Common Core State Standards
What’s It All About?
Karen Kennedy, Ed.D.
Mathematics Consultant
“WHERE”
THE
MATHEMATICS
WORKS
Computational
& Procedural
Skills
Problem
Solving
DOING
MATH
Conceptual
Understanding
“HOW”
THE
MATHEMATICS
WORKS
“WHY”
THE
MATHEMATICS
WORKS
Content Coherence

Coherent progressions across grade levels.
Balance of Concepts and Skills

Content standards require both conceptual
understanding and procedural fluency.
Mathematical Practices

Practices foster reasoning and sensemaking in mathematics.
Standards for Mathematical Practice
Apply
•[1] Make sense of
problems and
persevere in solving
them.
•[4] Model with
mathematics.
•[5] Use appropriate
tools strategically.
Common
Core State
Standards
•[2] Reason abstractly and
quantitatively.
Understand
•[7] Look for and make use of
structure.
•[8] Look for and express
regularity in repeated
reasoning.
CaCCSS pp.1-2, 47-48
Evaluate
•[3] Construct viable arguments
and critique the reasoning of
others.
•[6] Attend to precision.
Standards for Mathematical Practice
Carry across all grade levels.
Describe habits of mind of a mathematically expert
student.
Describe varieties of expertise that educators
should seek to develop in their students.
Rest on important “processes and proficiencies”
from the National Council of Teachers of
Mathematics and National Research Council.
Relate to mathematical proficiency as defined by the
California Framework.

Mathematical Proficiency
Framework
SMP
 Develop fluency in basic computational
skills.
 Develop an understanding of mathematical
concepts.
 Become mathematical problem solvers who
can recognize and solve routine problems
readily and can find ways to reach a solution
or goal where no routine path is apparent.
 Communicate precisely about quantities,
logical relationships, and unknown values
through the use of signs, symbols, models,
graphs, and mathematical terms.
 Reason mathematically by gathering data,
analyzing evidence, and building arguments
to support or refute hypotheses.
 Make connections among mathematical
ideas and between mathematics and other
disciplines.
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.
Mathematical Proficiency
Framework
SMP
 Develop fluency in basic computational
skills.
 Develop an understanding of mathematical
concepts.
 Become mathematical problem solvers who
can recognize and solve routine problems
readily and can find ways to reach a solution
or goal where no routine path is apparent.
 Communicate precisely about quantities,
logical relationships, and unknown values
through the use of signs, symbols, models,
graphs, and mathematical terms.
 Reason mathematically by gathering data,
analyzing evidence, and building arguments
to support or refute hypotheses.
 Make connections among mathematical
ideas and between mathematics and other
disciplines.
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.
*Not identified as an explicit practice in the Framework.
Coherence
Topics and performances are logical over time.
 Reflect hierarchical nature of the content.
 Are based upon learning progressions’ research on how
students learn.
 Build upon learners’ schema (mental maps).

Progressions
Vertical articulation, i.e., domains progress over several
grades.

Organization
K-8 standards are presented by grade level.
 High school standards are organized by conceptual
themes (Number and Quantity, Algebra, Functions,
Modeling, Geometry, Statistics and Probability).

Grade Level Overviews
CaCCSS p. 12
Grade Level Overviews
CaCCSS p. 12



Content standards define what students should
understand and be able to do.
Clusters are groups of related content standards.
Domains are larger groups of related content
standards that progress across grade levels.
Standard
from
Grade 3
CaCCSS p.14
K-5 Domains
In grades K-5, students develop a solid foundation in
whole numbers, addition, subtraction, multiplication,
division, fractions, and decimals.
CaCCSS p. 3(K),6(1),9(2),12(3),16(4),20(5)
Middle Grades Domains
With a strong foundation of content knowledge from
grades K-5, middle school students are prepared for
robust learning in geometry and statistics and probability.
CaCCSS p. 24(6),29(7),42(CC8)
K-7 Standards
Focus on arithmetic and fluency with whole numbers at early
grades.
• In grades K-5, students develop a solid foundation in whole numbers,
addition, subtraction, multiplication, division, fractions, and decimals.
Fluency with fractions and decimals.
• In grade three, students begin to develop an understanding of
fractions as numbers and represent fractions on a number line
diagram.
• Addition and subtraction of fractions are introduced in grade four and
multiplication and division in grade five.
• The standards for grades six and seven extend work with fractions
and develop concepts such as rational numbers and proportional
relationships.
Domai
n
Cluster of
Standards
The Number System
[6.NS]
Apply
and extend previous understandings of
multiplication and division to divide fractions by
fractions.
Compute
fluently with multi-digit numbers and
find common factors and multiples.
Apply
and extend previous understandings of
numbers to the system of rational numbers.
CaCCSS p. 24
Grade 3

Develop an understanding of fractions as numbers [3.NF].
Grade 4

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.

