Transcript 1.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2014 SESSION 1 • 16 JUNE 2014 GETTING THE BIG PICTURE & DESCRIBING A DISTRIBUTION

1.1
WELCOME TO COMMON CORE HIGH SCHOOL
MATHEMATICS LEADERSHIP
SUMMER INSTITUTE 2014
SESSION 1 • 16 JUNE 2014
GETTING THE BIG PICTURE & DESCRIBING A
DISTRIBUTION
1.2
TODAY’S AGENDA
 Introductions, norms and administrative details
 CCSSM background
 MKT assessment
 Grade 9, Lesson 1: Distribution and Their Shapes
 Reflecting on CCSSM standards aligned to lesson 1
 Break
 Grade 9, Lesson 2: Describing the Center of a Distribution
 Reflecting on CCSSM standards aligned to lesson 2
 Homework and closing remarks
1.3
ACTIVITY 1
INTRODUCTIONS, NORMS AND ADMINISTRATIVE DETAILS
 Where do you teach?
 What do you teach?
 How long have you been teaching?
 What challenges does your district face related to high school mathematics?
 What is your experience/background with the CCSSM?
 What do you hope to learn about the CCSSM from this project?
1.4
ACTIVITY 1
INTRODUCTIONS, NORMS AND ADMINISTRATIVE DETAILS
Start on Time  End on Time
Silence cell phones.
No texting or Wi-Fi.
No sidebar
conversations . . .
Name Tents
Attention signal
Raise hand!!
Food
• Administrative fee
Restrooms
1.5
ACTIVITY 2
CCSSM BACKGROUND
www.corestandards.org
Focus: Unifying themes and
guidance on “ways of knowing” the
mathematics.
CCSSM Design Principles
Coherence: Progressions based on
mathematics and student learning.
Understanding: Deep, genuine understanding of
mathematics and ability to use that knowledge
in real-world situations.
Image: www.kidsgeo.com/geology
MPES Conference 2011/D. Huinker
1.6
1.7
Standards for Mathematical Practice
Standards for Mathematics Content
• Make sense of problems & persevere in
solving them
• Reason abstractly & quantitatively
K–8 Standards
by Grade Level
• Construct viable arguments & critique the
reasoning of others
• Model with mathematics
• Use appropriate tools strategically
High School Standards
by Conceptual Categories
________________________
• Attend to precision
 Domains
• Look for & make use of structure
 Clusters
• Look for & express regularity in repeated
 Standards
reasoning
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
6. Attend to precision.
1. Make sense of problems and
persevere in solving them.
STANDARDS FOR MATHEMATICAL PRACTICE
1.8
4. Model with mathematics.
Reasoning and
Explaining
Modeling and
Using Tools
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity
in repeated reasoning.
William McCallum, The University of Arizona
Seeing Structure
and Generalizing
1.9
1
2
3
4
5
6
7
8
HS
Counting
&
Cardinality
Algebra
Operations & Algebraic Thinking
Expressions and
Equations
Number & Operations in Base Ten
The Number System
Number &
Operations
Fractions
Ratios &
Proportional
Relationships
Measurement & Data
Functions
Statistics & Probability
Geometry
William McCallum, The University of Arizona
Number
and
Quantity
Modeling
K-8 Domains & HS
Conceptual Categories
K
1.10
WHY THE ENGAGENY/COMMON CORE BOOKS?
 First curriculum designed from the ground up for Common Core
(not an existing curriculum “aligned” to the standards)
 Features tasks of high-cognitive demand that require students to think,
reason, explain, justify, and collaborate
 Contains substantial teacher implementation support resources:
lesson plans, notes on student thinking, assessments and rubrics
 Developed by an exceptional group of educators
 Source material is available free and could be integrated with existing
programs your district may have
1.11
ACTIVITY 3
STATISTICS KNOWLEDGE ASSESSMENT
MKT Assessment
Go to: http://bit.ly/UWM-LOCUS orhttp://devartist.gotpantheon.com/quiz/djqJoGPi9u
Access code: djqJoGPi9u
1.12
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
 Use informal language to describe shape, center, and variability of a distribution displayed by
a dot plot, histogram, or box plot.
 Recognize that the first step in interpreting data is making sense of the context.
 Make meaningful conjectures to connect data distributions to their contexts.
 Calculate and interpret the mean and median based on the shape and spread of the data
 Explain why the mean and the median are approximately the same for a data distribution that
is nearly symmetrical and are not approximately the same for a skewed distribution.
1.13
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
 use appropriate language to describe and interpret a data set by its shape, its center, and its
variability.
 describe the context of a data set, based on the center and variability of a data distribution.
 explain why we have (at least) two measures of the center of a data set, and when it is
appropriate to use one rather than the other.
1.14
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
REVIEW OF DATA DISTRIBUTIONS AND REPRESENTATIONS
ENGAGENY/COMMON CORE GRADE 9, LESSON 1
1.15
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
1.16
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
1.17
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
1.18
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
Reflecting on CCSSM standards aligned to lesson 1
Review the following CCSSM High School content standards:
S-ID.1
S-ID.2
S-ID.3
 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?
1.19
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
S-ID.1:
Represent data with plots on the real number line (dot plots,
histograms, and box plots).
S-ID.2:
Use statistics appropriate to the shape of the data distribution to
compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets.
S-ID.3:
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points
(outliners).
1.20
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
Reflecting on CCSSM standards aligned to lesson 1
Read MP2, the second 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 MP2?
 Are there other standards for mathematical practice that were prominent as you and
your groups worked on the tasks?
1.21
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
CCSSM MP.2
engageny MP.2
MP.2 Reason abstractly and quantitatively
MP.2 Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and
their relationships in problem situations. They bring two
complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given
situation and represent it symbolically and manipulate the
representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to
contextualize, to pause as needed during the manipulation process
in order to probe into the referents for the symbols involved.
Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units
involved; attending to the meaning of quantities, not just how to
compute them; and knowing and flexibly using different properties of
operations and objects.
Students pose statistical questions
and reason about how to collect and
interpret data in order to answer these
questions. Student form summaries of
data using graphs, two-way tables,
and other representations that are
appropriate for a given context and the
statistical question they are trying to
answer. Students reason about
whether two variables are associated
by considering conditional relative
frequencies.
1.22
ACTIVITY 4
LESSON 1: DISTRIBUTIONS AND THEIR SHAPES
Closing questions for lesson 1
 What are some of the favorite televisions shows for high school students? Do
the commercials connect with the viewers?
 You walk into a store. You estimate that most of the customers are between
50 and 60. What kind of store do you think it is? Why?
 You are going to take a trip to Kenya. Do you think you will meeting several
people ninety or older? Why or why not?
Break
1.24
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A
DISTRIBUTION
MEASURES THAT SUMMARIZE DATA DISTRIBUTION SHAPE
ENGAGENY/COMMON CORE GRADE 9, LESSON 2
1.25
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Individually, and then with your small group, consider:
 What do you think a center should tell us about a data distribution?
 How are centers used in our summary of a data distribution?
1.26
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Can we assume that all students will interpret the question “How many pets do you
currently own?” in the same way?
1.27
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Why would the same hallway have different reported measures of length?
What measure of the length of the hallway do you think are the most accurate from
the data set? Why?
1.28
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
What number would you use to describe the typical age of cars in years
by the car owners in this group?
1.29
AN OVERVIEW OF THE HIGH SCHOOL CONCEPTUAL
CATEGORIES
Algebra
Functions
Number &
Quantity
Geometry
Statistics & Probability
1.30
THE MODELING FRAMEWORK
The Modeling Conceptual Category
(pages 72-73 of your Standards book)
1.31
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Reflecting on CCSSM standards aligned to lesson 2
Review the following CCSSM High School content standards:
S-ID.1
S-ID.2
S-ID.3
 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?
1.32
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
S-ID.1:
Represent data with plots on the real number line (dot plots,
histograms, and box plots).
S-ID.2:
Use statistics appropriate to the shape of the data distribution to
compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets.
S-ID.3:
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points
(outliners).
1.33
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Reflecting on CCSSM standards aligned to lesson 2
Read MP1, the first 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 MP1?
 Are there other standards for mathematical practice that were prominent as you and
your groups worked on the tasks?
1.34
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
CCSSM MP.1
MP.1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a
problem and looking for entry points to its solution. They analyze givens, constraints,
relationships, and goals. They make conjectures about the form and meaning of the solution
and plan a solution pathway rather than simply jumping into a solution attempt. They
consider analogous problems, and try special cases and simpler forms of the original
problem in order to gain insight into its solution. They monitor and evaluate their progress
and change course if necessary. Older students might, depending on the context of the
problem, transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient students can explain
correspondences between equations, verbal descriptions, tables, and graphs or draw
diagrams of important features and relationships, graph data, and search for regularity or
trends. Younger students might rely on using concrete objects or pictures to help
conceptualize and solve a problem. Mathematically proficient students check their answers
to problems using a different method, and they continually ask themselves, “Does this make
sense?” They can understand the approaches of others to solving complex problems and
identify correspondences between different approaches.
engageny MP.1
MP.1 Make sense of problems and persevere in
solving them.
Students choose an appropriate method of
analysis based on problem context. They
consider how the data were collected and
how data can be summarized to answer
statistical questions. Students select a
graphic display appropriate to the problem
context. They select numerical summaries
appropriate to the shape of the data
distribution. Students use multiple
representations and numerical summaries
and then determine the most appropriate
representation and summary for a given data
distribution.
1.35
ACTIVITY 5
LESSON 2: DESCRIBING THE CENTER OF A DISTRIBUTION
Closing questions for lesson 2
 Sketch a dot plot in which the median is greater than the mean. Could you
think of a context that might result in data where you think that would happen?
 Sketch a dot plot in which the median and the mean are approximately equal.
Could you think of a context that might result in data were you think that
would happen?
1.36
LEARNING INTENTIONS AND SUCCESS CRITERIA
We are learning to…
 Use informal language to describe shape, center, and variability of a distribution displayed by
a dot plot, histogram, or box plot.
 Recognize that the first step in interpreting data is making sense of the context.
 Make meaningful conjectures to connect data distributions to their contexts.
 Calculate and interpret the mean and median based on the shape and spread of the data
 Explain why the mean and the median are approximately the same for a data distribution that
is nearly symmetrical and are not approximately the same for a skewed distribution.
1.37
LEARNING INTENTIONS AND SUCCESS CRITERIA
We will be successful when we can:
 use appropriate language to describe and interpret a data set by its shape, its center, and its
variability.
 describe the context of a data set, based on the center and variability of a data distribution.
 explain why we have (at least) two measures of the center of a data set, and when it is
appropriate to use one rather than the other.
1.38
ACTIVITY 6
HOMEWORK AND CLOSING REMARKS
 Complete the Lesson 2 Problem Set in your notebook (pages S.14-S.16)
 Extending the mathematics:
Sketch a histogram or dot plot or box plot of data collected from an imaginary
population (ages of people in a church or temple, ages of people attending a
movie, number of text messages sent per day from a grade 9 math class). Do
not indicate the population of your graph. In our next class, we will guess the
population based on your graph.
 Reflecting on teaching:
Consider a typical class of 9th grade algebra students in your district. What
aspects of these two lessons are likely to connect to their prior knowledge?
What concepts in these lessons might be new to them?