Transcript 3.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2014 SESSION 3 • 18 JUNE 2014 VARIABILITY: DESCRIBING IT, DISPLAYING IT, AND MODELING WITH.

3.1
WELCOME TO COMMON CORE HIGH SCHOOL
MATHEMATICS LEADERSHIP
SUMMER INSTITUTE 2014
SESSION 3 • 18 JUNE 2014
VARIABILITY: DESCRIBING IT, DISPLAYING
IT, AND MODELING WITH IT
3.2
TODAY’S AGENDA
 Special Guest: Adam Guttridge, Milwaukee Brewers
 Homework review and discussion
 Grade 6, Lessons 6 and 9: Mean and MAD
 Reflecting on CCSSM standards aligned to lessons 6 and 9
 Break
 Grade 6, Lessons 12 and 13: The IQR and Box Plots
 Reflecting on CCSSM standards aligned to lessons 12 and 13
 Group presentation planning time
 Homework and closing remarks
3.3
SPECIAL GUEST
ADAM GUTTRIDGE
MILWAUKEE BREWERS BASEBALL CLUB
MANAGER–BASEBALL RESEARCH & DEVELOPMENT
3.4
ACTIVITY 1
HOMEWORK REVIEW AND DISCUSSION
Table discussion
Discuss your write ups for the Day 2 homework tasks:
 Compare your strategies with others at your table
 Reflect on how you might revise your own solution and/or presentation
3.5
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
 Describe, conceptualize, and calculate measures of center in
context
 Describe the variability of a set of data relative to measures of
center
3.6
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
 Calculate the mean and median in a data set
 Understand the mean related to “fair shares” and use a fair shares
strategy to calculate the mean
 Calculate, display, and describe interquartile range in a data set
3.7
ACTIVITY 2
LESSONS 6 AND 9: MEAN & MAD
MEASURES OF VARIABILITY IN NEAR-SYMMETRIC DISTRIBUTIONS
ENGAGENY/COMMON CORE GRADE 6, LESSONS 6 AND 9
3.8
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
 On the large white board, put a sticky note up that corresponds to the number
of hours of sleep you got last night.
 How would you describe the center of the distribution of our dot plot?
 How might we determine the mean without calculating it?
3.9
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
 Give each person at your table the same number of Unifix cubes as they
reported hours of sleep last night.
 Use a fair share strategy to find the mean number of hours of sleep at your
table.
3.10
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
 Complete the Lesson 6 Exit ticket with a partner or group of 3.
MP.3
different orderings. Several orderings are reasonable – focus on the students’ explanations for ordering the
distributions. What is important is not their suggested orderings but rather their arguments to support their
3.11orderings.
Also, the goal for this example is for students to realize that they need to have a more formal way of deciding the best
ordering. Sabina suggests that a formula is needed, and she proceeds in this lesson to develop one.
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
Exercises 1–3
The following temperature distributions for seven other cities all have a mean temperature of approximately
degrees.
They do not have the same variability. Consider the following dot plots of the mean yearly temperatures of the seven
cities in degrees Fahrenheit.
City B
City A
 Complete Lesson 9,
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Temperature (degrees F)
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City C
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exercises 1-3.
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City E
City D
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Temperature (degrees F)
Temperature (degrees F)
City F
 In what order would you
classify the 7 cities’
temperatures, from least
variability to most variability?
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Temperature (degrees F)
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City G
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Temperature (degrees F)
1.
Which distribution has the smallest variability of the temperatures from its mean of
degrees? Explain your
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3.12
ACTIVITY 2 Exercises 4–6
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
The dot plot for the temperatures in City
answer the following questions.
is shown below. Use the dot plot and the mean
 Find the mean temperature
City G
for City G
 For each month’s
temperature, find the
deviation from the mean
temperature.
 What do you notice about
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Temperature (degrees F)
your deviation values?
Mean absolute deviation = (sum of the absolute values of the deviations from the mean)
4. Fill in the following table for City temperature deviations.
÷ (number of data points)
Temp Deviation Result
3.13
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
 Complete Lesson 9, Exercise 7 with a partner or group of three.
