Probable Pen in the Cereal Box
Math, Science, Social Studies
(The idea for this lesson came from the "Fun With Probability" website found at http://lrs.ed.uiuc.edu/students/mcornell/cerealbox/)

 Objectives:

    1. Students will recognize that there is an equal probability of finding any of the six prizes.
    2. Students will predict how many boxes of cereal they must buy in order to receive all six prizes.
    3. Students will simulate the number cereal boxes they would have to buy in order to receive all six prizes and compare their results to their predictions.
Focus/Set Induction: Ask students if they have ever bought a cereal or other product just to receive a prize. Discuss prizes as incentives for buying products. Rationale: This lesson gives students a real-life picture of equal probability. It also helps students to understand how companies use prizes to sell their products. Materials:

                    1 die per pair of students
                    Data collection worksheet
                    Pencils
                    6 different colored pens
                    Cereal box (decorated as desired)

Activities:

Instructional Input:

    1. Tell students that a particular cereal is offering one of 6 different pens in each box of cereal.
    2. Put pens in the cereal box.
    3. Ask students: Is there an equal chance that I could draw any color pen?
    4. Explain that since there are an equal number of each color, the probability of getting any one color is the same.
Guided Practice:
    1. Put a copy of the data collection worksheet on the overhead.
    2. Demonstrate buying a box of cereal by pulling a pen from the box. Mark a tally in the appropriate box.
    3. Replace the pen and draw again. Note to students that there is still an equal chance of drawing any color. Mark the appropriate box.
    4. Continue until each color’s box has at least one tally. Stress to students that they must stop when the last color has a mark!
    5. Tell students that they will now do the same thing, but instead of using actual pens, they will use a die. Each side of the die will represent a different color pen. (Demonstrate this if needed.)
Independent Practice:
    1. Break students into pairs.
    2. Have students predict how many boxes they will "buy" and write this number on their worksheet.
    3. Students take turns doing the experiment while the other student keeps track of the tally.
    4. Students complete the worksheet questions.
                    Challenge: Have students repeat the experiment. Allow them to predict if their results will be the same or different. After repeating the experiment, have them answer why they think their results are the same or different. If they are competent with division, have them find a class or group average. Was this around the same number every time? Do they think if they did the experiment several times, and added the results to their previous tries, would the average change?

For those who need help:

Some students may not get the connection between rolling the die and "buying" a box of cereal. These students should be allowed to actually draw pens from the box as in guided practice in order to find their results.

 Evaluation: Students will be evaluated on following directions and completing the worksheet properly. They will also be assessed on their reasoning for the difference (if any) between prediction and actual values. Closure: Ask students to describe why there was an equal chance of receiving any color pen. Have students share the number of boxes they had to "buy" and write this on the overhead (the numbers will be used in the next lesson). Do they think that offering prizes is an incentive for buying a particular cereal?

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