Download MATH II Unit 9 STATISTICS

Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
Enduring understanding (Big Idea):
Students will be able to use probability practices to solve real-life statistics problems.
Essential Questions:
1. What is the difference between a permutation and a combination?
2. What is the difference between theoretical and experimental probability?
3. How do independence and dependence of events affect the computation of probabilities in two-stage experiments?
4. How is probability used in real-world settings?
BY THE END OF THIS UNIT:
Students will know…
Students will be able to:
 The difference between combination and
 Determine if theoretical or experimental probability
permutation problems.
is the best course of action to solve a problem.
 The difference between independent and
 Use dependent and independent computations to
dependent probabilities.
solve probabilities
Vocabulary:
Population, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study,
controlled experiment, survey, Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally
likely outcomes, outcome, event, complement of an event, odds, conditional probability, relative frequency, probability distribution,
uniform distribution, cumulative frequency, cumulative probability, two-way frequency table, Compound event, Independent and
Dependent event, mutually exclusive events, overlapping events, Fundamental Counting Principal, permutation, combination, n
factorial
Unit Resources:
Performance Task:
Pearon Alg 2 probability performance tasks.pdf
probability activity.pdf
Project: l21_probability_statements_beta_complete.pdf
Test Specification Weights for the Common Exams in
Common Core Math II:
Standard
S-IC
S-CP
%
Constructed
Response
0%
0%
%
MultipleChoice
7% 10%
Category
Percentage
(Statistics)
7% - 10%
Suggested Order/Pacing:
Geometric Probability: Section 10.8
Theoretical and Experimental Probability: CC-21,
Algebra 1BK: Section 12.7, CB 12.7, ER 12.7
Algebra 2 BK: Section 11.2
Probability Distribution and Frequency Tables: CC-22
Algebra 2 BK: CB 11.3
Permutations and Combinations: CC-23,
Algebra 1 BK: Section 12.6, ER 12.6,
Algebra 2 BK: Section 11.1
Compound Probability and Probability of Multiple Events: CC-24, and
Algebra 1 BK: Section 12.8, ER 12.8
Algebra 2 BK: Section 11.3
Contingency Tables: CC-25
Conditional Probability: CC-26,
Algebra 1 BK: CB 12.8 and Algebra 2 BK: Section 11.4
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving
them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the
reasoning of others
4. Model with mathematics
6. Attend to precision
CCSS-M Included:
S.IC.2, S.IC.6, S.CP.1 – S.CP.9
Abbreviation Key:
CC – Common Core Additional Lessons found in the
Pearson online materials.
CB- Concept Bytes found in between lessons in the Pearson
textbook.
ER – Enrichment worksheets found in teacher resources per
chapter.
Merge information from Geometry, Algebra 1, and
Algebra 2 Books to complete this unit.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 1
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand and evaluate random processes underlying statistical experiments.
Standard S-IC.2 Decide if a specified model is consistent with results from a given data generating process, e.g., using
simulation.
For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you
to question the model?
Concepts and Skills to Master




Find the experimental probability of an event
Find the theoretical probability of an event
Use of a simulation to model an event
Make decisions about probability based on simulated events
SUPPORTS FOR TEACHERS
Critical Background Knowledge:



Event, possibilities, successes
Sample space, trials, outcomes
Cards in a deck, faces of a die
Academic Vocabulary:
Experimental probability, simulation, sample space, equally likely outcomes, theoretical probability
Suggested Instructional Strategies:
Starting Resources:
 Utilized the TI-84 Probability Simulation App
Algebra 1 Textbook Correlation:
 Remind students that they did simple probability in middle school
CB 12.7


Use a coin toss experiment to introduce the concepts but quickly move to
simulations
Use your calculator to do the simulations like coin toss and random number
generator
Algebra 2 Textbook Correlation:
Section 11.2, ER 11.2, CB 11.3
NCDPI Unpacking:
What does this standard mean that a student will know and be able to do?
1) Explain how well and why a sample represents the variable of interest from a population.
2) Demonstrate understanding of the different kinds of sampling methods.
