Transcript Document 7125405

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Implementing
Common Core
State Standards
in the Classroom
High School
Day 1
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Overall Outcomes
 Recognize
the interconnectedness of the Standards
for Mathematical Practice and content standards in
developing student understanding and reasoning.
 Illuminate
practices that establish a culture where
mistakes are a springboard for learning, risktaking is the norm, and there is a belief that all
students can learn.
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Effective Classrooms
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What research says about effective
classrooms
 The
activity centers on mathematical under-standing,
invention, and sense-making by all students.

The culture is one in which inquiry, wrong answers, personal
challenge, collaboration, and disequilibrium provide
opportunities for mathematics learning by all students.

The tasks in which students engage are mathematically
worthwhile for all students.

A teacher’s deep knowledge of the mathematics content she/he
teaches and the trajectory of that content enables the teacher to
support important, long-lasting student understanding
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Effective implies:
 Students
are engaged with important mathematics.
 Lessons
are very likely to enhance student
understanding and to develop students’ capacity to
do math successfully.
 Students
are engaged in ways of knowing and
ways of working consistent with the nature of
mathematicians ways of knowing and working.
+
Outcomes Day 1:
 Reflect
on teaching practices that support the
shifts (Focus, Coherence, & Rigor) in the
Common Core State Standards for
Mathematics.
 Understand
the four SBAC Assessment Claims
for Mathematics.
 Deepen
understanding of the progression of
learning and coherence around the CCSS-M
Conceptual Category Functions
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Common Core State Standards:
Mathematics
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Why CCSS?
 Greta’s Video
Clip
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What We are Doing Doesn’t Work
Almost half of eighth-graders in Taiwan, Singapore and
South Korea showed they could reach the “advanced”
level in math, meaning they could relate fractions,
decimals and percents to each other; understand algebra;
and solve simple probability problems.
In the U.S., 7 percent met that standard.

