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Florida K-8 Mathematics Standards April 28, 2008 Grade 3 Adapted from a presentation given by Julie Kay Dixon, Ph.D, UCF – a member of the K-8 Writers Group Perspective… 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. 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 K12 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 2006 - 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 state’s 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 Singapore’s 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 Subject Grade-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 2nd 3rd Number of Old GLE’s 67 78 84 88 4th 5th 89 77 6th 7th 8th 78 89 93 K 1st Number of New Benchmarks Describing the Standards Grade Level K 1st 2nd 3rd 4th 5th 6th 7th 8th Number of Old GLE’s 67 78 84 88 89 77 78 89 93 Number of New Benchmarks 11 14 21 17 21 23 19 22 19 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. Intent of the Standards 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. This does not necessarily mean that students are incapable of learning at an earlier grade. Instead, it is an attempt to streamline the focus of content at each grade level. For Example… Old Standards Decimals introduced in grade 3 Knows multiples of whole numbers with products of 60 or more & determines factors to 100 in grade 3 Measures of Central Tendency introduced in grade 3 New Standards For Example… Old Standards New Standards Decimals introduced in grade 3 Decimals introduced in grade 4 Knows multiples of whole numbers with products of 60 or more & determines factors to 100 in grade 3 Determines factors and multiples for specified whole numbers in Grade 4 Measures of Central Tendency introduced in grade 3 Measures of Central Tendency introduced in grade 6 Big Ideas for Third Grade: Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts 2: Develop an understanding of fraction and fraction equivalence 3: Describe and analyze properties of two-dimensional shapes 1: Third Grade Supporting Ideas Algebra: – Create, analyze, and represent patterns and relationships using words, variables, tables and graphs. Third Grade Supporting Ideas Geometry & Measurement: – Select appropriate units, strategies and tools to solve problems involving perimeter. – Measure objects using fractional parts of linear units such as 1/2, 1/4, and 1/10. – Tell time to the nearest minute and to the nearest quarter hour, and determine the amount of time elapsed. Third Grade Supporting Ideas Numbers and Operations: – Represent, compute, estimate and solve problems using numbers through hundred thousands. – Solve non-routine problems by making a table, chart, or list and searching for patterns. Third Grade Supporting Ideas Data Analysis: – Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments. 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 won’t 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 realworld 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: – http://www.floridastandards.org Florida Department of Education, Office of Mathematics and Science – http://www.fldoestem.org Florida Council of Teachers of Mathematics – http://www.fctm.net National Council of Teachers of Mathematics – http://www.nctm.org Santa Rosa County Mathematics Department – http://www.santarosa.k12.fl.us/currinst/ 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 3 Selection from a PowerPoint presented by Linda Oaksford Test Development Center Grade 3 ~ Big Idea 1 Multiplication & division strategies for basic facts Real-life situations as repeated addition, arrays, combinations, measurement … Commutative, associative, distributive, identity, & inverse properties Facts through 9 X 9 Understanding, Understanding as well as fluency MA.3.A.1.3 Identify, describe, and apply division and multiplication as inverse operations MA.3.A.1.3 Sample Ms. Sali placed 24 desks into 4 rows. Each row has the same number of desks. Which of the following can be used to find the number of desks in each row? A) __ 4 = 24 B) 4 X ___= 24 B C) 24 X 4= ____ D) __ + 4 = 24 Previous Benchmark: MA.A.3.2.2 The student selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers. Grade 3 ~ Big Idea 3 Describe and analyze properties of two-dimensional shapes Classification of shapes, using sides and angles Composition, decomposition and transformation of polygons to make other polygons Congruency and symmetry MA.3.G.3.2 Compose, decompose, and transform polygons to make other polygons, including concave and convex with three, four, five, six, eight, or ten sides. MA.3.G.3.2 Sample How many of the small green triangles are needed to make the larger red triangle? Previous Benchmark: MA.C.1.2.1 The student, given a verbal description, draws and/or models two- and threedimensional shapes and uses appropriate geometric vocabulary to write a description of a figure or a picture composed of geometric figures. Sample: MA.C.1.2.1 Which figure has exactly 2 right angles? A B B C D As of 2011. . . NOT assessed at 3rd grade Measurement of weight/mass, capacity, temperature, area, etc. Coordinates Measures of central tendency – median, mode, and range Probability – likeliness of outcome