Each group must prove the validity of probability using the ball bucket experiment.
Setup Time: 15 minutes
Time: 40 – 50 minutes
Instruction: Whole class, pairs and Individual
1. After dividing the students into groups, each group should use the following steps to build the ball bucket.
2. Insert a 24” Toobeez tube into both ends of all four curtains.
3. Attach spheres to both ends of the 24” tubes in two of the curtains from Step 2.
4. Using four 36” Toobeez tubes, construct two rectangular panels with the two curtains from Step 3.
5. Connect the two panels from Step 4 with the remaining two curtains from Step 2.
6. Stand the resulting box up with one open end facing the floor (see below). This will serve as the ball bucket for the experiment.
7. Using the remaining spheres in the Toobeez set and an erasable marker, students should write one letter (A, B or C) on each sphere or on a label taped to each sphere. Teacher Note:Be sure to have students record the total number of each type of lettered sphere (see below).
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8. Toss the lettered spheres into the ball bucket.
1. After setting up, divide the students into groups.
2. Begin with a mini-lesson on probability.
3. Read aloud the following Activity Challenge Box to the group.
Challenge: Each group must prove the validity of probability using the ball bucket experiment.
4. As a group, students should define the three possible outcomes (A, B or C) for drawing a ball from the bucket. Teacher Note: This should be a student-led discussion. Allow students to self discover the possible outcomes.
5. The students should calculate the probability of each event using the following equations:
1. P(A)= # of ways to choose “A”/total # of spheres
2. P(B)= # of ways to choose “B”/total # of spheres
3. P(C)= # of ways to choose “C”/total # of spheres
Teacher Note: Students should be invited to try and solve the probability of each event using the master probability equation provided during the mini-lesson.
6. Groups should conduct an experiment by removing one sphere, recording the letter, and replacing the sphere in the bucket. Students should repeat this procedure at least 20 times. Teacher Note: The more attempts conducted, the more accurate the calculated probabilities.
7. Using the equations in Step 5, students should calculate the actual frequency of each event.
8. Students should compare the predicted probability and actual frequency of each event. Each group should record any interesting observations.
9. Each group should compare and share their results with the entire class.
10. After the activity, circle up the group and ask them the following question: “Were the actual experimental frequencies similar to the calculated probabilities? What does this information tell you about probability?”
11. Finally, move to the “Activity Discussion and Processing” section of the activity.
To close the lesson, end with a group discussion about what was learned during the activity. Circle up the group and work through the following questions. If possible, record the group’s responses on flip chart paper so all comments are displayed.
Here are some additional topics for discussion:
1. Increasing accuracy.
Have the students conduct the same experiment, but with 40 trials rather than 20. Let the students compare this result to the original experimental result and the calculated probabilities.
2. Additional challenge.
Have students repeat the activity with four types of lettered spheres (A, B, C & D).
3. Extension/Follow up
Have the students conduct the experiment by removing only ten spheres from the ball bucket without replacing them. Determine the effect on the calculated probability.