Transcript Grade 8 Math Standards - Santa Rosa County School District
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
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 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. Curriculum 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 Focal Points specific standards.
Curriculum within a set of grade-level
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, United States can Learn from Singapore’s World-class Mathematics System .
What the 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.
Subject 5.
Grade-Level A.
Body of Knowledge 1.
Big Idea/ Supporting Idea 1 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 K 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th Number of Old GLE’s 67 78 84 88 89 77 78 89 93 Number of New Benchmarks
Describing the Standards
Grade Level K 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 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.
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 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
Eighth Grade Supporting Ideas
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:
– 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:
– 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:
– 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 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 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: – 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 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.3.3.1
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
Revised SSS Standard Used in Transition
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 MC
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
MAA333 adds, subtracts, multiplies, and divides
MC, GR 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
DRAFT
Assessed Until 2011
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 2011. . .
NOT assessed at 8th grade
Derivation of formulas for geometric figures Effects of change in dimensions Scale drawings Relative size of rational numbers Equivalent forms of numbers Select appropriate operations Probability & Odds Number sequences