Transcript Slide 1

Agenda

CCSS math shifts – digging in deep for high school

Smarter Balanced Assessment

Resources and professional learning opportunities
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CCSS Math Webinar Part 4: 5/28/13
OSPI CCSS Quarterly Webinar Series
http://www.k12.wa.us/CoreStandards/UpdatesEvents.aspx#Webinar
Year 2 Topics: 2012-13
CCSS Systems for District
and Building Leaders
1. September 2012: Recap / State Context / Resources /
Where to Start / Professional Learning Systems
2. December 2012: The Basics for School Boards
3. March 2013: Focus on Instructional Materials / Principal
Leadership
4. May 2013: Focus on Communications and Smarter Balanced
Digital Library
CCSS-M Content for Leaders 1. September 2012: Recap / Math Shifts and Resources
and Cross-Content Teams
2. December 2012: Diving into the Math Shifts for Elementary
3. March 2013: Diving into the Math Shifts for Middle School
4. May 2013: Diving into the Math Shifts for High School
CCSS-ELA for Leaders and
Cross-Content Teams
3
1. September 2012: Recap / ELA Shifts and Resources
2. December 2012: Diving into ELA and Text Selection /
Implications for ELA in History/Social Studies
3. March 2013: Diving into the ELA: A Focus on Evidence in
Reading/Writing/Speaking & Listening
4. May 2013: Diving into ELA: Academic Vocabulary and ELA
across
the Part
Subjects
(Science, the Arts, etc.)
CCSS Math
Webinar
4: 5/28/13
Before we begin…About You

We’d like to know a little about who is out there.

Time for a poll (one more time…)
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CCSS Math Webinar Part 4: 5/28/13
ESEA Flexibility
CAREER AND COLLEGE READY LEARNING
STANDARDS FOR K-12
Vision
Every Washington
Student and Educator
Purpose
Core Values
All
students
leave
high
school
college
and career
ready
Our Purpose: To develop a statewide system with resources that
support partners at all levels in their preparation of ALL educators
and ALL students to implement the CCSS.
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Washington’s State Learning Goals are the
Foundation (HB 1209+; RCW 28A.150.210)
1. Read with comprehension, write effectively, and communicate
successfully in a variety of ways and settings and with a variety of
audiences;
2. Know and apply the core concepts and principles of mathematics;
social, physical, and life sciences; civics and history, including
different cultures and participation in representative government;
geography; arts; and health and fitness;
3. Think analytically, logically, and creatively, and to integrate
technology literacy and fluency as well as different experiences
and knowledge to form reasoned judgments and solve problems;
and
4. Understand the importance of work and finance and how
performance, effort, and decisions directly affect future career
and educational opportunities.
5.
Updated in 2011: SSB 5392)
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CCSS Implementation Timeline
Phase 1: CCSS Exploration
Phase 2: Build Awareness & Begin
Building Capacity
Phase 3: Build State & District
Capacity and Classroom Transitions
Phase 4: Statewide Application and
Assessment
Ongoing: Statewide Coordination
and Collaboration to Support
Implementation
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Our guiding beliefs and approach for CCSS
Implementation in WA
2-Prongs:
1. The What: Content Shifts (for students and educators)

The How: System “Remodeling”
2.



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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.
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
CCSS Math Webinar Part 4: 5/28/13
Ongoing: Statewide Coordination and
Collaboration to Support Implementation
Washington
Including:
• School Districts (CCSS District Implementation Network)
• Higher Education
• Education and Educator Content Associations
• Business
Partners
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“These standards
are not intended
to be new names
for old ways of
doing business.”
CCSSM, page 5
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The 3 Shifts in CCSSM



Focus strongly where the
standards focus
Coherence: Think across
grades and link to major
topics within grades
Rigor: In major topics,
pursue with equal
intensity:



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Conceptual understanding
Procedural skill and fluency
Application
CCSS Math Webinar Part 4: 5/28/13
Shift One: Focus
strongly where the Standards focus
• Move away from "mile wide, inch deep" curricula
identified in TIMSS.
• Learn from international comparisons.
• Teach less, learn more.
“Less topic coverage can be associated with higher scores
on those topics covered because students have more time
to master the content that is taught.”
– Ginsburg et al., 2005
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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.”
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CCSS Math Webinar Part 4: 5/28/13–
Ginsburg et al., 2005
Focus in Early Grades
Materials do not assess any of the following topics before
the grade level indicated.
Grade
Introduced
Topic
Probability, including chance, likely outcomes, probability models.
7
Statistical distributions, including center, variation, clumping, outliers,
mean, median, mode, range, quartiles, and statistical association or
trends, including two-way tables, bivariate measurement data, scatter
plots, trend line, line of best fit, correlation.
6
Similarity, congruence, or geometric transformations.
8
Symmetry of shapes, including line/reflection symmetry, rotational
symmetry.
4
Additionally, materials do not assess pattern problems in K-5
that do not support the focus on arithmetic, such as “find the
CCSS Math Webinar Part 4: 5/28/13
next one” problems.
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Shift Two: 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.
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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)
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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.
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CCSS Math
Webinar Part
4: 5/28/13
-Mathematical
Education
of Teachers report (2012)
Coherence with Functions
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. 3.OA.D.9
3rd Grade
Use variables to represent two quantities in a real-world problem that change in relationship to
one another; write an equation to express one quantity, thought of as the dependent variable, in
terms of the other quantity, thought of as the independent variable. Analyze the relationship
between the dependent and independent variables using graphs and tables, and relate these to the
equation. 6.EE.C.9 6th Grade
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial
value of the function from a description of a relationship or from two (x, y) values, including reading these from a
table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it
models, and in terms of its graph or a table of values. 8.F.B.4 8th Grade
Write a function that describes a relationship between two quantities.
Combine standard function types using arithmetic operations.
F-BF.A.b
F-BF.A
HS Functions
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.
Shift Three: Rigor Equal intensity in conceptual
understanding, procedural skill/fluency, and
application

The CCSSM require:




Solid conceptual understanding
Procedural skill and fluency
Application of skills in problem solving situations
In the major work of the grade, this requires equal
intensity in time, activities, and resources in pursuit of all
three
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It starts with Focus



The current U.S. curriculum is ‘a mile wide and an inch
deep.’
Focus is necessary in order to achieve the rigor set forth
in the standards
More in-depth mastery of a smaller set of things pays off
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The Structure is the Standards
A Grecian urn
You have just purchased an expensive Grecian urn and asked the dealer
to ship it to your house. He picks up a hammer, shatters it into pieces,
and explains that he will send one piece a day in an envelope for the
next year.You object; he says “don’t worry, I’ll make sure that you get
every single piece, and the markings are clear, so you’ll be able to glue
them all back together. I’ve got it covered.” Absurd, no? But this is the
way many school systems require teachers to deliver mathematics to
their students; one piece (i.e. one standard) at a time.”
Adapted from “The Structure is the Standards”
by Bill McCullum, Phil Daro and Jason Zimba
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Standards for Mathematical Practice








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Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
CCSS Math Webinar Part 4: 5/28/13
Standards for Mathematical Practices
Graphic
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Some Old Ways of Doing Business
•
A different topic every day
•
Every topic treated as equally important
•
Elementary students dipping into advanced topics at the
expense of mastering fundamentals
•
Infinitesimal advance in each grade; endless review
•
Incoherence and illogic – bizarre associations, or lacking a
thread
CCSS Math Webinar Part 4: 5/28/13
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Traditional Ways of Doing Business
Finding Intercepts by Substitution
Find the intercepts of the line y = 13 – x
Solution
The first intercept is easy to find. The y-intercept occurs when
x = 0. Substituting gives us y = 13-0 = 13, so the y-intercept is
(0, 13).
Similarly, the x-intercept occurs when y = 0. Plugging in 0 for y
gives us 0 = 13 - x, and adding x to both
sides gives us x = 13. So (13, 0) is the x-intercept.
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Traditional Ways of Doing Business
Finding Intercepts for Standard Form Equations Using the Cover- Up
Method
Find the intercepts of 7x - 3y = 21
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Traditional Ways of Doing Business

