Office of Math and Science

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2. Office of Math and Science Rob Schoen robert.schoen@fldoe.org (850)245-5143

3. Coming Events FCR-STEM Mathematics Standards Workshops Florida Math Day PAEMST PD3 Development

4. FCR-STEM Mathematics Teaching Workshops 6 locations in Florida in January/February 2008 Focus of workshops are understanding and implementation of 2007 Sunshine State Standards with a focus on instructional decisions Collaboration between the Office of Math and Science, FCR-STEM, University Professors, and Classroom Teachers Will explore Sunshine State Standards, NCTM Process Standards, NRC strands of mathematics proficiency, and Depth of Knowledge/Cognitive Complexity Will do an abbreviated version on Tuesday from 3pm-6pm

5. Florida Math Day First Annual: May 1, 2008 Financial Literacy Theme All schools in Florida invited to participate Call for Lesson Proposals by February 15 Lesson plans and materials will be disseminated through the Standards Database

6. FCTM Math Day Award

7. FCTM Math Day Award FCTM sponsoring one award per lesson for Florida Math Day lesson writers Award includes a one-year membership to FCTM, complimentary registration at the FCTM Annual Meeting October, 16-18, 2008 in Jacksonville, FL, and $500 to be used for travel to the annual meeting.

8. Presidential Award for Excellence in Mathematics and Science Teaching Nomination and application processes are now online (no longer hardcopy) 2008 award year is for K-6 teachers Nominations due before March 1, 2008 Teacher applications due May 1, 2008 Information available at: www.paemst.org

9. Professional Development Decisions with Data (PD3) Gather data on instruction (NOT for collection by the Dept. of Education) �Needs-sensing� tool Mathematics section divided into two aspects: Content and Instruction Expected to be available on a larger scale starting Fall 2008

10. Professional Development Decisions with Data (PD3) Improve PD decisions by looking at classroom practice Increase PD relevance at a local level Enhance the role of school-based instructional teams Provide a vehicle to track, over time, the impact of PD on classroom practice

11. PD3 Design Team Developed initially for site administrator/school leadership team SRI International Miami Science Museum Florida Department of Education Miami-Dade Public Schools/Reading

13. PD3 Screenshot

14. PD3 Screenshot

15. PD3 Screenshot

17. Sunshine State Standards Written by mathematics stakeholders across the state and nation: framers, writers, reviewers Average number of grade level expectations (benchmarks) changed from ~83 per grade to ~18 per grade for K-8 Number of benchmarks increased in high school to provide more guidance and improve equity

18. Sunshine State Standards Big Ideas and Supporting Ideas: grades K-8 Bodies of Knowledge at grades 9-12 �Fair-game Principle� very important Standards are adopted, focus shift to learning, implementation, and instruction

19. How Do We Connect These? Content Standards Mathematics Understanding, Ability, and Achievement

20. Sunshine State Standards

21. Teaching and Learning Mathematics The five process standards (NCTM, 2000): Problem Solving Reasoning and Proof Communication Connections Representations The five �strands� of mathematics proficiency (NRC, 2001): Conceptual Understanding � comprehension of mathematical concepts, operations, and relations Procedural Fluency � skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic Competence � ability to formulate, represent, and solve mathematical problems Adaptive Reasoning � capacity for logical thought, reflection, explanation, and justification Productive Disposition � habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one�s own efficacy

22. Activity Farmer Davis grows watermelons. Yesterday, he had a watermelon in the field that weighed 100 pounds and was 99% water. Yesterday was a very hot day, some of the water evaporated from the watermelon. Today, the watermelon is 98% water. What is the weight of the watermelon today?

