Florida K-8 Mathematics Standards May 1, 2008 Grade 8 Adapted from a presentation given by Julie Kay Dixon, Ph.D, UCF – a member of the K-8 Writers Group

A student said this… When asked to compare 4/5 and 2/3, a student said, I know that 4/5 is greater than 2/3. How would you respond? Hopefully you would ask the student how he or she knew. Perspective…

The student said… I made both fractions using manipulatives. I knew that 4/5 was bigger because 4/5 has 4 pieces and 2/3 only has 2 pieces and since 4 is greater than 2 then 4/5 is greater than 2/3. What would this response tell you? Perspective…

Would you ask this student to compare 2/5 and 1/2? According to the intent of the new standards, the answer should be yes. This problem is appropriate for a student in grade 3. Perspective…

Developing the Standards The new Florida K-8 Mathematics Standards are framed by the recently released NCTM Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics and informed by the Singapore Standards, the SSS Grade Level Expectations, and standards from other states that received high grades for rigor, focus, specificity and clear progression of content. There are clear differences between the new standards and the 1996 K-8 mathematics SSS.

Developing the Standards The framers, a group that represented K- 12 teachers, K-12 mathematics supervisors, mathematicians, and mathematics educators, were convened to address issues related to the current standards and to establish a framework for the design of the new standards. The framers recommended that the Curriculum Focal Points be used as the foundation for the new K-8 standards.

Developing the Standards The writers, a group that represented the same set of stakeholders, were convened to generate the revised standards. The writers of the K-8 standards had the task of actualizing the intent of the Curriculum Focal Points within a set of grade-level specific standards.

Developing the Standards September 2006: Framers met with experts to learn about task and conceptualize new standards. October January 2007: Writers wrote draft of standards. February - March 2007: New standards posted for public review period. April - May 2007: Standards revised by writers and representation from framers based on comments received during review September 2007: Standards approved by State Board of Education.

Who were the experts? Dr. Barbara Reys: Center for the Study of Mathematics Curriculum (CSMC); shared a review of 42 states mathematics standards. Dr. Jane Schielack: Chaired NCTM committee that wrote the Curriculum Focal Points. Dr. Kaye Forgione: Senior Associate of Mathematics Benchmarking Initiative with Achieve, Inc. Dr. Alan Ginsburg: US Dept. of Education, What the United States can Learn from Singapores World-class Mathematics System. Dr. R. James Milgram: Wrote the California Mathematics Standards.

Describing the Standards Big Ideas---Standards which are aligned with the Curriculum Focal Points. – –They should be the primary focus of mathematics instruction for each grade level, K - 8. – –There are three Big Ideas for each grade. – –The Big Ideas are not the same for each grade. – –Instructional time may not be evenly divided among the three Big Ideas. The order of the Big Ideas does not determine the order of instruction nor does it indicate that one idea requires greater instructional emphasis.

Describing the Standards Supporting Ideas---standards that serve one or more of the following purposes: – –Establish connections to and between the strands of mathematics as defined by NCTM; – –Prepare students for future mathematics teaching and learning; and – –Address gaps in instruction that are important to the understanding, fluency, and application of mathematics ideas to problem solving. The Supporting Ideas are not less important than the Big Ideas, but are key components to a structurally sound mathematics education.

Describing the Standards 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 –Include three levels of complexity: participatory, supported, and independent with the participatory level being the least complex

Describing the Standards Access Points – –The Access points were not written by the Mathematics Standards Writing Committee and are not intended for mainstream students.

Describing the Standards Coding Scheme for Kindergarten through Grade 8 MA.5.A.1.1 SubjectGrade-Level Body of Knowledge Big Idea/ Supporting Idea Benchmark

Describing the Standards Body of Knowledge Key: A - Algebra C - Calculus D - Discrete Mathematics F - Financial Literacy G - Geometry P - Probability S - Statistics T - Trigonometry

Describing the Standards Grade Level Number of Old GLEs Number of New Benchmarks K67 1 st 78 2 nd 84 3 rd 88 4 th 89 5 th 77 6 th 78 7 th 89 8 th 93

Describing the Standards Grade Level Number of Old GLEs Number of New Benchmarks K st nd rd th th th th th 9319

Describing the Standards Old Standards had an average of 83.3 Grade Level Expectations (GLEs) per grade. The new Standards have an average of 19 benchmarks per grade. What is the importance of having fewer expectations per grade????

Intent of the Standards A member of the Florida Department of Education shared a reaction by a teacher during an open forum regarding the new Florida standards. The teacher looked at the short list of curricular topics in a grade and said, I can teach this in 20 days, what do I do the rest of the year?

Intent of the Standards How do we help teachers with similar views come to understand what is meant by facilitating deep understanding, mathematical fluency, and an ability to generalize (NCTM, 2006, p. 5)?

Describing the Standards To enable the development and mastery of a few key concepts in each grade level it was necessary to make decisions about the placement of topics. As a result, some topics are not introduced until later grades. In addition, some topics have been moved to earlier grades. This helps to streamline the focus of content at each grade level.

