Transcript 4.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2014 SESSION 4 • 19 JUNE 2014 INVESTIGATING THE CENTER, VARIABILITY, AND SHAPE OF A.

4.1
WELCOME TO COMMON CORE HIGH SCHOOL
MATHEMATICS LEADERSHIP
SUMMER INSTITUTE 2014
SESSION 4 • 19 JUNE 2014
INVESTIGATING THE CENTER, VARIABILITY,
AND SHAPE OF A DATA DISTRIBUTION
4.2
TODAY’S AGENDA
 Activity 1: Homework review and discussion
 Activity 2: Grade 6, Lesson 20: Describing Center, Variability, and Shape of a Data
Distribution from a Graphic Representation
 Reflecting on CCSSM standards aligned to lesson 20
 Break
 Activity 3: Grade 6, Lesson 21: Summarizing a Data Distribution by Describing
Center, Variability, and Shape, along with Grade 6, Lesson 22: Presenting a
Summary of a Statistical Project
 Reflecting on CCSSM standards aligned to lessons 21 and 22
 Activity 4: Group presentation planning time and updates to instructors
 Activity 5: Homework and closing remarks
4.3
ACTIVITY 1
HOMEWORK REVIEW AND DISCUSSION
Table discussion
Discuss your write ups for the Day 3 homework tasks:
 Compare your strategies with others at your table
 Reflect on how you might revise your own solution and/or presentation
4.4
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
• Describe how a given data set was collected.
• Describe the center and variability from a frequency histogram.
• Present a summary of a statistical investigation based on collected
data.
4.5
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
• summarize a given data set from a graphic representation of the
data.
• pose statistical questions that involve collecting and interpreting
data.
• summarize the 4-step process of a statistical study from a given
data set or from data collected.
4.6
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND
SHAPE OF A DATA DISTRIBUTION FROM A GRAPHIC
REPRESENTATION
REVIEW OF A GRAPHIC REPRESENTATION OF A DATA DISTRIBUTION AND HOW TO
ESTIMATE ITS CENTER AND VARIABILITY FROM THE GRAPH
ENGAGENY/COMMON CORE GRADE 6, LESSON 20
4.7
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
Scientists captured yellow perch from a lake in this region. They recorded data on each
fish, and then returned each fish to the lake. Consider the following histogram of data on
the length (in centimeters) for a sample of yellow perch.
4.8
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
 What data do you think researchers might want to collect about perch?
 How many fish captured had a length of 20 to 25 centimeters?
 Do you know how many fish had a length of 22 centimeters? Explain.
 Why do you think scientists were concerned about what they saw in the
histogram of the lengths of yellow perch?
4.9
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
In small groups, complete exercises 1 – 11 of Lesson 20.
After you have complete the exercises, discuss as a whole group
what you expect would be some of the challenges with students
completing these exercises.
Discuss Example 2: What Would Better Distribution Look Like?
(And, of course, why?)
4.10
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
Complete exercises 12 - 17.
Work in small groups. After you have complete the exercises,
discuss as a whole group what you expect would be some of the
challenges with students completing these exercises.
4.11
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
Summary questions:
 What is the problem with the yellow perch length distribution show in the
opening histogram?
 What is a typical yellow perch length?
 What unit of measure do you sue to describe the variability of yellow perch
lengths?
4.12
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
Reflecting on CCSSM standards aligned to lesson 20
Review the following CCSSM grade 6 content standards:
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?
4.13
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
6.SP.B.4: Display numerical data in plots on a number, including dot plots, histograms, and box
plots.
6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of
measurement.
c. Giving quantitative measures of center (median and/or mean) and variability interquartile range and/or
mean absolute deviation), as well as describing any overall pattern and any striking deviations from the
overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the
context in which the data were gathered.
4.14
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
Reflecting on CCSSM Standards for Mathematical Practice aligned to
lesson 20
Read MP4, the fourth CCSSM standard for mathematical practice.
 Recalling that the standards for mathematical practice describe student behaviors,
how did you engage in this practice as you completed the lesson?
 What instructional moves or decisions did you see occurring during the lesson that
encouraged greater engagement in MP4?
 Are there other standards for mathematical practice that were prominent as you and
your groups worked on the tasks?
4.15
ACTIVITY 2
LESSON 20: DESCRIBING CENTER, VARIABILITY, AND SHAPE OF A DATA DISTRIBUTION
FROM A GRAPHIC REPRESENTATION
CCSSM MP.4
MP.4 Model with Mathematics
Mathematically proficient students can apply the mathematics they know to
solve problems arising in everyday life, society, and the workplace. In early
grades, this might be as simple as writing an addition equation to describe a
situation. In middle grades, a student might apply proportional reasoning to
plan a school event or analyze a problem in the community. By high school, a
student might use geometry to solve a design problem or use a function to
describe how one quantity of interest depends on another. Mathematically
proficient students who can apply what they know are comfortable making
assumptions and approximations to simplify a complicated situation, realizing
that these may need revision later. They are able to identify important
quantities in a practical situation and map their relationships using such tools
as diagrams, two-way tables, graphs, flowcharts and formulas. They can
analyze those relationships mathematically to draw conclusions. They
routinely interpret their mathematical results in the context of the situation and
reflect on whether the results make sense, possibly improving the model if it
has not served its purpose.
engageny MP.4
MP.4 Model with Mathematics .
Students create graphs of data distributions.
