The Witch Virus

Grade Levels: 11, 12

Subject: Mathematics, English

Learner Outcomes:

Time Frame: 3 days

Technology Tools:

  • Word version to be entered into the calculator
  • TI-83 program to simulate the virus: Witches.83p
  • Microsoft Excel or another spreadsheet program
  • Microsoft Word
  • Microsoft PowerPoint
    • Materials: TI-83 graphing calculators for each student

    Teacher Notes:

    Procedures:
    This activity will be difficult with a small class.  Because of the speed at which the Witch Virus will spread through the class, getting enough data for a regression analysis may be difficult even in a class of 30.  The simulation should be started to emphasize the manner in which the virus spreads; a TI-83 program is included.  It will permit much larger population sizes than can be achieved in a classroom.
    Prior to performing the activity, have a container with the names of all of the students in the class.  In order to avoid personality conflicts, it is suggested that students draw names to determine whom they accuse.
  • Discuss the following information with the class:
    1. Explain:  We are going to select names.  Those whose names are selected will be accused of being a witch.  Since a witch would lie, denying being a witch will do no good because your testimony is not credible.  If found guilty (which is a foregone conclusion.) you will be hung on Gallows Hill unless you confess and repent.  One of the conditions of confessing and a demonstration of  repentance, is to accuse at least two others in the class of being a witch.  Try to imagine yourself in this situation.  You WILL be hung unless you confess
      1. Draw the name of two students, these will be the first accused of being a witch..
      2. Have the student indicate whether he confesses or continues to deny being a witch. (At least one of the students must confess; otherwise the simulation is over.)
      3. This concludes a round of the simulation.  Record the round number, number of students accused, and the number executed.
      4. Begin the next round .
      5. Record the round number, the total number accused, and the total executed.
      6. Graph the number accused each round as a function of the round number.
      7. Examine the graph and have the students write a short analysis of the results.

        8. Since there is a random factor in this simulation the results will be different each time the simulation is run. One thing probably appear, at the beginning, only a few were accused, this increased in the middle rounds and dropped off at the end.  Some questions the students may discuss are the following:
        1. What did you notice about the number accused each round?
        2. Did this same thing happen with the number executed?
        3. If this simulation were conducted again, would you expect the same thing to happen?
        4. Why do you think the results were as they were?
        5. In a real witch trial, do you expect the same thing to happen? Why or why not?
      8. If you have sufficient data, you may wish to enter this information into the TI-83 calculator and perform a regression analysis.


      TI-83 simulation:

      A program is included that can be run on the TI-83 calculator, which will give an approximate simulation.
       

      1. When you start the program, you will be asked if you want to accept the default parameters or enter your own.  Enter 0 for NO or 1 for YES.
      2. The parameters are:
      3. On the first trial you will enter the number accused of being a witch. (2 to 4 works well.  If you plan on using the scatter gram activity, see the scatter gram notes.)
      4. Create a chart showing the number accused each trial from number 3 above.  (The calculator cannot keep track of this because all of the lists are being used for other data.  (See 5-e below.)
      5. If an accused confesses, he must accuse others of being a witch. You will then enter the number each confessed witch will accuse of being a witch (2 to 4 works well.  If you plan on using the scatter gram, see the scatter gram notes.)

        6. The calculator then does the following:
        1. Using the probability entered above, the accused may confess. If he confesses, he must accuse others as designated in 4 above.  (The calculator randomly selects from the entire population.  It may select members who have already been accused, have not yet been accused, or have been executed.)
        2. If he does not confess, he is executed. (There is no second chance to confess in the calculator simulation.)
        3. Based on the probability entered above, the newly accused may confess and must accuse others of being a witch, (This is how the witch virus spreads.  If it does not kill its victim, it must infect others.). Enter the number each of the confessing witches will accuse of being a witch.  This may be the same as entered in 3 above but does not need to be the same.  (If you plan on using the scatter gram activity, see the scatter gram notes.  2 works well.)
        4. During the next trial, those who have confessed may change their mind.  The probability of changing ones mind and denying being a witch is 1/10 of the original probability of denying being a witch.  This will not happen often.  If the accused now denies being a witch, he is executed.
        5. The calculator records the trial number in L1, the total number accused in L2, the total number executed in L3, the number accused each trial in L4, the number executed each trial in L5, and the population condition in L6.
      6. The calculator will report the total number accused and the total number executed. The simulation will continue until 0 is entered for the number to be accused or the entire population has been accused.  If you use the default population size, you should continue the simulation for 15 to 20 trials.