3) Design simulations of random sampling: assign digits in appropriate proportions for
events, carry out the simulation using random number generators and random number tables
and explain the outcomes in context of the population and the known proportions. Use datagenerating processes such as simulations to evaluate the validity of a statistical model.
Additional note from DPI for Level II:
Ex. Jack rolls a 6 sided die 15 times and gets the following results:
4, 6, 1, 3, 6, 6, 2, 5, 6, 5, 4, 1, 6, 3, 2
Based on these results, is Jack rolling a fair die? Justify your answer using a simulation.
Sample Assessment Tasks
Skill-based task:
On a multiple choice test, each item has 4 choices, but only one choice
is correct. How can you simulate guessing the answers? Based on
your simulation of at least 20 trials, what is the probability that you will
pass the test by guessing at least 6 of 10 answers correctly?
Problem Task:
On a multiple-choice test, each item has 4 choices, but only
one choice is correct. How can you simulate guessing the
answer? What is the probability that you will pass the test
by guessing at least 6 of 10 answers correctly?
Teacher Created Argumentation Tasks (W1-MP3&6): Assume that an event is neither certain nor impossible. Then the odds in
favor of the event is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. Would you rather play a
game in which your odds of winning are ½, or a game in which your probability of winning is ½? Sate your answer, support your
answer with relevant data and be prepared to defend your position.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 2
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Standard: S-IC.6 Evaluate reports based on data.
Concepts and Skills to Master:
 Evaluate reports based on data
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Academic Vocabulary:
Population, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational
study, controlled experiment, survey
Suggested Instructional Strategies:
Starting Resources:
What does this standard mean that a student will know
Algebra 2 Textbook Correlation:
and be able to do?
Section 11.7
Read and explain in context data from outside reports. Evaluate
reports based on data on multiple aspects (e.g. experimental
design, controlling for lurking variables, representativeness of
samples, choice of summary statistics, etc.)
Sample Assessment Tasks
Skill-based task:
A survey asks, “Aren’t handmade gifts always better than
tacky purchased gifts?” Does this survey question have any
bias? Explain.
Problem Task:
What sampling method could you use to find the percent of
adults in your community who support building more nuclear
power plants? What is an example of a survey question that
is likely to yield unbiased information?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 3
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand independence and conditional probability and use them to interpret data.
Standard: S.CP.1 Describe events and subsets of a sample space using characteristics of the outcomes, or as unions,
intersections, and complements of other events ("or," "and," "not.")
Concepts and Skills to Master:
 The probability of an impossible event is 0, (0%), the probability of a certain event is 1 (100%), and all other
probabilities are between 0 and 1.
 The probability that an event will occur + the probability it will not occur = 1.
 Define a sample space and events within the sample space. Identify subsets from sample space given defined
events, including unions, intersections and complements of events.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Find the area of
polygons and circles.
Academic Vocabulary:
Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally likely outcomes,
outcome, event, complement of an event, odds
Suggested Instructional Strategies:
Starting Resources:
 Use Venn diagrams to remind students how to
Geometry Textbook Correlation:
determine the difference between “and” and “or”.
10.8, CC.21
NCDPI Unpacking:
What does this standard mean that a student will know
and be able to do?
1) Define the sample space for a given situation.
Additional note from DPI for Level II:
Ex. What is the sample space for rolling a die?
Ex. What is the sample space for randomly selecting one
letter from the word MATHEMATICS?
2) Describe an event in terms of categories or
characteristics of the outcomes in the sample
space.
Additional note from DPI for Level II:
Ex. Describe different subsets of outcomes for rolling a die
using a single category or characteristic.
3) Describe an event as the union, intersection, or
complement of other events.
Additional note from DPI for Level II:
Ex. Describe the following subset of outcomes for choosing
one card from a standard deck of cards as the intersection
of two events: {queen of hearts, queen of diamonds}.
Sample Assessment Tasks
Skill-based task:
If the probability an event will occur is 74%, what is the
probability it will not occur?
