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KITES: Food for Thought, 7 - 9

Activity

KITES: Food for Thought, 7 - 9

Grade Levels

7th Grade, 8th Grade, 9th Grade

Course, Subject

Mathematics
Related Academic Standards
CC.2.1.HS.F.3 CC.2.1.HS.F.3
Apply quantitative reasoning to choose and Interpret units and scales in formulas, graphs and data displays.
CC.2.1.HS.F.5 CC.2.1.HS.F.5
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
CC.2.4.HS.B.1 CC.2.4.HS.B.1
Summarize, represent, and interpret data on a single count or measurement variable.
CC.2.4.HS.B.3 CC.2.4.HS.B.3
Analyze linear models to make interpretations based on the data.
CC.2.4.HS.B.4 CC.2.4.HS.B.4
Recognize and evaluate random processes underlying statistical experiments.
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Objectives

Students will:
  • Use estimation to check the reasonableness of results obtained by computation, algorithms, or the use of technology.
  • Estimate the probability of events.
  • Use simulation techniques to estimate probabilities.
  • Determine probabilities of independent events and mutually exclusive events.

    • Source

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

    Description

    Uncertainty incorporates estimation as well as methods for calculating probabilities and predicting outcomes of future events. Students can perform experiments that examine possible outcomes involving repeated trials. Empirical and theoretical probability, along with estimation, are major components of the mathematical prekindergarten to grade 12 experience with uncertainty. Activities about uncertainty investigate problems incorporating manipulatives, including number cubes, spinners, cards, marbles, and coins. Students learn how to set up tables, document outcomes, and tally results. Use of frequency tables and practice in expressing probability as a fraction, decimal, or percent are all a part of the curriculum in prekindergarten to grade 6. In the intermediate levels, opportunities for experiments in uncertainty are extended. Arrangements involving order become more prevalent. Empirical versus theoretical probability is explored. Tree diagrams introduce students to uncertainty activities and provide clues for identifying relationships among independent events. As the student progresses into high school, technical terms specific to uncertainty (combinations, permutations, counting principle, Bernoulli experiment) can be developed within the context of activities. Through the use of experimentation with tasks increasing in difficulty, a deeper understanding of the topic of uncertainty can be attained.

    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.

    Procedure

      Part 1:
    1. The teacher will create a deck of 20 food cards, any combinations of 3 or 4 food types (e.g., 4 turkey, 2 steak, 5 corn, and 9 carrots) for each student pair. Larger quantities of cards are suggested for advanced classes.
    2. Students should NOT look at the cards! Have one student draw a card, record the food type in a frequency table, replace the card, and shuffle the deck. Repeat this process for a total of 10 trials. The students will then calculate the empirical (experimental) probabilities, P(E), of each food type from their tables and express these results as a fraction, decimal, and percent.
    3. Have the students predict the makeup of the 20-card deck on the basis of their tabulated results. Have the groups compare their predictions.
    4. The whole process should be repeated using a larger sampling size (e.g., 36 draws). Their predictions should be modified if desired.
    5. The class counts can then be combined to get a very large sampling, and the class can once again modify their prediction, if needed.
    6. Have the students take an actual count of the deck after all sampling size trials have been completed. Discussion should take place about why the small sampling might have given different results from the larger sample sizes.
    7. Class discussions should includes choosing appropriate sample sizes, cumulative and relative frequency, empirical versus theoretical probability.
    8. This problem can lead to discussion of how polls can be fairly accurate.
      Part 2:
    1. Each student receives 4 cards (1 turkey, 1 broccoli, 1 pasta, and 1 strawberry). Students should discuss how many ways these four cards can be arranged.
    2. Investigate, using the cards, the actual number of ways this can be accomplished. Students should be recording the ways as they manipulate the four cards.
    3. The students should discuss what they discovered; discussion should lead to the concept of factorial and its symbol. NOTE: Students should practice using this symbol (!) on a calculator.
    4. The students should discuss the number of ways these four cards can be arranged if they can use only 3 cards. What happens if they can use only 2 cards?
    5. Have the students investigate these scenarios using their four cards (recording their results as they go).
    6. Have the students share their results; this should lead to a discussion of permutations (order matters) versus combinations (order doesn't matter).
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