Probably Pistachio by Stuart J. Murphy

Mathematical Strand:

Probability

Topic:

Students will use manipulatives and examine situations where probability can be used.

Grade level:

6-8

Lesson Created by:

Kathy Buyle, Susan B. Anthony Middle School, Manhattan, KS

Launching the lesson (engage):

1. Materials - Book: Probably Pistachio, game cube, checkers, coins

1. Read the story
2. Discuss the part of the story where Jack wants to stand next to his friend, Alex. How could Jack have positioned himself in order to stand next to Alex when the coach decided to count off by 3’s instead of 2’s?
3. How could Jack have increased his chances of getting a bag of popcorn when they were choosing snacks?
4. From the students’ knowledge about the predictability of school lunches, ask them to predict what lunch will be tomorrow.
5. As a follow-up to the previous item, ask the students to keep track of school lunches for a couple of weeks to see if there is a predictable pattern to the order in which certain items are served. I save the daily menus so we can refer to the menus for the past few weeks to test the predictability.
   

2. Developing the lesson

1. Introduce probability mathematically: The probability of a particular event occurring equals the number of ways the event can occur divided by the total number of possible events.
2. Do some simple probability exercises using one die. Roll the die 50 times and keep track of how many times an odd and even number shows up. Theoretically, each should occur half the time.
3. Using a checker (each side will be different), flip the checker in the air once and let it fall on a table. Observe to see which side faces up. There are only two possibilities. This can be expressed as a ratio of ½.
4. In the story there were 15 total bags of snacks. Set this up as a probability problem: What is the probability of Jack getting his favorite snack (popcorn) if he were first to choose? There were 3 bags of popcorn, 7 bags of pretzels, and 5 bags of crunch.
5. Put different numbers of several flavors of lollipops in a container. Each student knows the numbers of each flavor. Have the students keep track with pencil and paper as each takes a turn removing one lollipop. The probability will change each time depending on which color of lollipop was taken out.

3. Closure/Discussion/Elaboration

1. Discussing Pascal’s triangle and tossing different numbers of checkers or coins and keeping track of tosses on a chart can extend this experience.
2. Record the results when a checker is flipped many times (10, 20, 50 100) when doing these experimental trials the results should be very close to the theoretical probabilities of occurrences.