Factoring Methods



Factoring out a monomial
Factoring by grouping
Factoring x2 + bx + c



Factoring ax2 + bx + c




When c is postivie
When c is negative
When a is negative
Factoring Special cases


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When c is positive
When c is negative
Difference of two squares
Perfect square trinomials
CCSS Math Webinar Part 4: 5/28/13
New Ways of Doing Business
Teacher: To avoid mile wide factoring, I’m thinking CCSS intends for us to narrow down
the toolbox but I need to know what to cut. I taught factoring monomials from bi, then
grouping, then turning trinomials into four factors for grouping and relating special cases
to grouping, all the while motivating toward guess and check for shortcuts. The CCSS do
not seem to include grouping which wipes out the rest of my sequence. Can someone
please clarify what factoring tools will be used, particularly if don’t factor by grouping? Is
there a connected sequence?
Bill McCallum: I would say that CCSS is not so much narrowing down the toolbox, as
encouraging students to see that all the different tools work on the same principle, so
that you don’t have to remember so many different tools.Your progression is fine, and
can be understood as progressively more sophisticated applications of the distributive
property. I don’t know exactly what you mean when you say that the “CCSS does not
seem to include grouping.” If I understand correctly what you mean by grouping, it is an
instance of the distributive property, which is fundamental from early grades (even if it
does not go by that name).
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CCSS Math Webinar Part 4: 5/28/13
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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A Look at Assessment
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CCSS Math Webinar Part 4: 5/28/13
CCSS Assessment System Transitions


Our change to Common Core is at the heart of
assessment changes for ELA and Math
NCLB requires states to assess state standards

We’ve changed standards so we need to change assessments


What we change to is our choice
Smarter Balanced is where we are headed for ELA and Math


Graduation requirements are a state’s choice


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IMPT: There are currently no assessment consortia established for Science
Supt Dorn is proposing reduced graduation requirements
ESEA Waiver changes expectation that all students are
proficient next year (2014) – it gives us more time and
more individualized school-based goals
CCSS Math Webinar Part 4: 5/28/13
Smarter Balanced Assessment System
Components
Common
Core State
Standards
specify
K-12
expectations
for college
and career
readiness
Summative
assessments
Benchmarked to
college and career
readiness
Teachers and
schools have
information and
tools they need to
improve teaching
and learning
Teacher resources for
formative assessment
practices
to improve instruction
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All students
leave
high school
college
and career
ready
Interim assessments
Flexible, open, used for
actionable feedback
CCSS Math Webinar Part 4: 5/28/13
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
COMPUTER
ADAPTIVE TESTS
• ELA/Literacy
• Mathematics
Re-take option
*Time windows may be adjusted based on results from the research agenda and final implementation decisions.
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Claims for the Mathematics
Summative Assessment
Overall Claim for Grades 3-8
Overall Claim for Grade 11
“Students can demonstrate progress toward college and career
readiness in mathematics.”
“Students can demonstrate college and career readiness in
mathematics.”
Claim #1 - Concepts &
Procedures
“Students can explain and apply mathematical concepts and
interpret and carry out mathematical procedures with precision and
fluency.”
Claim #2 - Problem Solving
“Students can solve a range of complex well-posed problems in pure
and applied mathematics, making productive use of knowledge and
problem solving strategies.”
Claim #3 - Communicating
Reasoning
“Students can clearly and precisely construct viable arguments to
support their own reasoning and to critique the reasoning of others.”
Claim #4 - Modeling and Data
Analysis
“Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and solve
problems.”
CCSS Math Webinar Part 4: 5/28/13
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Smarter Balanced Timeline –
Washington’s Involvement
(http://www.k12.wa.us/SMARTER/default.aspx)








OSPI staff involved in workgroups 2010-2014
Teachers involved in item writing Summer/Fall 2012
Sample Released Items and Performance Tasks – October 2012
(view the OSPI webinar!)
Small Scale Trials in Oct/Nov 2012
Pilot in Spring 2013
Practice Test widely available May 29
Comprehensive field test in 2013-14
Operational use in 2014-15
The Digital Library…

Work begins late spring 2013

State Network of Educators to be recruited in May 2013 to populate
the
digital library
CCSS Math Webinar Part 4: 5/28/13
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Smarter’s Vision for the Digital
Library



