Subject/Course: Math 2
Topic: “The Multiplication
Rule When Events are not
Independent”
Grade: High School
Designer(s): Simpson
Stage 1- Desired Results
Standards: Standard: 3. Data Analysis, Statistics, and Probability
3. Probability models outcomes for situations in which there is inherent randomness
Understandings (Big Ideas):
Essential Questions:
 Students will be performing the multiplication rule for  I can find the probability of two events when they
non-independent events.
are not independent.
Vocabulary/toolkit notes:
 Put rule for finding probability of non-independent
events into toolkit.
Performance Tasks:
 U8L1I3, pg. 532
 CYU, pg. 535
Learning Objectives:
Students will be able to …
 Find the probability of non-independent events
using the multiplication rule.
Stage 2- Assessment Evidence
Other Evidence:
 Pg. 538, #7
 Pg. 539, #10
 Pg. 540, #11
Stage 3- Learning Plan
Where is the investigation headed?
Final step in finding probability using multiplication rule.
Hook the learner with engaging work.
Equip for understanding, experience, and explore the big ideas. (prerequisites)
Students need to be able to find conditional probability.
Rethink options, revise ideas and work. (student misconception)
Show/give the formula to students if needed after the investigations
Evaluate your work and adjust as needed.
The teacher will walk around answering questions and checking in on students and use the CYU as a
measuring tool.
Tailor the work to reflect individual needs, interests, and styles.
Students get a wide variety of teaching tools from direct instruction to class discussion. Also students are
allowed time to work individually as well as in a group.
Organize the work flow to maximize in-depth understanding and success at the summative tasks.
1. Warm-up
2. As a class do and discuss the first problem
3.
a. Teacher will explain how to find the probability of events using “and” with the multiplication rule.
b. Put in notes both multiplication rules and independence
4.
5. Final Problem-Monty Hall
Game description: This game is based on the old television show “Let’s Make a Deal” hosted by
Monty Hall. At the end of each show, the contestant who had won the most money was invited to
choose from among 3 doors: Door #1, Door #2, and Door #3. Behind one of the three doors was a
very nice prize, let’s say a car. Behind the other 2 doors there was a goat. The contestant selected
a door. Monty then revealed what was behind one of the OTHER doors (always a goat). The
contestant was then offered a choice: stick with his current door, or switch to the remaining unrevealed door. He won what was behind his final choice of door.
Before beginning the simulation, ask yourself: intuitively, does it make any difference to the
chance of winning a car if the contestant switches of not?
http://www.grand-illusions.com/simulator/montysim.htm
Combine your data with your partner’s data.
# of trials switched __________
# of cars won
(after switching)
# of trials “stuck” __________
# of cars won
__________
(after “sticking”)
total # of trials
# of cars won
(grand total)
__________
__________
__________
Now pool the class results. Don’t double-count your data and your partner’s!
# of trials switched __________
# of cars won
(after switching)
# of trials “stuck” __________
# of cars won
__________
(after “sticking”)
total # of trials
# of cars won
(grand total)
__________
Questions:
1. What proportion of all trials resulted in a win?
__________
__________
2. What proportion of all “switch” trials resulted in a win?
3. What proportion of all “stick” trials resulted in a win?
4. What proportion of all wins (i.e., all cars) were the result of the switching strategy?
What do these probabilities tell you about your intuitive answer? Does switching improve your
chance of winning the car?
Part II: MATHEMATICAL PROBABILITY
We will now construct a tree diagram. First consider the “prize” behind the first door the
contestant selects. This will form the first part of the tree diagram. The two options are “CAR”
and “GOAT.”
What is P(GOAT)? __________
What is the P(CAR)? __________
Second, consider the decision made by the contestant. This will form the second part of the tree
diagram. The two options are “SWITCH” and “STICK.” To be fair in our calculations, we
assume that the probability of switching is 0.5. Fill in the remaining probabilities and complete
your tree diagram below.
Finally, use the tree diagram:
What is P(CAR|SWITCH)? ___________
Is there an advantage to switching? Does this agree with your original opinion?
http://www.youtube.com/watch?v=mhlc7peGlGg Explanation of the Monty Hall problem
Summative Assessment Plan
Probability Summative Assessment
Choose one of the following assessments to demonstrate your understanding of
probability.
1. Take Home Unit Exam: students will complete a take-home exam showing their
knowledge of probability
2. Game Show Research Report: you will research a popular television game show to find
the theoretical probability of winning. Then you will watch at least 3 episodes and record
the experimental results. Compare the theoretical probability to the experimental
probability in each episode. Discuss the devise used in the game and discuss whether it
is fair or unfair. Discuss the likelihood of a contestant winning the game.
3. Board Game Research Report: you will research a popular children’s’ board game show
to find the theoretical probability of winning. Then you will play the board game three
times and record the experimental results. Compare the theoretical probability to the
experimental probability in each game. Discuss the devise used in the game and discuss
whether it is fair or unfair. Discuss the likelihood of a contestant winning the game.
