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  

Carry across all grade levels. Describe habits of mind of a mathematically expert student.

Standards for Mathematical Content  

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