Florida K-8 Mathematics Standards April 30, 2008 Grade 6 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.

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 StandardsNew Standards Knows proportional relationships in scale drawings and uses scale drawings to solve real world problems in grade 6

For Example… Old StandardsNew Standards Knows proportional relationships in scale drawings and uses scale drawings to solve real world problems in grade 6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed in grade 7

For Example… Old StandardsNew Standards Expresses whole numbers in exponential notation or in factored form in grade 6

For Example… Old StandardsNew Standards Expresses whole numbers in exponential notation or in factored form in grade 6 Simplify real number expressions using the laws of exponents in grade 8

For Example… Old StandardsNew Standards Solves problems involving the changes of dimensions in a two- dimensional figure and how those changes effect the area or perimeter of the given figure in grade 6

For Example… Old StandardsNew Standards Solves problems involving the changes of dimensions in a two- dimensional figure and how those changes effect the area or perimeter of the given figure in grade 6 Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and apply these relationships to solve problems in grade 7

Big Ideas for Sixth Grade: 1: Develop an understanding of and 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals 2: Connect ratio and rates to multiplication and division 2: Connect ratio and rates to multiplication and division 3: Write, interpret, and use mathematical expressions and equations 3: Write, interpret, and use mathematical expressions and equations

Sixth Grade Supporting Ideas Geometry & Measurement: Geometry & Measurement: –Understand the concept of pi, know common estimates of pi (3.14; 22/7) and use these values to estimate and calculate the circumference and area of circles –Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies

Sixth Grade Supporting Ideas Geometry & Measurement: Geometry & Measurement: –Determine a missing dimension of a plane figure or prism, given its area or volume and some of the dimensions, or determine the area or volume given the dimensions

Sixth Grade Supporting Ideas Numbers and Operations: Numbers and Operations: –Use equivalent forms of fractions, decimals and percents to solve problems –Compare and order fractions, decimals, and percents, including finding their approximate location on a number line –Estimate the results of computations with fractions, decimals, and percents and judge the reasonableness of the results

Sixth Grade Supporting Ideas Data Analysis: Data Analysis: –Determine the measures of central tendency (mean, median, mode) and variability (range) for a given set of data –Select and analyze the measure of central tendency or variability to represent, describe, analyze and/or summarize a data set for the purpose of answering questions appropriately

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 6 Selection from a PowerPoint Presented by Heather McKenzie Test Development Center

Grade 6 ~ Big Idea 1 Develop an understanding of and fluency with multiplication and division of fractions and decimals. Explain and justify procedures for multiplying and dividing fractions and decimals. Multiply and divide fractions and decimals efficiently. Solve real-world problems involving multiplication and division of fractions and decimals. May include mixed numbers, improper fractions, proper fractions, and decimals

MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals.

MA.6.A.1.1 Sample Which of the following numbers, when multiplied by itself, would give an answer greater than itself? A)4/5C) 0.05 B)5/3 D) 0.7

Previous Benchmark: MA.A The student 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.

Grade 6 ~ Big Idea 2 Connect ratio and rates to multiplication and division. Use reasoning about multiplication and division to solve ratio and rate problems. Interpret and compare ratios and rates.

MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems.

MA.6.A.2.1 Sample Maria began hiking on a trail at a rate of 4 miles per hour for 30 minutes. For the next 1 hour and 15 minutes, she hiked at a rate of 3 miles per hour and completed the trail. What is the total distance Maria hiked? A)3.50 milesC) 5.75 miles B)3.75 miles D) 7.00 miles

Previous Benchmark: MA.B The student uses concrete and graphic models to derive formulas for finding rates, distance, time, and angle measure. At Grade 6, this benchmark was assessed with MA.C

As of NOT assessed at 6th grade Change in dimensions Change in dimensions Scale drawings Scale drawings Direct/indirect measurement (in isolation) Direct/indirect measurement (in isolation) Scientific notation Scientific notation Coordinate plotting (in isolation) Coordinate plotting (in isolation) Similarity, congruency, symmetry, transformations and other geometric concepts & properties Similarity, congruency, symmetry, transformations and other geometric concepts & properties Probability & odds Probability & odds Circle graphs & stem-and-leaf plots Circle graphs & stem-and-leaf plots