Results from the 2011 TIMMS
+ Theory of Practice
for CCSS Implementation in WA
2-Prongs:
1.
2.
The What: Content Shifts (for students and educators)
 Belief that past standards implementation efforts have
provided a strong foundation on which to build for
CCSS; HOWEVER there are shifts that need to be
attended to in the content.
The How: System “Remodeling”
 Belief that successful CCSS implementation will not take
place top down or bottom up – it must be “both, and…”
 Belief that districts across the state have the conditions
and commitment present to engage wholly in this work.
 Professional learning systems are critical
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WA CCSS Implementation Timeline
2010-11
Phase 1: CCSS Exploration
Phase 2: Build Awareness & Begin
Building Statewide Capacity
Phase 3: Build State & District
Capacity and Classroom Transitions
Phase 4: Statewide Application and
Assessment
Ongoing: Statewide Coordination
and Collaboration to Support
Implementation
2011-12
2012-13
2013-14 2014-15
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Transition Plan for Washington State
Year 1- 2
2012-2013
K-2
3-5
School districts that can, should
consider adopting the CCSS for K-2
in total.
3 – Number and Operations –
Fractions (NF); Operations
and Algebraic Thinking (OA)
K – Counting and Cardinality (CC);
Operations and Algebraic Thinking
(OA); Measurement and Data (MD)
4 – Number and Operations –
Fractions (NF); Operations
and Algebraic Thinking (OA)
1 – Operations and Algebraic
Thinking (OA); Number and
Operations in Base Ten (NBT);
5 – Number and Operations –
Fractions (NF); Operations
and Algebraic Thinking (OA)
2 – Operations and Algebraic
Thinking (OA);
Number and Operations in Base
Ten (NBT);
and remaining 2008 WA
Standard
and remaining 2008 WA Standards
6-8
6 – Ratio and Proportion
Relationships (RP); The
Number System (NS);
Expressions and
Equations (EE)
7 – Ratio and Proportion
Relationships (RP); The
Number System (NS);
Expressions and
Equations (EE)
8 – Expressions and
Equations (EE); The
Number System (NS);
Functions (F)
and remaining 2008 WA
Standards
High School
Algebra 1- Unit 2: Linear
and Exponential
Relationships; Unit 1:
Relationship Between
Quantities and Reasoning
with Equations and Unit 4:
Expressions and
Equations
Geometry- Unit 1:
Congruence, Proof and
Constructions and
Unit 4: Connecting
Algebra and Geometry
through Coordinates;
Unit 2: Similarity, Proof,
and Trigonometry and
Unit 3:Extending to Three
Dimensions
and remaining 2008 WA
Standards
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Focus, Coherence & Rigor
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The Three Shifts in
Mathematics
Focus: Strongly
where the
standards focus
Coherence: Think
across grades
and link to major topics within
grades
Rigor: Require
conceptual
understanding, fluency, and
application
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Focus on the Major
Work of the Grade
Two levels of focus ~
•
•
What’s in/What’s out
The shape of the content
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Focus in International Comparisons
TIMSS and other international comparisons suggest that
the U.S. curriculum is ‘a mile wide and an inch deep.’
“…On average, the U.S. curriculum omits only 17 percent
of the TIMSS grade 4 topics compared with an average
omission rate of 40 percent for the 11 comparison
countries.
The United States covers all but 2 percent of the TIMSS
topics through grade 8 compared with a 25 percent
noncoverage rate in the other countries.
High-scoring Hong Kong’s curriculum omits 48
percent of the TIMSS items through grade 4, and 18
percent through grade 8.”
– Ginsburg et al., 2005
ALGEBRA 1
The Real Number System (N-RN)
Use properties of rational and irrational numbers (3)
Quantities(N-Q)
Reason quantitatively and use units to solve problems (1,
2, 3)
Seeing Structure in Expressions (A-SSE)
Interpret the structure of expressions (1, 2)
Write expressions in equivalent forms to solve problems (3)
Arithmetic with Polynomials and Rational Expressions (A-APR)
Perform arithmetic operations on polynomials (1)
Understand the relationship between zeros and factors
of polynomials (3)
Creating Equations (A-CED)
Create equations that describe numbers or relationships (1, 2, 3, 4)
Reasoning with Equations and Inequalities (A-REI)
Understand solving equations as a process of reasoning
and explain the reasoning (1)
Solve equations and inequalities in one variable (3, 4)
Solve systems of equations (5, 6)
Represent and solve equations and inequalities
graphically (10, 11, 12)
Interpreting Functions (F-IF)
Understand the concept of a function and use function notation (1, 2, 3)
Interpret functions that arise in applications in terms of the context (4, 5, 6)
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Engaging with the HS Content
 How
would you summarize the major work of HS?
 What
would you have expected to be a part of the
major work that is not?
 Give
an example of how you would approach
something differently in your teaching if you
thought of it as supporting the major work, instead
of being a separate, discrete topic.
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Coherence Across
and Within Grades
 It’s
about math making sense.
 The
power and elegance of math comes out
through carefully laid progressions and
connections within grades.
+ Coherence
Think across grades, and link to major
topics within grades
 Carefully
connect the learning within and
across grades so that students can build new
understanding onto foundations built in
previous years.
 Begin
to count on solid conceptual
understanding of core content and build on it.
Each standard is not a new event, but an
extension of previous learning.
+How do students perceive
mathematics?
• Doing mathematics means following the rules laid down
by the teacher.
• Knowing mathematics means remembering and
applying the correct rule when the teacher asks a
question.
• Mathematical truth is determined when the answer is
ratified by the teacher.
-Mathematical Education of Teachers report (2012)
+How do students perceive
mathematics?
 Students
who have understood the mathematics they
have studied will be able to solve any assigned
problem in five minutes or less.
 Ordinary
students cannot expect to understand
mathematics: they expect simply to memorize it and
apply what they have learned mechanically and without
understanding.
-Mathematical Education of Teachers report (2012)
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Looking For Coherence Within
Grades
 Examples:
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



