Grade 8 Math Standards - Santa Rosa County School District

Report
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 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.
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 boxand-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 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 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.
B.
C.
D.
all
all
all
all
numbers
numbers
numbers
numbers
less than 5
between 0 and 10
between 5 and 25
greater than 25
Assessment Crosswalk
Revised SSS Standard
Used in Transition
DRAFT
Assessed Until 2011
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 multistep 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 numbers
MC
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 calculator
MC, 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 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 threedimensional 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

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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

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