Instructional Unit
Part I: Unit Information
Unit Title: Probability
Grade Level: 9-10
Time Frame: 10 days
Prerequisite Knowledge (where this unit sits in a scope and sequence):
N-Q.2: Define appropriate quantities for the purpose of descriptive modeling.
S-ID.1: Represent data with plots on the real number line (dot plots, histograms,
and box plots).
S-ID.5: Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data.
S-ID.6: Represent data on two quantitative variables on a scatter plot, and
describe how the variables are related.
Unit Overview:
The purpose of this unit is to build on probability concepts that began in the
middle grades, students use the languages of set theory to expand their ability to
compute and interpret theoretical and experimental probabilities for compound
events, attending to mutually exclusive events, independent events, and
conditional probability. Students should make use of geometric probability
models wherever possible. They use probability to make informed decisions.
Essential Question:
How do I understand independence and conditional probability and use them to
interpret data?
CCSS Mathematical Content Standards Addressed:
S.CP.1 Describe events as subsets of a sample space (the set of outcomes)
using characteristics (or categories) of the outcomes, or as unions, intersections,
or complements of other events (“or,” “and,” “not”).
S.CP.2 Understand that two events A and B are independent if the probability of
A and B occurring together is the product of their probabilities, and use this
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characterization to determine if they are independent.
S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B),
and interpret independence of A and B as saying that the conditional probability
of A given B is the same as the probability of A, and the conditional probability of
B given A is the same as the probability of B.
S.CP.4 Construct and interpret two‐way frequency tables of data when two
categories are associated with each object being classified. Use the two‐way
table as a sample space to decide if events are independent and to approximate
conditional probabilities.
S.CP.6 Find the conditional probability of A given B as the fraction of B’s
outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and
interpret the answer in terms of the model.
S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model,
P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the
model.
S.CP.9 (+) Use permutations and combinations to compute probabilities of
compound events and solve problems.
CCSS Mathematical Practice Standards Addressed:
*While all eight mathematical practices may not be used in the culminating task, they will all be used by
students at some point within the overall unit of instruction.
MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.
MP3: Construct viable arguments and critique the reasoning of others.
MP4: Model with mathematics.
MP6: Attend to precision.
MP8: Look for and express regularity in repeated reasoning.
Concepts





Conditional probability
Union of events
Combination,
Permutation,
Compound events,
Skills/Performances
• Understand independence and
conditional probability and use them to
interpret data.
• Use the rules of probability to compute
probabilities of compound events in a
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
Basic counting principal
uniform probability model.
• Use probability to evaluate outcomes of
decisions.
Part II: Evidence of Understanding
Culminating Performance Task: Friends You Can Count On
Practice Standards Addressed:
CCSS Mathematical Standards Addressed:
S.CP.1 Is the student able identify the subset of the sample space?
S.CP.2 Is the student able to determine if the 2 events are dependent or
independent?
Is the student able to find the probability of an event?
Is the student able to find the probability of multiple events?
S.CP.3 Is the student able to find conditional probabilities for two events?
S.CP.6 Is the student able to find probabilities using total outcomes?
Is the student able to find conditional probabilities by using subsets of
the sample space as a total?
S.CP.7 Is the student able to find probabilities for unions of events by adding
individual probabilities and subtracting overlaps?
S.CP.8 Is the student able to know and use the general multiplication rule?
S.CP.9 Is the student able determine the difference between combinations and
permutations?
Is the student able to use combinations and permutations to find
probabilities of events?
CCSS Mathematical Practices Addressed:
MP1: Make sense of problems and persevere in solving them.
Is the student able to read and digest the problem to understand what is
being asked of them?
Is the student able to take the information from each task to answer each
subsequent question?
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MP2: Reason abstractly and quantitatively.
Is the student able to express the problem symbolically?
Is the student able to apply the probability rules to other situations?
MP3: Construct viable arguments and critique the reasoning of others.
Is the student able to provide justification to support reasoning for
improving their chances of winning a pizza party?