1st grade – 5th grade: Represent and Interpret Data
3rd grade & 5th grade: “Relate area (volume) to
multiplication and to addition.”
6th grade: Solve problems by graphing in all 4
quadrants. (1st year of rational numbers)
8th grade: “Understand the connections between
proportional relationships, lines and linear
equations.”
HS: “Understand that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers.”
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Coherence Within A Grade
Functions – Connections to Expressions, Equations, Modeling
and Coordinates
Determining an output value for a particular input involves
evaluating a an expression; finding inputs that yield a given
output involves solving an equation. Questions about when two
functions have the same value for the same input lead to
equations, whose solutions can be visualized from the
intersection of their graphs. Because functions describe
relationship between quantities, they are frequently used in
modeling. Sometimes functions are defined by a recursive
process, which can be displayed effectively using a
spreadsheet or other technology.
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Looking for Coherence Across
Grades
 Coherence
is an important design element of the
standards.
 “The
Standards are not so much built from topics as
they are woven out of progressions.”
Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix
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Rigor:
Illustrations of Conceptual
Understanding, Fluency, and
Application
 Here
rigor does not mean “difficult problems.”
 It’s
a balance of three fundamental components that
result in deep mathematical understanding.
 There
must be variety in what students are asked to
produce.
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Some Old Ways of Doing Business
•
Lack of rigor
 Reliance
 Lack
on rote learning at expense of concepts
of or excessive use of repetitious practice
 Severe
restriction to stereotyped problems lending
themselves to mnemonics or tricks
 Lack
of quality applied problems and real-world
contexts
 Lack
of variety in what students produce
 E.g., overwhelmingly
only answers are produced,
not arguments, diagrams, models, etc.
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Some New Ways of Doing Business
A.SEE Interpret the structure of expressions.
Suppose P and Q give the sizes of two different animal populations,
where Q>P.
In (a)–(d), say which of the given pair of expressions is larger. Briefly
explain your reasoning in terms of the two populations.
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+Instructional order leads to concept
development which leads to flexible
thinking about models
Concrete
Conceptual and
Procedural
Understanding
Abstract
SemiConcrete
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Frequently Asked Questions

How can we assess fluency other than
giving a timed test?

Is it really possible to assess conceptual
understanding? What does it look like?

Are the Common Core State Standards for
Math all about application and meaningful
tasks?
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Standards for Mathematical
Practice and Depth of
Knowledge
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Lets’s
Do Some Math!
Figure Height
Write an equation that solves for the height, h, in terms of b. Show all
work necessary to justify your answer.
+
Whole group discussion
Share
solutions
Identify
domain(s) and cluster(s)
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Standards for Mathematical
Practices (SMP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of
others.
4.
Model with mathematics
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
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Standards for Mathematical
Practices (SMP)
What
Standards for Mathematical
Practice (SMP) could be promoted
with the Figure Height Task?
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Cognitive Rigor and Depth of
Knowledge (DOK)

The level of complexity of the cognitive demand.

Level 1: Recall and Reproduction


Level 2: Basic Skills and Concepts


Requires the engagement of some mental processing beyond
a recall of information.
Level 3: Strategic Thinking and Reasoning


Requires eliciting information such as a fact, definition, term,
or a simple procedure, as well as performing a simple algorithm
or applying a formula.
Requires reasoning, planning, using evidence, and explanations
of thinking.
Level 4: Extended Thinking