3.14
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
Reflecting on CCSSM standards aligned to lessons 6 and 9
Review the following CCSSM Grade 6 content standards:
6.SP.A.2
6.SP.A.3
6.SP.B.4
6.SP.B.5
 Where did you see these standards in the lesson you have just completed?
 What would you look for in students’ work to suggest that they have made progress
towards these standards?
3.15
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
6.SP.A.2: Understand that a set of data collected to answer a statistical question has a
distribution which can be described by its center, spread, and overall shape.
G.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its
values with a single number, while a measure of variation describes how its values vary with a
single number.
6.SP.B.4: Display numerical data on plots on a number line, including dot plots, histograms, and
box plots.
6.SP.B.5: Summarize numerical data sets in relation to their contexts.
3.16
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
Reflecting on CCSSM standards aligned to Lessons 6 and 9
Look across the set of Standards for Mathematical Practice.
 Recalling that the standards for mathematical practice describe student
behaviors, which practices did you engage in, and how?
 What instructional moves or decisions did you see occurring during the lesson
that encouraged greater engagement in the SMP?
Break
3.18
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
MEASURES OF VARIABILITY IN SKEWED DISTRIBUTIONS
ENGAGENY/COMMON CORE GRADE 6, LESSONS 12 & 13
3.19
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
Consider the following:
 In what situations might you want or need to know where the border between
the top half and the bottom half of a set of data is?
 What questions might you ask about your data when you know where this
border point lies?
3.20
How do we summarize a data distribution? What provides us with a good description of the data? The following
exercises help us to understand how a numerical summary answers these questions.
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
Example 1 (2 minutes): The Median—A Typical Number
The activity begins with a set of data displayed in a dot plot. Introduce the data presented in the example.
 With your pair or group of 3, work on exercises 1, 2, 3, 5, and 7 from Lesson 12.
Example 1: The Median – A Typical Number
Suppose a chain restaurant (Restaurant A) advertises that a typical number of french fries in a large bag is
shows the number of french fries in selected samples of large bags from Restaurant A.
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Number of French Fries in a Bag (Restaurant A)
Number of French Fries in a Large Bag (Restaurant A)
Lesson 12:
Date:
Describing the Center of a Distribution Using the Median
10/25/13
95
. The graph
Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
ACTIVITY 3
Then have students find the medians of each half by counting from the top and bottom of the list, noting that a value for
LESSONS
12 & 13: THE IQR AND BOX PLOTS
bags with the same count can be in both halves. It might help to think about the individual bags – one of the bags with
78 fries is in the first half, one of the bags with 78 fries is in the second half, and one of the bags divides the two halves
and marks the median of the data set. At this point, the important idea is that students get a sense of how to find a
median: order the values and find a midpoint for the ordered values.
 Using frequency tables to find median…
Exercises 8–10: Finding Medians from Frequency Tables
8.
A third restaurant (Restaurant C) tallied a sample of bags of french fries and found the results below.
Number of fries
Frequency
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a.
How many bags of fries did they count?
3.21
3.22
approximate the number of elements in each section in terms of
or 25% of the data or by giving an estimate of the
ACTIVITY
3
actual number data values as well as knowing that or 50% of the data values are between the two quartiles. They
should also recognize
that13:
the IQRTHE
is a measure
of spreadAND
around theBOX
median (thePLOTS
length of the interval that captures the
LESSONS
12
&
IQR
middle 50% of the data).
Consider the following questions as you discuss the example questions with students:
 How do you Approximately
think thehow
data
these
restaurants
wasExplain
collected,
and what
manyfrom
data values
would be
between the quartiles?
your reasoning.
Answers will
depending
the data.
problems might there
bevary
with
the on
data?
What other measures of center and spread have you studied and how do you think they would compare to the
median and IQR? (If you want to pursue this question, you could have students compute the mean and MAD
for one of the data sets.)