MP4: Model with mathematics.
Is the student able to apply the principles of probability to daily life
situations?
Is the student able to use mathematical formulas, diagrams, and
connections to justify results.
MP6: Attend to precision.
Is the student able to clearly articulate mathematical reasoning behind
their solution?
MP8: Look for and express regularity in repeated reasoning.
Is the student able to maintain oversight of the process of solving a
problem, while attending to the details.
Is the student able to continually evaluate the reasonableness of
intermediate results.
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Interim/Formative Performance Tasks
Pre-Assessment: N/A
Interim Performance Task: (Middle of Unit)
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Performance Task: (End of Unit)
Friends You Can Count On
Your school has a lunchtime spirit rally each month. To encourage students to attend the
rally, there is a drawing for a pizza lunch with you and your five friends. You and your
friends have decided that no matter whose ticket is selected, the six of you will choose
each other to share in the pizza party. You estimate that about 150 students attend the
rally.
What is the probability that you personally win the lunch for your friends?
What is the probability that you will get to attend the pizza lunch this month?
What are the chances that none of you get a pizza lunch this month? Show how you
found your answers.
What are the chances that you and your friends will win three pizza lunches three months
in a row? Explain your solution.
In your history class, you are studying exploration to the New World. Your teacher has
planned to celebrate Columbus Day by awarding a pizza lunch for two to the best essay
writer on the life and voyages of the explorer. You and your best friend are in the same
class and have agreed to share lunch with each other if either essay is selected. Suppose
all of the 28 students have an equal chance of having their essay selected, what are your
chances of having a free pizza lunch during the month of October? Explain your method.
Explain how you might improve your chances of winning a free pizza lunch. Use
mathematics in your explanation.
Part III: Instructional Pathway
Learning Map
Timeframe
Learning
Objectives
Week 1:
I can describe
events.
I can identify
independent and
dependent events.
I can find
probabilities and
determine
independence for
events.
Evidence of
Performance
Interim Performance
Task I (Mid Unit)
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Week 2:
I can find conditional
probabilities using
basic counting
principals.
Performance Task
(End of Unit)
I can find
probabilities for
unions of events
with the addition rule
of
probability.
I can use the
general
multiplication rule for
probabilities.
I can use
combinations and
permutations to find
probabilities for
compound events.
Part IV: Scaffolding
Students need many opportunities to state comparisons and define these using
Challenges and Barriers
Content / Concept
Barrier
Scaffold
Universal Design for Learning
Representation
Action and
Engagement
Expression
 Use pictures in situations
 Manipulati  Have students create their
ves
own
 Have tactile manipulatives
available to model
 Graphic
 Reinforce classroom
comparative situations
organizers
norms
 Use color to highlight
 Sentence  Ask students to draw
comparison words in
starters
diagrams
situations
and
 Do not always ask for
language
 Have students model
answers
objectives
comparisons
 Culture of
a
“complete
answer”
Language
Language Objectives:
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Sentence Frames:
Academic Language:
Part V: Resources
Texts:
1. http://map.mathshell.org/materials/index.php
2. http://www.insidemathematics.org/index.php/standard-1
Instructional Unit
Culminating Task
Rubric for Culminating Task
Criteria of
Standard
S-CP.1 Describe
events as subsets of
a sample space (the
set of outcomes)
using
characteristics (or
categories) of the
outcomes, or as
unions,
intersections, or
complements of
other events (“or,”
“and,” “not”).
S-CP.2 Understand
that two events A and
B are independent if
the probability of A
and B occurring
together is the
product of their
probabilities, and use
this characterization
to determine if they
are independent.
S-CP.3 Understand
the conditional
probability of A given
B as P(A and B)/P(B),
and interpret
independence of A
and B as saying that
the conditional
probability of A given
B is the same as the
probability of A, and
the conditional
probability of B given
A is the same as the
probability of B.
Friends You Can Count On Rubric
Evidence of Meeting
Evidence of
Standard
Approaching Standard
Accurately identify the
Identifies some subsets
subsets of the sample
of the sample space.
space.