Requires complex reasoning, planning, developing, and
thinking most likely over an extended period of time.
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Depth of Knowledge
What
is the depth of knowledge
(DOK) of the Figure Height task?
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DOK Distribution on SBAC
DOK 2 DOK 3 DOK 4
Grade 4
DOK
1
25%
40%
26%
9%
Grade 8
18%
43%
27%
12%
High
School
27%
41%
23%
9%
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BREAK TIME!!!
15 minutes….Go
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Smarter Balanced
Assessment Consortium
aka ….SBAC
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Using SBAC for High School Graduation Tests –
Policy Questions Abound…
Grade
Subject
Tested
2012–13 and
2013–14
2014–15
and Beyond
Measure current Reading,
Writing, Algebra, Geometry ,
and
Biology Standards
Measure Common
Core State Standards and current
Biology Standards
10
Reading
HSPE
10
Writing
HSPE
10
E/LA
10
Algebra
EOC
10
Geometry
EOC
10
Math
10
Biology
11
E/LA
SBAC
11
Math
SBAC
SBAC
*SBAC
EOC
EOC
Note: 10th grade exams measure high school proficiency with passage required for
graduation; 11th grade exams measure career and college-ready standards.
* 10th grade math exams could be separate Algebra and Geometry EOC exams.
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A Balanced Assessment System
English Language Arts/Literacy and Mathematics, Grades 3-8 and High School
School Year
Last 12 weeks of the year*
DIGITAL CLEARINGHOUSE of formative tools, processes and exemplars; released items and tasks; model
curriculum units; educator training; professional development tools and resources; scorer training modules; and
teacher collaboration tools.
Optional Interim
Assessment
Computer Adaptive
Assessment and
Performance Tasks
Optional Interim
Assessment
Computer Adaptive
Assessment and
Performance Tasks
PERFORMANCE
TASKS
• ELA/Literacy
• Mathematics
Scope, sequence, number and timing of interim assessments locally determined
*Time windows may be adjusted based on results from the research agenda and final implementation decisions.
COMPUTER
ADAPTIVE TESTS
• ELA/Literacy
• Mathematics
Re-take option
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Time and format
 Summative:
For each content area - ELA & Math
 Computer
Adaptive Testing (CAT)
 Selected response (SR), Constructed Response
(open-ended—CR, ECR), Technology enhanced
(e.g., drag and drop, video clips, limited webinterface)
 Performance Tasks (like our CBAs) (PT)
 1 per content area in grades 3-8
 Up to 3 per content area in High School
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Section 4
THE CLAIMS
+SBAC Assessment Claims for Mathematics
Overall Claim (Gr. 3-8)
Overall Claim (High School)
Claim 1
Concepts and Procedures
Claim 2
Problem Solving
Claim 3
Communicating Reasoning
Claim 4
Modeling and Data Analysis
“Students can demonstrate progress toward college and
career readiness in mathematics.”
“Students can demonstrate college and career readiness in
mathematics.”
“Students can explain and apply mathematical concepts and
interpret and carry out mathematical procedures with
precision and fluency.”
“Students can solve a range of complex well-posed problems
in pure and applied mathematics, making productive use of
knowledge and problem solving strategies.”
“Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique
the reasoning of others.”
“Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and
solve problems.”
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What is a claim?
 “Claims” are
the broad statements of the assessment
system’s learning outcomes, each of which requires
evidence that articulates the types of
data/observations that will support interpretations of
competence towards achievement of the claims.
 “assessment
targets” describe the expectations of
what will be assessed by the items and tasks within
each claim.
+
Claim 1
Concepts and Procedures
Students can explain and apply mathematical
concepts and interpret and carry out mathematical
procedures with precision and fluency.
Grade
Level
Number of
Assessment Targets
3
11
4
12
5
11
6
10
7
9
8
10
11
17
Assessment
Targets =
Clusters
+
Claim 1 Targets
Number and Quantity (9-12.N)
Target A: Extend the properties of exponents to rational exponents. (DOK 1, 2) [a/s]
Target B: Use properties of rational and irrational numbers. (DOK 1, 2) [a/s]
Target C: Reason quantitatively and use units to solve problems. (DOK 1, 2) [m]
Algebra (9-12.A)
Target D: Interpret the structure of expressions. (DOK 1) [m]
Target E: Write expressions in equivalent forms to solve problems. (DOK 1, 2) [m]
Target F: Perform arithmetic operations on polynomials. (DOK 1) [a/s]
Target G: Create equations that describe numbers or relationships. (DOK 1, 2) [a/s]
Target H: Understand solving equations as a process of reasoning and explain the reasoning. (DOK 1, 2) [m]
Target I: Solve equations and inequalities in one variable. (DOK 1, 2) [m]
Target J: Represent and solve equations and inequalities graphically. (DOK 1, 2) [m]
Functions (9-12.F)
Target K: Understand the concept of a function and use function notation. (DOK 1) [m]
Target L: Interpret functions that arise in applications in terms of a context. (DOK 1, 2) [m]
Target M: Analyze functions using different representations. (DOK 1, 2, 3) [m]
Target N: Build a function that models a relationship between two quantities. (DOK 1, 2) [m]
Geometry (9-12.G)
Target O: Prove geometric theorems. (DOK 2) [m]
.
Statistics and Probability (9-12.SP)
Target P: Summarize, represent and interpret data on a single count or measurement variable. (DOK 2) [m]
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+
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Claims Task Analysis Jigsaw
3 Rounds: Claims
At your current table: Count off by 3
–move to numbered tables for “focus group”
Each Round, we will focus on a Claim. Focus groups will
rotate their focus: SMP, CCSS or DOK
 Do tasks together
 Analyze tasks focusing on assigned aspect for that round
 Briefly Share after each round
Return to “home” table at end of all 3 rounds to more fully
share ideas from your groups and complete Task Analysis
Form
 Please
Count off and Move: 1’s, 2’s, 3’s
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Task Analysis Protocol Sheet
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Task Analysis Round 1 (Claim 1)
 Do “New
Computers” task on claims
handout. Discuss and justify the SBAC
details listed:



1’s: What content domain/cluster does the task address?
2’s: What is the depth of knowledge (DOK) of the task?
3’s: What Standards for Mathematical Practices (SMP) can
it promote?
 Do “Rewrite
Functions” task. Determine and
justify the same SBAC aspect your group
focused on for “New Computers”
+
New Computers



1’s: Domain/Cluster
2’s: DOK
3’s: SMP
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Rewrite Functions



1’s: Domain/Cluster
2’s: DOK
3’s: SMP
+
Share & justify!
1’s: Domain/Cluster
2’s: DOK
3’s: SMP
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Claim 2 – Problem Solving
Claim 2: Students can solve a range of complex well-posed
problems in pure and applied mathematics, making productive
use of knowledge and problem solving strategies.
A. Apply mathematics to solve well-posed problems
arising in everyday life, society, and the workplace
B. Select and use tools strategically
C. Interpret results in the context of the situation
D. Identify important quantities in a practical situation
and
map their relationships.
+
+
Claim 2 Item Specs
Task Types
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Task Analysis Round 2
 Review “Figure
Height” task on claims
handout. Discuss and justify (also a review
from earlier!) the SBAC details listed:



1’s: What is the depth of knowledge (DOK) of the task?
2’s: What Standards for Mathematical Practices (SMP) can
it promote?
3’s: What content domain/cluster does the task address?
 Do “Graph
Inverse” task. Determine and
justify the same SBAC aspect your group
focused on for “Figure Height”
+
Figure
Height
Write an equation that solves for the height, h, in terms of b. Show all
work necessary to justify your answer.



1’s: DOK
2’s: SMP
3’s: Domain/Cluster
+
Graph Inverse



1’s: DOK
2’s: SMP
3’s: Domain/Cluster
+
Share & justify!



1’s: DOK
2’s: SMP
3’s: Domain/Cluster
+
Claim 3 – Communicating Reason
Claim 3: Students can clearly and precisely construct
viable arguments to support their own reasoning and to
critique the reasoning of others.
A.
Test propositions or conjectures with specific examples.
B.
Construct, autonomously, chains of reasoning that justify or refute propositions or
conjectures.
C.
State logical assumptions being used.
D.
Use the technique of breaking an argument into cases.
E.
Distinguish correct logic or reasoning from that which is flawed,
and—if there is a flaw in the argument—explain what it is.
F.
Base arguments on concrete referents such as objects, drawings, diagrams, and
actions.
G.
Determine conditions under which an argument does and
does not apply.
+
+
Task Analysis Round 3
 Review “Parking
Lot” task on claims
handout. Discuss and justify the SBAC
details listed:



1’s: What Standards for Mathematical Practices (SMP) can
it promote?
2’s: What content domain/cluster does the task address?
3’s : What is the depth of knowledge (DOK) of the task?
 Review
“Decibels” task. Determine and
justify the same SBAC aspect your group
focused on for “Figure Height”
+



1’s: SMP
2’s: Domain/Cluster
3’s:DOK
+
DECIBELS



1’s: SMP
2’s: Domain/Cluster
3’s:DOK

The noise level at a music concert must be no more than 80
decibels (dB) at the edge of the property on which the concert is
held.

Melissa uses a decibel meter to test whether the noise level at the
edge of the property is no more than 80 dB.

Melissa is standing 10 feet away from the speakers and the noise
level is 100 dB.

The edge of the property is 70 feet away from the speakers.

Every time the distance between the speakers and Melissa
doubles, the noise level decreases by about 6 dB.

Rafael claims that the noise level at the edge of the property is no
more than 80 dB since the edge of the property is over 4 times the
distance from where Melissa is standing. Explain whether Rafael is
or is not correct.
+
Share & justify!