 What would you consider typical and what would you consider atypical for each
restaurant?
This question provides students an opportunity to discuss what they might recall about the mean as a
center and the MAD as a measure of variability.
Data from Lesson 12: Number of french fries
Restaurant A: 80, 72, 77, 80, 90, 85, 93, 79, 84, 73, 87, 67, 80, 86, 92, 88, 86, 88, 66, 77
Restaurant B: 83, 83, 83, 84, 79, 78, 80, 81, 83, 80, 79, 81, 84, 82, 85, 85, 79, 79, 83
Restaurant C: 75, 75, 77, 85, 85, 80, 80, 80, 80, 81, 82, 84, 84, 84, 85, 77, 77, 86, 78, 78, 78, 79, 79, 79, 79, 79
Exercises 1–4
1.
In Lesson 12, you thought about the claim made by a chain restaurant that the typical number of french fries in a
large bag was . Then you looked at data on the number of fries in a bag from three of the restaurants.
3.23
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
 With your pair or group of three, work on exercises 2, 4, 5, and 6 from Lesson
13.
NOT a statistical question.
3.24
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
Consider the following:
 What are the conditions under which you might choose to summarize a set of
data using:
 The mean
 The MAD
 The IQR?
 How does the statistical question you are investigating relate to this decision?
3.25
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
Create three different contexts for which a set of data collected related
to those contexts could have an IQR of 𝟐𝟎. Define a median for each
context. Be specific about how the data might have been collected
and the units involved. Be ready to describe what the median and IQR
mean in each case.
3.26
ACTIVITY 3
LESSONS 12 & 13: THE IQR AND BOX PLOTS
 Complete the Exit Ticket for Lesson 13.
3.27
ACTIVITY 2
LESSONS 12 & 13: THE IQR AND BOX PLOTS
Reflecting on CCSSM standards aligned to lessons 12 & 13
Review the following CCSSM Grade 6 content standards:
6.SP.A.2
6.SP.A.3
6.SP.B.4
6.SP.B.5
 In what ways did the work on these two lessons add to your understandings
of the standards?
3.28
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
6.SP.A.2: Understand that a set of data collected to answer a statistical question has a
distribution which can be described by its center, spread, and overall shape.
G.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its
values with a single number, while a measure of variation describes how its values vary with a
single number.
6.SP.B.4: Display numerical data on plots on a number line, including dot plots, histograms, and
box plots.
6.SP.B.5: Summarize numerical data sets in relation to their contexts.
3.29
ACTIVITY 2
LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION
Reflecting on CCSSM standards aligned to Lessons 6 and 9
Look across the set of Standards for Mathematical Practice.
 Recalling that the standards for mathematical practice describe student
behaviors, which practices did you engage in, and how?
 What instructional moves or decisions did you see occurring during the lesson
that encouraged greater engagement in the SMP?
3.30
ACTIVITY 4
GROUP PRESENTATION PLANNING TIME
 During Week 2 of the institute, you will present (in groups) one of the following
engageny lessons:
 Grade 6, Lessons 2, 3, 4, 5, 16
 Grade 8, Lesson 6
 Grade 9, Lessons 3, 17
 For the rest of our time today, you should study these lessons, decide which
one you wish to present, and find a group with which you will present.
3.31
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
 Describe, conceptualize, and calculate measures of center in
context
 Describe the variability of a set of data relative to measures of
center
3.32
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
 Calculate the mean and median in a data set
 Understand the mean related to “fair shares” and use a fair shares
strategy to calculate the mean
 Calculate, display, and describe interquartile range in a data set
3.33
ACTIVITY 5
HOMEWORK AND CLOSING REMARKS
 Due to our tight timeframe, no content homework this evening.
 In your reflection tonight, address the following:
Tonight, we touched on mean, mean absolute deviation, median, and
interquartile range. As students learn to calculate and represent these
quantities, how might we support them in developing both the procedural
fluency with these quantities alongside the conceptual understanding that
will help them know when and how to make use of them?