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Todd Clark, Office of Math and Science FL Department of Education February 19, 2008 © 2008, Florida Department of Education

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Floridas Office of Math & Science Established by Governor Crist in February 2007 Responsible for implementing K-12 mathematics and science standards and education policies that improve student achievement and prepare students for success Website:

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An Era of Standards NCTM publishes standards in 1989 (content), 1991 (teaching), 1995 (assessment), and 2000 (revision) Florida adopts first set of Sunshine State Standards for Math in 1996 Grade Level Expectations written in 1999

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Revision Process September 2006 – Framers convene October 2006 through January 2007 – Writers draft K-8 standards and secondary content standards with comment and review from framers February through March 2007 – Individual, Public, and Committees review drafts April through June 2007 – Revisions of drafts based on public review June 2007 – Evaluation of cognitive complexity of Benchmarks August 2007 – Present new standards to the State Board of Education September 2007 – Standards are approved by the State Board of Education

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Modeled From the Worlds Leading Mathematics Curriculum – World-Class Curriculum Standards Singapore – top on the TIMSS Finland – top on the PISA Massachusetts, California, Indiana – standards that were graded A National Council Teachers of Mathematics Curriculum Focal Points

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What the Researchers said about Our Mathematics Standards A Mile Wide, An Inch Deep For Floridas Grades 1-7, the average number of mathematics grade level expectations (GLEs) = 83.3 Singapore, the highest performing nation as measured by Trends in International Math and Science Study (TIMSS), has 15 GLEs per grade level

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College Board Define grade-level expectations for grade Increase rigor of middle through high school standards Increase specificity of standards, showing a progressive development across grade levels Increase the depth of knowledge required as grades progress

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Recommendations From International and National Experts Increase rigor and specificity all the way around K-8 - By grade level up to Algebra 1 Let NCTMs Focal Points be a guide Reduce number of GLEs, focused in-depth instruction Secondary - By Bodies of Knowledge Algebra, Geometry, Probability, Statistics, Trigonometry, Discrete Math, Calculus, Financial Literacy Upper level mathematics courses will use standards set by AP, IB, College Board, Dual Enrollment course guidelines/standards

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Terms in the 1996 and 2007 Standards 1996 Standards Grade Band Strand Benchmark Grade Level Expectation 2007 Standards Body of Knowledge Supporting Idea Big Idea Access Points Benchmark

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Coding Scheme MA.5.A.1.1 SubjectGrade-LevelBody of Knowledge Big Idea/ Supporting Idea Benchmark MA.912.G.1.1 SubjectGrade-LevelBody of Knowledge StandardBenchmark Secondary Kindergarten through Grade 8

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Standard 2 Standard 4 Standard 5 Standard 3 Sunshine State Mathematics Standards Standard 1 Benchmark MA.912.T.1.1 Benchmark MA.912.T.1.3 Benchmark MA.912.T.1.4 Benchmark MA.912.T.1.6 Benchmark MA.912.T.1.7 Benchmark MA.912.T.1.8 Benchmark MA.912.T.1.5 Benchmark MA.912.T.1.2 Trigonometry Body of Knowledge Benchmark MA.912.T.5.3 Benchmark MA.912.T.3.1 Benchmark MA.912.T.3.2 Benchmark MA.912.T.3.3 Benchmark MA.912.T.3.4 Benchmark MA.912.T.2.3 Benchmark MA.912.T.2.4 Benchmark MA.912.T.2.1 Benchmark MA.912.T.2.2 Benchmark MA.912.T.4.1 Benchmark MA.912.T.4.4 Benchmark MA.912.T.4.3 Benchmark MA.912.T.4.2 Benchmark MA.912.T.5.2 Benchmark MA.912.T.5.1

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and TRIGONOMETRY BODY OF KNOWLEDGE Standard 1: Trigonometric Functions Students extend the definitions of the trigonometric functions beyond right triangles using the unit circle and they measure angles in radians as well as degrees. They draw and analyze graphs of trigonometric functions (including finding period, amplitude, and phase shift) and use them to solve word problems. They define and graph inverse trigonometric functions and determine values of both trigonometric and inverse trigonometric functions. Benchmark CodeBenchmark MA.912.T.1.1Convert between degree and radian measures. MA.912.T.1.2Define and determine sine and cosine using the unit circle. MA.912.T.1.3State and use exact values of trigonometric functions for special angles, i.e. multiples of MA.912.T.1.4Find approximate values of trigonometric and inverse trigonometric functions using appropriate technology. MA.912.T.1.5Make connections between right triangle ratios, trigonometric functions, and circular functions. MA.912.T.1.6Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology. MA.912.T.1.7Define and graph inverse trigonometric relations and functions. MA.912.T.1.8Solve real-world problems involving applications of trigonometric functions using graphing technology when appropriate. (degree and radian measures)

