School Improvement in Maryland

Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 3 Data Analysis And Probability

Expectation 3.1 The student will collect, organize, analyze, and present data.

Indicator 3.1.3 The student will calculate theoretical probability or use simulations or statistical inference from data to estimate the probability of an event.

Lesson Content

Designing Models to Simulate Actual Events Using a Table of Random Digits

Objectives

  • The student will design models to simulate actual events using a table of random digits.
  • The student will estimate the likelihood of a particular outcome using results of simulation.

Other Indicators Addressed

3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

Materials Needed

Note: The "Table of Random Digits" is included with the worksheet "Guessing on a Multiple-Choice Test"

Assessment

Summary Questions: A girl has six sweaters that she can wear to school. Explain how you could use the table of random digits to determine whether it is likely that she will wear the same sweater more than once in a five-day week. Assume that each sweater selection is independent of the others.
(Use the digits 1-6 to represent the six sweaters, disregard the digits 0, 7, 8, and 9. Begin at a random point in the table and look at the following five numbers, ignoring any of the unused digits. These five numbers represent each day of the week. The number of 1s that appear will correspond to the number of times she wore the first sweater. The number of 2s that appear will correspond to the number of times she wore the second sweater, and so forth.)

Lesson Structure

    Warm-Up/Opening Activity

    Students will estimate the likelihood of an event using results of a simulation.
    A couple decides to have two children. They want to determine the probability of having two girls, so they simulate the births of their children by flipping 2 coins 50 times. The results of the simulation are shown in the table.
     
    Possible FamilyFrequency
    2 boys
    1 boy and 1 girl
    2 girls    		13
    26
    11
    Total50

     
    Using the results of the simulation, estimate the likelihood of the couple having two girls. (according to simulation: 11/50 = 0.22 or 22%)

    Exploration

    Students will investigate how to use a random digit table. They will conduct simulations using a random digit table. At first, teachers may want to instruct students to begin at the same point in the random digit table when conducting simulations. As students become more comfortable, they should begin at different points in the table.

    Class Discussion

    Students need to understand that selecting pairs of numbers at a time or skipping numbers in the table will not affect the "randomness" of their results. Teachers may want to discuss how to simulate events with outcomes that are more complex.

    Additional Practice

    Modeling Using a Table of Random Digits

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