They select an appropriate measure of center to
describe a typical data value for a given data
distribution. They also calculate and interpret
an appropriate measure of variability based on
the shape of the data distribution.
Break
4.17
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION
BY DESCRIBING CENTER, VARIABILITY, AND SHAPE
DEVELOPING A POSTER PRESENTATION OF A DATA DISTRIBUTION
ENGAGENY/COMMON CORE GRADE 6, LESSONS 21-22
4.18
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
These two lessons conclude our work with 6th graders in statistics. They are
also considered exploratory lessons. Statistics is about using data to answer
questions. Recall how we started our work with data:
Step 1: Pose a question that can be answered by data.
Step 2: Determine a plan to collect the data.
Step 3: Summarize the data with graphs and numerical summaries.
Step 4: Answer the question (the statistical question) posed using the data and
the summaries.
4.19
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
Think of a statistical study that could be conducted around some of
the following questions.
 What is the typical rainfall for New York?
 How many states has the typical participant in our class visited?
 How any countries (other than the USA) has the typical participant in our class visited?
 What is the typical number of years of teaching in our class? (This may be a more
interesting data distribution than you think.)
 How many text messages did a typical person in our class receive yesterday?
 Other?
4.20
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
As a class, we will collect data from our group on the questions
selected. The data will be recorded on a the whiteboard.
In small groups, use the templates provided in Lesson 21 and Lesson
22 do develop a statistical study of one of the questions. Develop a
poster that summarizes your selected statistical study.
4.21
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
Present your poster to the class.
Outline how your poster addressed the 4-steps of a statistical study.
We will also display the posters and have a short gallery walk.
4.22
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
Reflecting on CCSSM standards aligned to lessons 21-22
Review the following CCSSM grade 6 content standards:
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?
4.23
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
6.SP.B.4: Display numerical data in plots on a number, including dot plots, histograms, and box
plots.
6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of
measurement.
c. Giving quantitative measures of center (median and/or mean) and variability interquartile range and/or
mean absolute deviation), as well as describing any overall pattern and any striking deviations from the
overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the
context in which the data were gathered.
4.24
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
Reflecting on CCSSM Standards for Mathematical Practice aligned to
lessons 20-21
Read MP4, the fourth CCSSM standard for mathematical practice.
 Recalling that the standards for mathematical practice describe student behaviors,
how did you engage in this practice as you completed the lesson?
 What instructional moves or decisions did you see occurring during the lesson that
encouraged greater engagement in MP4?
 Are there other standards for mathematical practice that were prominent as you and
your groups worked on the tasks?
4.25
ACTIVITY 3
LESSONS 21-22: SUMMARIZING A DATA DISTRIBUTION BY DESCRIBING CENTER,
VARIABILITY, AND SHAPE
CCSSM MP.4
MP.4 Model with Mathematics
Mathematically proficient students can apply the mathematics they know to
solve problems arising in everyday life, society, and the workplace. In early
grades, this might be as simple as writing an addition equation to describe a
situation. In middle grades, a student might apply proportional reasoning to
plan a school event or analyze a problem in the community. By high school, a
student might use geometry to solve a design problem or use a function to
describe how one quantity of interest depends on another. Mathematically
proficient students who can apply what they know are comfortable making
assumptions and approximations to simplify a complicated situation, realizing
that these may need revision later. They are able to identify important
quantities in a practical situation and map their relationships using such tools
as diagrams, two-way tables, graphs, flowcharts and formulas. They can
analyze those relationships mathematically to draw conclusions. They
routinely interpret their mathematical results in the context of the situation and
reflect on whether the results make sense, possibly improving the model if it
has not served its purpose.
engageny MP.4
MP.4 Model with Mathematics .
Students create graphs of data distributions.
They select an appropriate measure of center to
describe a typical data value for a given data
distribution. They also calculate and interpret
an appropriate measure of variability based on
the shape of the data distribution.
4.26
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
• Describe how a given data set was collected.
• Describe the center and variability from a frequency histogram.
• Present a summary of a statistical investigation based on collected
data.
4.27
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
• summarize a given data set from a graphic representation of the
data.
• pose statistical questions that involve collecting and interpreting
data.
• summarize the 4-step process of a statistical study from a given
data set or from data collected.
4.28
ACTIVITY 4
GROUP PRESENTATION PLANNING TIME AND UPDATES
 During Week 2 of the institute, you will present (in groups of no more than
three) one of the following Engage NY lessons:
 Grade 6, Lessons 2, 3, 4, 5, 16
 Grade 8, Lesson 6
 Grade 9 (Algebra 1), 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.
4.29
ACTIVITY 4
GROUP PRESENTATION AND UPDATES
 Update instructors on the progress of your lesson. Instructors will meet with
each group and assist with your questions. Provide instructors a general
outline of your planning and development of the selected lessons. A tentative
schedule of presentations will be considered.
4.30
ACTIVITY 5
HOMEWORK AND CLOSING REMARKS
 Complete the problem set problems in grade 6, Lesson 20.
 Extending the mathematics:
Write a 3 to 5 sentence summary of the perch data that was presented in
Lesson 20. Pretend you are a report for the Milwaukee Journal. Develop a
headline that would go along with your short article.
 Reflecting on teaching:
Conducting a genuine statistical study with students in the middle to high
school ages poses some challenges. Explain how you would develop a
statistical study with your students that would involve collecting numerical
data from other students. Be attentive in your plan to how you would
supervise students’ process in collecting the data.