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Subject

Math, Science & Technology

Related Activities

1. The teacher will create a deck of 10 food cards (3 meats, 2 fruits, and 5 vegetables) for each pair of students.
2. Have the students predict (using the cards, if neccessary) how many combinations of one meat, one vegetable, and one fruit can be made.
3. Have students construct tree diagrams of these combinations to determine the accuracy of their predictions (see Activity Sheet 4).
4. Using the 3 meat, 2 fruit, and 5 vegetable cards, experimentation and discussion can take place regarding the probability that an event will occur, such as P(meat)=3/10. These probabilities can be expressed as fractions, decimals, and precents. The teacher should show how these probabilities are related to the tree diagram.
5. The teacher should lead student exploration of the concepts of experimental probability (number of times a desired event occurs/total number of trials) and theoretical probability (number of desired outcomes/total number of possible outcomes).

Author

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

Description

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.

Resource/Materials

Activity Sheet

Related Academic Standards

New York State

NY-7.EE.3 Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.

NY-7.SP.8 Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

NY-7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

NY-7.SP.8b Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event.

NY-7.SP.8c Design and use a simulation to generate frequencies for compound events.

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