CCSSI FOR MATHEMATICS
“STANDARDS OF PRACTICE”
Collegial Conversations
GRADES 2 - 3
Today’s Goal
 To explore the Standards for Content and
Practice for Mathematics
 Begin to consider how these new CCSS
Standards are likely to impact your classroom
practices
What are the Common Core State
Standards?
 Aligned with college and work expectations
 Focused and coherent
 Included rigorous content and application of
knowledge through high-order skills
 Build upon strengths and lessons of current state
standards
 Internationally benchmarked so that all students are
prepared to succeed in our global economy and society
 Research and evidence based
 State led- coordinated by NGA Center and CCSSO
Focus
• Key ideas, understandings, and skills are
identified
• Deep learning of concepts is emphasized
– That is, time is spent on a topic and on
learning it well. This counters the “mile wide,
inch deep” criticism leveled at most current
U.S. standards.
Benefits for States and Districts
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Allows collaborative professional development based
on best practices
Allows development of common assessments and other
tools
Enables comparison of policies and achievement
across states and districts
Creates potential for collaborative groups to get more
economical mileage for:
– Curriculum development, assessment, and
professional development
Common Core Development
• Initially 48 states and three territories
signed on
• As of November 29, 2010, 42 states have
officially adopted
• Final Standards released June 2, 2010, at
www.corestandards.org
• Adoption required for Race to the Top
funds
Michigan’s Implementation Timeline
• Held October and November of 2010 rollouts
• District curricula and assessments that provide a
K-12 progression for meeting the MMC
requirements will require minimal adjustments to
meet CCSS
• Curriculum and assessment alignment in SY10-11
• Implementation SY11-12
• New assessment 2014-15 (Smarter Balanced
Assessment Consortium or SBAC – replaces MEAP
and MME)
Background
Responsibilities of States in the Consortium
Each State that is a member of the Consortium in 2014–
2015 also agrees to do the following:
 Adopt common achievement standards no later than the 2014–2015 school
year,
 Fully implement the Consortium summative assessment in grades 3–8 and
high school for both mathematics and English language arts no later than
the 2014–2015 school year,
 Adhere to the governance requirements,
 Agree to support the decisions of the Consortium,
 Agree to follow agreed-upon timelines,
 Be willing to participate in the decision-making process and, if a Governing
State, final decisions, and
 Identify and implement a plan to address barriers in State law, statute,
regulation, or policy to implementing the proposed assessment system and
address any such barriers prior to full implementation of the summative
assessment components of the system.
Technology Approach
SBAC Item Bank
• Partitioned into a secure item bank for
summative assessments and a non-secure
bank for the interim/benchmark assessments:
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Traditional selected-response items
Constructed-response items
Curriculum-embedded performance events
Technology-enhanced items (modeled after
assessments in use by the U.S. military, the
architecture licensure exam, and NAEP)
HOW TO READ THE GRADE LEVEL
STANDARDS
Domains are large groups of related
standards. Standards from different
domains may sometimes be closely
related. Look for the name with the code
number on it for a Domain.
Common Core Format
Clusters are groups of related standards.
Standards from different clusters may
sometimes be closely related, because
mathematics is a connected subject.
• Clusters appear inside domains.
Standards
define what
students
should be
Common
Core
Format
able to understand and be able to do –
part of a cluster.
•They are content statements. An example content
statement is: “Identify arithmetic patterns (including
patterns in the addition table or multiplication table), and
explain them using properties of operations. For example,
observe that 4 times a number can be decomposed into two
equal addends”, 3.OA.9. The “OA” stands for “Operations and Algebraic
Thinking”. Please refer to page three in your grade level appropriate Common Core
document.