23. Activity

24. What does this look like? Grade 4 Example Lesson � Day 1 Provide each student with 30 cm2 tiles and several sheets of cm2 paper Reintroduce cm2 tiles and the concepts of squares and rectangles, request student volunteers build and share models of squares and rectangles and articulate the definitions for each Request students build as many rectangles and squares as possible using one up to all of the tiles and draw these models on their graph paper

25. Day 2 Ask students individually to identify for each number of tiles used, how many rectangles or squares can be built Pair students and have them compare and discuss their findings Have students share with the class their findings and justify correctness When the correct total is agreed upon (58), provide students the opportunity to review their work to make any necessary improvements prior to the next step (teacher reviews for correctness)

26. Day 3 Students list the numbers of tiles from which: only one square or rectangle could be built a square could be built multiple rectangles and/or squares could be built Students and have them compare and discuss their findings Have student pairs share with the class their findings and communicate their defense for correctness When the correct responses are agreed upon, provide students the opportunity to review their work to make any necessary improvements prior to the next step (teacher reviews for correctness)

27. Here are the solutions: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 tiles only build one rectangle 1, 4, 9, 16, 25 tiles build squares 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30 tiles build multiple rectangles and/or squares What mathematical concepts do these models represent?

28. More and More and MoreThis example lesson should take several more days to complete. Primes, composites, perfect squares Other concepts by continuing this lesson: Number patterns Perimeter and addition facts Repeated addition (precursor to multiplication) Area and multiplication facts (precursor to factoring in algebra and use of algebra tiles) Prime factorization and factors

29. Applying These Concepts Make these concepts relevant by applying them: Using one sheet of your graph paper, design a floor plan for your first home that includes eight square and rectangular rooms. Your plan must include at least one perfect square and one rectangle with a prime area. Label all perimeters, areas, and room purposes. Write a defense for your plan.

30. Related Benchmarks Grade 4: MA.4.A.1.1 Use and describe various models for multiplication in problem-solving situations and demonstrate recall of basic multiplication and related division facts with ease Grade 4: MA.4.G.3.2 Justify the formula for the area of the rectangle �area= base x height� Grade 5: MA.5.A.2.4 Determine the prime factorization of numbers (a concept needed to add and subtract fractions with unlike denominators)

31. Transition to 2007 Math Standards: Crosswalk

32. Crosswalk The Office of Math and Science has a complete DRAFT crosswalk between the 1999 GLE�s and the 2007 Benchmarks Available at www.fldoestem.org Development of FL Standards Attempted a fine-grained analysis of the 2007 Standards �Fair-game Principle� very important

33. What is the purpose of crosswalk? Help teachers make transition to 2007 math standards and understand new arrangement of topics Clarify the new benchmarks Highlight the progression of concepts across different grade levels Different from assessment crosswalk

34. How to read the crosswalk Placements based on the new benchmarks Every old grade level expectation is matched to a new benchmark Crosswalk and explanation of columns available at www.fldoestem.org on the Florida Math Standards page The crosswalk document is in DRAFT form. Your feedback will be appreciated.

35. Examples from the Crosswalk Third grade, Big idea 2, MA.3.A.2.3 Sixth grade, Number and Operations (Supporting Idea), MA.6.A.5.3 Sixth grade, Number and Operations (Supporting Idea), MA.6.A.5.1

36. Remarks/Examples Reviewers submitted feedback for all grade levels Remarks and examples will soon be available in standards database Remarks and examples will continue to clarify the new benchmarks

37. 2008-2009 Course Descriptions Submitted revision of existing courses in the course code directory to Florida Board of Education List of benchmarks define courses Board approval anticipated February 2008

39. Outstanding Issues Pacesetter Math Applied Math III Explorations in Math II Financial Literacy (level 2) 6th grade Algebra Preparation Course Equivalencies

40. District Contacts List If you have not received emails from Rob (Sunshine State Scholars, State Math Day Announcement, etc.), then you are not on the Office of Math and Science district contacts list If you wish to be on this list, please send an email to Rob to request to be added Please include your name, email address, district, position, and phone number

42. Standards Database (+) Live starting Monday, January 14, 2008 Course descriptions Drafts will be available to print Downloadable options/features to come Intend to populate with remarks and examples, model lessons, glossary and other resources

43. Standards Database Tasks Find the MA.K.G.3.1 benchmark and look at the different fields in the benchmark view. Find the course description for your favorite course and print it. Find all course description that include the benchmark MA.8.G.5.1. Use the search or browse feature to find benchmarks that illustrate the progression of the concept of factoring across grade levels.