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?”
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:
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:
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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Sandi