Evidence of Below
Standard
Cannot identify any
subsets of the sample
space.
Determines if the events
are dependent or
independent and
accurately determines
the probability of those
events.
Find the individual
probability of one event
but not the other.
Or they are unable to
determine if they are
independent from their
results.
Cannot state if the events
are dependent or
independent and cannot
determine the
probabilities.
The students find the
conditional probability.
The students find the
individual probabilities
but not the probability of
both events.
The students find no
probabilities.
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S-CP.6 Find the
conditional
probability of A
given B as the
fraction of B’s
outcomes that also
belong to A, and
interpret the answer
in terms of the
model.
S-CP.7 Apply the
Addition Rule, P(A
or B) = P(A) + P(B)
– P(A and B), and
interpret the answer
in terms of the
model.
Identify the sample
space and a subset of the
sample space and use it
to calculate conditional
probability.
They identify the correct
sample space and/or
subset but do not
determine the correct
probability.
Does not use the correct
sample space and subset
in calculating the
probability.
The student shows all
elements needed to
calculate probabilities
for unions of events by
adding individual
probabilities and
subtracting overlaps.
The student shows some
elements needed to
calculate probabilities
for unions of events by
adding individual
probabilities and
subtracting overlaps.
The student does not
show elements needed to
calculate probabilities
for unions of events by
adding individual
probabilities and
subtracting overlaps.
S-CP.8 Apply the
general
Multiplication Rule
in a uniform
probability model,
P(A and B) =
P(A)P(B|A) =
P(B)P(A|B), and
interpret the answer
in terms of the
model.
S-CP.9 Use
permutations and
combinations to
compute
probabilities of
compound events
and solve problems.
Practices
P1. Make sense of
problems and
persevere in
solving them.
The student is able to
correctly use the general
multiplication rule.
The student is able to
display some knowledge
of the general
multiplication rule, but
does not apply the
concept correctly.
The student does not
display knowledge of the
general multiplication
rule.
The student is able to
correctly identify the
combination/permutation
rule. The student is able
to relate the combination
rule to the multiplication
rule.
Supports each claim
with mathematics
and forms a
conclusion
The student is able to
correctly identify the
combination/permutation
rule. The student is not
able to relate the
combination rule to the
multiplication rule.
Supports some
claims with
mathematics but
does not support
all claims.
Student does not
come to a
conclusion.
The student is not able to
correctly identify the
combination/permutation
rule. The student is not
able to relate the
combination rule to the
multiplication rule.
Uses the same
strategy to compare all
claims regardless of
whether the strategy
supports the
mathematics
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P2. Reason
abstractly and
quantitatively.
Sets up each probability
accurately.
Some probabilities are
set up properly .
Uses probabilities that
do not represent the
problem.
P3. Construct
viable arguments
and critique the
reasoning of
others.
P4. Model with
mathematics.
Provides a justification
to find a way to improve
the chances of winning.
Provides some
mathematical reason for
their conclusions.
Offers no support for
their conclusions.
Uses mathematical
formulas, diagrams
and connections to
support their claim
Uses procedures
to support claims.
Uses procedures
inaccurately and does
not model with
mathematics
P6. Attend to
precision
Uses academic
language and
mathematics to
clearly articulate
their claim. There
may be minor
arithmetic errors but
the overall claim is
justified.
Offers a
statement to
defend a point of
view but does not
connect all claims
to mathematics or
support all points
of view
Offers a statement that
does not align with the
mathematics presented
or the problem. Does
not support all claims
P8. Look for and
express regularity
in repeated
reasoning.
The student is
able to maintain
oversight Is the
student able to
maintain
oversight of the
process of
solving a
problem, while
attending to the
details.
Is the student
able to
continually
evaluate the
reasonableness of
intermediate
results.
The student is
able to maintain
some oversight Is
the student able
to maintain
oversight of the
process of
solving a
problem, while
attending to the
details.
The student is
not able to
maintain
oversight of the
process of
solving a
problem.
.
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