Thursday, September 6, 2012

Introducing Probability to 30-2

I will be modelling a lesson in two weeks, introducing probability to Math 30-2 students.  I brainstormed a bit and knew that I wanted to do a hands-on activity based on the Monty Hall problem.  I raced to the internet, did some research and came up with a rough-draft below.  I would love some input regarding a) better questions I could be asking and b) the ordering.  It seems a little weird to throw the card question in the middle.  Not sure if I want it there are at the end.  Would love your input!

Note:  I still need to check that it's ok to bring candy for students.  I've never been told no in the past as I'm a guest but...I haven't been to this school yet and better dot my i's and cross my t's and all that.


My rough draft lesson plan.

30-2 Probability Intro
Monty Hall Problem
Based on:
·         Monty Hall problem
·         And blog write up and comments listed at Point of Inflection
·         And lesson plan shown here:  http://www.ms.uky.edu/algebracubed/lessons/Monty_Hall_Lesson.pdf

Materials:
·         Candy - would be a toy car if not allowed to use candy
·         Bowls with lids, labeled 1, 2, 3
·         Blocker so they can’t see which one I’m changing
·         Cards
·         Envelope you can’t see through
·         3 cups per group
·         1 object per group (represent candy) – or candy

Instructions:
·         Place 3 bowls on table.  One has candy inside of it.
      Ask “Who wants to play?”
o   Don’t give out rules yet
·         “One of these three bowls has candy in it.  If you can guess which one, you get the candy.”
·         Play
·         “Who else wants to play?”
·         Play a few times.
·         “What’s the probability of winning?”
·         Next time, say “Your guess was as good as any other.  But I want to give you another chance.  I will show you that this bowl <lift an empty one> is empty.  Do you want to keep your original guess or switch?”  Finish
·         Play again but this time stop after showing an empty bowl.
·         Ask “what are the odds now?”  They will probably answer 50%.
·         “Interesting” Finish game.
·         Play again, stopping again after showing the bowl.
·         Ask “when you chose at first, you had a 1/3 chance of winning.  Now you say that the same bowl you picked has a 50% chance of winning.  How could flipping over an empty bowl over here improve the chances that this bowl is a winner?”
·         Allow for discussion.

Switch to cards:
·         Let’s try this with cards.  <Student> pick a card but don’t look at it.” Put in envelope.
·         “Who do you think probably has the Ace of Spades?
·         “What’s the probability that it’s the Ace of Spades?” 1/52
·         “I’m going to get rid of a card that is not the Ace of Spades.”  Look at 3 and discard 1.
·         “Do you think you’re more likely, equally likely, or less likely to have the Ace of Spades now?”
·         Run through deck, discussing probability as you go.  

Back to the bowls:
·         When finished, return to 3 bowl problem.
·         Ask students “We’re going back to the question - Should you switch or stay?  In partners, I’d like you to discuss how to PROVE if the contestant should switch or stay.”


Provide groups of two with student handout, 3 cups and candy/other object.  Explain that they will be creating data based on the Monty Hall problem.  Make sure they understand that they need to do the test 50 times each (a total of 100 times) - 50 for switching and 50 for staying.



Student Handout

Names:_________________
            _________________

Let’s Make a Deal


1.       Do you think you will win more often if you switch or stay?  Explain.





2.      Play the Monty Hall Game with a partner. Record your results in the table below. Be sure to play 50 times WITH switching doors and 50 times WITHOUT switching doors.
Strategy
Switch Doors
Stay
WINS











LOSSES











Winning Percentage



1.      Do your results display a difference in your chance of winning based on whether or not you switched doors?  Explain.





2.      How do your results compare with your prediction?





3.      What is the probability of winning the Monty  Hall Game?  Explain.





4.      Do you believe that you have a better chance of winning if you switch doors?  Why?






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