MATH Model Content Frameworks

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The PARCC Model Content Frameworks
Mathematics
Grades 3-8, Algebra I, Geometry, and
Algebra II
Version 3.0—November 2012
Common Core State Standards for
Mathematics
• 8 Standards for Mathematical Practice
– Describe areas of expertise for students at all grade levels
– Rest on important processes and proficiencies
• Mathematics Content Standards
– Grade specific in 3-8
– Domain specific for high school standards
Key Shifts in Mathematics
• Content Shifts
– Big ideas at each grade band
• Fluency (K-4)
• Algebraic Thinking and Proportional Reasoning (5-8)
• Functions and Modeling (9-12)
Key Shifts in Mathematics
• Instructional Shifts
– Teachers should move away from “coverage” toward deeper
understanding.
– Greater emphasis is placed on the 8 Standards for Mathematical
Practice.
– Instructional emphasis is placed on natural learning progressions as
well as clusters of information.
– Discrete bits of information are no longer the strategy for instruction.
– Test preparation is no longer the focus of instruction.
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Approach of the Model Content Frameworks
for Mathematics
• Analysis of CCSS on how focus, coherence, content and practices all work
together
• Frame the critical advances in the standards:
– Focus and coherence
– Content knowledge, conceptual understanding, and expertise
– Content and mathematical practices
• Grades 3-8; Algebra I, Geometry, Algebra II; Mathematics I, Mathematics II,
Mathematics III
Purpose and Audience of the Model
Content Frameworks
Purpose
• Inform development of PARCC assessments
• Support implementation of the Common Core State
Standards
Audience
• State and local curriculum directors
• Teachers and building administrators
Purposes for the PARCC Model Content Frameworks
• To serve as a bridge between the Common Core State
Standards and the PARCC assessments by
– Supporting implementation of the Common Core
State Standards
– Informing development of item specifications and
blueprints for the PARCC assessments
• To serve as one model for teachers, curriculum
directors, and administrators
A Model for Curriculum Developers and Teachers
• Illustrates one way of organizing the content of the standards over
the course of the school year without prescription
• Reflects the key shifts in the standards
• Provides insight into the development of the PARCC Assessment
System
• Presents standards in an integrated fashion
• Focuses on essential knowledge, skills, and understandings
students must develop for college and career readiness
Note: The Frameworks are NOT a complete guide for curriculum.
What is Different about PARCC’s Development
Process?
• PARCC states first developed the Model Content Frameworks to
provide guidance on key elements of excellent instruction
aligned with the Standards.
• The Model Content Frameworks informed the assessment
blueprint design.
So, for the first time. . .
• PARCC is communicating in the same voice to teachers as it is to
assessment developers!
• PARCC is designing the assessments around the exact same
critical content the standards expect of teachers and students.
An Aligned System
Common Core State Standards
Model Content Frameworks
Model Instructional Lessons/Units
PARCC Assessment System
CCSS Goal:
All Students College and Career Ready
• Students will solve problems related to the content at their
grade level with connections to the practices.
• Students express mathematical reasoning by constructing
mathematical arguments and critiques.
• Students solve real-world problems engaging particularly in
the modeling practice.
• Students demonstrate fluency in areas set forth in the
Standards for Content in grades 3-6.
Key Elements of the Model Content Frameworks
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Examples of Key Advances from Previous Grades
Fluency Expectations
Examples of Major Within-Grade Dependencies
Opportunities for Connections
Opportunities for In-Depth Focus
Opportunities for Connecting Content and Practices
Content Emphasis by Cluster
Assessment Limitations
Key Advances from Previous Grades
• Why?
– Diagnostic in Nature
– Embedded Assessment of Securely Held Content
– Early Intervention to Close Curricular Gaps
– Opportunity to Remediate Areas of Concern From
Earlier Grades
– Opportunity for Vertical Alignment
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Key Advances from Previous Grades
• Grade 5 Example
– Students use their understanding of fraction
equivalence and their skill in generating
equivalent fractions, including fractions
with unlike denominators.
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Key Advances from Previous Grades
• Imperative in Order To
– Add and Subtract Fractions with Unlike Denominators
– Understand Equal Fractions as a Scaling of the
Numerator and Denominator
– Solidify the Foundation Needed to Perform
Operations on Algebraic Fractions (Rational
Expressions)
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Fluency Expectations and Examples of
Culminating Standards
• Why?
