Module Focus: Grade 9 – Module 2
Sequence of Sessions
Overarching Objectives of this November 2013 Network Team Institute

Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate
how these modules contribute to the accomplishment of the major work of the grade.

Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom
teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.

Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding
how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.

Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the
mid-module assessment and end-of-module assessment.
High-Level Purpose of this Session
●
●
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Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons.
Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the
module addresses the major work of the grade.
Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module.
Related Learning Experiences
●
This session is part of a sequence of Module Focus sessions examining the Grade 9 curriculum, A Story of Functions.
Key Points
• Students use informal language to describe the shape, center and variability of a distribution based on a dot plot, histogram, or box
plot.
• Students recognize that a first step in interpreting data is making sense of the context.
• Students make meaningful conjectures to connect data distributions to their context and the questions that could be answered by
studying the distribution.
• Data distributions are represented by dot plots, histograms, and box plots.
• Data distributions are defined by their shape, center, and spread.
• Distributions that are skewed use the median and interquartile range (IQR) for measures of center and variability
• Distributions that are nearly symmetrical use the mean and the mean absolute deviation (or MAD) for measures of center and
variability
• Categorical bivariate data are summarized by two-way frequency tables.
• Conditional relative frequencies are used to evaluate the possible association between two categorical variables.
• Many of the 9th grade standards and learning expectations are started in grade 6, 7, and 8, and are continued in this grade.
• Topic D continues to present scatter plots. Students particularly focus on deciding whether or not a scatter plot has a linear model
and that that model tells us about the data.
• A linear model is introduced in grade 8, and then expanded in grade 9 as students develop a “best-fitting” line.
• The decision of whether or not the linear model is a good model is based on a residual plot.
• The next slides introduce the topic of a residual and a residual plot. The topic involving residuals concludes Topic D and the
module.
Session Outcomes
What do we want participants to be able to do as a result of this
session?
 Participants will develop a deeper understanding of the sequence of
mathematical concepts within the specified modules and will be able to
articulate how these modules contribute to the accomplishment of the major
work of the grade.
 Participants will be able to articulate and model the instructional approaches
that support implementation of specified modules (both as classroom
teachers and school leaders), including an understanding of how this
instruction exemplifies the shifts called for by the CCLS.
 Participants will be able to articulate connections between the content of the
specified module and content of grades above and below, understanding how
the mathematical concepts that develop in the modules reflect the
connections outlined in the progressions documents.
 Participants will be able to articulate critical aspects of instruction that
prepare students to express reasoning and/or conduct modeling required on
the mid-module assessment and end-of-module assessment.
How will we know that they are able to do this?
Participants will be able to articulate the key points listed above.
Session Overview
Section
Topic A: Shapes and
Centers of
Distributions
Topic B: Describing
Variability and
Comparing
Distributions
Mid-Module
Assessment
Topic C: Categorical
Data on Two
Variables
Topic D: Numerical
Data on Two
Variables
End-of-Module
Assessment
Time
Overview
Prepared Resources
Facilitator Preparation
Examination of the conceptual
understandings that are
developed in Topic A.


Grade 9 Module 2
Grade 9 Module 2 PPT

Review Topic A.
Examination of the conceptual
understandings that are
developed in Topic B.


Grade 9 Module 2
Grade 9 Module 2 PPT

Review Topic B.
Examination of the conceptual
understandings that are
developed in Topic C.


Grade 9 Module 2
Grade 9 Module 2 PPT

Review Topic C.
Examination of the conceptual
understandings that are
developed in Topic D.


Grade 9 Module 2
Grade 9 Module 2 PPT

Review Topic D.
Exploration of the End-of-Module
Assessment.


