Florida K-8 Mathematics
Standards
April 29, 2008
Grade 4
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”?




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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
Division of Whole
Numbers (1 digit divisor
and up to 3 digit
dividends) - Explains,
demonstrates, and
solves real world
problems using
manipulatives, drawings,
and algorithms
New Standards
For Example…
Old Standards
New Standards
Division of Whole
Numbers (1 digit divisor
and up to 3 digit
dividends) - Explains,
demonstrates, and
solves real world
problems using
manipulatives, drawings,
and algorithms
Divide multi-digit whole
numbers fluently,
including solving realworld problems,
demonstrating
understanding of the
standard algorithm and
checking the
reasonableness of
results.
For Example…
Old Standards
Addition and
subtraction of
decimals and
common fractions in
grade 4
New Standards
For Example…
Old Standards
New Standards
Addition and
subtraction of
decimals and
common fractions in
grade 4
Develop an
understanding of and
fluency with addition
and subtraction of
fractions and
decimals in grade 5
Big Ideas for Fourth Grade:



Develop quick recall of multiplication
facts and related division facts and
fluency with whole number multiplication
2: Develop an understanding of decimals,
including the connection between
fractions and decimals
3: Develop an understanding of area and
determine the area of two-dimensional
objects
1:
Fourth Grade
Supporting Ideas

Algebra:
– Generate algebraic rules and use all four
operations to describe patterns, including
nonnumeric growing or repeating
patterns
– Describe mathematics relationships using
expressions, equations, and visual
representations
– Recognizes and writes algebraic
expressions for functions with two
operations
Fourth Grade
Supporting Ideas

Geometry & Measurement:
– Classify angles of two-dimensional shapes using
benchmark angles (i.e., 45°, 90°, 180°, and
360°)
– Identify and describe the results of translations,
reflections and rotations of 45, 90, 180, 270 and
360 degrees, including those with line and
rotational symmetry.
– Identify and build a three-dimensional object
from two-dimensional representations of that
object and vice versa.
Fourth Grade
Supporting Ideas

Numbers and Operations:
– Use and represent numbers through millions in
various contexts, including estimation of relative
sizes of amounts or distances
– Use models to represent division as the inverse
of multiplication, as partitioning, or as successive
subtraction
– Generate equivalent fractions and simplify
fractions
– Determine factors and multiples of specified
whole numbers
Fourth Grade
Supporting Ideas

Numbers and Operations:
– Relate halves, fourths, tenths and
hundredths to decimals and percents
– Estimate and describe reasonableness of
estimates; determine the appropriateness
of estimate versus an exact answer
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 4
Selection from a PowerPoint
Presented by
Linda Oaksford
Test Development Center
Big Ideas
~ Grade 4
1. Multiplying multi-digit whole numbers~
check for reasonableness of products
2. Decimals (through thousandths)
and fractions
3. Area of two-dimensional shapes based
on unit square, including rectangle
formula
Grade 4 ~
MA.4.A.4.3
Supporting Idea:
Algebra
Recognizes and writes algebraic
expressions for functions with two
operations
MA.4.A.4.3
Sample
Alex is 4 years more than twice as old as
Sam. Which expression shows Alex’s age,
using s for Sam’s age?
A) (4 + 2) x s
B) (s + 4) x 2
C) 4s x 2
D) 2s + 4 B
Previous Benchmark:
MA.D.1.2.1
The student describes a wide variety of
patterns and relationships through
models, such as manipulatives, tables,
graphs, and rules using algebraic
symbols.
(Student extended patterns and
relationships; limited to one operation)
Sample: MA.D.1.2.1
The students in Mrs. Jay’s Notebooks
class need a notebook for
4
5
every subject. According to
6
the table what would be
7
the price of 6 notebooks?
A)16
C)19
B) 18 B
D)20
Price
$12
$15
$21
As of 2011. . .
NOT assessed at 4th grade

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Measurement of weight/mass,
capacity, temperature,
(perimeter), etc.
Coordinates
Measures of central tendency –
mean, median, mode, and range
Probability – likeliness of outcome
Data Analysis
Combinations