It

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Its Not the Same Old Algebra and Geometry

• Dr. Joyce Bernstein
• East Williston UFSD
• LIASCD
• October 19, 2007

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(No Transcript)
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Investigate/Explore - Students will be given
situations in which they will be asked to look
for patterns or relationships between elements
within the setting. Discover - Students will make
note of possible patterns and generalizations
that result from investigation/exploration. Conjec
ture - Students will make an overall statement,
thought to be true, about the new
discovery. Reasoning - Students will engage in a
process that leads to knowing something to be
true or false. Argument - Students will
communicate, in verbal or written form, the
reasoning process that leads to a conclusion. A
valid argument is the end result of the
conjecture/reasoning process. Justify/Explain -
Students will provide an argument for a
mathematical conjecture. It may be an intuitive
argument or a set of examples that support the
conjecture. The argument may include, but is not
limited to, a written paragraph, measurement
using appropriate tools, the use of dynamic
software, or a written proof. Proof - Students
will present a valid argument, expressed in
written form, justified by axioms, definitions,
and theorems. Apply - Students will use a
theorem or concept to solve an algebraic or
numerical problem.
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   Math A Math B Algebra Geometry Algebra 2 and Trigonometry
2006-07 X X             
2007-08 X X X First admin. in June 2008          
2008-09 X Last admin. in January 2009 X X X First admin. in June 2009    
2009-10   X Last admin. in June 2010 X X   X First admin. in June
2010-11     X X X
2011-12     X X X
 
 
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Important Websites Math Toolkit grades 9
12 http//emsc32.nysed.gov
/3-8/guidance912.htm Sample Tasks NYS
Mathematics Core Curriculum
Curriculum Performance Indicators Implementation
Timeline Glossary for Teachers by Grade
Level Regents Approved Commencement-Level Course
Descriptions Template for Analysis of
Mathematics Program Series Commencement Level
Crosswalk Powerpoint Overview Test Samplers
Late October prior to each test
http//www.emsc.nysed.gov/osa Test
Specifications
http//www.emsc.nysed.gov/osa/mathre/testspecsalge
bra.pdf http//www.emsc.nysed.gov/osa/mathre/tests
pecs-geometry.pdf http//www.emsc.nysed.gov/osa/ma
thre/testspecs-alger2trig.pdf Association of
Math Assistant Principals of NYC
http//www.amaps.org/
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Integrated Algebra In implementing the Algebra
process and content performance indicators, it is
expected that students will identify and justify
mathematical relationships. The intent of both
the process and content performance indicators is
to provide a variety of ways for students to
acquire and demonstrate mathematical reasoning
ability when solving problems. Local curriculum
and local/state assessments must support and
allow students to use any mathematically correct
method when solving a problem. Throughout this
document the performance indicators use the words
investigate, explore, discover, conjecture,
reasoning, argument, justify, explain, proof, and
apply. Each of these terms is an important
component in developing a students mathematical
reasoning ability.
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Crosswalks To Algebra Other than from Math A From
Middle School A.N.5 - Solving Algebraic problems
involving fractions, decimals, percents
(decrease/increase and discount), and
proportionality/direct variation Math 8 does not
use the term direct variation. A.N.6 -
Evaluating expressions involving factorial(s),
absolute value(s), and exponential
expression(s) Factorials and absolute value in
grade 7 Math 8 handles expressions with
exponents. A.A.9 - Analyze and solve verbal
problems that involve exponential growth and
decay Start from scratch! A.A.21 - Verifying a
value as a solution to a linear equation or
inequality in one variable A.A.45 - Application
of Pythagorean theorem (grade 7) A.M.1 -
Calculations of rate (grade 7)
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Crosswalks To Algebra Other than from Math A From
Math B A.G.3 - Determine when a relation is a
function A.G.5 - How coefficient change in a
function effects its graph (Associate with
graphs of parabolas. Use the calculator.) A.S.3
- Determine when collected data or display may be
biased A.S.4 - Compare and contrast the
appropriateness of different measures of central
tendency for a given data set A.S.8 - Line of
best fit for a scatter plot and its equation
(The line drawn depends on the 2 points chosen to
define the line. Or.. Stat..calc4LinReg(ax
b)) A.S.15 - Identify and describe sources of
bias and its effect, drawing conclusion from
data A.S.17 - Use a reasonable line of best fit
to make a prediction involving interpolation or
extrapolation
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Crosswalks To Algebra- New to 2005
Standards A.A.3 - Difference between an
Algebraic expression and an Algebraic equation
(Now a Middle School topic Is there an
equal sign?) A.A.28 - Relation between roots
and factors of a quadratic equation (Not really
new) A.A.29 - Set builder notation and/or
interval notation to represent the elements of a
set A.A.30 - Complement of a set A.A.31
Intersection of sets A.A.32 - Slope as a rate of
change (not really new)
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Highlights from the Specifications for
Integrated Algebra Content Strand Number
Sense Operations 6 10 Algebra 50
55 Geometry 14 19 Measurement 3
8 Probability Statistics 14 19
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Highlights from the Specifications for
Integrated Algebra Question Type Number of
Questions Multiple Choice (2 pt) 30 2-credit
open ended 3 3-credit open ended 3 4-credit
open ended 3 87 Points 60 points are
Multiple Choice
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• Highlights from the Specifications for
• Integrated Algebra
• Reference Sheet
• Trig Ratios
• Selected area, volume, surface area formulas
• Slope
• Reminder about graphing calculators