Algebra 1 Textbook Correlation:
Section 12.7
Algebra 2 Textbook Correlation:
Section 11.2, ER 11.2
http://www.shodor.org Interactive Venn Diagram Shape
Sorter
Problem Task:
What is the probability that a quarterback will complete his
next pass if he has completed 30 of his last 40 passes?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 4
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand independence and conditional probability and use them to interpret data.
Standard S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is
the products of their probabilities, and use that characterization to determine if they are independent.
Concepts and Skills to Master
 Explain properties of Independence and Conditional Probabilities in context and simple English.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Understand basic properties of probability. (7.SP.5)
 Approximate probabilities of chance events through experiment. (7.SP.6)
 Use Venn diagrams (II.4.S.CP.1) and two-way frequency tables. (I.S.ID.5)
 (A ∩ B) is the equivalent of the probability of event A and event B occurring together. (II.4.S.CP.1)
Academic Vocabulary:
Conditional probability,
Suggested Instructional Strategies:
Starting Resources:
Geometry Textbook Correlation:
NCDPI Unpacking:
CC-26
What does this standard mean that a student will know
and be able to do?
Algebra 1 Textbook Correlation:
1) Understand that two events A and B are
CB 12.8
independent if and only if P(A and B)= 𝑃(𝐴) ∙ 𝑃(𝐵).
Algebra 2 Textbook Correlation:
2) Determine whether two events are independent
Section 11.4
using the Multiplication Rule (stated above).
3) Explain properties of Independence and Conditional
Probabilities in context and simple English.
Additional note from DPI for Level II:
Ex. For the situation of drawing a card from a standard deck
of cards, consider the two events of “draw a diamond” and
“draw an ace.” Determine if these two events are
independent.
Ex. Create and prove two events are independent from
drawing a card from a standard deck.
Sample Assessment Tasks
Skill-based task:
C and D are independent events, P  C  
P  D 
1
. What is P(C and D)?
3
2
, and
7
Problem Task:
Suppose you randomly select a shape
from this circle. What is the probability
that the shape is black and has five
points?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 5
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand independence and conditional probability and use them to interpret data.
Standard 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 P(A) and the conditional probability of B given
A is the same as P(B).
Concepts and Skills to Master:
 The probability that an event B will occur given that another event, A, has already occurred.
 Conditional probability occurs when two events are dependent.
 Define and calculate conditional probabilities. Use the Multiplication Principal to decide if two events are independent and
to calculate conditional probabilities.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
Academic Vocabulary:
Conditional Probability
Suggested Instructional Strategies:
Starting Resources:
Use Venn diagrams to explore and compute conditional probabilities. Geometry Textbook Correlation:
CC-26
NCDPI Unpacking:
What does this standard mean that a student will know and be
Algebra 1 Textbook Correlation:
able to do?
CB 12.8
1) Understand that the conditional probability of event A given event
B has already happened is given by the formula: 𝑷(𝑨|𝑩) =
𝑷(𝑨 𝒂𝒏𝒅 𝑩)
𝑷(𝑩)
Understand that two events A and B are independent if and only
if 𝑷(𝑨|𝑩) = 𝑷(𝑨)𝒂𝒏𝒅 𝑷(𝑩|𝑨) = 𝑷(𝑩). In other words, the
fact that one of the events happened does not change the
probability of the other event happening.
3) Prove that two events A and B are independent by showing that
𝑷(𝑨|𝑩) = 𝑷(𝑨)𝒂𝒏𝒅 𝑷(𝑩|𝑨) = 𝑷(𝑩).
Additional note from DPI for Level II:
Ex. For the situation of drawing a card from a standard deck of cards,
consider the two events of “draw a spade” and “draw a king.” Prove that
these two events are independent.
Ex. Create and prove two events are dependent from drawing a card from
a standard deck.
Algebra 2 Textbook Correlation:
Section 11.4
2)
Sample Assessment Tasks
Skill-based task:
Given the following Venn
diagram, determine whether
events A and B are
independent.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 6
Cut the Knot – Conditional Probability and
Independent Events:
http://www.cut-theknot.org/Curriculum/Probability/ConditionalProbabilit
y.shtml
Texas A&M – Conditional Probability Applet:
http://www.stat.tamu.edu/~west/applets/Venn1.html
Problem Task:
A box contains 10 blue cubes, 5 red cubes, 5
blue marbles and 10 red marbles. You
randomly pick a blue shape from the box.