Provide an online, interactive clearinghouse with all the
formative tools and resources necessary to transform
classroom practices to support student success.
Prior to summative assessment, primary focus
professional development.
With the summative, data from summative and interim
score reports integrated into resources for teachers,
students, and parents.
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CCSS Math Webinar Part 4: 5/28/13
Digital Library Features
One Stop:
 The Digital Library will have links to all test engine systems through a single
sign-on with user permission levels so teachers, parents, and students have
access to all of the curriculum and professional learning resources.
 Assessment literacy
 Formative assessment resources
 Links to other resources and other components of the Smarter online
system
Interactive Teacher Space
 Opportunities to keep journals of practices
 Key words or phrases in the journals will generate suggested lists of
resources.
 Record resources consulted and suggest others.
 Teachers can request resources matched to student assessment results.
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Digital Library Deliverables

Teaching and Learning Resources for Educators
Modules for Grades K-2, 3-5, 6-8, 9-12

Assessment Literacy Modules


144 Assessment Literacy professional learning modules that
include:


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how to build, administer, score, evaluate, interpret, and use data from
formative, interim, and summative assessments
Includes resources for each grade band that address English
Language Learners and Students With Disabilities
CCSS Math Webinar Part 4: 5/28/13
Digital Library Deliverables

Exemplar Instruction Modules

50 instructional modules for each grade band (Grades K-2, 3-5,
6-8, 9-12)
ELA/Literacy – Proposed Modules
Mathematics – Proposed Modules
Balance of Inf. and Literary Text
Focus
Literary in the Content Areas
Coherence
Increased complexity of text
Fluency
Text-Based questions and answers
Duel Intensity
Academic Vocabulary
Deep Understanding
Writing using evidence
Math Practices across various standards
Writing using evidence
(Wireless Generation Response pg. 97)
Page 41
CCSS Math Webinar Part 4: 5/28/13
Deliverables –
Exemplar Instruction Modules
…each instructional module will:

Start by identifying the learning targets for the lesson, which align with the CCSS in
ELA or Math.

Begin lesson with a formative pre-assessment to determine the level of knowledge
students have about the learning target. (ASSESS)

Use formative assessment data/information to plan the lesson so that the teacher
knows individual students’ needs related to the learning targets. (PLAN)

Provide examples of instruction that can teach the learning target and also meet the
needs of diverse learners.(TEACH)

Conclude the lesson with a formative post- assessment whose data will determine
the plan for the next lesson (ASSESS)

Contain embedded links to the Digital Library resources, Assessment Literacy
modules and glossary, and additional resources as available.
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(Wireless Generation Response pg. 108 )
CCSS Math Webinar Part 4: 5/28/13
Deliverables – Exemplar Instruction
Each module will show video clips on:

Classroom instruction of the learning targets

Formative assessment (pre and post instruction) of the learning targets

Teacher and student reflections following the lesson

The length of each video will be between 1–3 minutes, with the final length of each
module no longer than 15–25 minutes.
Each module will include a Teacher Resource Guide with:

Graphic/visual and text versions of the full cycle of instruction using formative
assessment practices; and key CCSS-M/ELA instructional shifts

Student work samples (by grade band) from diverse student groups

Examples of the writing required in each grade level

Evidence gathering tools and techniques (by content and grade band) including preassessments (prior to lesson), post-assessments(following the lesson)

Links to resources on CCSS, formative assessments, appropriate accommodations for
CCSS content and meeting needs of diverse learners.
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(Wireless Generation Response pg. 109)
CCSS Math Webinar Part 4: 5/28/13
State Network of Educators (SNE)
http://www.k12.wa.us/SMARTER/EducatorInvolvement.aspx
Overview:

70-100 members per state and a minimum of 2700+ across all governing states (WA will have 92)

Participate in web-based review and feedback cycles to develop (2 year commitment)

Digital Library Application

Quality Criteria Policies

Inventory of Currently Available Resources

Smarter Balanced Professional Learning Resources

Educator Training Materials

Identify and recommend additional resources for the Digital Library

Disseminate web-based educator training to state professional learning networks

Receive stipends from Contractor
Timeline:

Statewide recruitment process in May 2013 – APPLY TODAY!

