cab ride or receive a free ride.) Ask students if they agree that a coin toss is fair to everyone. “Can you think of a game we played in class that proves that a coin toss gives everyone a fair chance?” Step 4: Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them to listen closely as the kids play the worm game in R Fair City. Ask students to write down the “rap” the kids used to determine if a game is fair (everyone has an equal chance of winning.) RESUME PLAYING the tape from its previous pause point until the end of the segment showing the kids and Lucky at Grubby’s Wacky Worm game stand. STOP the tape. Check for comprehension. Allow students to describe the Wacky Worm game and tell how this game is similar to the roll one number cube game. Write Lucky’s rap on chart paper and discuss it with the students. (LUCKY’S RAP: “TO BE SURE IT’S FAIR LOOK AT THE GAME, EVERYONE’S CHANCE OF WINNING MUST BE THE SAME.) Allow students to apply Lucky’s rule to the roll one number cube game. “Is it fair?” “Use Lucky’s rule to test the roll two number cubes game. Is it fair?” Step 5: Provide your students with a FOCUS FOR
MEDIA INTERACTION. Tell students to write down the numbers
on the zergons. “What are the rules for Hacker’s
game?” “Do you think it is a fair game?” Step 6: Instruct students to make a frequency table showing the possible products.
Ask students to answer the questions: “Is Hacker’s game fair? How many chances are there to get an even product? How many ways are there to get an odd product? Is everyone’s chance of winning the same? Tell why or why not.” Allow students to record their answers in their math journals. Discuss student findings as a whole group. Step 7: Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that they will be allowed to watch the next segment to find out the results of Jackie and Inez’s “fairness” test. “Did their findings match the class results?” RESUME PLAYING the tape from its previous stopping point until the girls “outsmart” Hacker and force him to fall into the water. Tell students “We’ve had the opportunity to play a variety of probability games. We’ve also learned how to test a game to find out if everyone has a fair chance of winning. You are going to work with a group of your friends to design a game that gives everyone a fair chance. Allow time for students to review and discuss some of the games from the other lesson activities. List each game and discuss the probability of “winning” for each game. Remind students of the coin toss and worm game from the Cyberchase episode. Write Lucky’s rap on chart paper and remind students that they may want to use the rap to test their games. Divide students into groups of four; distribute cardstock, markers, paper, and other school supply items. Have number cubes and coins available for student use also. Allow students to work on designing their games. Allow students to present their games to another group when the games are completed. Each group should evaluate the games to make certain that everyone has a fair chance of winning. Step 8: Assessment Procedures CROSS-CURRICULAR EXTENSIONS: COMMUNITY CONNECTIONS: STUDENT MATERIALS:
|
•
LPB NTTI • Master
Teachers • Handheld Resources •
Lesson Plans • Professional
Development •
• LPB Interactive • National
NTTI •
