Is It Really Fair?

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SWBAT apply principles of probability to make fair decisions.

Big Idea

Are random number generators and tables really random and is random really fair? Try them out for yourself and find out.

Set the Stage

5 minutes

I've found that students are willing to accept that a coin flip or drawing straws is a truly random and "fair" method for choosing, but often challenge a random number table or random number generator as not being as "fair".  To help them better understand this I begin this class with the following question on the board:

"What is a random number?" (MP6)

We just finished a lesson looking a methods for random selection so I'm anticipating several responses in the form "It has an equal chance of being selected".  My next question requires a bit more thinking: "When you say "equal chance" what are you comparing your random number to?" This usually follows a discussion as my students explore the difference between a method of random selection and a random number.  I facilitate the discussion for a few minutes or as long as it's productive, then tell them that today they will be exploring a random number table and a random number generator to better understand how they can be used to simulate random selection.


Put It Into Action

35 minutes

For this part of the lesson each student should have a graphing calculator (we use TI84s) to generate random numbers, but if there are not enough available you can have students share.  If you don't have calculators you can do this activity using a Random Digits Table or find a web site such as this one

I might need to explain or refresh students' knowledge about how to use the random number generator so I distribute the Using a TI 84 Calculator as a Random Number Generator handout , ask if there are any questions, and tell them they have about 10 minutes to work through all the different options.  (MP5)  While they're working I walk around offering encouragement and trouble-shooting as necessary.  It is likely that some students are still not comfortable with their calculators and will need more support. In this case rather than "hold their hand" through the worksheet, I using prompts like "What do you need to do next?" and "Does your calculator screen look like the example on the worksheet?"

After about 10 minutes or when everyone is done I distribute the Random Numbers Table and walk the entire class through a few examples of how to use the table to generate a list of random numbers.  I check for understanding about the random number table using fist-to-five, then  tell my students that they will be working with their left-shoulder partner to complete the next activity. 

I distribute the Is Random Fair challenge and tell them they have about 20 minutes to complete the worksheet.  I copy the class data table on the board and explain that each student needs to post their data for the calculator and for the random numbers table. (MP5)  I also clarify that I want each student to complete the table of class data on their worksheet and answer the essay questions in their own words.  (MP1, MP2) While they're working I walk around offering encouragement and assistance as necessary.  The biggest struggle most students have with this is answering the final questions.  For those who say they "don't get it" or something similar, I might ask "Do you remember the definition of random selection? How does that relate to a random number?"  When everyone is done or after about 20 minutes I ask them to turn in their papers.

Wrap It Up

10 minutes

I use two different things to close this lesson.  First, I post the following definition of random numbers on the board and elicit class discussion. 

Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones

I ask my students for a show of open/closed fist to indicate whether they agree or disagree to get the discussion started, then ask if there are any additions or corrections needed.  When we have thoroughly discussed this definition, I distribute notecards and ask my students to write a "text" message to an absent classmate defining random number in their own words.  (MP3)