Understand decimal notation for fractions and compare decimal
fractions [4.NF].
Grade 5

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and
division to multiply and divide fractions [5.NF].
Grade 6

Apply and extend previous understandings of multiplication and
division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors
and multiples [6.NS].
Grade 3

Develop an understanding of fractions as numbers [3.NF].
Grade 4

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.

Understand decimal notation for fractions and compare decimal
fractions [4.NF].
Grade 5

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and
division to multiply and divide fractions [5.NF].
Grade 6

Apply and extend previous understandings of multiplication and
division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors
and multiples [6.NS].
Grade 8 Standards
Algebra readiness by grade eight or Algebra 1.
• The CCSS are consistent with California’s goal that all
students succeed in Algebra 1.
• Students who master the content and skills through grade
seven will be well-prepared for algebra in grade eight.
• With an expectation that all students continue their study
of mathematics, the CCSS moves students forward with
grade eight standards that prepare them for higher math
(Algebra 1 and beyond).
SBE’s Goal for Eighth Grade
Students is Algebra 1


After taking Algebra in eighth grade, students could,
theoretically, take three or four years of high school
math to assure their placement at a UC or CSU campus.
Because not all students have the prerequisite skills for
Algebra, the SBE adopted two sets of standards for
grade 8.


Existing CA Algebra 1 Standards
Common Core Standards for eighth grade (published June 2,
2010), which spread the instruction of Algebra 1 over Grades 8
and 9 and introduce Geometry in Grade 8.
High School Standards: Conceptual Categories
Are arranged by conceptual cluster, not by course.
• Number and Quantity
• Algebra
• Functions
• Modeling*
• Geometry
• Statistics and Probability
Eighth grade Algebra 1 standards are organized around these themes as well.
*Modeling Standard for Mathematical Practice
is emphasized at the high school level. Students are
expected to use mathematics to analyze situations,
understand them more fully, and make decisions related to
their everyday lives. (pp.60-61)
CaCCSS p. 49(N),52(A),56(F),60(M),62(G),67(S)
Theme
High School
Conceptual Theme
Notation
Domain
Cluster of
Standards
CaCCSS p. 63
Grades 9-12 Standards
Real world applications using modeling.
• Throughout the standards, students apply the
mathematics they have learned to solve problems that
arise in everyday life, society, and the workplace.
• The Standards for Mathematical Practice emphasize this
skill and provide specific suggestions for modeling realworld situations using mathematics.
• The high school standards include modeling standards
throughout the other conceptual categories; these
standards are identified with a star () symbol.*
*Example: CaCCSS p. 53(A)
High School Standards
College and Career Readiness Preparation
Standards specify the mathematics that all students
should study in order to be college and career ready.
 Standards demand that students develop a depth of
understanding and ability to apply mathematics outside of
their classrooms.
 Standards are designated with a “+” to indicate material
that students should learn in order to take advanced
courses such as calculus, advanced statistics, or discrete
mathematics. (The “+” standards may also be incorporated
into courses that states require for all students.)*

*Example: CaCCSS p. 53(A)
Examples of California’s Additional 15%:
CA added standards to develop ideas in…
Grade 2: Operations and Algebraic Thinking
5. Use repeated addition and counting by multiples to
demonstrate multiplication.
6. Use repeated subtraction and equal group sharing to
demonstrate division.
High School Geometry: Geometric Measurement
and Dimension
5. Determine how changes in dimensions affect the
perimeter, area, and volume of common geometric
figures and solids (CA Standard Geometry 11.0).
Examples of California’s Additional 15%:



Some Common Core Standards from Grade 8 were
shifted to Grade 7, and some Common Core
Standards from Grade 7 were shifted to Grade 6.
CA added its own Algebra 1 Standards to achieve
the state’s goal of Algebra 1 for all eighth grade
students.
Like the high school standards, Grade 8 Algebra 1
standards are also organized by the high school
conceptual themes.
Examples of California’s Additional 15%*:



CA also supplemented Common Core Standards in
Algebra II, trigonometry, and geometry with key CA
standards.
CaCCSS include the addition of two courses:
Calculus and Advanced Statistics and Probability.
Development of course descriptions will be done by
CDE as part of their long-range implementation
plan.
*Underlined standards in the CCSS document represent California’s additional 15%.
What Now?




Recognize that there are more similarities than
differences in the current state standards and CCSS.
Implement a truly balanced math program as this will
support the Standards for Mathematical Practice.
Continue to use quality assessments to inform and
drive effective instruction.
Provide opportunities for teachers to collaborate and
plan.
Resources
California Department of Education
• http://www.cde.ca.gov/ci/cc/
Sacramento County Office of Education
• http://scoe.net/castandards
Common Core Standards
• http://corestandards.org
Los Angeles County Office of Education
• http://cis.lacoe.edu/common_core/