florida k-8 mathematics standards april 28, 2008 grade 3 adapted from a presentation given by julie...
TRANSCRIPT
Florida K-8 Florida K-8 Mathematics Mathematics StandardsStandards
April 28, 2008April 28, 2008
Grade 3Grade 3
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…
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…
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…
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.
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.
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.
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.
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.
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.
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.
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
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.
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
Describing the Describing the StandardsStandards
Body of Knowledge Key:A - AlgebraC - CalculusD - Discrete MathematicsF - Financial LiteracyG - GeometryP - ProbabilityS - StatisticsT - Trigonometry
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
Describing the Describing the StandardsStandardsGrade LevelGrade Level Number of Number of OldOld
GLE’sGLE’sNumber 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
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.
Intent of the Intent of the StandardsStandards What is the importance of having
fewer expectations per grade????
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?”
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)?
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. 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…For Example…
Old Standards New 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
For Example…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 Determines factors and multiples for specified multiples for specified whole numbers in Grade whole numbers in Grade 44
Measures of Central Tendency introduced in grade 3
Measures of Central Tendency introduced in grade 6
Big Ideas for Third Big Ideas for Third Grade:Grade:
1:1: Develop understandings of Develop understandings of multiplication and division and multiplication and division and
strategies for basic multiplication strategies for basic multiplication facts and related division factsfacts and related division facts
2: 2: Develop an understanding of Develop an understanding of fraction and fraction equivalencefraction and fraction equivalence
3: 3: Describe and analyze properties of Describe and analyze properties of two-dimensional shapestwo-dimensional shapes
Third Grade Third Grade Supporting IdeasSupporting Ideas
Algebra:Algebra: – Create, analyze, and represent Create, analyze, and represent
patterns and relationships using patterns and relationships using words, variables, tables and graphs.words, variables, tables and graphs.
Third Grade Third Grade Supporting IdeasSupporting Ideas
Geometry & Measurement:Geometry & Measurement: – Select appropriate units, strategies and Select appropriate units, strategies and
tools to solve problems involving tools to solve problems involving perimeter.perimeter.
– Measure objects using fractional parts Measure objects using fractional parts of linear units such as 1/2, 1/4, and of linear units such as 1/2, 1/4, and 1/10.1/10.
– Tell time to the nearest minute and to Tell time to the nearest minute and to the nearest quarter hour, and the nearest quarter hour, and determine the amount of time elapsed.determine the amount of time elapsed.
Third Grade Third Grade Supporting IdeasSupporting Ideas
Numbers and Operations:Numbers and Operations: – Represent, compute, estimate and Represent, compute, estimate and
solve problems using numbers solve problems using numbers through hundred thousands.through hundred thousands.
– Solve non-routine problems by Solve non-routine problems by making a table, chart, or list and making a table, chart, or list and searching for patterns.searching for patterns.
Third Grade Third Grade Supporting IdeasSupporting Ideas
Data Analysis: Data Analysis: – Construct and analyze frequency Construct and analyze frequency
tables, bar graphs, pictographs, and tables, bar graphs, pictographs, and line plots from data, including data line plots from data, including data collected through observations, collected through observations, surveys, and experiments.surveys, and experiments.
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.”
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.
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.
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.
RemarksRemarks
Remarks were not included with the
standards presented to the State
Board of Education.
Remarks are currently included in
course descriptions.
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/
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)
Assessment…
How will itchange?
FCAT Crosswalk~
Impact on Assessment
Grade 3Selection from a
PowerPoint presented by Linda Oaksford
Test Development Center
Grade 3 ~ Big Idea 1
Real-life situations as repeated addition, arrays, combinations, measurement …
Commutative, associative, distributive, identity, & inverse properties
Facts through 9 X 9Understanding, as well as fluencyUnderstanding
Multiplication & division strategies for basic facts
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 rowhas the same number of desks. Which of the following can be used to find the number of desks in each row?
A) __ 4 = 24 C) 24 X 4= ____B) 4 X ___= 24 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.
How many of the small green
triangles are needed to make the
larger red triangle?
MA.3.G.3.2 Sample
Previous Benchmark: MA.C.1.2.1
The student, given a verbal description, draws and/or models two- and three-dimensional 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 C D
As of 2011. . .As of 2011. . .NOT assessed at 3NOT assessed at 3rdrd grade grade
Measurement of weight/mass, Measurement of weight/mass, capacity, temperature, area, etc.capacity, temperature, area, etc.
CoordinatesCoordinates Measures of central tendency –Measures of central tendency –
median, mode, and rangemedian, mode, and range Probability – likeliness of Probability – likeliness of
outcomeoutcome