What is the probability you picked a cube?
ANS: 67%
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand independence and conditional probability and use them to interpret data.
Standard S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each
object being classified. Use the table as a sample space to decide if events are independent and to approximate conditional
probabilities.
For example, collect data from a random sample of students in your school on their favorite subject among math, science,
and English. Estimate the probability that a randomly selected student from your school will favor science given that the
student is in tenth grade. Do the same for other subjects and compare the results.
Concepts and Skills to Master:
 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.
 Use a two-way table as a sample space to decide if events are independent
 Use a two-way table to approximate conditional probabilities.
SUPPORTS FOR TEACHERS
Critical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
Academic Vocabulary:
Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally likely outcomes, outcome,
event, complement of an event, conditional probability, relative frequency, probability distribution, uniform distribution, cumulative
frequency, cumulative probability, two-way frequency table
Suggested Instructional Strategies:
NCDPI Unpacking:
What does this standard mean that a student will know and be able to do?
Starting Resources:
Geometry Textbook Correlation:
CC.21,CC.22, CC.25
1.Construct and interpret a two-way frequency table from a set of data on two categorical variables.
Additional note from DPI for Level II:
Ex.Make a two-way frequency table for the following set of data. Use the following age groups:
3-5,6-8,9-11,12-14,15-17.
Algebra 1 Textbook Correlation:
Section 12.7 (see next page for
more resources.)
Algebra 2 Textbook Correlation:
CB 11.3, Section 11. 4
2.Determine if two categorical variables are independent by analyzing a two-way table of data
collected on the two variables.
3.Calculate conditional probabilities based on two categorical variables from a table and interpret in
context.
Additional note from DPI for Level II:
Ex. Use the frequency table to answer the following questions.
a. Given that a league member is female, how likely is she to be 9-11 years old?
b. What is the probability that a league member is aged 9-11?
c. Given that a league member is aged 9-11, what is the probability that a member of this league is
a female?
d. What is the probability that a league member is female?
e. Are the events “9-11 years old” and “female” independent? Justify your answer.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 7
Source for problem task:
http://wiki.warren.kyschools.us/gr
oups/wcpscommoncorestandards
/wiki/45424/images/75b78.png#6
97x251
Course Name: Geometry/Math II
Sample Assessment Tasks
Skill-based task:
Unit 9
Unit Title: Probability and Statistics
Problem Task:
Use the table below to determine if being a girl and never having a part-time job are
independent or dependent events. Then approximate the probability that a student is
a girl, given that the student never had a part-time job.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 8
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Understand independence and conditional probability and use them to interpret data.
Standard S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language
and everyday situations.
For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have
lung cancer.
Concepts and Skills to Master:
 Recognize the concepts of conditional probability and independence in everyday language and everyday situations.
 Explain the concepts of conditional probability and independence in everyday language and everyday situations.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
Academic Vocabulary:
relative frequency, probability distribution, uniform distribution, cumulative frequency, cumulative probability, two-way
frequency table, conditional probability
Suggested Instructional Strategies:
Resources:
 Give an example of a situation where conditional probability
Geometry Textbook Correlation:
would be used. Explain why conditional probability applies to a
CC.22, CC.26
situation.
 Give an example of two independent events. What constitutes the Algebra 1 Textbook Correlation:
independence of two events?
CB 12.8
Instructional Expectations
In both pathways, the expectation in Geometry and CCSS Mathematics II is to
build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop
understanding of conditional probability and independence.
What does this standard mean that a student will know and be able to do?
Given an everyday situation describing two events, use the context to construct
an argument as to whether the events are independent or dependent.
Algebra 2 Textbook Correlation:
Section 11.3, 11.4
Read more: Examples of Real Life Probability |
eHow.com
http://www.ehow.com/list_7719506_real-lifeprobability-examples.html#ixzz1wvNUV1st
Additional note from DPI for Level II:
HONORS:
Ex. Felix is a good chess player and a good math student. Do you think
http://myweb.cableone.net/surgett/nmmi/webq
that the events “being good at playing chess” and “being a good math
uests/probability/ research project for real
student” are independent or dependent? Justify your answer.
life applications of probability.
