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Algebra 2 | Unit G: Probability and Statistics
Unit Overview
Common Core State Standards
Content Standards
Major Focus: Students will understand intermediate probability ideas having to do leading up to conditional
probability and using probability models. Students will also understand the language of statistics leading up
to the creation of a survey/experiment/observational study and the normal curve.
Tasks:
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Determine if events A and B are independent by multiplying their probabilities.
Construct two-way frequency tables and use them to decide if events are independent.
Use the addition rule P(A or B) = P(A) + P(B) – P(A and B)
Recognize the differences between sample surveys, experiments and observational studies.
Use data to estimate a population mean or proportion and develop a margin of error using simulation models.
Use the mean and standard deviation of a set to fit it in a normal distribution curve and to estimate
population percentages.
Textbook Resources
Tasks: Pearson Prentice Hall Algebra 2 copyright 2011
Sections: CC12, CC13, CC14, CC15, CC16, CC17, CC18,
CC19, CC20, CC21
CC-12: Theoretical and Experimental Probability
CC-13: Probability of Compound Events
CC-14: Probability Distributions
CC-15: Conditional Probability
CC-16: Probability Models
CC-17: Standard Deviation
CC-18: Samples and Surveys
CC-19: Normal Distributions
CC-20: Margin Of Error
CC-21: Drawing Conclusions from Samples
Honors Additional Sections: CC-12H (Combinations and
Permutations)
Mathematics Formative Assessment System Tasks
The system includes tasks or problems that teachers can
implement with their students, and rubrics that help the
teacher interpret students' responses. Teachers using
MFAS ask students to perform mathematical tasks,
explain their reasoning, and justify their solutions.
Rubrics for interpreting and evaluating student responses
are included so that teachers can differentiate instruction
based on students' strategies instead of relying solely on
correct or incorrect answers. The objective is to
understand student thinking so that teaching can be
adapted to improve student achievement of
mathematical goals related to the standards. Like all
formative assessment, MFAS is a process rather than a
test. Research suggests that well-designed and
implemented formative assessment is an effective
strategy for enhancing student learning.
http://www.cpalms.org/resource/mfas.aspx
This a working document that will continue to be revised and improved taking your feedback into consideration.
MAFS.912.S-CP.1.1
MAFS.912.S-CP.1.2
MAFS.912.S-CP.1.3
MAFS.912.S-CP.1.4
MAFS.912.S-CP.1.5
MAFS.912.S-CP.2.6
MAFS.912.S-CP.2.7
MAFS.912.S-IC.1.1
MAFS.912.S-IC.1.2
MAFS.912.S-IC.2.3
MAFS.912.S-IC.2.4
MAFS.912.S-IC.2.5
MAFS.912.S-IC.2.6
MAFS.912.S-ID.1.4
Standards for
Mathematical Practice
MAFS.K12.MP.1.1
MAFS.K12.MP.2.1
MAFS.K12.MP.3.1
Additional Honors
Content Standards
MAFS.912.S-CP.2.8
MAFS.912.S-CP.2.9
MAFS.912.S-MD.2.6
MAFS.912.S-MD.2.7
Other Resources
Kuta Software
Purple Math
Algebra Nation
Online Graphing Calculator
National Library of Virtual Manipulatives
Geogebra
Virtual Nerd
YouTube
Khan Academy—Math
Engage NY
TI Nspired Resource Center for Educators
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for
measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1,
“What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps
students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the
academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and
declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
4.0
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these
standards. Examples:

