Introduction to Probability

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Objective

The students will be able to define, determine, and apply probability in decisions involving fairness.

Big Idea

Roll out this probability unit with a "hands on" introduction!

Dice Game Entry Activity: What is probability?

10 minutes

The lesson hook has students playing a die game which I describe in the video narrative: Entry Dice Game Activity. This has students looking  for structure and patterns (MP7) from the game outcomes right from the start of the unit!

A quick summary of the two games mentioned in the video:

Game #1:  (10 rolls)  Player A wins if sum is even.  Player B wins if sum is odd.

Discussion.  Post results on board.

Game #2:  (10 rolls)  Player A wins if product is even.  Player B wins if product is odd.

Discussion.  Post results on board.

 

Introductory Probability Problems

20 minutes

The opening activity gets students talking about and defining the concept of probability and student’s definitions will likely revolve around the “fairness” of the game.  As you can see in my Introduction to Probability PowerPoint, we take this introductory understanding and build on it throughout the lesson. 

Guiding the lesson, I make sure to include student involvement.  Periodically, I ask students to turn and talk with their thinking groups or people sitting nearest to them. Some strategies and questioning I use to help promote student dialogue include:

  • In example #1, I have students collaborate to  devise a third option that would be a fair way of assigning food. Students are very creative with this!  It is fun to critique the ideas that are brought to the table for discussion (MP3)! 
  • In example #2, I ask the students if they ever “pulled a fast one” on a brother or sister that is similar to the situation in the example.  The students like to share these stories, and many of them will bring a lot of laughs!
  • Many of the students will have suggested the idea of a random number generator in conversation from the first examples, #1 and #2, prior to seeing example #3! 
  • In examples #5 and #6, I introduce the students to the mathematical notation used when determining probabilities.  I intentionally hold off and waiting until the end to do this. I like to use the concepts to motivate the mathematics, not vice versa!  

If I have additional time, I like to ask the students what principals from our statistics unit can might apply as we study probability.  You should not be surprised to find that they come up with content tied directly to the math practice standards we have been emphasizing throughout the course!

Homework Time

15 minutes

I allow students to work collaboratively on the homework assignment - Introduction to Probability Worksheet .  To me, homework is meant to be a first opportunity to grapple with the complexity of the mathematics.  This first opportunity is best explored through conversations with others.  As long as my students are involved in professional collaboration, I have no issues with them helping each other out. 

Students will likely struggle with the openness of the random number generator in #7 and #8.  I prefer to give the students the opportunity to explore and search for how to use a random number generator on their iPads or calculator.  I have purposefully kept this problem open and find this is far more beneficial to the students than giving them all the same random number list.  As you rotate the room helping students, really encourage them to be specific in their explanations of the fair/unfair scenarios.  Details and reasoning are important mathematical skills!