Theoretical Probability vs. Experimental Probability
Math 7

Objective:	Find and compare theoretical probability and experimental probability.

Common Core:    7.SP.7, 7.SP.7a, 7.SP.7b

Previous Knowledge:    Finding simple probability

Vocabulary:	theoretical probability, experimental probability, fair, unfair

Prep Work:  	Download and print spinners clip-art found here: http://etc.usf.edu/clipart/galleries/551-spinners
	This site is copyrighted by Florida Center for Instructional Technology which you can find here:  http://fcit.usf.edu/  , however they will allow anyone to download 50 educational clipart items without further permission.

	Choose how many spinners you would like to use, I am choosing to use 5 different spinners as I have 5 students in each group.  Make a set of spinners for each group of students you have.  After downloading and putting the spinner together, label each section of the spinners with colors or letters, I plan to use letters making sure that each one has the letter A included.

Activation:	Have the students find the simple probability of spinning an A on each spinner.  Have the students in each group pass the spinners around in order for them to find the 5 different probabilities.

Demonstration:  	Ask the students if they have seen prize wheels at amusements parks, fun centers, or as part of a contest.  Ask?  How difficult was it to spin the winning space?  Why do you think it was so difficult/easy?  Looking at the spinners you have found the probabilities for, how would the probabilities change if we change the A section to be twice the size?  What would happen if we made the A section half the size?  How would we test to see if our probabilities were accurate?
Review the vocabulary with the students.  Explain that theoretical probability is what should happen and experimental probability is what actually happens.  A fair game is a game in which each participant has and equal chance at winning.  An unfair game is a game in which at least one participant has a greater chance of winning than another participant.  Explain that the simple probabilities they found with the spinners in the activation portion of the lesson were the theoretical probabilities of each spinner.

Application:		Have students make a table for each spinner with columns for the number of sections on each spinner. 
		Ex:   Spinner #
A	B	C	
			
		Have students spin each wheel 20 times and notate their results on each table coordinating to the designated spinner.  Then have students determine the experimental probability of spinning the A on each spinner.

Integration:		Have each student compare their experimental probabilities with their theoretical probabilities they found at the start of the lesson.  Ask?  Were the probabilities close?  Why or why not?  Do you think spinning the wheels 20 times were enough to get an accurate experimental probability?  Why or why not?  What would happen to the experimental probability if we spun the wheels 50 times, 1000 times?  Would the experimental probabilities and theoretical probabilities get closer?