Grade 6 Math Standards - Santa Rosa County School District

Report
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
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 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 K12 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 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, What the
United States can Learn from Singapore’s 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
Subject
Grade-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
K
Number of Old
GLE’s
67
1st
2nd
78
84
3rd
88
4th
5th
89
77
6th
7th
8th
78
89
93
Number of New
Benchmarks
Describing the Standards
Grade Level
K
1st
Number of Old
GLE’s
67
78
Number of New
Benchmarks
11
14
2nd
3rd
84
88
21
17
4th
5th
89
77
21
23
6th
7th
8th
78
89
93
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.
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 Standards
Knows proportional
relationships in scale
drawings and uses scale
drawings to solve real
world problems in grade
6
New Standards
For Example…
Old Standards
New 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 Standards
Expresses whole
numbers in
exponential notation
or in factored form in
grade 6
New Standards
For Example…
Old Standards
New 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 Standards
Solves problems
involving the changes of
dimensions in a twodimensional figure and
how those changes
effect the area or
perimeter of the given
figure in grade 6
New Standards
For Example…
Old Standards
New Standards
Solves problems
involving the changes of
dimensions in a twodimensional 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
fluency with multiplication and
division of fractions and decimals
2: Connect ratio and rates to
multiplication and division
3: Write, interpret, and use
mathematical expressions and
equations
Sixth Grade
Supporting Ideas

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:
– 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:
– 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:
– 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 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 realworld 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:




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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) 4/5
B) 5/3
C) 0.05
D) 0.7
Previous Benchmark:
MA.A.3.3.1
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 miles
C) 5.75 miles
B)3.75 miles
D) 7.00 miles
Previous Benchmark:
MA.B.1.3.2
 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.1.3.1.
As of 2011. . .
NOT assessed at 6th grade

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Change in dimensions
Scale drawings
Direct/indirect measurement (in
isolation)
Scientific notation
Coordinate plotting (in isolation)
Similarity, congruency, symmetry,
transformations and other geometric
concepts & properties
Probability & odds
Circle graphs & stem-and-leaf plots

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