Notifications in early July 2013

Work begins in Summer 2013
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Tools and Supports
What’s new and what’s next
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Washington State Common Core State Standards
Year 2 Professional Learning Opportunities
In partnership with OSPI, Regional Math and English Language Arts
Coordinators from each ESD across the state, have created consistent, equitable
professional development opportunities to support implementation of the Common
Core State Standards. These workshops align with the transition plans set out by the
collective group.
Mathematics
Grades
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CCSS Focus Domain:
K-2
Counting and Cardinality
Numbers and Operations
in Base Ten and Algebraic Thinking
3-5
Numbers and Operations - Fractions
6-8
Ratio and Proportional Relationships
HS
Linear Relationships and Functions
Description
Teachers across all grade bands will deepen their
understanding of the major shifts to the Common
Core State Standards (CCSS):

Embed Standards for Mathematical Practices with
grade specific content

Analyze, adapt and implement tasks with the
intended rigor of the CCSS

Understand the Smarter Balanced Assessment
System

Analyze student work to identify next steps for
learning
CCSS Math Webinar Part 4: 5/28/13
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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Algebra Progression Document
Seeing Structure in Expressions
Seeing structure in expressions entails a dynamic view of an algebraic expression, in which
potential rearrangements and manipulations are ever present.A-SSE.2 An important skill for college
readiness is the ability to try out possible manipulations mentally without having to carry them
out, and to see which ones might be fruitful and which not.
CCSS Math Webinar Part 4: 5/28/13
Algebra Progression Document
Reasoning with Equations and Inequalities
The danger in learning algebra is that students emerge
with nothing but the moves, which may make it difficult to detect
incorrect or made-up moves later on. Thus the first requirement in
the standards in this domain is that students understand that solving
equations is a process of reasoning. A-REI.
It is traditional for students to spend a lot of time on various
techniques of solving quadratic equations, which are often presented
as if they are completely unrelated (factoring, completing the square,
the quadratic formula). In fact, as we have seen, the key step in
completing the square, going from 𝑥 2 = 2 𝑡𝑜 𝑥 = ± 𝑞 , involves at
its heart factoring. And the quadratic formula is nothing more than
an encapsulation of the method of completing the square. Rather
than long drills on techniques of dubious value, students with an
understanding of the underlying reasoning behind all these methods
are opportunistic in their application, choosing the method that bests
suits the situation at hand. A-REI.4b
http://commoncoretools.me/wpcontent/uploads/2012/12/ccss_progression_algebra_2012_12_04.pdf
CCSS Math Webinar Part 4: 5/28/13
Resources for Considering Instructional
Materials

OSPI Instructional Materials Web Site:


http://www.k12.wa.us/CurriculumInstruct/InstructionalMaterialsReview.aspx
OSPI’s Open Educational Resources Project:

http://digitallearning.k12.wa.us/oer/
From CCSS Developers…
CCSS Publisher’s Criteria – ELA and Math (http://engageny.org/resource/publishers-criteria-for-elaliteracy-and-math/)


CCSS Evidence Guides: Common Core-aligned practice made clear (from
Achieve the Core)

These tools provide specific guidance for what the CCSS for ELA / literacy and math looks like in
planning and practice. They are designed as developmental tools for teachers and those who support
teachers. http://www.achievethecore.org/leadership-tools-common-core/instructional-practice/
Going deeper with other states…
 EQuip Review Rubrics and Process (http://engageny.org/resource/tri-state-quality-review-rubric-and-rating-process/)
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CCSS Math Webinar Part 4: 5/28/13
2012-13 CCSS Implementation
Resources & Activities
Opportunities and Resources
CCSS Awareness and Professional Learning Opportunities and
Materials (http://www.k12.wa.us/CoreStandards/Resources.aspx)
OSPI CCSS Webinar Series
PD Offered through all 9 ESDs
CCSS District Implementation Network Collaborations
Instructional Materials Quality Considerations & Supports
Assessment System Resources
Smarter Balanced Released Sample Items / Perf. Tasks
Dynamic Learning Map Assessment Literacy Supports
Teacher-Leader Capacity Building Opportunities
Math and ELA “Fellows” build capacity around common learning (Spring 2013)
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CCSS Math Webinar Part 4: 5/28/13
Thank YOU!
Common Core Supports:
OSPI Lead Team:
General Support / Overall CCSS Leadership:
- General email: [email protected]
- Jessica Vavrus, [email protected]
Math Support / CCSS Coordination Lead:
- Greta Bornemann, [email protected]
ELA Support:
- Liisa Moilanen Potts, [email protected]
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