1’s: SMP
2’s: Domain/Cluster
3’s:DOK
+
Return to Original groups
 Jigsaw
debrief
+
+ Functions
Progression of Learning:
How does coherence manifest itself in
the standards?
+
Common Core Format
K-8
High School
Grade
Domain
Cluster
Standards
Conceptual Category
Domain
Cluster
Standards
(There are no preK Common Core
Standards)
+
Conceptual Category: Functions
 (Function)
 F-IF:
Domains:
Interpreting Functions
(3 clusters under Interpreting Functions domain)
 F-BF: Building Functions (2 clusters)
 F-LE: Linear, Quadratic, and Exponential
Models* (2 clusters)
 F-TF: Trigonometric Functions (3 clusters)
+
Functions
 Assign
one Domain to each table group
1. Interpret Functions 2. Build Functions or 3. Linear, Quadratic,& Exp Models
 Think:
 Individually
read the Conceptual Category Functions overview from CCSS
 In

Pairs:
Brainstorm: What do students need to know for
each of the clusters in your assigned Functions
Domain?
 Share: In table groups, share your lists with
each other & create a “group list”
+
Functions: Grade 8
What do students learn about functions in
grade 8?
 Read
Functions Progression, Grade 8 Section
 Compare
with your group list
 Notate any items on your group list that are
addressed in grade 8
+
Grade 8 Functions Clusters
 Major:
Define, evaluate and compare
functions
 Supporting:
Use functions to model
relationships between quantities
Functions:
Connections
+
What connections are there between the Functions
domains/clusters and the other high school conceptual
categories?
 Read
the CCSS document for assigned
function domain

Find & enhance details for aligned items on your group list
 Look
for connections to other high
school conceptual categories in the
CCSS document—where are the other
items from your list?

Notate on your list the cluster(s)/standard(s) where these related
items are located in the CCSS
+ Functions Domain Poster &
Presentation
 Meet
with other tables working on the same
domain.
 Poster:
Create a poster to represent the
information you gathered for your Functions
Domain, making sure to include:
Key cluster and standard language in the domain
 Progression of learning from 8th grade
 Connections to other high school conceptual
categories

 Presentation:
Select one person to talk about
each of the above bullets for @ 2 minutes each
+
BREAK TIME!!!
10 minutes….Go
Instructional Shifts to Develop
+
the Standards for
Mathematical Practices
+
Mathematical Practices
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning
of others.
4.
Model with mathematics
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
+
Standards of Student Practice in
Mathematics Proficiency Matrix
+
Digging Deeper:
Constructing Viable
Arguments & Critiquing Reasoning of Others
and Modeling with Mathematics
 In
groups of 4
 Each
person reads one side of the Mathematical
Practices (#3 & #4) handouts.
 Highlight three new ideas found in your assigned
reading
 Share in your group and use the ideas to
“enhance” the Proficiency matrix using the blank
matrix
+
Planning for Instructional
Action
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Implications for your students
 Consider
your lessons over the next few
weeks
 Develop
an instructional action intended to
improve your instructional practice for
critiquing the reasoning of others.
 Use
think-pair-share as one of your
strategies.
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
Homework
Use one of the 2 given tasks as a learning activity in at least 1
class before next session.
Complete the Rich Task Classroom Implementation
Preplanning worksheet before doing the lesson – be
sure to include using Think-Pair-Share
 Capture
evidence of several students development of
SMP 3&4 during the lesson using the Proficiency
Matrix
 Reflect
on instructional strategies you implemented
during lesson to support MSP 3&4 (including those on
preplanning worksheet)
 Select
3 samples of student work to share at next
class: 1 high, 1 low
 Bring
back all handouts to next session
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Top Resources for Math Educators

Inside Mathematics Video excerpts of mathematics lessons correlated with the
practice standards, resources on content standards alignment, and videos of
exemplary lessons in both elementary and secondary settings.

Illustrative Mathematics Guidance to states, assessment consortia, testing
companies, and curriculum developers by illustrating the range and types of
mathematical work that students experience in a faithful implementation of the
Common Core State Standards.

Progressions Documents for the Common Core Math Standards Narrative
documents describing the progression of a topic across a number of grade levels.

Publishers Criteria Provides criteria for aligned materials to CCSS. Based on the two
major evidence-based design principles of the CCSSM, focus and coherence, the
document intends to guide the work of publishers and curriculum developers, as
well as states and school districts, as they design, evaluate, and select materials or
revise existing materials.

