Probability of Childhood Games
   
Robert Foote                   Disney Magnet School
                               4140 N. Marine Drive
                               Chicago IL 60613
                               (312) 534-5844

Objective:

     Students will find probability of several different events theoretically 
and experimentally.  This lesson is intended for junior high students. 

Materials Needed:

 1. 5 or 6 spinners evenly divided into 6 colors.
 2. Three-color spinner divided into a half and two quarters. 
 3. A bag of fifteen marbles (five of one color, four of another, etc.).
 4. A set of dice and a Monopoly board.

Strategy:
     
     Students in groups will migrate from one station to another during the 
period with about ten minutes given to each task.  Each group should have a 
recorder to write down the results of each experiment. 

     The following is a description of each experiment and what to do for each:

Experiment 1:  The four color spinner experiment involves a spinner for each 
participant and the participants will spin the spinner twenty times and record 
on which color the spinner landed.

Experiment 2:  The six color spinner follows the same procedure as the four 
color spinner of Experiment 1.  A total of twenty spins per group is again
suggested.

Experiment 3:  When I did this experiment as my mini-teach, I used a unique 
spinner.  The spinner with marbles is a spinner from the game The Magnificent 
Race, a favorite game of my childhood.  Unfortunately, the game is no longer 
being made.  However, you can simulate the results using a bag of marbles 
with five of one color, four of another, three of a third, two of a fourth and 
one of a fifth.  This will give you a total of 15 marbles.  Have each group draw 
a marble from the bag, replace it, and draw again until they have drawn a total 
of twenty times.  Record the results.  
    
Experiment 4:  The Monopoly board task is for students to determine which space 
on the Monopoly board is landed on the most.  To do this, starting at Go, roll 
the dice and record where on the board the player would land.  Continue doing 
this starting at Go each time until the dice have been rolled twenty times. 

    After students have finished all the experiments and recorded them, the next 
step is to compare the experimental probability from the results of the 
experiment to the theoretical probability.  The theoretical probability can be 
determined for each of the experiments in this way:


Experiment 1:  This spinner is broken up into one half and two fourths, so 
theoretically, the probability for landing in each of the spaces should be one 
half, one fourth, and one fourth.  This means that theoretically the spinner 
should land in the half space half the time and so on.

Experiment 2:  This spinner has evenly divided spaces, so theoretically the 
spinner should land in each space the same number of times.  This may or may not 
happen in reality.  You need a whole lot of trials to match the theoretical 
probability.

Experiment 3:  This spinner holds a a total of fifteen marbles with more of some 
marbles than others so the theoretical probability depends on the number of 
marbles of each color.  The theoretical probability is the number of marbles 
of a particular color over the total number of marbles.  For example, if you 
have five marbles of one color, the probability of that color being picked is 
five over fifteen. 

Experiment 4:  The Monopoly experiment is rooted in the classic probability 
experiment of rolling two dice.  Students can make a chart to determine which
rolls come up more frequently than others and then match the rolls to the spaces 
on the Monopoly board.  The most common roll should be seven.

After the groups have finished with their individual experiments, compile the 
data for each experiment from all the groups.  You should find that the compiled 
data of the entire class should be closer to the theoretical probability than 
the data of the individual groups.