Transcript Mathematics - Riverside County Office of Education

Common Core State Standards
What’s It All About?
Karen Kennedy, Ed.D.
Mathematics Consultant
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 sense-making
in mathematics.
Standards for Mathematical Practice
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
Carry across all grade levels.
Describe habits of mind of a mathematically
expert student.
Standards for Mathematical Content

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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).

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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.
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.
Evaluate
•[3] Construct viable arguments
and critique the reasoning of
others.
•[6] Attend to precision.
Coherence


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Topics and performances are logical over time;
Reflect hierarchical nature of the content;
Based upon learning progressions research on how
students learn; and
Build upon learners’ schema (mental maps).
Progressions

Vertical articulation: Domains progress over several
grades.

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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.
K-5 Domains
In grades K-5, students develop a solid
foundation in whole numbers, addition,
subtraction, multiplication, division,
fractions, and decimals.
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.
SBE’s Goal for Eighth Grade
Students is Algebra 1

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Purpose of California’s common core standards for eighth
grade is to finalize students’ preparation for high school
mathematics.
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.
SBE’s Goal for Eighth Grade
Students is Algebra 1
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As augmented, the K-7 standards prepare students for
either set of standards.
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.
Pre-Algebra would be available to students who require
further content knowledge and skills in Algebra.
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.
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.)

High School Standards
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 where students are expected to use
mathematics to analyze situations, understand
them more fully, and make decisions related to
their everyday lives.
California’s Additional 15%:
Are based upon the following criteria:
The CCSS substantively enhance the common core
standards.
Address a perceived gap.
Are defensible to classroom practitioners.
Keep the original standards intact.
Insure that the rigor of California’s existing
standards is maintained.
Examples of California’s Additional 15%:
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Underlined standards in the CCSS document represent
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.
Examples of California’s Additional 15%:
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Like the high school standards, Algebra 1 standards are
also organized by the high school conceptual themes.
CA also supplemented common core standards in
Algebra II, trigonometry, and geometry with key CA
standards.
CCSS include the addition of two courses from
California: Calculus and Advanced Statistics and
Probability.
Development of course descriptions will be done by CDE
as part of their long-range implementation plan.
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).
Grade Level Overviews
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.
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].
What Now?

Recognize that there are more similarities than
differences in the current state standards and CCSS.
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Implement a truly balanced math program as this will
support the Standards for Mathematical Practice.
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Continue to use quality assessments to inform and
drive effective instruction.
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Provide opportunities for teachers to collaborate and
plan.
Standards: Important but insufficient
To be effective in improving education and
getting all students ready for college, workforce
training, and life, the Standards must be
partnered with a content-rich curriculum and
robust assessments, both aligned to the
Standards.
The Promise of Standards
These Standards are not intended to be new
names for old ways of doing business. They are a
call to take the next step. It is time for states to
work together to build on lessons learned from
two decades of standards-based reforms. It is
time to recognize that standards are not just
promises to our children, but promises we intend
to keep.
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