Download Module 4 Guidance

Algebra II Module 4
Inferences and Conclusions From Data
Topic A
Probability
13 Days
Topic B
Modeling Data Distributions
12 Days
Topic C
Drawing Conclusions Using
Data From a Sample
10 Days
1
Overview
The concepts of probability and statistics covered in Grade 11 build on students’ previous work in Grades 7 and 9. Topics A and B
address standards S-CP.A.1–5 and S-CP.B.6–7, which deal primarily with probability. In Topic A, fundamental ideas from Grade 7 are
revisited and extended to allow students to build a more formal understanding of probability. More complex events are considered
(unions, intersections, complements) (S-CP.A.1). Students calculate probabilities based on two-way data tables and interpret them
in context (S-CP.A.4). They also see how to create “hypothetical 1000” two-way tables as a way of calculating probabilities.
Students are introduced to conditional probability (S-CP.A.3, S-CP.A.5), and the important concept of independence is developed (SCP.A.2, S-CP.A.5). The final lessons in this topic introduce probability rules (S-CP.B.6, S-CP.B.7).
Topic B is a short topic consisting of four lessons. This topic introduces the idea of using a smooth curve to model a data
distribution, describes properties of the normal distribution, and asks students to distinguish between data distributions for which it
would be reasonable to use a normal distribution as a model and those for which a normal distribution would not be a reasonable
model. In the final two lessons of this topic, students use tables and technology to find areas under a normal curve and interpret
these areas in the context of modeling a data distribution (S-ID.A.4).
Topics C develops students’ understanding of statistical inference and introduce different types of statistical studies (observational
studies, surveys, and experiments) (S-IC.B.3). In Topic C, students explore using data from a random sample to estimate a
population mean or a population proportion. Building on what they learned about sampling variability in Grade 7, students use
simulation to create an understanding of margin of error. Students calculate the margin of error and interpret it in context (SIC.B.4). Students also evaluate reports from the media using sample data to estimate a population mean or proportion (S-IC.B.6).
2
Lesson
Big Idea
Emphasize
Suggested
Problems
Exit
Ticket
# of Days
TOPIC A Probability
2
Students calculate probabilities given
a two-way table of data.
Students interpret probabilities in
context.
Data organized in a two-way
frequency table can be used to
calculate probabilities.
Exercises 1-14
Problem Set 1a-f
Yes
3
Students calculate conditional
probabilities given a two-way data
table or using a hypothetical 1000
two-way table.
How to calculate conditional
probability using a two way table
(not formula yet).
Exercises 1-6, 10-14
Problem Set 1, 2, 4, 6
Yes
Two events are independent when
knowing that one event has occurred
does not change the likelihood that
the second event has occurred.
Exercises 1-11
Problem Set 2-3
Yes
2
Combinations of events s using
“and,” “or,” and “not” are
represented by different regions of a
Venn Diagram.
Opening Exercise
Examples 1-3
Exercises 1-3
Problem Set 1-2
Yes
2
2
2
Students interpret probabilities,
including conditional probabilities, in
context.
4
Students use two-way tables to
determine if two events are
independent.