Achieve The Core Guidance and templates on how to begin implementing the shifts,
assembled by the nonprofit Student Achievement Partners.
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Reflections
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Reflection
 What
is your current reality around classroom
culture?
 What
can you do to enhance your current reality?
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Wrap up Activity
 Feedback
Thank You!
See you next session…………..
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Day 2
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Outcomes Day 2 & 3:
 Analyze
student work with the Standards for
Mathematical Practice and content standards.
 Analyze, adapt, and
implement a task with the
integrity of the Common Core State Standards.
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Welcome Back Activity
Success, challenge, barrier, breakthrough
Reflect on your experience using one of the
assigned tasks in your classroom.
Use separate post-it notes to capture your successes,
challenges, barriers, and/or breakthroughs
Post on appropriate poster
Read post-it notes on all posters and select one that
resonates with you.
Quick share of selected post-its.
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Homework Review
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Collaboration Protocol-Looking at
Student Work (55 minutes)
Select one group member to be today’s facilitator to help move the group through the steps of the protocol.
Teachers bring student work samples with student names removed.
1. Individual review of student work samples (10 min)
•
All participants observe or read student work samples in
silence, making brief notes on the form “Looking at
Student Work”
2. Sharing observations (15 min)
The facilitator asks the group
4. Discussing implications-teaching & learning (10 min)
• The facilitator invites all participants to share any thoughts
they have about their own teaching, students learning, or ways
to support the students in the future.
• How might this task be adapted to further elicit student’s use
of Standards for Mathematical Practice or mathematical
content.
• What do students appear to understand based on evidence?
• Which mathematical practices are evident in their work?
• Each person takes a turn sharing their observations about
student work without making interpretations, evaluations
of the quality of the work, or statements of personal
reference.
3. Discuss inferences -student understanding (15 min)
• Participants, drawing on their observation of the student
work, make suggestions about the problems or issues of
student’s content misunderstandings or use of the
mathematical practices.
Adapted from: Steps in the Collaborative Assessment Conference developed by
Steve Seidel and Project Zero Colleagues
5. Debrief collaborative process (5 min)
• The group reflects together on their experiences using this
protocol.
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Homework Strategy Sharing
 How
did using the Proficiency matrix work? Are
there changes you’d like to make?
 How
did your students respond to Think-PairShare?
 What
other strategies did you try out to improve
your instructional practice so that student’s had the
opportunity to critiquing the reasoning of others?
 Say
It, Know It Structures handout – choose 1 to try
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BREAK TIME!!!
15 minutes….Go
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Rich Tasks
What makes a rich task?
1.
Is the task interesting to students?
2.
Does the task involve meaningful mathematics?
3.
Does the task provide an opportunity for students to
apply and extend mathematics?
4.
Is the task challenging to all students?
5.
Does the task support the use of multiple strategies
and entry points?
6.
Will students’ conversation and collaboration about
the task reveal information about students’
mathematics understanding?
Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al
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Environment for Rich Tasks
 Learners
are not passive recipients of
mathematical knowledge.
 Learners
are active participants in creating
understanding and challenge and reflect on
their own and others understandings.
 Instructors
provide support and assistance
through questioning and supports as
needed.
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Is this a rich task?
Is this a rich task?
In (a)–(e), determine whether the quantity is changing in a
linear or exponential fashion. Be prepared to justify your
answer.
a. A savings account, which earns no interest, receives a
deposit of $723 per month.
b. The value of a machine depreciates by 17% per year.
c. Every week, 9/10 of a radioactive substance remains
from the beginning of the week.
d. A liter of water evaporates from a swimming pool every
day.
e. Every 124 minutes, ½ of a drug dosage remains in the
body.
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SBAC Claim 4
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Claim 4 – Modeling and Data Analysis
Claim 4: Students can analyze complex, real-world
scenarios and can construct and use mathematical
models to interpret and solve problems.
A.
B.
C.
D.
E.
F.
G.
Apply mathematics to solve problems arising in everyday life, society, and
the workplace.
Construct, autonomously, chains of reasoning to justify mathematical models
used, interpretations made, and solutions proposed for a complex problem.
State logical assumptions being used.
Interpret results in the context of a situation.
Analyze the adequacy of and make improvement to an existing model
or develop a mathematical model of a real phenomenon.
Identify important quantities in a practical situation and map their
relationships.
Identify, analyze, and synthesize relevant external resources to pose
or solve problems.
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Task Analysis

What content cluster is addressed in this task?