Ex. Juanita flipped a coin 10 times and got the following results: T, H, T,
T, H, H, H, H, H, H. Her math partner
Harold thinks that the next flip is going to result in tails because there
have been so many heads in a row. Do you agree? Explain why or why
not.
Sample Assessment Tasks
Skill-based task:
Problem Task:
If you are using a game spinner with four sections -- red, blue, green and yellow -Have students find and interpret
you have a 25 percent chance of landing on red, since one of the four sections is
probability statements in media.
red. What is the probability that you're going to roll one die and get an even
number? You have a 50 percent chance, since three of the six numbers on a die
are even.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 9
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model.
Standard S.CP.6 Find the conditional probability of A given B as the fractions of B's outcomes that also belong to A, and interpret the
answer in terms of the model.
Concepts and Skills to Master:

Find and interpret conditional probabilities using a two-way table, Venn diagram, or tree diagram.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
Find probabilities of compound events. (7.SP.8)
Summarize categorical data in two-way frequency tables. (I.4.S.ID.5)
Academic Vocabulary: Conditional Probability
Suggested Instructional Strategies:
Starting Resources:
• Make a “human Venn diagram” where the sample space is all the students in the class. Use lengths
Geometry Textbook
of rope to create three overlapping circles. Assign an event to each of the three circles, such as: ate
Correlation:
breakfast, brought a cell phone to school, and got at least 7 hours of sleep. Have students place
CC.26
themselves in the appropriate locations. Using correct probability notation, identify each of the spaces in
the Venn diagram (don’t forget to include the space outside the circles). Analyze, explore and record the
Algebra 2 Textbook
results in terms of conditional probabilities.
Correlation:
• Connect to probability models from other standards.
Section 11.4
NCDPI Unpacking:
What does this standard mean that a student will know and be able to do?
1) Understand that when finding the conditional probability of A given B, the sample space is
reduced to the possible outcomes for event B. Therefore, the probability of event A happening
is the fraction of event B’s outcomes that also belong to A.



2)
Understand that drawing without replacement produces situations involving conditional
probability.
3) Calculate conditional probabilities using the definition. Interpret the probability in context.
Additional note from DPI for Level II:
Ex. Peter has a bag of marbles. In the bag are 4 white marbles, 2 blue marbles, and 6 green marbles.
Peter randomly draws one marble, sets it aside, and then randomly draws another marble. What is the
probability of Peter drawing out two green marbles?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 10
Course Name: Geometry/Math II
Unit 9
Sample Assessment Tasks
Skill-based task:
Problem Task:
From the table, determine the probability of getting the flu, and compare that to
the probability of getting the flu given that an individual takes high doses of
vitamin C.
Placebo
Vitamin C
Total
Cold
31
17
48
Unit Title: Probability and Statistics
No cold
109
122
231
total
140
139
279
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 11
Life is like a box of chocolates. Suppose your box of
36 chocolates have some dark and some milk
chocolate, divided into cream or nutty centers. Out of
the dark chocolates, 8 have nutty centers. Out of the
milk chocolates, 6 have nutty centers. One-third of
the chocolates are dark chocolate. What is the
probability that you randomly select a chocolate with
a nutty center? Given that it has a nutty center, what
is the probability you chose a dark chocolate? Show
how you determined your answers.
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model.
Standard 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.
Concepts and Skills to Master:
 Mutually exclusive events P(A and B) = P(A) + P(B)
 Dependent events P(A or B) = P(A) + P(B) - P(A and B)
OR
 Identify two events as disjoint (mutually exclusive). Calculate probabilities using the Addition Rule.
 Interpret the probability in context.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
 Computing independent events
Academic Vocabulary:
Compound event, Independent and Dependent event, mutually exclusive events, overlapping events
Suggested Instructional Strategies:
Starting Resources:
11.3 Algebra 2 Pearson Game: The Probability Path
Geometry Textbook Correlation:
NCDPI Unpacking:
CC.24
What does this standard mean that a student will know and be able to do?
