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1 Common Core State Standards for Mathematics

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2 Overview of the Initiative State-led and developed common core standards for K- 12 in English/language arts and mathematics Focus on learning expectations for students, not how students get there.

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3 What momentum is there for the initiative? 48 states, the District of Columbia, and two territories have signed on to the Common Core State Standards Initiative

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4 July 2010 South Carolina was the 25th state to adopt Common Core (SBE Approved in July 2010) Developed by the National Governors Association and the Council of Chief State School Officers Implement the new standards during the school year, with planning and training carried out during the next two school years.

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5 SC is currently part of 2 consortia Smarter Balanced Assessment Consortium (SBAC) Partnership for Assessment of Readiness for College and Careers (PAARC)

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6 Assessment will change Both consortia plan to use computer- based assessment. (Paper-pencil will be available for a while.) Testing may be computer-adaptive. Both plan to include open-ended and/or constructed response items with computer and human scoring. Money will be saved by teaming up and using computer scoring. Formative, interim, benchmark and summative may/will be included.

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7 SC is currently part of 2 consortia Smarter Balanced Assessment Consortium (SBAC) Lead state- Washington 31 member states SC would be “Advisory” not “Governing”

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8 SC is currently part of 2 consortia Partnership for Assessment of Readiness for College and Careers (PAARC) Lead state- Florida 25 member states SC would be “Participating” not “Governing”

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9 Design and Organization Standards for Mathematical Content K-8 standards 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)

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10 Focal points at each grade level

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11 Overview Pages

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12 Fractions, Grades 3–6 3. Develop an understanding of fractions as numbers. 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.

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13 Fractions, Grades 3–6 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.

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14 Algebra, Grade 8 Focus on linear equations and functions in Grade 8 (ramp up to Algebra) Expressions and Equations Work with radicals and integer exponents. Proportional relationships, lines, and linear equations. Solve linear equations and pairs of simultaneous linear equations. Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities.

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15 High School College and career readiness threshold (+) standards indicate material beyond the threshold; can be in courses required for all students. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle (+) Compose functions. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. (+) Add and subtract vectors.

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16 Design and Organization High school assessment has not been “pinned down.” Change requires legislative action. HSAP – no changes for , , and probably Algebra I EOCEP – no changes for , , and probably

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17 Conclusion 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.

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18 More Information Visit

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19 Credit to: rds_June_2010_Webinar_Final_v_2.ppt#410,34,Conclusion Harriet Pritchard

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20 Assessment Issues Definition of “Regular” polygons Inequalities with or Sum of probabilities = one whole (complements) “Corresponding” parts of similar shapes addressed in focus of Grade 7 but no standard lists it

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