•Progressions of increasing complexity from grade to
grade
Common Core - Clusters
• May appear in multiple grade levels in the K-8
Common Core. There is increasing development
as the grade levels progress
• What students should know and be able to do
at each grade level
• Reflect both mathematical understandings and
skills, which are equally important
Common Core Format
K-8
High School
Grade
Conceptual Category
Domain
Domain
Cluster
Cluster
Standards
(There are no preK Common Core Standards)
Standards
Format of K-8 Standards
Grade Level
Domain
Format of K-8 Standards
Standard
Cluster
Standard
Cluster
Mathematics » Grade 2 » Introduction
In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation;
(2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and
analyzing shapes.
1.
Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and
multiples of hundreds, tens, and ones, as well as number relationships involving these units, including
comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing
that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds +
5 tens + 3 ones).
2.
Students use their understanding of addition to develop fluency with addition and subtraction within 100. They
solve problems within 1000 by applying their understanding of models for addition and subtraction, and they
develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of
whole numbers in base-ten notation, using their understanding of place value and the properties of operations.
They select and accurately apply methods that are appropriate for the context and the numbers involved to
mentally calculate sums and differences for numbers with only tens or only hundreds.
3.
Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other
measurement tools with the understanding that linear measure involves an iteration of units. They recognize
that the smaller the unit, the more iterations they need to cover a given length.
4.
Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and
reason about decomposing and combining shapes to make other shapes. Through building, drawing, and
analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume,
congruence, similarity, and symmetry in later grades.
Mathematics » Grade 3 » Introduction
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and
strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with
numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing twodimensional shapes.
1. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and
problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding
an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups
or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly
sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By
comparing a variety of solution strategies, students learn the relationship between multiplication and division.
2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out
of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that
the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint
than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is
divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions
to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual
fraction models and strategies based on noticing equal numerators or denominators.
3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number
of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the
standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into
identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify
using multiplication to determine the area of a rectangle.
4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and
angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of
part of a shape as a unit fraction of the whole.
Fractions, Grades 3–6
 3. Develop an understanding of fractions as numbers.
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4. Extend understanding of fraction equivalence and ordering.
4. Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
4. Understand decimal notation for fractions, and compare
decimal fractions.
5. Use equivalent fractions as a strategy to add and subtract
fractions.
5. Apply and extend previous understandings of multiplication
and division to multiply and divide fractions.
6. Apply and extend previous understandings of multiplication
and division to divide fractions by fractions.
K – 5 DOMAINS
Domains
Grade Levels
Counting and Cardinality
K only
Operations and Algebraic
Thinking
1-5
Number and Operations in
Base Ten
1-5
Number and Operations Fractions
3-5
Measurement and Data
1-5
Geometry
1-5
MIDDLE GRADES DOMAINS
Domains
Grade Levels
Ratio and Proportional
Relationships
6-7
The Number System
6-8
Expressions and Equations
6-8
Functions
8
Geometry
6-8
Statistics and Probability
6-8
Michigan GLCE vs. CCSS
Grade
Topic
Whole Number: Meaning
Whole Number: Operations
Measurement Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Perimeter, Area & Volume
Rounding & Significant Figures
Estimating Computations
Whole Numbers: Properties of Operations
Estimating Quantity & Size
Decimal Fractions
Relation of Common & Decimal Fractions
Properties of Common & Decimal Fractions
Percentages
Proportionality Concepts
Proportionality Problems
2-D Geometry: Coordinate Geometry
Geometry: Transformations
Negative Numbers, Integers, & Their Properties
Number Theory
Exponents, Roots & Radicals
Exponents and Orders of Magnitude
Measurement: Estimation & Errors
Constructions Using Straightedge & Compass
3-D Geometry
Geometry: Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Proportionality: Slope & Trigonometry
Uncertainty & Probability
Real Numbers: Their Subsets & Properties
Topic intended in Michigan GLCE
Topic intended in CCSS
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MAJOR SHIFTS K - 5
Numeration and operation intensified, and introduced
earlier
•Early place value foundations in Kindergarten
•Regrouping as composing/decomposing in Grade 2
•Decimals to hundredths in Grade 4
All three types of measurement simultaneously
•Non-standard, English and metric
Emphasis on fractions as numbers
Emphasis on number line as visualization/structure
Observations About Place Value
and Base Ten in the Early Grades
•Kindergarten
Foundation in bundling
Emphasis on the teen numbers
•Grade 1
•Extends to 10, 20, 30…
•Learn to compare
•Grade 2
•Extend to 100 as a bundle of ten 10s
•Extend to 100, 200, 300…
•Expanded notation and comparison
HOW IS THERE LESS?