Grade 9 Module 2
Grade 9 Module 2 PPT

Review the End-of Module
Assessment.
Session Roadmap
Section: Topic A: Shapes and Centers of Distributions
Time: 2 hours and 15 minutes
HAVE ASKED HENRY TO ADD TIMING NOTES FOR EACH SLIDE
[minutes] In this section, you will…
Examine the conceptual understandings that are built in Grade 9
Module 2, Topic A.
Time Slide # Slide #/ Pic of Slide
1
1
0
2
Materials used include:
Script/ Activity directions
Introduce the module as the second module of the 9th grade A Story of
Functions. The module title, Modeling with Descriptive Statistics, continues
students’ work with data distributions and data representations.
This module extends the introduction to data distributions started in grade
6, and continued in grades 7 and 8.
GROUP
0
3
2
4
Introduce the objectives of this presentation. Discuss with participants that
the primary objective of this session is to learn more about the lessons in
this module and what students will investigate. These objectives will be
developed by working through a few problems, and connecting these
problems to the standards.
5
Summarize the next two slides as the organization of the grade 9 module,
and the connections to the standards.
6
7
Explore with the participants the general questions posted on the slide.
Chart their responses. There may be several responses, and then there may
be very few. After several questions or comments have been stated (and
posted), provide a general answer if possible. Move to a specific topic as
outlined in this powerpoint (Topic A or Topic B or Topic C or Topic D) that
would best address the questions. If participants have just started the
module, and question the overall goals of the Module, start with Topic A. If
several questions indicate that participants have completed the first 4
lessons and are asking about the other topics, begin with Topic B or C or D
based on participants’ comments.
8
Point out to participants that the first activity is to complete selected
problems from Lesson 1 of the module. Briefly go over the format of the first
lesson, namely, it is series of questions connected to data distributions
represented by either a dot plot, a histogram, or a box plot. Summarize the
primary goal of the lesson is to provide students a bridge from what they
learned in their previous grades to where they are going with this work. The
data distributions provided in this lesson include distributions from their
work in the statistics and probability modules of grades 6, 7, and 8. It also
opens up new questions that will be addressed in this module.
9
After participants complete lesson 1, summarize the points made in this slide
as the primary goals of the problems in lesson 1.
10
Use the question on this slide as a way for participants to connect the
problems they completed in Lesson 1 to the goals of this module.
11
Ask participants to summarize what they think is the story behind this data
distribution. Essentially summarize that this is a skewed distribution, with a
tail to the right. The distribution indicates that most of the delays of an
airline were around 20 minutes. 20 minutes would be approximately the
median delay time. If necessary, review with participants how to find the
median.
12
The above distribution is summarized by a histogram. A summary would
indicate a skewed distribution, with a tail to the right. Ask participants what
they can summarize about the data from this histogram. They may indicate
various descriptions of the population based on different age groups; for
example, 17% of the population of Kenya is 0 to 4 years old. Or, they main
summarize that a fraction of a percent of the population are 80 or older.
Discuss any summary that participants suggest can be derived from this
graph. Also ask participants what summaries cannot be determined from
this graph (for example how many people are in this data distribution or
how many people are a specific age category).
13
Ask participants again to summarize what is indicated by this graph. Look
for descriptions that include the median number of pets owned, or the
minimum number of pets owned, or a summary that indicates 50% of the
people surveyed owned 2 or less pets. Ask participants to summarize what
they think the “ *” at the end of the box plot means (an outlier). Ask them to
suggestion an interpretation of the outlier.
14
Carefully read through this slide as it summarizes the primary questions that
are investigated in Topic A. The slides that follow indicate how these
questions are investigated.
15
Ask the questions in the slide. Summarize this shape as a data distribution
that is skewed.
Section: Topic B: Describing Variability and Comparing
Time:
Distributions
[minutes] In this section, you will…
Examine the conceptual understandings that are built in Grade 9
Module 2, Topic B.
Materials used include:
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
16
Describe the center of a distribution as the value that provides a typical
description of the distribution. For a skewed distribution, the median is
considered a typical description. In this example, an estimate of the median
age would be located within the interval of 15 to 19 years old
(approximately 17 years old). This age would describe the typical age of the
people in this sample. Indicate that if the distribution was nearly
symmetrical, the mean would be a description of the typical age.
17
Variability is linked to the shape of the distribution. For a distribution that
is skewed, the variability is described by the interquartile range (IQR), or
the difference of Q3 (upper quartile) and Q1 (lower quartile). The IQR is
