School Improvement in Maryland
Designing Models to Simulate Actual Events Using a Random Number Generator on a Graphing Calculator
 
Data Analysis and Probability .
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Objectives
 
  • The student will design models to simulate actual events using a random number generator on a calculator.
  • The student will estimate the likelihood of a particular outcome using results of simulations.
     
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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
 
  • If you roll a single die, what is the probability that:
    1. you roll a 5?
    2. you roll an odd number?
      (1. 1/6 2. 3/6 or 1/2)
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materials
 
  • Activities: "Simulation", "Conducting Simulations", "Simulations on the Graphing Calculator", and "What's Your Sign? Designing the Simulation"
  • Graphing calculators
     
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Calculator Skills
 
  • Use randInt to generate a random integer within a range specified by lower and upper integer bounds
  • Use randBin to generate a random integer from a specified binomial distribution (OPTIONAL EXTENSION)
  • .  Print Version: (Acrobat 31k)
    The print version contains all student worksheets and answer keys needed to complete the lesson.
     

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activities
 
  1. Drill. Have the students work individually to complete this drill. This is designed to be a quick check on the students' understanding of probability. If this drill is hard for students, more work on probability needs to be done before students are ready for simulations.
  2. Introducing Simulation - Before giving students any handouts, give them Problem 1. Ask students to discuss this problem with their group to determine what they think the answer is or how one could go about solving this type of problem. Get the group responses and explain that simulations are often used to determine the answer to this type of problem. (Note: Students should do simulations with hands-on materials such as coins, number cubes, and/or random number tables before using the calculator.) Review the basic steps involved in a simulation and model those steps using Problem 1. Demonstrate the randInt feature of the calculator by showing the student what happens when you enter randInt (1, 10) and press enter several times. Students will see that the calculator generates a random integer between 1 and 10 each time enter is pressed. The next step is to add one more number to speed up the process. Type randInt (1, 10, 3) and then randInt (1, 10, 5) and ask the students to explain what is happening. They will see that the additional number allows you to generate and display more than one number at a time. The students are ready to explain the command randInt(1, 2, 7) and carry it out. Have pairs of students collect their results and share them with the class.
  3. Investigating Simulation - Allow the students to work Problem 2 and Problem 3 with their groups. Discuss the results with the entire class and make
  4. sure that the students understand the calculator commands as well as how the simulations work.
  5. Additional problems - "Conducting Simulations" & "Simulations on the Graphing Calculator"
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Assessment
 
  • Summary Questions: (Context may need to be explained.)
    A goalie saves half of the shots on goal. Suppose there were twelve shots in a game.
    1. Describe how you would conduct one trial of a simulation that models the results of the shots on goal.
      (Using the digits 1 and 2, let 1 represent saving the shot and 2 represent missing the shot. Generate 12 of these digits to represent each of the twelve shots on goal.)
    2. Suppose the goalie saved 2/3 of the shots on goal. Describe how you would conduct one trial of a simulation that models the results of the shots on goal.
      (Using the digits 1, 2, and 3, let 1 and 2 represent saving the shot and 3 represent missing the shot. Generate 12 of these digits to represent each of the twelve shots on goal.)
    3. How many trials should be conducted to obtain reasonable results? Use mathematics to justify your answer.
      (One hundred trials should be reasonable for this situation. In practice, the more critical the situation, the more trials are preformed. For instance, more trials would need to be performed for medical research than for a taste test on soda preference.)
       
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Homework
 
  • "What's Your Sign? Designing the Simulation"
     
Objective Objective Core Learning Goals Core Learning Goals Drill Drill Materials Materials Calculator Skills Calculator Skills Activities Activities Assessment Assessment Homework Homework