Adapted from the NYS Department of Education publication, A Toolkit for Mathematics Educators: Key Idea Tasks to Enhance Success (KITES)

Through the use of teacher-made food cards the students will explore the concepts involved in the world of uncertainty. Students in the primary grades begin with the simple notion of “more than, less than, or same as.” As students progress through the middle and high school grades, they develop an understanding of the concepts of tree diagrams, counting principle, combinations, permutations, and Bernoulli principle. The series of activities presented will help students develop a deeper understanding of probability and the place it has in their lives. Food cards are used as the theme for these activities, but any topic can easily be substituted to fit the needs of an individual classroom.

1. The teacher will create a deck of 32 food cards containing one meat, one vegetable, one dairy, and one fruit (8 copies of each). Working in pairs, have the students shuffle the deck, remove one card, record its type, and replace it. The students will then draw a second card and record it as the second card of an ordered pair (e.g., turkey, corn). The students should repeat this process several times, recording the ordered pairs formed and always replacing the card removed. Discuss the concept "with replacement".
2. Have the class discuss what patterns they notice.
3. Have the students investigate all the possible outcomes by laying out the pairs, using their 32 cards; then have students record the results on paper.
4. Discuss the student's findings. Possible questions include: What is P(meat and vegetable)? P(meat or vegetable)? p( ~ meat)? Discuss combinations versus permutations and introduce the formulas. Calculate the probabilities both manually and by using the calculator.
5. Discuss how they think things would be different without replacement. In this discussion, the concept of mutuallly exclusive should be investigated.