Florida K-8 Mathematics Standards May 1, 2008 Grade 8 Adapted from a presentation given by Julie Kay...

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

Transcript of Florida K-8 Mathematics Standards May 1, 2008 Grade 8 Adapted from a presentation given by Julie Kay...

Page 1: 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.

Florida K-8 Florida K-8 Mathematics Mathematics StandardsStandards

May 1, 2008May 1, 2008

Grade 8Grade 8

Adapted from a presentation given by Julie Kay Dixon, Ph.D, UCF – a member of the K-8 Writers Group

Page 2: 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…A student said this…

When asked to compare 4/5 and 2/3, When asked to compare 4/5 and 2/3, a student said, “I know that 4/5 is a student said, “I know that 4/5 is greater than 2/3.”greater than 2/3.”

How would you respond?How would you respond?

Hopefully you would ask the Hopefully you would ask the student how he or she knew.student how he or she knew.

Perspective…Perspective…

Page 3: 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.

The student said…The student said…

I made both fractions using manipulatives. I I made both fractions using manipulatives. I knew that 4/5 was bigger because 4/5 has 4 knew that 4/5 was bigger because 4/5 has 4 pieces and 2/3 only has 2 pieces and since 4 pieces and 2/3 only has 2 pieces and since 4 is greater than 2 then 4/5 is greater than 2/3.is greater than 2 then 4/5 is greater than 2/3.

What would this response tell you?What would this response tell you?

Perspective…Perspective…

Page 4: 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.

Would you ask this student to Would you ask this student to compare 2/5 and 1/2?compare 2/5 and 1/2?

According to the intent of the new According to the intent of the new standards, the answer should be yes. standards, the answer should be yes. This problem is appropriate for a This problem is appropriate for a student in grade 3. student in grade 3.

Perspective…Perspective…

Page 5: 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.

Developing the Developing the StandardsStandards 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.

Page 6: 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.

Developing the Developing the StandardsStandards 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.

Page 7: 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.

Developing the Developing the StandardsStandards 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.

Page 8: 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.

Developing the Developing the StandardsStandards

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.

Page 9: 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.

Who were the Who were the “experts”?“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.

Page 10: 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.

Describing the Describing the StandardsStandards 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.

Page 11: 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.

Describing the Describing the StandardsStandards 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.

Page 12: 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.

Describing the Describing the StandardsStandards Access Points

– Written for students with significant cognitive Written for students with significant cognitive disabilities to access the general education disabilities to access the general education curriculumcurriculum

– Reflect the core intent of the standards with reduced Reflect the core intent of the standards with reduced levels of complexitylevels of complexity

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

Page 13: 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.

Describing the Describing the StandardsStandards Access Points

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

Page 14: 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.

Describing the Describing the StandardsStandards Coding Scheme for Kindergarten through

Grade 8

MA.MA. 5.5. A.A. 1.1. 11

SubjectSubject Grade-Grade-LevelLevel

Body of Body of KnowledgKnowledg

ee

Big Idea/ Big Idea/ SupportinSupportin

g Ideag Idea

BenchmarBenchmarkk

Page 15: 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.

Describing the Describing the StandardsStandards

Body of Knowledge Key:A - AlgebraC - CalculusD - Discrete MathematicsF - Financial LiteracyG - GeometryP - ProbabilityS - StatisticsT - Trigonometry

Page 16: 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.

Describing the Describing the StandardsStandardsGrade LevelGrade Level Number of Number of OldOld

GLE’sGLE’sNumber of Number of NewNew

BenchmarksBenchmarks

KK 6767

11stst 7878

22ndnd 8484

33rdrd 8888

44thth 8989

55thth 7777

66thth 7878

77thth 8989

88thth 9393

Page 17: 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.

Describing the Describing the StandardsStandards

Grade LevelGrade Level Number of Number of OldOld GLE’sGLE’s

Number of Number of NewNew BenchmarksBenchmarks

KK 6767 1111

11stst 7878 1414

22ndnd 8484 2121

33rdrd 8888 1717

44thth 8989 2121

55thth 7777 2323

66thth 7878 1919

77thth 8989 2222

88thth 9393 1919

Page 18: 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.

Describing the Describing the StandardsStandards 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????

Page 19: 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.

Intent of the Intent of the StandardsStandards 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?”

Page 20: 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.

Intent of the Intent of the StandardsStandards 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)?

Page 21: 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.

Describing the Describing the StandardsStandards 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.

Page 22: 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.

Big Ideas for Eighth Big Ideas for Eighth Grade:Grade:

1: Analyze and represent linear 1: Analyze and represent linear functions functions and solve linear equations and solve linear equations and and systems of linear equationssystems of linear equations

2: Analyzes two- and three-2: Analyzes two- and three-dimensional dimensional figures by using figures by using distance and angledistance and angle

3: Select, organize and construct 3: Select, organize and construct appropriate data displays, including appropriate data displays, including box-box- and-whisker plots, scatter plots, and-whisker plots, scatter plots, and and lines of best fit to convey lines of best fit to convey information information and make conjectures and make conjectures about possible about possible relationshipsrelationships

Page 23: 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.