5
Students represent events by shading
appropriate regions in a Venn
diagram.
Students use a Venn Diagram to
calculate probabilities.
3
Lesson
6
Big Idea
Emphasize
Students use the complement rule to
calculate the probability of the
complement of an event and the
multiplication rule for independent
events to calculate the probability of
the intersection of two independent
events.
Suggested
Problems
Examples 1-3
Exercises 1-2
Problem Set 1, 3-6
Exit
Ticket
Yes
# of Days
3
Students recognize that two events 𝐴
and 𝐵 are independent if and only if
𝑃(𝐴 and 𝐵) = 𝑃(𝐴)𝑃(𝐵) and interpret
independence of two events 𝐴 and 𝐵
as meaning that the conditional
probability of 𝐴 given 𝐵 is equal to
𝑃(𝐴).
Students use the formula for
conditional probability to calculate
conditional probabilities and
interpret probabilities in context.
7
Students use the addition rule to
calculate the probability of a union of
two events.
Opening Exercise
Exercises 1-3
Examples 1-2
Problem Set 1-3, 5
4
Yes
2
Lesson
Big Idea
Emphasize
Suggested
Problems
Exit
Ticket
# of Days
TOPIC B – Modeling
Data Distributions
*S.D.
Topic B assumes that students are
familiar with standard deviation,
which students may or may not have
learned in Algebra 1. Teachers may
need to teach the concept of
standard deviation prior to lesson 8.
How to calculate mean and standard
deviation using a graphing calculator.
eMath Instruction
Algebra 1 Unit 10 Lesson 4
8
Students describe data distributions
in terms of shape, center, and
variability.
The mean of a distribution is
interpreted as a typical value and is
the average of the data values that
make up the distribution.
Exercises 1-3, 7-9
Problem Set 1-2
eMath Instruction
Unit 13 Lesson 2
Yes
2
Students use the mean and standard
deviation to describe center and
variability for a data distribution that
is approximately symmetric.
The standard deviation is a value that
describes a typical distance from the
mean.
Exercises 1-9
Problem Set 1-3
eMath Instruction
Unit 13 Lesson 3
Yes
2
9
Students draw a smooth curve that
could be used as a model for a given
data distribution.
Students recognize when it is
reasonable and when it is not
reasonable to use a normal curve as a
model for a given data distribution.
A normal curve is symmetric and bell
shaped. The mean of a normal
distribution is located in the center of
the distribution. Areas under a
normal curve can be used to estimate
the proportion of the data values
that fall within a given interval.
When a distribution is skewed, it is
not appropriate to model the data
distribution with a normal curve.
5
2
10
Students calculate 𝑧 scores.
z score is defined as
Exercises 1-4
Examples 1-2
Problem Set 1-2, 5
eMath Instruction
Unit 13 Lesson 4
Yes
3
Probabilities associated with normal
distributions can be found using 𝒛
scores or directly without using zscores.
Examples 1-2
Exercises 1-2
Problem Set 2-3
Yes
3
To avoid bias in observational studies
and surveys, it is important to select
subjects randomly.
Exercises 1-3
Problem Set 1,2,4
eMath Instruction
Unit 13 Lesson 1
Yes
2
Students use technology and tables
to estimate the area under a normal
curve.
Probabilities associated with normal
distributions are determined using
scores and can be found using a
graphing calculator or tables of
standard normal curve areas.
11
Students use tables and technology
to estimate the area under a normal
curve.
Topic C -Drawing
Conclusions Using
Data from a Sample
12
Students distinguish between
observational studies, surveys, and
experiments
Students explain why random
selection is an important
consideration in observational
studies and surveys and why random
assignment is an important
consideration in experiments.
6
Lesson
13
Big Idea
Students differentiate between a 
population and a sample.

14
15
18
19
Suggested
Problems
Examples 1-3
A population is the entire set of
subjects in which there is an interest Exercises 1-3
Problem Set #1
Emphasize
Students recognize statistical

questions that are answered by
estimating a population mean or a 
population proportion.
A sample is a part of the population
from which information (data) is
Students understand the term
“sampling variability” in the context
of estimating a population
proportion.
The vast majority of the statistics that
you've done so far has been
descriptive. With descriptive
statistics, we summarize how a data
set "looks" with measures of central
tendency, like the mean, and
measures of dispersion, like the
standard deviation. But, the more
powerful branch of statistics is known
as inferential where we try to
infer properties about a population
from samples that we take. We do
this by using probability and
sampling variability to estimate how
likely the sample is given a certain
population.
Students understand that the
standard deviation of the sampling
distribution of the sample proportion
offers insight into the accuracy of the
sample proportion as an estimate of
the population proportion.
Exit
Ticket
Yes
# of Days
2
gathered, often for the purpose of
generalizing from the sample to the
population.
7
eMath Instruction
Unit 13 Lesson 5
eMath Instruction
Unit 13 Lesson 6
eMath Instruction
Unit 13 Lesson 7
No
6