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Riverside Test Publishing has overall
responsibility for the Regents exams for the next
few years. New York State teachers are the
question writers, trained by Riverside.
Riverside is responsible for final format. State
Ed Update For standard-setting the new exams,
the Department will use the same processes that
were used for the Grades 3 8 Testing Program,
including standard setting AFTER the test has
been administered using operational testing data
(rather than field testing data). Administration
Tuesday, June 17 Return with scaled scores
Thursday, June 26
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Geometry There is no other school mathematics
course that offers students the opportunity to
act as mathematicians.  Within this course,
students will have the opportunity to make
conjectures about geometric situations and prove
in a variety of ways, both formal and informal,
that their conclusion follows logically from
their hypothesis.  The variety of approaches to
verification and proof is what gives curriculum
developers and teachers the flexibility to adapt
strategies to address these performance
indicators in a manner that meets the diverse
needs of our students. Local curriculum and
local/state assessments must support and allow
students to use any mathematically correct method
when solving a problem. It is intended that
students will use the traditional tools of
compass and straightedge as well as dynamic
geometry software that models these tools more
efficiently and accurately, to assist in these
investigations. 
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Crosswalks to Geometry Solid Geometry NOT
Previously Addressed G.G.1 A line perpendicular
to each of two intersecting lines at their point
of intersection is perpendicular to the plane
determined by them G.G.2 Through a given point
there passes one and only one plane perpendicular
to a given line G.G.3 Through a given point
there passes one and only one line perpendicular
to a given plane G.G.4 Two lines perpendicular
to the same plane are coplanar
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G.G.5 Two planes are perpendicular to each other
if and only if one plane contains a line
perpendicular to the second plane G.G.6 If a
line is perpendicular to a plane, then any line
perpendicular to the given line at its point of
intersection with the given plane is in the given
plane G.G.7 If a line is perpendicular to a
plane then every plane containing the line is
perpendicular to the given plane G.G.8 If a
plane intersects two parallel planes, then the
intersection is two parallel lines
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G.G.9 Two planes perpendicular to the same
line are parallel. GG.10 The lateral edges of a
prism are congruent and parallel G.G.11 Two
prisms have equal volumes if their bases have
equal areas and their altitudes are equal G.G.12
The volume of a prism is the product of the area
of the base and the altitude
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Concurrency Theorems NOT Previously
Addressed G.G.21 Investigate and apply the
concurrence of medians, altitudes, angles
bisectors, and perpendicular bisectors of
triangles. That means centroids, orthocenters,
incenters, and circumcenters
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Highlights from the Specifications for
Geometry Content Band Geometric
Relationships 8 12 Constructions 3
7 Locus 4 8 Informal and Formal Proofs 41
47 Transformational Geometry 23 - 28
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Highlights from the Specifications for
Geometry Question Type Number of
Questions Multiple Choice (2 pt) 28 2-credit
open ended 6 4-credit open ended 3 6-credit
open ended 1 86 Points 56 points
are Multiple Choice
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Algebra 2 and Trigonometry This course is a
continuation and extension of the two courses
that preceded it. While developing the algebraic
techniques that will be required of those
students that continue their study of
mathematics, this course is also intended to
continue developing alternative solution
strategies and algorithms. For example,
technology can provide to many students the means
to address a problem situation to which they
might not otherwise have access. In implementing
the Algebra 2 and Trigonometry process and
content performance indicators, it is expected
that students will identify and justify
mathematical relationships, formally and
informally. The intent of both the process and
content performance indicators is to provide a
variety of ways for students to acquire and
demonstrate mathematical reasoning ability when
solving problems. Local curriculum and
local/state assessments must support and allow
students to use any mathematically correct method
when solving a problem
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Crosswalks to Algebra 2 and Trigonometry Topics
NOT Previously Addressed
(my edited list) A2.A.12 Evaluate exponential
expressions, including those with base e A2.A.24
Know and apply the technique of completing the
square A2.A.50 Approximate the solution to
polynomial equations of higher degree by
inspecting the graph
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A2.A.63 Restrict the domain of the sine, cosine,
and tangent functions to ensure the existence of
an inverse function A2.A.65 Sketch the graph of
the inverses of the sine, cosine, and tangent
functions A2.A.70 Sketch and recognize one
cycle of a function of the form y AsinBx or y
Acos Bx A2.A.71 Sketch and recognize the graphs
of the functions y sec(x), y csc(x), y
tan(x), and y cot(x)
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Highlights from the Specifications for Algebra
2/Trigonometry Content Strand Number
Sense Operations 6 10 Algebra 70
75 Measurement 2 5 Probability
Statistics 13 17
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Highlights from the Specifications for Algebra
2/Trigonometry Question Type Number of
Questions Multiple Choice (2 pt) 27 2-credit
open ended 8 4-credit open ended 3 6-credit
open ended 1 88 Points 54 points are
Multiple Choice
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• Questions from Our Curriculum Leaders
• Lets Discuss
• In what grade are you starting Algebra?
• How are you providing AIS?
• How are you providing staff development?
• How are you selecting textbooks?
• In what order are you offering Integrated
  Algebra, Geometry, and Algebra 2/Trigonometry?
• Are Regents Examinations counted in final
  averages?