1) Understand that two events A and B are mutually exclusive if and only if P(A
Algebra 1 Textbook Correlation:
and B) = 0. In other words, mutually exclusive events cannot occur at the
Section 12.8
same time.
2) Determine whether two events are disjoint (mutually exclusive).
Additional note from DPI for Level II:
Ex. Given the situation of rolling a six-sided die, determine whether the following pairs
of events are disjoint:
a. rolling an odd number; rolling a five
b. rolling a six; rolling a prime number
c. rolling an even number; rolling a three
d. rolling a number less than 4; rolling a two
3) Given events A and B, calculate (𝐴 𝑜𝑟 𝐵) using the Addition Rule. Interpret
the probability in context.
Additional note from DPI for Level II:
Ex. Given the situation of drawing a card from a standard deck of cards, calculate the
probability of the following:
a. drawing a red card or a king
b. drawing a ten or a spade
c. drawing a four or a queen
d. drawing a black jack or a club
e. drawing a red queen or a spade
Sample Assessment Tasks
Skill-based task:
Classify each pair of events as dependent or independent.
 A month is selected at random; a number from 1 to 30 is selected at
random.
 A letter of the alphabet is selected at random; another letter is selected
at random.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 12
Algebra 2 Textbook Correlation:
Section 11.3
Problem Task:
Suppose a number from 1 to 100 is
chosen. What is the probability that a
multiple of 4 or 5 is chosen?
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model.
Standard 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.
What does this standard mean that a student will know and be able to do?
Calculate probabilities using the General Multiplication Rule. Interpret in context.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Academic Vocabulary:
Compound events, Independent and Dependent events, mutually exclusive events, overlapping events
Suggested Instructional Strategies:
Starting Resources:
Geometry Textbook Correlation:
CC-24
Algebra 1 Textbook Correlation:
Section 12.8
Algebra 2 Textbook Correlation:
Section 11.4
Sample Assessment Tasks
Skill-based task:
The probability that a car has two doors, given that it is red
is 0.6. The probability that a car has two doors and is red is
0.2. What is the probability that a car is red?
Problem Task:
Sixty percent of a company’s sales representatives have
completed training seminars. Of these, 80% have had
increased sales. Overall, 56% of the representatives
(whether trained or not) have had increased sales. Use a
tree diagram to find the probability of increased sales, given
that a representative has not been trained.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 13
Course Name: Geometry/Math II
Unit 9
Unit Title: Probability and Statistics
CORE CONTENT
Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model.
Standard S.CP.9 Use permutations and combinations to compute probabilities of compound events.
Concepts and Skills to Master:
 Use multiplication to quickly count the number of ways certain things can happen.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities
Academic Vocabulary:
Fundamental Counting Principal, permutation, combination, n factorial, Compound events, Independent and Dependent
events, mutually exclusive events, overlapping events
Suggested Instructional Strategies:
Starting Resources:
Geometry Textbook Correlation:
 Get a lunch menu from the cafeteria for the day and find the
CC.23, CC.24
number of different lunches that can be served
 Explain a deck of cards. Many students don’t know how many
Algebra 1 Textbook Correlation:
suits, colors; face cards are in a deck of cards.
Section 12.6
NCDPI Unpacking:
What does this standard mean that a student will know and be able
Algebra 2 Textbook Correlation:
to do?
Identify situations as appropriate for use of a permutation or combination Section 11.1 , ER 11.1
to calculate probabilities. Use permutations and combinations in
conjunction with other probability methods to calculate probabilities of
compound events and solve problems.
Sample Assessment Tasks
Skill-based task:
 Find 6!
 Find 8! / 3!
 Find the permutation of 5 pick 2.
 Find the combination of 6 choose 3
Problem Task:
A restaurant offers chicken, tuna or roast beef sandwiches,
sides of chips, fruit, fries or slaw, and desserts of banana
pudding or apple pie. If you can choose one sandwich, side
and dessert, how many different meals can you make?
Teacher Created Argumentation Tasks (W1-MP3&6)
Can a permutation and a combination with the same total and choices have the same solution? Justify your answer.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 14