•Backed off of algebraic patterns K – 5
•Backed off of statistics and probability in
K–5
•Delayed content like percent and ratios
and proportions
THE REASON
WHY WE ARE HERE
TODAY!
CCSSM
Mathematical
Practices
The Common Core proposes a set of
Mathematical Practices that all teachers should
develop in their students. These practices are
similar to NCTM’s Mathematical Processes from
the Principles and Standards for School
Mathematics.
Design and Organization
Mathematical Practice – expertise students
should acquire: (Processes & proficiencies)
• NCTM five process standards:
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Problem solving
Reasoning and Proof
Communication
Connections
Representations
NCTM Process Standards and the
CCSS Mathematical Practice Standards
NCTM Process Standards
CCSS Mathematical Practices
Problem Solving
Make sense of problems and persevere
in solving them.
Use appropriate tools strategically
Reasoning and Proof
Reason abstractly and quantitatively.
Critique the reasoning of others.
Look for and express regularity in
repeated reasoning
Communication
Construct viable arguments
Connections
Attend to precision.
Look for and make use of structure
Representations
Model with mathematics.
Design and Organization
• Mathematical proficiency (National Research
Council’s report Adding It Up)
– Adaptive reasoning
– Strategic competence
– Conceptual understanding (comprehension of
mathematical concepts, operations, relations)
– Procedural fluency (skill in carrying out procedures flexibly,
accurately, efficiently, and appropriately)
– Productive disposition (ability to see mathematics as
sensible, useful, and worthwhile
Mathematics/Standards for Mathematical
Practice
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
Mathematics/Standards for Mathematical Practice
“The Standards for Mathematical Practice describe varieties of expertise that
mathematics educators at all levels should seek to develop in their students.
These practices rest on important “processes and proficiencies” with
longstanding importance in mathematics education.” CCSS, 2010
Standards for Mathematical Practice
• Carry across all grade levels
• Describe habits of a mathematically expert student
Standards for Mathematical Content
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K-8 presented by grade level
Organized into domains that progress over several grades
Grade introductions give 2-4 focal points at each grade level
High school standards presented by conceptual theme (Number &
Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability
Standards of Mathematical Practice
1. Choose a partner at your table and “Pair Share” the
Standards of Practice between you and your partner.
2. When you and your partner feel you understand
generally each of the standards, discuss the following
question:
What implications might the standards
of practice have on your classroom?
Transition from Current State Standards & Assessments
to New Common Core Standards
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Develop Awareness
Needs Assessment/Gap Analysis
Planning
Capacity Building
Job-embedded Professional Development
Transition Planning
Next Steps:
• Alignment of CCSS with curriculum
• Gap analysis (content and skills that vary from
the MEAP and MME)
• What instructional practices will facilitate the
transition?
• What new assessment strategies will be
needed?
• Professional development needs?
Transition Planning
• Gather in teams from your schools and discuss
– What are your immediate needs as a classroom teacher
being asked to implement the CCSS?
– What professional development is needed?
– What initial gaps come to mind and how do you address
these gaps?
– As a school team, look at the eight Standards for
Mathematical Practice. What do they look like? Sound
like? What will students need in order to implement them?
What will teachers need? What are the implications for
assessment and grading?
Select a recorder, time keeper and someone to report out for
your group.
Questions?
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INFORMATION HERE!
Have a great day!