Transcript Grades 9-12 Math Standards - Santa Rosa County School District

Todd Clark, Office of Math and Science
FL Department of Education
February 19, 2008
© 2008, Florida Department of Education
Florida’s Office of Math & Science
Established by Governor Crist in February
2007
Responsible for implementing K-12
mathematics and science standards and
education policies that improve student
achievement and prepare students for
success
Website: www.fldoestem.org
An Era of Standards
NCTM publishes standards in 1989
(content), 1991 (teaching), 1995
(assessment), and 2000 (revision)
Florida adopts first set of Sunshine State
Standards for Math in 1996
Grade Level Expectations written in 1999
Revision Process
September 2006 – Framers convene
October 2006 through January 2007 – Writers draft K-8
standards and secondary content standards with
comment and review from framers
February through March 2007 – Individual, Public, and
Committees review drafts
April through June 2007 – Revisions of drafts based on
public review
June 2007 – Evaluation of cognitive complexity of
Benchmarks
August 2007 – Present new standards to the State
Board of Education
September 2007 – Standards are approved by the State
Board of Education
Modeled From the World’s Leading
Mathematics Curriculum –
World-Class Curriculum Standards
Singapore – top on the TIMSS
Finland – top on the PISA
Massachusetts, California, Indiana –
standards that were graded “A”
National Council Teachers of
Mathematics Curriculum Focal Points
What the Researchers said about
Our Mathematics Standards
“A Mile Wide, An Inch Deep”
For Florida’s Grades 1-7, the average
number of mathematics grade level
expectations (GLEs) = 83.3
Singapore, the highest performing nation
as measured by Trends in International
Math and Science Study (TIMSS), has 15
GLEs per grade level
College Board
Define grade-level expectations for grade 912
Increase rigor of middle through high school
standards
Increase specificity of standards, showing a
progressive development across grade
levels
Increase the depth of knowledge required
as grades progress
Recommendations From
International and National Experts
“Increase rigor and specificity all the way around”
K-8 - By grade level up to Algebra 1
Let NCTM’s Focal Points be a guide
Reduce number of GLEs, focused in-depth
instruction
Secondary - By Bodies of Knowledge
Algebra, Geometry, Probability, Statistics,
Trigonometry, Discrete Math, Calculus, Financial
Literacy
“Upper level” mathematics courses will use
standards set by AP, IB, College Board, Dual
Enrollment course guidelines/standards
Terms in the 1996 and 2007
Standards
1996
Standards
Grade Band
Strand
Benchmark
Grade Level
Expectation
2007
Standards
Body of Knowledge
Supporting Idea
Big Idea
Access Points
Benchmark
Coding Scheme
Kindergarten through Grade 8
MA.
5.
A.
1.
1
Subject
Grade-Level
Body of
Knowledge
Big Idea/
Supporting
Idea
Benchmark
Secondary
MA.
912.
G.
1.
1
Subject
Grade-Level
Body of
Knowledge
Standard
Benchmark
Sunshine State Mathematics Standards
Trigonometry
Body of Knowledge
Benchmark
MA.912.T.2.2
Standard 2
Benchmark
Benchmark
MA.912.T.1.2
Benchmark
MA.912.T.1.1
MA.912.T.1.3
Benchmark
Benchmark
MA.912.T.2.1
Benchmark
Benchmark
MA.912.T.1.4
MA.912.T.1.5
MA.912.T.2.4
Standard 1
Benchmark
MA.912.T.1.6
MA.912.T.2.3
Benchmark
Benchmark
Benchmark
MA.912.T.1.8
MA.912.T.1.7
Standard 4
Benchmark
MA.912.T.3.1
Standard 3
Benchmark
MA.912.T.4.1
Benchmark
Standard 5
Benchmark
MA.912.T.4.2
Benchmark
MA.912.T.4.3
Benchmark
Benchmark
MA.912.T.3.2
MA.912.T.3.4
Benchmark
MA.912.T.5.1
Benchmark
MA.912.T.3.3
Benchmark
MA.912.T.5.2
Benchmark
MA.912.T.5.3
MA.912.T.4.4
TRIGONOMETRY BODY OF KNOWLEDGE
Standard 1: Trigonometric Functions
Students extend the definitions of the trigonometric functions beyond right triangles using the unit
circle and they measure angles in radians as well as degrees. They draw and analyze graphs of
trigonometric functions (including finding period, amplitude, and phase shift) and use them to solve
word problems. They define and graph inverse trigonometric functions and determine values of
both trigonometric and inverse trigonometric functions.
Benchmark Code
Benchmark
MA.912.T.1.1
Convert between degree and radian measures.
MA.912.T.1.2
Define and determine sine and cosine using the unit circle.
MA.912.T.1.3
State and use exact values of trigonometric functions for special angles, i.e. multiples of