Big Ideas for Eighth Grade: 1: Analyze and represent linear functions and solve linear equations and systems of linear equations 1: Analyze and represent linear functions and solve linear equations and systems of linear equations 2: Analyzes two- and three-dimensional figures by using distance and angle 2: Analyzes two- and three-dimensional figures by using distance and angle 3: Select, organize and construct appropriate data displays, including box- and-whisker plots, scatter plots, and lines of best fit to convey information and make conjectures about possible relationships 3: Select, organize and construct appropriate data displays, including box- and-whisker plots, scatter plots, and lines of best fit to convey information and make conjectures about possible relationships

Eighth Grade Supporting Ideas Algebra: Algebra: –Solve literal equations for a specified variable –Solve and graph one- and two-step inequalities in one variable

Eighth Grade Supporting Ideas Geometry & Measurement: Geometry & Measurement: –Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)) and dimensions including temperature, area, volume, and derived units to solve problems

Eighth Grade Supporting Ideas Number and Operations: Number and Operations: –Use exponents and scientific notation to write large and small numbers and vice versa and to solve problems –Make reasonable approximations of square roots and mathematical expressions that include square roots, and use them to estimate solutions to problems and to compare mathematics expressions involving real numbers and radical expressions

Eighth Grade Supporting Ideas Number and Operations: Number and Operations: –Simplify real number expressions using laws of exponents –Perform operations on real numbers (including integer exponents, radicals, percents, scientific notations, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems

Describing the Standards Mathematics instruction at each subsequent grade will continue to use concepts and understandings learned in earlier grades as needed. When asked at a recent Florida Council of Teachers of Mathematics meeting, a representative from FCAT said, students would still need to know concepts from previous grades. They just wont be tested in isolation. When asked at a recent Florida Council of Teachers of Mathematics meeting, a representative from FCAT said, students would still need to know concepts from previous grades. They just wont be tested in isolation.

Describing the Standards Some prerequisite knowledge and skills, not specifically identified in the standards, may need to be added to the curriculum to meet the standards. Students who move to Florida from other states may need exposure to topics not addressed at their grade of entry.

Real-World Problems To the extent possible, it is expected that the relevance of mathematics would be made clear to students by illustrating how mathematics is used in the real world. To this end, the curriculum should include real- world contexts in addition to mathematical contexts. The overall goal is to help students relate mathematics to the real world and their experiences.

Remarks are provided to: Clarify what is described in the standards. Provide context to be addressed as part of the standards. Provide examples of the types of problems that the standards address. Provide content limits when deemed appropriate.

Remarks Remarks were not included with the standards presented to the State Board of Education. Remarks are currently included in course descriptions.

Important Links Florida Mathematics Standards & Course Descriptions: Florida Mathematics Standards & Course Descriptions: – Florida Department of Education, Office of Mathematics and Science Florida Department of Education, Office of Mathematics and Science – Florida Council of Teachers of Mathematics Florida Council of Teachers of Mathematics – National Council of Teachers of Mathematics National Council of Teachers of Mathematics – Santa Rosa County Mathematics Department Santa Rosa County Mathematics Department –

Next steps should include: Statewide communication regarding new standards (ongoing). A comprehensive crosswalk between the new and existing standards (currently available in draft form). District-by-district plans for transitioning to the new standards (work together!). District curriculum plan for each grade level, K – 8 Professional development for teachers in order to provide tools and knowledge necessary to implement new standards with success (ongoing)

Assessment… How will it change?

FCAT Crosswalk ~ Impact on Assessment Grade 8 Selection from a PowerPoint Presented by Steve Ash Test Development Center

Grade 8 ~ Supporting Idea Number and Operations MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.

Previous Benchmark: MA.A MAA331 understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers MC

MA.8.A.6.4 Sample Which of the following, when divided by 5, will always be greater than 5? A.all numbers less than 5 B.all numbers between 0 and 10 C.all numbers between 5 and 25 D.all numbers greater than 25

Assessment Crosswalk DRAFT Revised SSS StandardUsed in Transition Assessed Until 2011 MA.8.A.6.3 Simplify real number expressions using the laws of exponents. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi- step and real world problems. MAA331 understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers MC MAA333 adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator MC, GR MAA132 understands the relative size of integers, fractions, and decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios MC

Grade 8 BIG IDEA 1: Analyze and represent linear functions and solve linear equations and systems of linear equations. 7 benchmarks BIG IDEA 2: Analyze two- and three- dimensional figures by using distance and angle. 4 benchmarks BIG IDEA 3: Analyze and summarize data sets. 2 benchmarks

Grade 8 Supporting Idea: Algebra literal equations Inequalities in one variable Supporting Idea: Geometry and Measurement dimensional analysis Supporting Idea: Number and Operations exponents and scientific notation reasonable approximations of square roots laws of exponents operations on real numbers

As of NOT assessed at 8th grade Derivation of formulas for geometric figures Derivation of formulas for geometric figures Effects of change in dimensions Effects of change in dimensions Scale drawings Scale drawings Relative size of rational numbers Relative size of rational numbers Equivalent forms of numbers Equivalent forms of numbers Select appropriate operations Select appropriate operations Probability & Odds Probability & Odds Number sequences Number sequences