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The Common Core State
Standards
August 2010
Common Core Development
• Initially 48 states and three territories
signed on
• Final Standards released June 2, 2010,
and can be downloaded at
www.corestandards.org
• As of August 10, 2010, 32 states had
officially adopted
• Adoption required for Race to the Top
funds
Common Core Development
• Each state adopting the Common Core either
directly or by fully aligning its state standards
may do so in accordance with current state
timelines for standards adoption, not to
exceed three (3) years.
• States that choose to align their standards
with the Common Core Standards accept
100% of the core in English language arts
and mathematics. States may add additional
standards.
Benefits for States and Districts
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Allows collaborative professional development to be
based on best practices
Allows the 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
mileage from:
– Curriculum development, assessment, and
professional development
Characteristics
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Fewer and more rigorous. The goal was increased clarity.
Aligned with college and career expectations – prepare all
students for success on graduating from high school.
Internationally benchmarked, so that all students are
prepared for succeeding in our global economy and
society.
Includes rigorous content and application of higher-order
skills.
Builds on strengths and lessons of current state
standards.
Research based.
Intent of the Common Core
• The same goals for all students
• Coherence
• Focus
• Clarity and specificity
Coherence
• Articulated progressions of topics and
performances that are developmental and
connected to other progressions
• Conceptual understanding and procedural skills
stressed equally
NCTM states coherence also means that
instruction, assessment, and curriculum are
aligned.
Focus
• Key ideas, understandings, and skills are
identified
• Deep learning of concepts is stressed
– That is, adequate time is devoted to a topic
and learning it well. This counters the “mile
wide, inch deep” criticism leveled at most
current U.S. standards.
Clarity and Specificity
• Skills and concepts are clearly defined.
• An ability to apply concepts and skills to
new situations is expected.
CCSS Mathematical Practices
The Common Core proposes a set of
Mathematical Practices that all teachers
should develop in their students. These
practices are similar to the mathematical
processes that NCTM addresses in the
Process Standards in Principles and
Standards for School Mathematics.
CCSS Mathematical Practices
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.
Common Core Format
K-8
High School
Grade
Conceptual Category
Domain
Domain
Cluster
Standards
(No pre-K Common Core Standards)
Cluster
Standards
Grade Level Overview
Mathematics | Grade 1
In Grade 1, instructional time should focus on four critical areas: (1)
developing understanding of addition, subtraction, and strategies for
addition and subtraction within 20; (2) developing understanding of
whole number relationships and place value, including grouping in
tens and ones; (3) developing understanding of linear measurement
and measuring lengths as iterating length units; and (4) reasoning
about attributes of, and composing and decomposing geometric
shapes.
(1) Students develop strategies for adding and subtracting whole numbers
based on their prior work with small numbers. They use a variety of models,
including discrete objects and length-based models (e.g., cubes connected
to form lengths), to model add-to, take-from, put-together, take-apart, and
compare situations to develop meaning for the operations of addition and
subtraction, and to develop strategies to solve arithmetic problems with
Grade Level Overview
Mathematics | Grade 1
In Grade 1, instructional time should focus on four critical areas: (1)
developing understanding of addition, subtraction, and strategies for
addition and subtraction within 20; (2) developing understanding of Crosswhole number relationships and place value, including grouping in Cutting
tens and ones; (3) developing understanding of linear measurement Themes
and measuring lengths as iterating length units; and (4) reasoning
about attributes of, and composing and decomposing geometric
shapes.
(1) Students develop strategies for adding and subtracting whole
numbers based on their prior work with small numbers. They use a
variety of models, including discrete objects and length-based models
(e.g., cubes connected to form lengths), to model add-to, take-from,
put-together, take-apart, and compare situations to develop meaning
for the operations of addition and subtraction, and to develop
strategies to solve arithmetic problems with these operations. Students
understand connections between counting and addition and
subtraction
Critical Areas
Format of K-8 Standards
Operations and Algebraic Thinking
Domain
1.OA
Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart,
and comparing, with unknowns in all positions, e.g., by using objects,
drawings, and equations with a symbol for the unknown number to
represent the problem.2
2. Solve word problems that call for addition of three whole numbers
whose sum is less than or equal to 20, e.g., by using objects, drawings,
and equations with a symbol for the unknown number to represent the problem.
Understand and apply properties of operations and the relationship
between addition and subtraction.
3. Apply properties of operations as strategies to add and subtract. Examples: If
8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of
addition.) To add 2 + 6 + 4, the second two numbers can be added to make a
ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
4. Understand subtraction as an unknown-addend problem. For example,
subtract 10 – 8 by finding the number that makes 10 when added to 8.
Grade
Level
Format of K-8 Standards
Operations and Algebraic Thinking
1.OA
Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart,
and comparing, with unknowns in all positions, e.g., by using objects,
drawings, and equations with a symbol for the unknown number to
represent the problem.2
2. Solve word problems that call for addition of three whole numbers
whose sum is less than or equal to 20, e.g., by using objects, drawings,
and equations with a symbol for the unknown number to represent the problem.
Understand and apply properties of operations and the relationship
between addition and subtraction.
Standard
Cluster
Standard
3. Apply properties of operations as strategies to add and subtract. Examples: If
8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of
addition.) To add 2 + 6 + 4, the second two numbers can be added to make a
ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
4. Understand subtraction as an unknown-addend problem. For example,
subtract 10 – 8 by finding the number that makes 10 when added to 8.
Cluster
Common Core - Domain
• Overarching “big ideas” that connect topics
across the grades
• Descriptions of the mathematical content to
be learned, elaborated through clusters and
standards
Common Core - Standards
• Content statements
• Progressions of increasing complexity from
grade to grade
Common Core - Clusters
• May appear in multiple grade levels with
increasing developmental standards as the
grade levels progress
• Indicate WHAT students should know and
be able to do at each grade level
• Reflect both mathematical understandings
and skills, which are equally important
Additional Information
• For grades preK-8, a model of
implementation can be found in NCTM’s
Curriculum Focal Points for Prekindergarten
through Grade 8 Mathematics
www.nctm.org/cfp
• For the secondary level, please see NCTM’s
Focus in High School Mathematics:
Reasoning and Sense Making
www.nctm.org/FHSM
Acknowledgments
• Thanks to the Ohio Department of Education
and Eric Milou of Rowan University for
providing content and assistance for this
presentation