      Analysis

      1. Each student must record the values from L1, L2, L3, and L4 on the chart started above.
      2. Graph the number accused each trial, as a function of the trial number.
        1. Press Y= and remove any functions by pressing "clear"
        2. Press 2nd Y= (Stat plot)
        3. Select Plot 1
        4. Turn Plot 1 On
        5. Select the connected line graph under Type
        6. Select L1 as the Xlist
        7. Select L4 as the Ylist
        8. Select either the square or the + as the Mark
        9. Select Zoom 9 (Zoomstat)
        10. Sketch the graph carefully, on your own paper.
      3. Graph the number executed each trial, as a function of the trial number.  Repeat number 2 above but use L1 and L5. If you want to place both plots on the same graph, use Plot 2 for this plot.
      4. Use Stat Calc and use different regression analysis to find best fit functions for the plot. The following is the process for doing a Quadreg for number 2 above.
        1. Press Stat
        2. Select Calc
        3. Select Quadreg
        4. Enter 2nd L1 , 2nd L4 (The home screen should show Quadreg L1,L2)
        5. Press Enter
        6. To place the function into Y= do the following:
          1. Press Y=
          2. After Y1= press Vars
          3. Select Statistics
          4. Select EQ
          5. Select RegEQ. (The regression equation will be entered after Y=.)
          6. Press GRAPH
      5. Create a written report based on the results of the two graphs above.  The report may contain, but should not be limited to the following (Depending on the ability level, you may need to be more or less specific about the requirements for this report.):
        1. The results must contain a complete graph of each simulation discussed. A complete graph will contain, a title and adequate labeling and legends so anyone can look at the graph and recreate the data.
        2. What is the average number accused each trial?
        3. What is the median number accused each trial?
        4. In what trial is the most number accused/executed?  (Is this the same for both accused and executed?)
        5. What did you notice about the shape of the graph.
        6. Which regression equation worked best for your graph? (LinReg, QuadReg, CubicReg, QuartReg)
        7. How do you think this simulation is similar and different from the results of the actual Salem Witch Trials or other witch trials in history?
        8. Perform the simulation a second time using exactly the same parameters.  How does the results compare? Is the same regression equation best for both simulations?
        9. Is your simulation the same or different from the results of other class members? Why?
    Scatter gram
      1. Collect the results of each member of the class (See Scatter gram Notes below)
      2. Create a scatter gram for the for the number accused each trial and the number executed each trial.
      3. Draw a best fit line for the results.
      4. Have the class members create a written report explaining the similarities and differences of the results of the class members.  The report may contain but should not be limited to the following:
        1. A complete graph of the results must be included in the report.  See the definition of a complete graph above.
        2. Use the TI-83 and place values from the best fit line into L4 and L5.
        3. Use the regression analysis and find a best fit function.
        4. How does this best fit function compare with the ones found above?
    Evaluation: Evaluation Rubric

    Modifications:

    Add or delete the report requirements based on the ability level of the students and any I.E.P. that may apply.
    Enrichment: IGO'S: National Standards

    References:

    Chronology of the Salem Witch Trials
    Witches Dungeon
    The Crucible
    Comments:

    Created by:
    Rusty Campbell
    David Underwood
                              Carol White

    North Marion High School
    Rt. 1, Box 100
    Farmington, WV  26571Date Created: April 1, 1999


    Date Modified: April 1, 1999
     
     


     
     

    Attachments:

    Word version to be entered into the calculator
    Witches.83p
    Evaluation Rubric
    The three graphs below are based on the TI-83 simulation