– Always Good to Know Where You Are Going
– Frames the Key Take-Aways at Each Grade Level
– Helps to Prioritize Scope and Sequence
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Fluency Expectations and Examples of
Culminating Standards
• Grade 7 Example
– Students solve multistep problems posed
with positive and negative rational numbers
in any form, using tools strategically.
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Fluency Expectations and Examples of
Culminating Standards
• How does this help me as a teacher?
– Helps me to understand overarching goals of the
grade level
– Helps me to see the culmination of multiple
progressions as well as the integration of math
practices and problem solving
– Helps me to think of instruction in terms of something
other than discrete bits of information
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Examples of Major Within Grade
Dependencies
• Why?
– Highlights Body of Content Within a Grade Where
Conceptual Understanding of One Body of
Knowledge Depends on Another Body of
Knowledge at the Same Grade Level
– Stresses the Need to Organize Coherently
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Examples of Major Within Grade
Dependencies
• Grade 6 Example
– Equations in the form px=q (6.EE.7) are unknown
factor problems and solutions could sometimes be
the result of dividing a fraction by another fraction
(6.NS.1).
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Examples of Major Within Grade
Dependencies
• Outcomes for teachers and students
– Thoughtful organization allows teachers to
develop and deliver more meaningful lessons and
units.
– Students are able to use knowledge already
mastered to engage in more complex problems.
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Examples of Opportunities for Connections
Among Standards, Clusters, or Domains
Why?
–Opportunities to Connect Content in
Assessments, Curriculum, and Instruction
–Stresses the Need to Avoid Checklist
Mentality
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Examples of Opportunities for Connections
Among Standards, Clusters, or Domains
• Grade 8 Example
– Students’ work with proportional relationships,
lines, linear equations, and linear functions can be
enhanced by working with scatter plots and linear
models of association in bivariate measurement
data (8.SP.1-3)
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Examples of Opportunities for Connections
Among Standards, Clusters, or Domains
• What is the Value?
– Excellent opportunity to integrate real world
applications as well as mathematical modeling.
– Provides opportunities for students to engage in
rich mathematical tasks, in turn preparing them
for the rigors of the PARCC Assessments.
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Examples of Opportunities for In-Depth
Focus
• Why?
– Highlights standards that play an important role in
the content at a grade level
– Frames important considerations such as
assessment questions, time devoted to the
standard, amount of student practice, etc.
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Examples of Opportunities for In-Depth
Focus
• Grade 3 Example
– Continuous measurement quantities such as
volume and mass are important context for
fraction addition.
– Students should experience whole number
problems involving continuous measurement
quantities to help establish foundation for future
problems in Grades 4 and 5.
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Examples of Opportunities for Connecting
Mathematical Content and Mathematical Practice
• Why?
– Happens in the context of solving a problem
– Practices interact and overlap with each other
– Reminder that content and practices are never
really separate when engaging in real and
meaningful learning
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Examples of Opportunities for Connecting
Mathematical Content and Mathematical Practice
• Grade 8 Examples
– Solving an equation requires students to see and
make use of structure.
– Much of the mathematics in grade 8 lends itself to
modeling especially around linear relationships
with functions.
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Content Emphasis By Cluster
• Why?
– Provided so that curriculum, instruction, and
assessment reflect the focus and emphasis of the
standards
– Separated into Major, Additional, and Supporting
clusters
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Content Emphasis By Cluster
• Grade 5 Example
– Converting like measurement units within a given
measurement system supports computation with
decimals. (Metric system)
– Major emphasis on performing the operations
with supporting content of conversion within a
system.
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High School Frameworks
• Divides content into Major, Supporting and
Additional clusters
• Key Advances from K-8
• Mathematical Practices Related to Course
Content
• Fluency Recommendations
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High School Frameworks
• The Pathway Summary Table outlines where
specific standards are housed.
• For standards that are “cross-cutting” or that
appear in multiple courses, assessment
limitations are also presented.
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Supporting Programs/Initiatives
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MDC
CGI
UBD
EQuIP Rubric
Arkansas IDEAS
Cooperatives and STEM Centers
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Challenges
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Planning
Expectation
Content
Fear of the Unknown
Autonomy and Creativity
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Rewards
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Meaningful Mathematics
Greater Conceptual Development
In-Depth Focus
Greater Student Achievement
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PARCC’s Fundamental Advance
PARCC is designed to reward quality
instruction aligned to the Standards,
so the assessment is worthy of
preparation rather than a distraction
from good work.
Contact Information
Dr. Tracy Tucker
[email protected]
Thomas Coy
[email protected]
Anthony Owen
[email protected]
Janie Hickman
[email protected]
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