Eighth Grade Eighth Grade Supporting IdeasSupporting Ideas

Algebra:Algebra: – Solve literal equations for a specified Solve literal equations for a specified

variablevariable– Solve and graph one- and two-step Solve and graph one- and two-step

inequalities in one variableinequalities in one variable

Page 24: 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.

Eighth Grade Eighth Grade Supporting IdeasSupporting Ideas

Geometry & Measurement:Geometry & Measurement: – Compare, contrast, and convert Compare, contrast, and convert

units of measure between different units of measure between different measurement systems (US measurement systems (US customary or metric (SI)) and customary or metric (SI)) and dimensions including temperature, dimensions including temperature, area, volume, and derived units to area, volume, and derived units to solve problemssolve problems

Page 25: 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.

Eighth Grade Eighth Grade Supporting IdeasSupporting Ideas

Number and Operations:Number and Operations: – Use exponents and scientific notation Use exponents and scientific notation

to write large and small numbers and to write large and small numbers and vice versa and to solve problemsvice versa and to solve problems

– Make reasonable approximations of Make reasonable approximations of square roots and mathematical square roots and mathematical expressions that include square expressions that include square roots, and use them to estimate roots, and use them to estimate solutions to problems and to solutions to problems and to compare mathematics expressions compare mathematics expressions involving real numbers and radical involving real numbers and radical expressionsexpressions

Page 26: 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.

Eighth Grade Eighth Grade Supporting IdeasSupporting Ideas

Number and Operations:Number and Operations: – Simplify real number expressions Simplify real number expressions

using laws of exponentsusing laws of exponents– Perform operations on real numbers Perform operations on real numbers

(including integer exponents, (including integer exponents, radicals, percents, scientific radicals, percents, scientific notations, absolute value, rational notations, absolute value, rational numbers , and irrational numbers) numbers , and irrational numbers) using multi-step and real world using multi-step and real world problemsproblems

Page 27: 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.

Describing the Describing the StandardsStandards 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 When asked at a recent Florida Council of Teachers of Mathematics meeting, a of Teachers of Mathematics meeting, a representative from FCAT said, representative from FCAT said, “students would still need to know “students would still need to know concepts from previous grades. They concepts from previous grades. They just won’t be tested in isolation.” just won’t be tested in isolation.”

Page 28: 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.

Describing the Describing the StandardsStandards 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.

Page 29: 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.

Real-World ProblemsReal-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.

Page 30: 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.

Remarks are provided to: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.

Page 31: 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.

RemarksRemarks

Remarks were not included with the

standards presented to the State

Board of Education.

Remarks are currently included in

course descriptions.

Page 32: 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.

Important LinksImportant Links

Florida Mathematics Standards & Course Florida Mathematics Standards & Course Descriptions: Descriptions: – http://http://www.floridastandards.orgwww.floridastandards.org

Florida Department of Education, Office of Florida Department of Education, Office of Mathematics and ScienceMathematics and Science– http://www.fldoestem.orghttp://www.fldoestem.org

Florida Council of Teachers of MathematicsFlorida Council of Teachers of Mathematics– http://www.fctm.nethttp://www.fctm.net

National Council of Teachers of MathematicsNational Council of Teachers of Mathematics– http://www.nctm.orghttp://www.nctm.org

Santa Rosa County Mathematics Santa Rosa County Mathematics DepartmentDepartment– http://www.santarosa.k12.fl.us/currinst/http://www.santarosa.k12.fl.us/currinst/

Page 33: 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.

Next steps should Next steps should include: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)

Page 34: 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.

Assessment…

How will itchange?

Page 35: 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.

FCAT Crosswalk~

Impact on Assessment

Grade 8

Selection from a PowerPoint Presented by

Steve AshTest Development Center

Page 36: 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.

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.

Page 37: 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.

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 numbersMC

Page 38: 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.

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 5B. all numbers between 0 and 10C. all numbers between 5 and 25D. all numbers greater than 25

Page 39: 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.

Assessment Crosswalk DRAFTRevised SSS

StandardUsed in Transition

Assessed Until 2011MA.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 numbersMC

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 calculatorMC, 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 ratiosMC

Page 40: 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.

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

Page 41: 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.

Grade 8 Supporting Idea: Algebra

literal equations Inequalities in one variable

Supporting Idea: Geometry andMeasurement dimensional analysis

Supporting Idea: Number and Operations exponents and scientific notation reasonable approximations of square

roots laws of exponents operations on real numbers

Page 42: 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.

As of 2011. . .As of 2011. . .NOT assessed at 8th gradeNOT assessed at 8th grade

Derivation of formulas for Derivation of formulas for geometric figuresgeometric figures

Effects of change in dimensionsEffects of change in dimensions Scale drawingsScale drawings Relative size of rational numbersRelative size of rational numbers Equivalent forms of numbersEquivalent forms of numbers Select appropriate operationsSelect appropriate operations Probability & OddsProbability & Odds Number sequencesNumber sequences