To do this part of the lesson, you will need:

  • dice
  • pencil and paper

In this activity, you will use a die and a tally sheet to model the cereal box problem. One roll will represent a trip to the supermarket. Each number on the die will represent one of the prizes. You should do at least 30 trials. One trial is complete when you have all six prizes.

Below is a table that illustrates 5 trials. The first trial turned up prize #1 three times, and prize #3 five times. Can you tell which was the last prize for each trial? How?

Now make your own table like this one. Instead of numbers, you will probably have tally marks in your table.

Trial Prize #1 Prize #2 Prize #3 Prize #4 Prize #5 Prize #6 Total Number of Rolls
Trial #131522316
Trial #222222111
Trial #323122212
Trial #414243418
Trial #522133920

An empty table is available for print out.

After you have have completed your table, find the average of all the trials done by your class. (For example, in the table above, the average is 77/5 = 15.4) This is your experimental expected value. Now check and see how close this is to the theoretical value.

Interested in the mathematics of the cereal box problem?
Check out the following article by Jesse "Jay" Wilkins, Wilkins, J. L. M. (1999).
The cereal box problem revisited . School Science and Mathematics, 99(3), 117-123.
Click on the title to download the article in Adobe Acrobat format.

Special thanks to School Science and Mathematics, for allowing us to distrubute the article in this manner.