4. Design a Game: design a game using a fair device. Discuss the theoretical probability of
winning the game. Play the game at least three times and record the experimental
probability. Decide whether your game is fair or unfair.
5. Write a story: create a story which includes your understanding of events that are certain
to happen, likely, unlikely, and impossible.
-----------------------------------------------------------------------------------------------------------------------------------
I will complete the ____________________________________________________.
Parent Signature_____________________________________________________
Date _____________________________
Probability Summative Assessment Rubric-Students Self-Assessment
Take Home Exam
MYP Criterion
A: Knowledge
and
Understanding
0
1-2
I don’t
understand
anything and
did not
complete the
test.
I can solve
simple
probability
problems. I can
try to think
mathematically
if I have seen
the problem
before.
3-4
5-6
7-8
I can solve simple
and more difficult
probability problems.
I can think
mathematically
sometimes if I have
seen the problem
before.
I can solve
challenging probability
problems.
I can think
mathematically if I
have seen these types
of problems before.
I can solve challenging
probability problems.
I always think
mathematically correctly
even if I have not seen
that kind of problem
before.
Game Show Research Report, Board Game Research Report or Design a Game
Reflection in
Mathematics
0
I can’t explain
anything in writing.
0
1-2
3-4
5-6
I tried to explain
why my answers
make sense.
I try to explain the
importance of
probability in reallife.
I correctly
explain why my
answer makes
sense
I can explain the
importance of
probability in
real-life.
.
I can correctly
explain why my
answers make sense
in details.
I can explain the
probability
connection to real life
in details.
I offer suggestions or
hints to make
understanding easier
for others.
1
2
3
4
Research
My research is not
evident.
My research is not
evident. I only use
my prior knowledge
and do not include
any sources of
information.
My research may
not be evident. I
used sources but
site them
incorrectly.
My research is
evident. I used at
least two reliable
sources and site them
correctly using MLA
format.
My research is
evident. I used at
least three reliable
sources and site
them correctly
using MLA format.
Content
I did not address any
of the
questions/statements.
I did not
compare/contrast
theoretical and
experimental
probabilities but
may discuss the
devise used, and
the likelihood of the
contestant winning.
I left out important
information.
I
compare/contrast
theoretical and
experimental
probabilities, the
devise used, and
the likelihood of
the contestant
winning but may
be missing some
information.
I compare/contrast
theoretical and
experimental
probabilities, the
devise used, and the
likelihood of the
contestant winning
I
compares/contrasts
theoretical and
experimental
probabilities, the
devise used, and
the likelihood of the
contestant winning
and included
additional
.
information.
Presentation
My report may is
illegible or appears to
be thrown together.
My report is
handwritten and
may be difficult to
read or missing
important
information such as
title, name, period,
and the name of
the game
researched, has
many grammatical
errors.
My report is
handwritten,
includes title,
name, period,
name of game
researched may
not include
tables, graphs
and charts with
explanations,
may have some
grammatical
errors.
My report is typed,
includes title, name,
period, name of game
researched may not
include tables, graphs
and charts with
explanations, may
have a few
grammatical errors
but it is neatly stapled.
My report is typed,
includes title,
name, period,
name of game
researched tables,
graphs and charts
with explanation,
free of grammatical
errors sand is
neatly stapled.
Write a Story or Write a Letter
MYP Criterion
C:
Communication
in Mathematics
0
I did not try to
complete the
assignment.
0
Content
Grammar
I did not try to
complete the
assignment.
I did not try to
complete the
assignment.
1-2
I try to use some
math vocabulary,
but they may not
be used correctly.
I try to use
pictures, diagrams
or chats but I have
a hard time
explaining them.
I try to explain but
it may be
confusing.
1
3-4
I use most math
vocabulary
correctly.
If I use pictures,
diagrams or
charts, I can
explain most of it
in a way that
makes some
sense.
5-6
I use math
vocabulary
correctly to show
I understand
how math works.
If I use pictures,
diagrams or
charts, I can
explain all of it in
writing.
2
3
4
My story/letter
includes some
math vocabulary
terms. My
story/letter appears
to be written last
minute. The story
may include a
character. The plot
is undefined and
undeveloped; the
events of the story
are unclear.
My story/letter
may lack in detail
and may not make
sense`. My
story/letter
includes some
math vocabulary
terms. The story
includes one main
character. The
plot includes some
important events,
but may lack a
climax, and/or
resolution,
My story/letter
includes math
vocabulary terms
and reflects the
students
understanding of
probability.
My story/letter
immediately grabs the
readers attention,
shows creativity
through figurative
language (such as
similes, metaphors,
hyperboles or
personification) at least
once. The story/letter
includes math
vocabulary terms and
reflects the student’s
accurate understanding
of probability. In the
story the main
character is well
developed. The plot
includes several
important events, a
climax, and resolution.
My story/letter has
many grammatical
and spelling errors.
My story/letter has
some grammatical
and spelling
errors.
The story
includes one
main character.
The plot includes
several important
events, a climax,
and resolution.
My story/letter
has a few
grammatical and
spelling errors.
My story/letter is free of
grammatical and
spelling errors.