approximated by making a box plot of the distribution.
18
The next example is a comparison of two data distributions. In this example,
students compare the populations of Kenya and the United States.
GROUP
19
Read the slide. Challenge participants to provide 3 questions that they
might ask of students as they compare two data distributions represented
by histograms. Similarly, ask them to compare the data distributions
represented by box plots. Indicate that they should consider questions that
can be answered by a histogram and not a box plot, or questions answered
by a box plot and not a histogram.
20
Allow participants to examine the two distributions from the histogram.
These two histograms are also part of Lesson 8. Encourage participants to
discuss in small groups the exercises related to histograms in Lesson 8, or
exercises 1 – 8..
21
Discuss the two box plots. Ask participants, “What can you summarize
about the data from a box plots that you could not from the histograms?”
Encourage participants to work through the exercises involving box plots in
Lesson 8, or exercises 9 - 16.
22
Read and summarize this slide.
Section: Topic C: Categorical Data on Two Variables
Time:
[minutes] In this section, you will…
Examine the conceptual understandings that are built in Grade 9
Module 2, Topic C.
Materials used include:
Time Slide Slide #/ Pic of Slide
#
23
Script/ Activity directions
The following example is from Topic C of the module. It indicates how
students also work with categorical data. The categorical data is
summarized using a two-way frequency table, and examined by
frequencies, relative frequencies, and conditional relative frequencies. If
time permits, read and discuss the standards connected to the two-way
table, or S-ID.5. If time permits, organize participants in small groups to
discuss and work through the exercises of Lesson 9.
GROUP
24
Continue discussion of the two-way table. Ask the questions in the slide
and discuss with participants. Introduce the terms frequency, relative
frequency, and conditional relative frequency. Point out to participants that
the terms frequency and relative frequency begin in grade 8. The terms
conditional relative frequency and association are introduced in grade 9,
and further developed in grade 11 as conditional probability.
25
Read and summarize this slide. If time permits, move to a discussion of the
mid-module assessment. Ask participants to complete the first problem.
Discuss with participants the connection to the standards.
Section: Topic D: Numerical Data on Two Variables
Time:
[minutes] In this section, you will…
Examine the conceptual understandings that are built in Grade 9
Module 2, Topic D.
Materials used include:
Time Slide Slide #/ Pic of Slide
#
Script/ Activity directions
GROUP
26
The example presented on this slide is from Topic D, or Numerical Data on
Two Variables. The opening problem from Lesson 12 summarize the focus
of this topic. Discuss with participants how this investigation involves SID.6, or “Represent data on two quantitative variables on a scatter plot, and
describe how the variables are related.”
27
The scatter plot does not have a strong pattern. Participants may respond
that it looks like the data points are randomly scattered. If participants look
carefully, however, there is a pattern that suggests as elevation increase, the
number of clear days also appears to increase. Direct participants to work
in small groups to complete the exercises of lesson 12, or exercises 1 - 3. If
time permits, encourage participants to work on exercises 4 – 7, or
“Thinking about Linear Relationships.” After discussion of the exercises,
direct participants to work on exercises 8 - 13, or “Not Every Relationship is
Linear.”
28
Read and discuss the points presented in this slide. There will not be
enough time to fully develop the topic of residuals, however, this may be a
topic unfamiliar with participants. As a result, introduce that a residual
“looks like” and a general summary of a residual plot. (An entire session
could be developed just on these topics!) If interest is expressed by the
participants and time is available, encourage small groups work through
the exercises in lessons 15 - 16.
29
30
Discuss with participants that a special scatter plot of the residual is used to
decide if a linear model is a good model for the scatter plot. The topic of
how to use the residual plot in deciding whether or not to use a linear
model is developed in lessons 15, 16 and 17. If time permits. Involve
participants in selected problems from those lessons.
Section: End-of-Module Assessment
Time:
[minutes] In this section, you will…
Materials used include:
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
GROUP
29
30
Discuss with participants that a special scatter plot of the residual is used to
decide if a linear model is a good model for the scatter plot. The topic of how
to use the residual plot in deciding whether or not to use a linear model is
developed in lessons 15, 16 and 17. If time permits. Involve participants in
selected problems from those lessons.
31
Discuss with participants the points that were developed in the overview of
this module. Read the points on the slide and ask if there are any questions
related tot them. If time permits, move to the End-of-Module Assessment
and ask participants to complete the first problem.
Use the following icons in the script to indicate different learning modes.
Video
Reflect on a prompt
Active learning
Turn and talk
Turnkey Materials Provided
●
Grade 9 Module 2 PPT
Additional Suggested Resources
●
A Story of Functions Curriculum Overview