3.0
Design and conduct a sample survey/experiment/observational study, interpret the results, and present the findings.
The Student will:
 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”). (MAFS.912.S-CP.1.1)
 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. (MAFS.912.S-CP.1.2)
 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. (MAFS.912.S-CP.1.3)
 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. 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. (MAFS.912.S-CP.1.4)
 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. (MAFS.912.S-CP.1.5)
 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.
(MAFS.912.S-CP.2.6)
 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. (MAFS.912.S-CP.2.7)
 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
(MAFS.912.S-IC.1.1)
 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? (MAFS.912.S-IC.1.2)
 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
(MAFS.912.S-IC.2.3)
 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random
sampling. (MAFS.912.S-IC.2.4)
 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics
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2.0
(MAFS.912.S-IC.2.5)
Evaluate reports based on data. (MAFS.912.S-IC.2.6)
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data
sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
(MAFS.912.S-ID.1.4)
Honors
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. (MAFS.912.S-CP.2.8)
Use permutations and combinations to compute probabilities of compound events and solve problems. (MAFS.912.S-CP.2.9)
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (MAFS.912.S-MD.2.6)
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
(MAFS.912.S-MD.2.7)
The student will recognize or recall specific vocabulary, such as:
Probability, events, set, subset, sample space, complementary events, independent events, conditional probability, two-way frequency table, Addition
Rule, statistics, population, sample, sample survey, experiment, observational study, mean, population mean, margin of error, standard deviation, normal
distribution
The student will perform basic processes, such as:
 Utilize a sample space; find the complement of an event
 Calculate the probability of two independent events
 Find probability of A given B
 Construct a frequency table
 Apply conditional probability in an everyday situation
 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.
 Application of the Addition Rule
 Infer about population parameters based on a random sample from the population
 Know how to create a simulation
 Compare/contrast sample surveys, experiments, and observational studies
 Determine the population mean
 Compare/contrast the results from two experimental treatments
 Evaluate reports based on data
1.0
With help, partial success at 2.0 content but not at score 3.0 content
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question
#1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what
student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional
scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are
essential for mastery.
Domain: Making Inferences and Justifying Conclusions
Cluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. (Major)
Standard: MAFS.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to
each.
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.
Understand that in statistics, there are various methods used to explore an idea and randomization must be used to eliminate bias.
Know
Declarative knowledge: Facts, vocab., information
Do
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.
Determine if data is a survey, an experiment or an observational study.
Sample survey, experiment, observational
study, randomization, sampling techniques,
stratified sampling, systematic sampling,
cluster sampling, convenient sampling,
simple random sampling, simulation, random
number generator, census
Identify the type of sampling used.
Describe why data is random.
Identify problems with data (being random or not, is it faulty data due to pitfalls, sample is too broad/narrow,
etc.)
Choose and explain the best method to collect random data for a given purpose
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
Data, randomization, measures of central tendency, percentages,
Vocabulary: sample survey, experiment, observational study, randomization, sampling techniques, stratified sampling, systematic sampling, cluster sampling,
convenient sampling, simple random sampling, simulation, random number generator, census
Skills: data collection
Learning Goals: To recognize the purposes of and differences among sample surveys, experiments, and observational studies; and to explain how randomization relates to
each.
Moving Beyond: Students will examine reasonableness of data, draw conclusions from data and calculate correlation factors; they will also represent the data using different
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics
models.
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of
knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown
below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to
further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1,
“Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the
actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level,
not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
MAFS.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Learning Progression
Score
4.0
3.5

2.5
Create an appropriate survey, experiment, or study and carry out the process
using sampling and randomization concerning the following question:
What type of new food should be added in the school cafeteria?
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.

3.0
I can… make a random sample for a specific purpose in the real world
and interpret the data.
Sample Tasks
I can… recognize the purposes and differences among sample surveys,
experiments, and observational studies; AND explain how
randomization relates to each.
Which data technique (sampling, experiment, simulation, or census) for gathering data
do you think was used in the following studies?
a) An analysis of a sample of 31000 patients from New York Hospitals suggests
that the poor and the elderly sue for malpractice at 1/5 the rate of wealthier
patients (Journal of American Medical Association) ANS: sampling
b) The effects of wind sheer on airplanes during both landing and takeoff are
studied by using complex computer programs that mimic actual flight ANS:
simulation
c) A study of football scores attained through touchdowns and field goals was
conducted by the National Football League to determine whether field goals
account for more scoring evens than touchdowns (USA Today) ANS: census
d) An Australian study included 588 men and women who had already had
some pre cancerous skin lesions. Half got a skin cream containing a sunscreen
with a sun protection factor of 17; half got an inactive cream. After 7 months,
those using the sunscreen with the sun protection had fewer new pre
cancerous skin lesions. (New England Journal of Medicine) ANS: experiment
- Understandable Statistics, Brase and Brase page 27 #3
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics

2.0
I can… recognize some purposes and some differences among sample
surveys, experiments, and observational studies; or I can explain how
randomization relates to each with some help.
Find a newspaper or web site article that uses statistics. Are the data from the
entire population or just for a sample? What are the variables?
- Understandable Statistics, Brase and Brase page 29 #1
1.0
I need prompting and/or support to complete 2.0 tasks.
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply
demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them
as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and
common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?”
and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New
Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
CCSS Mathematical Content Standard(s)
Design Question 1; Element 1
CCSS Mathematical Practice(s)
Design Question 1; Element 1
Marzano’s Taxonomy
Teacher Notes
MAFS.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each.
MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.
Level 3—Analysis: “Classifying”
Students may be inclined to answer these tasks in a sentence or two—make sure that they explain the situation fully, citing
the original situation given.
For students who are extending, have them create a hypothesis for the experiment and write about why they think a
certain outcome could be determined.
For students who are struggling, provide definitions of experiment, observational study, and randomization with examples.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit G: Probability and Statistics
A student interested in comparing the effect of different types of music on short-term memory conducted the following
study: 80 volunteers were randomly assigned to one of two groups. The first group was given five minutes to memorize a
list of words while listening to rap music. The second group was given the same task while listening to classical music. The
number of words correctly recalled by each individual was then measured, and the results for the two groups were
compared.
Task
Design Question 3; Element 17
a.
b.
A. Is this an experiment or an observational study? Justify your answer.
B. In the context of this study, explain why it is important that the subjects were randomly assigned to the two
experimental groups (rap music and classical music).
*Taken from Illustrative Mathematics.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015