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Fun with Probability!The Probable Pen in the Cereal BoxProject Overview |
How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop? One - Two - Three. THREE!
How many boxes of cereal do you have to buy until you have received six pens of different colors? Well, that's what the "Probable Pen in the Cereal Box" project is all about. In only 1 to 3 hours, your class can participate in a world-wide experiment to calculate this value, have some fun, and learn a little about probability. Read below for:
Snowflakes Cereal is having a promotion. Each box of Snowflakes has a colored pen in it. Collect all six!
The Fun with Probability Project is a joint effort among interested schools worldwide to experimentally solve a simple probability problem. Simply stated, we are calculating the number of boxes of cereal one needs to purchase to receive a complete set of six colored pens.
Each student rolls a six-sided die to simulate buying one box of cereal. Each face of the die corresponds to a colored pen. The student counts the number of rolls it takes until each side (colored pen) has appeared at least once. Once that number is known, it is tabulated with the other students' results, and submitted to the Fun with Probability! web site.
The web site will compile local, regional and world-wide averages to provide an experimental result. This can be compared to the theoretical result which is calculated using statistical formulas.
Probability can be a difficult concept for students to understand. Your students will learn, via experimentation, that each student must buy a different number of boxes to get a set of six pens. Some will get the set in only six tries, but others will have to buy 30 or more boxes. Is that fair? What is the average number of boxes our class had to buy? What is the average number of boxes schools in our state had to purchase? What is the average for my country? Does the value vary from state to state? What if there were seven colors of pens -- would we have to buy more or less boxes?
More importantly, your students will learn about these concepts alongside students from around the world! Through the connectivity of the Internet, your students' results will be combined with the results of students from far-away locations to create a genuinely international solution.
This is not one of those projects where you have to wait weeks for the compiled results. As you submit your results to the Fun with Probability! web site, they are combined with previous trials into an updated solution. See the running average of all submissions immediately.
If you are one of the early submitters, come back to the site later to see who else has participated! If you don't have access to the world wide web, results can be mailed via electronic mail. Final results will be posted on the Fun with Probability! web site, and can be downloaded for your own processing.
This project is open to all grades. Lesson suggestions are available for grades K-2, 3-5, and 6-9. Math is optional!!! The earlier grades might be interested in the concept of proability without the actual calculations, while pre-algebra classes will be able to compare their calculations with experimental results.
There are three ways to participate:
The entire time required to prepare, present and execute the experimentranges from 1 to 3 hours, and can be split over several days. Submitting the results takes about 30 minutes.
The Fun with Probability! site will be in operation for three weeks, beginning Monday, April 22nd and ending Friday, May 10th. Registration is being accepted immediately. Approximately one week after your registration information is received, you will receive an e-mail with the URL of the Fun with Probability! web site. There you will find interesting information about the project, as well as lesson plans.
To register, please send the following information to mcornell@uiuc.edu:
Approximately one week after your registration information is received, you will receive an e-mail with the URL of the Fun with Probability! web site. There you will find interesting information about the project, as well as lesson plans, and instructions for submission.