What is the depth of knowledge of this task?

What mathematical practices does it promote?

Is this a rich task?
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Planning for Instructional
Action
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Deepen conceptual understanding
using tasks found in your Current
Materials
Change the tasks


Use richer tasks provided in
your instructional materials
(usually found at end of lesson
or in “extras” with book)
Adjust existing tasks – raise
DOK level
Change how you
implement the task
Refer to Standards for
Mathematical Practices
Compilations for strategies


Think, Pair, Share strategies
Ask good questions: teacher to
student, student to teacher,
student to student

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DOK 1 Task adjusted to DOK 2

Which statement is true about
the relation shown below?
[1] It is a function because there
exists one y-coordinate for each
x-coordinate.
[2] It is a function because there
exists one x-coordinate for each
y-coordinate.
[3] It is not a function because
there are multiple x-values for a
given y-value.
[4] It is not a function because
there are multiple y-values for a
given x-value.

Which statements are true
about the relation shown
below?
[1] It is a function because there
exists one y-coordinate for each
x-coordinate.
[2] It is a function because there
exists one x-coordinate for each
y-coordinate.
[3] It is a function because it
passes the vertical line test.
[4] It is not a function.
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Change this DOK 1 task to
DOK 2 or 3
What type of function is shown by the
graph at the right?

[1]
[2]
[3]
[4]
linear
exponential
quadratic
absolute value
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Planning to apply learning
 Review
upcoming lessons for mathematical
content
 Find
or create or adapt a rich task to use with one
of these lessons.
 Develop
an instructional action intended to
improve your instructional practice for critiquing
the reasoning of others.
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Homework
 Complete
the Rich Task Classroom Implementation
Preplanning worksheet before doing the lesson –
include your new Think-Pair-Share strategy.
 Capture
evidence of several students development of
SMP 3&4 during the lesson using the Proficiency
Matrix
 Reflect
on instructional strategies you implemented
during lesson to support MSP 3&4
 Bring
a copy of the task you used (both before and
after, if you adapted the task)
 Select
10-12 samples of student work to share at next
session: a mix of low to high
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Thanks…… are your students this
excited by rich tasks?
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Day 3
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Outcomes Day 2 & 3:
 Analyze
student work with the Standards for
Mathematical Practice and content standards.
 Analyze, adapt, and
implement a task with the
integrity of the Common Core State Standards.
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Welcome Back Activity
Success, challenge, barrier, breakthrough
Reflect on your experiences focusing on the
Standards for Mathematical Practices in your
classroom.
Use separate post-it notes to capture your successes,
challenges, barriers, and/or breakthroughs
Post on appropriate poster
Read post-it notes on all posters and select one that
resonates with you.
Quick share of selected post-its.
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Homework Review
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Looking at Tasks Used
Trade the task you used with another person.
 Do
a task analysis of each other’s tasks using the
following components:
Cluster/standard
 DOK
 Standards for Mathematical Practices
 Is it a rich task?

 Discuss
findings with each other.
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Looking at student work
With your same partner/group, complete the
following “Looking at Student Work” protocol.
 Sort one person’s classroom set of papers into
high, medium, and low piles (according to
student’s understanding of the mathematical
content) and come to agreement on which papers
belong in which piles. Record your criteria for
high, medium, & low.
 Repeat with the other group member’s set of
papers.
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BREAK TIME!!!
15 minutes….Go
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Critiquing the Reasoning of
Others in Action
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Video Task
5
minutes to work on independently
 Work
in table groups to discuss thinking
 Analyze
task using task analysis worksheet
(from Day 1 – add to bottom of sheet)
 Discuss
 Watch
whole group
video
Looking
into
a
high
school
classroom
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Inside Mathematics Public
Lesson: Quadratic Functions
• What makes this activity evidence of
critiquing the reasoning of others?
Modeling?
• What observable conditions supported
critiquing the reasoning of others?
Modeling?
• What observable conditions constrained
critiquing the reasoning of others?
Modeling?
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Publishers Criteria Shifts
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Key Shifts to look for….
Focus:
Coherence:
Rigor:
Underline one sentence from each of these sections that helps
you “make sense” of these shifts.
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Wrap up Activity
 Evaluations
Thank You!