# What are the Chances?

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## Objective

SWBAT apply principles of probability to make fair decisions

#### Big Idea

Is that random choice really random? This lesson explores the chances you'll be chosen by the flip of a coin, roll of a die or by drawing straws.

## Set the Stage

5 minutes

This lesson reinforces prior knowledge and builds a foundation for the next lessons which focus on using probability to make fair or good decisions.  it takes students beyond Algebra I content as  they attend to precision by explaining and understanding what random selection truly means rather than just applying it as a process.  I begin this unit with a brief review of key terms and concepts for probability as discussed in my video.  Instead of just posting a bunch of terms, I challenge my students to post as many terms related to probability as they can on the front board. (MP6) This usually generates an interesting list which in turn generates some interesting discussion.  One of the terms that always seems to spark some of the most heated debate is "random", because students want random to fit their personal definition of fair.  That leads into today's lesson, which focuses on what "random" really means in mathematics.  Again, I don't just give my students that basic definition here; "Every subject/object has an equal chance of being selected".  I want them to see for themselves that an equal chance of being selected is not the same thing as "Every object selected an equal number of times."

## Put It Into Action

40 minutes

For this part of the lesson I tell my students they will be working with their right-shoulder partner to explore multiple ways of "choosing" including drawing numbers from a paper bag, flipping coins, and rolling a die.  I distribute the Random worksheet and give them a few moments to read through the directions.  I ask if there are any questions then tell them they have about 25 minutes to complete this part of the activity.  (MP1, MP4)  I don't just put the materials out and let students come up to collect them because some teams would immediately start in with the data collection without really understanding what they're supposed to do.  Instead I keep control of the materials and when a student comes up to get them I ask to see their data table.  This is usually a pretty good indicator of whether or not they're ready to go.  If not I ask questions like "I see that you have space to record 40 coin flips, but where is the space for the dice and number strips?" or "I don't see your prediction or reasoning anywhere, did I miss it?"  Once everyone is collecting data, I walk around offering encouragement and redirection as necessary.  After about 25 minutes or when everyone is done I tell my students they get to evaluate the results of all their hard work and then share it with the class.  I distribute the Data Evaluation worksheet and tell them they have about 10 minutes to finish and be ready to share.  (MP2, MP3) When everyone is ready or after about 10 minutes, I randomly select teams to share, allowing about 2 minutes per team, while the remaining students critique their responses.   (MP3)  To summarize all their work, I a few leading questions like "Do you think these selection methods were random?  Why or why not?" and "Can a method be random even if every number doesn't get selected the same number of times? This should help my students recognize that "equal chance of being selected" and "selected an equal number of times" are not the same thing!

## Wrap It Up

5 minutes

I close this lesson by challenging my students to "text" a mathematically sound definition of random to friend. (MP6) This allows them to put what we've been talking about in this lesson into a written format, solidifying their understanding of the concept.  It also uses a method of communication that they're familiar and comfortable with, so it's an engaging challenge.