Name: Rachel Bender
Monty Hall
50 minutes
I. Contextual Factors
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This lesson is for an Advanced Quantitative Reasoning class, but can be done in a Statistics, Algebra I,
Algebra II, or PreCalculus class with some modifications as a primer on probability.
Students in Advanced Quantitative Reasoning classes will have been exposed to statistics in their previous
high school classes (Algebra I, Algebra II, and Geometry) as well as classes prior to high school
List of necessary materials: Computers with MS office and internet access, Pencils, Butcher Paper/Posters,
(Rulers-optional),
II. Learning Goals
 Form an original hypothesis (Hₒ) and alternative hypothesis (Hₐ) for Monty Hall
 Create a data set, frequency table, for Monty Hall probability
 Explain mathematically, visually, and in written form the best strategy for Monty Hall
TEKS 111.44. Advanced Quantitative Reasoning
c Knowledge and skills
4. Probabilistic and statistical reasoning
A. Use a two-way frequency table to identify whether two events are independent
B. Use the Addition rule in mathematical and real-world problems
D. Interpret conditional probabilities and probabilities of compound events by analyzing
representations to make decisions in problem situations
E. Use Probabilities to make and justify decisions about risks in everyday life
III. Assessment Plan
Use of multiple assessment modes and approaches aligned with learning goals to assess student learning before,
during (formative), and after instruction (summative).
Pre-Assessment:
Students will be asked: What is probability- what does it mean for making choices?
What are independent and conditional events?
Formative:
During the activity, students will be asked:
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Are you more likely to win by staying or switching door?
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What are your hypotheses?
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How can you represent the probability mathematically? (ie… P(A) = 1/3)
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How can you demonstrate the data? (tree diagrams, frequency table)
Summative
At the end, students will be asked (to be turned in):
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Did you accept or reject your original hypothesis? Why?
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How do you explain the probability you arrived at?
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Explain verbally, visually, and mathematically why you should switch doors (tree diagrams, frequency tables, P(A)
language should be incorporated here to explain/demonstrate why switching doors results in twice a likelihood of winning)
IV. Design for/Delivery of Instruction/Activities/Actions (of teacher and students)
Part I (8 minutes):
 Teacher “Today we will be playing games!”
 The teacher will ask students to name some game shows and games of chance, guiding them to ones
involving chance- (The price is Right, Deal or no Deal, poker, roulette, craps)
 Ask students how they would decide what to do, guiding them to probability
 Ask students what probability is and write their answers up on the board
 Ask students about independence in the context of the games (dice versus cards)
Name: Rachel Bender
Part II (7 minutes)
 Introduce the Monty Hall problem
 Go through assignment with students: Create hypotheses sets for whether they should switch doors to win
at Monty Hall, gather data by playing the game online, discuss the results in group, accept or reject original
hypothesis, and verbally and visually explain the results
 Split the students into heterogeneous groups based upon ability in computer use, mathematical
understanding, and ability to communicate ideas verbally/visually.
 Assign groups to a computer
 Help students get to Monty Hall web site:
http://www.shodor.org/interactivate/activities/SimpleMontyHall/
Part III (10 minutes)
 Groups should form their hypotheses on whether to keep the same door or switch doors
 Students should play Monty Hall in groups on the computer
 Teacher should walk around to make sure students are having input in the groups’ decision
 Teacher should ask students about why they are choosing to switch or stay, their hypotheses, what results
they are seeing, and why they think they are seeing those results
 Teacher should give the students a warning when there is only 2 minutes left on the computers so they can
record their results.
Part IV (10 minutes)
 Teacher should ask each group to records the number of wins and losses for staying and switching on the
board
 Teacher should ask class whether they would stay with the same door or switch doors
 Students should be guided to saying they were twice as likely to win if they switched doors and what the
probability is in each scenario (also how they arrived at that: wins/total)
 Teacher should prompt the students to ideas of why they think they would be more likely to win
 Teacher should guide students to the idea of conditional probability
 Teacher should introduce frequency table, tree diagram, and probability addition
Part V (25 min and hwk)
 Groups should decide if they want do a poster or do a Publisher or Word document
 Groups should discuss their hypotheses and accept or reject
 Teacher should float around class to assist students and answer questions they might have
 Teacher should observe and prompt to make sure participation and responsibility are shared throughout
group
 Groups should discuss the probabilities from group/class
 Groups should create a two-way frequency table
 Groups should create a tree diagram
 Groups should represent the probabilities both mathematically with probability addition and verbally
 Groups should put the hypotheses, frequency table, tree diagram, probability addition, and verbal
explanation of what happened and whether they accepted or rejected hypothesis in poster or document to
turn in and put up on walls. Turn-in should include what the group has decided is the best strategy to “win”
at Monty Hall.
Part VI (Wrap-up 5 min)
 Teacher should let students know when there are only 5 minutes left in class so students can wrap-up
 Groups should decide who/how should finish parts of project not completed in class
 Groups should sign out of computers and put up any markers or other supplies they have
Name: Rachel Bender
V. Design for/Delivery of Differentiated Instruction
 Putting the students in heterogeneous groups will allow them to assist each other and ensure there are no
especially “advanced” or “struggling” groups. Allowing students to work in groups will mean the
struggling students will receive assistance from their peers as well as the teacher while advanced students
will have to vocalize the concepts more clearly to their peers, ensuring they completely understand the
concepts.
 Allowing students to choose how to present their work (computer or poster) allows them to work in an
environment which supports them. For example, a student with a learning disability such as dyslexia may
be more comfortable using a computer for the assignment than writing it out. This may also mean students
with learning disabilities which are mitigated by either using the computer or writing out the information
can choose to do this and stay on a more equal footing with their peers.
Reflection and Self-Evaluation
Reflect on your lesson and establish at least two clear and explicit connections to course content related to these
suggested areas:
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Differentiating the product by allowing groups to choose between posters and computers and
which components each person is primarily responsible for is one of the classroom elements
Tomlinson and Strickland identify to maximize each individual students learning.
Grouping heterogeneously, as Routman suggests, will maximize the learning of individuals and
also help both high and low achieving individuals to feel part of the class via contribution and
participation.