School Improvement in Maryland
Designing Models to Simulate Actual Events Using a Table of Random Digits
 
Data Analysis and Probability .
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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.
     
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Core Learning Goals
 
  • 3.1.1 :The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.
  • 3.1.3: The student will calculate theoretical probability or use simulations or statistical inferences from data to estimate the probability of an event.
     
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Drill
 
    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%)
     
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materials
 
  • Activities: "Using Random Digit Tables," "Guessing on a Multiple-Choice Test," and "Modeling Using a Table of Random Digits"
  • Answer Keys
  • Table of Random Digits
  • .  Print Version: (Acrobat 36k)
    The print version contains all student worksheets and answer keys needed to complete the lesson.
     

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Calculator Skills
 
  • NONE
     
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activities
 
  • Drill. Students will estimate the likelihood of an event using results of a simulation.
  • 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 problems. "Modeling Using a Table of Random Digits"
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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.)
     
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Homework
 
  • "Modeling Using a Table of Random Digits"
     
Objective Objective Core Learning Goals Core Learning Goals Drill Drill Materials Materials Calculator Skills Calculator Skills Activities Activities Assessment Assessment Homework Homework