6

4
(degree and radian measures)
MA.912.T.1.4
Find approximate values of trigonometric and inverse trigonometric functions using
appropriate technology.
MA.912.T.1.5
Make connections between right triangle ratios, trigonometric functions, and circular
functions.
MA.912.T.1.6
Define and graph trigonometric functions using domain, range, intercepts, period,
amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing
technology.
MA.912.T.1.7
Define and graph inverse trigonometric relations and functions.
MA.912.T.1.8
Solve real-world problems involving applications of trigonometric functions using graphing
technology when appropriate.
Sunshine State Mathematics Standards
Grade 6
Benchmark
MA.6.A.1.1
Benchmark
Benchmark
Benchmark
MA.6.A.3.1
MA.6.A.3.2
Benchmark
MA.6.A.1.2
MA.6.A.3.3
Algebra
Big Idea 1
Body of Knowledge
Benchmark
Algebra
Body of Knowledge
Big Idea 3
MA.6.A.1.3
Benchmark
Benchmark
Benchmark
MA.6.A.3.5
MA.6.A.3.6
MA.6.A.3.4
Benchmark
MA.6.A.2.1
Big Idea 2
Benchmark
Algebra
MA.6.G.5.1
Body of Knowledge
Geometry
Benchmark
MA.6.A.2.2
Body of Knowledge
Supporting Idea
Benchmark
MA.6.G.5.2
Benchmark
MA.6.G.5.2
Benchmark
MA.6.A.6.1
Supporting Idea
Algebra
Body of Knowledge
Benchmark
Benchmark
MA.6.A.6.2
MA.6.A.6.3
Statistics
Body of Knowledge
Supporting Idea
Benchmark
MA.6.A.6.1
Benchmark
MA.6.A.1.3
Grade 6 Big Idea 1
BIG IDEA 1: Develop an understanding of and fluency with
multiplication and division of fractions and decimals.
BENCHMARK
CODE
BENCHMARK
MA.6.A.1.1
Explain and justify procedures for multiplying and dividing
fractions and decimals.
MA.6.A.1.2
Multiply and divide fractions and decimals efficiently.
MA.6.A.1.3
Solve real-world problems involving multiplication and
division of fractions and decimals.
What is a Supporting Idea?
Supporting Ideas are not subordinate
to Big Ideas
Supporting Ideas may serve to
prepare students for concepts or
topics that will arise in later grades
Supporting Ideas may contain critical
grade-level appropriate math
concepts that are not included in the
Big Ideas
What are 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
three levels of complexity include participatory,
supported, and independent with the
participatory level being the least complex
Access Points Coding Scheme
Kindergarten through Grade 8
MA.
5.
Subject
Grade Level
A.
1.
Body of
Big Idea/
Knowledge Supporting
Idea
ln.a
Access
Point
Secondary
MA.
912.
A.
1.
ln.a
Subject
Grade-Level
Body of
Knowledge
Standard
Access
Point
Comparing the Standards
Grade Level
K
1st
2nd
3rd
4th
5th
6th
7th
8th
Number of Old
GLE’s
67
78
84
88
89
77
78
89
93
Number of New
Benchmarks
11
14
21
17
21
23
19
22
19
How is this accomplished?
Fewer topics per grade due to less
repetition from year to year
Move from “covering” topics to teaching
them in-depth for long term learning
Individual teachers will need to know how
to begin each topic at the concrete level,
move to the abstract, and connect it to
more complex topics
Bodies Of Knowledge 9-12
Old 9-12 Benchmarks
(Same for all 9-12)
12 Benchmarks in Number
Sense, Concepts, and Operations
8 Benchmarks in Measurement
4 Benchmarks in Algebraic
Thinking
5 Benchmarks in Geometry and
Spatial Sense
7 Benchmarks in Data Analysis
and Probability
New Body of Knowledge
Benchmarks
84 Benchmarks for Algebra
52 Benchmarks for Calculus
41 Benchmarks for Discrete Math
41 Benchmarks for Financial Literacy
47 Benchmarks for Geometry
9 Benchmarks for Probability
28 Benchmarks for Statistics
24 Benchmarks for Trigonometry
Course Description Example:
ALGEBRA
ALGEBRA I
GEOMETR
Y
DISCRETE
MATH
MA.912.A.4.2 Add, subtract,
and multiply polynomials.
MA.912.G.1.4 Use coordinate geometry to
find slopes, parallel lines, perpendicular
lines, and equations of lines.
MA.912.D.7.2 Use Venn diagrams
to explore relationships and
patterns, and to make arguments
about relationships between sets.
Benchmark MA.912.A.4.3:
Factor polynomial expressions.
_______________________________
ex: Let a, b > 0, a > b, a,b Є 
Factor the following expression:
a2 – b2
Solution:
a2 – b2 = (a – b)(a + b)
Can this be done Geometrically
with manipulatives?