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Grade 6 Algebra Body of Knowledge Big Idea 1 Benchmark MA.6.A.1.3 Benchmark MA.6.A.1.2 Benchmark MA.6.A.1.1 Big Idea 3 Algebra Body of Knowledge Benchmark MA.6.A.3.3 Benchmark MA.6.A.3.5 Benchmark MA.6.A.3.4 Benchmark MA.6.A.3.2 Benchmark MA.6.A.3.1 Benchmark MA.6.A.3.6 Big Idea 2 Algebra Body of Knowledge Benchmark MA.6.A.2.2 Benchmark MA.6.A.2.1 Supporting Idea Benchmark MA.6.G.5.2 Benchmark MA.6.G.5.2 Benchmark MA.6.G.5.1 Geometry Body of Knowledge Supporting Idea Benchmark MA.6.A.6.1 Benchmark MA.6.A.6.2 Benchmark MA.6.A.6.3 Algebra Body of Knowledge Supporting Idea Benchmark MA.6.A.6.1 Benchmark MA.6.A.1.3 Statistics Body of Knowledge Sunshine State Mathematics Standards

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Grade 6 Big Idea 1 BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals. BENCHMARK CODE BENCHMARK MA.6.A.1.1Explain and justify procedures for multiplying and dividing fractions and decimals. MA.6.A.1.2Multiply and divide fractions and decimals efficiently. MA.6.A.1.3Solve real-world problems involving multiplication and division of fractions and decimals.

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What is a Supporting Idea? Supporting Ideas are not subordinate to Big Ideas Supporting Ideas may serve to prepare students for concepts or topics that will arise in later grades Supporting Ideas may contain critical grade-level appropriate math concepts that are not included in the Big Ideas

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What are Access Points? written for students with significant cognitive disabilities to access the general education curriculum reflect the core intent of the standards with reduced levels of complexity three levels of complexity include participatory, supported, and independent with the participatory level being the least complex

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Access Points Coding Scheme MA.5.A.1.ln.a SubjectGrade LevelBody of Knowledge Big Idea/ Supporting Idea Access Point MA.912.A.1.ln.a SubjectGrade-LevelBody of Knowledge StandardAccess Point Kindergarten through Grade 8 Secondary

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Comparing the Standards Grade LevelNumber of Old GLEs Number of New Benchmarks K st nd rd th th th th th 9319

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How is this accomplished? Fewer topics per grade due to less repetition from year to year Move from covering topics to teaching them in-depth for long term learning Individual teachers will need to know how to begin each topic at the concrete level, move to the abstract, and connect it to more complex topics

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Bodies Of Knowledge 9-12 Old 9-12 Benchmarks (Same for all 9-12) New Body of Knowledge Benchmarks 12 Benchmarks in Number Sense, Concepts, and Operations 8 Benchmarks in Measurement 4 Benchmarks in Algebraic Thinking 5 Benchmarks in Geometry and Spatial Sense 7 Benchmarks in Data Analysis and Probability 84 Benchmarks for Algebra 52 Benchmarks for Calculus 41 Benchmarks for Discrete Math 41 Benchmarks for Financial Literacy 47 Benchmarks for Geometry 9 Benchmarks for Probability 28 Benchmarks for Statistics 24 Benchmarks for Trigonometry

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ALGEBRA DISCRETE MATH GEOMETR Y Course Description Example: ALGEBRA I MA.912.A.4.2 Add, subtract, and multiply polynomials. MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. MA.912.D.7.2 Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.

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Benchmark MA.912.A.4.3: Factor polynomial expressions. _______________________________ ex: Let a, b > 0, a > b, a,b Є Factor the following expression: a 2 – b 2

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Solution: a 2 – b 2 = (a – b)(a + b) Can this be done Geometrically with manipulatives?

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