Algebra 
General
Description
In this course
students begin to master the craft of mathematical problem solving and to
develop an understanding of the power of abstraction in mathematics.
Algebra focuses on functions, their properties, and their use both in
mathematics as well as in other disciplines. Students will learn about
linear functions and their properties (e.g., slope and intercept),
functions of two or more variables, and, finally, quadratic equations.
Students will also become proficient in the use of graphing calculators.
In addition, they will create algebraic models for realworld situations.
By the conclusion of the course all students will be capable of explaining
and describing properties of linear and quadratic equations and where we
find them in the world. Finally, students will improve their mathematical
vocabulary.
Essential Questions
� What is algebra?
� In what ways can algebra be used to model
situations in the world?
� Why do we study algebra? Why do
mathematicians study algebra?
� How does algebra connect with other
disciplines?
� How is mathematics used to present
information in the media?
Units of
Study/Activities and Projects:
� Introduction to Algebra
�
Investigation of slope and intercept using graphing calculators
�
Description and interpretations of situations presented in two
dimensional graphs
� Linear Functions
�
solving systems of linear equations
�
modeling Distance=Rate
x Time problems
algebraically
� Quadratic Equations
� solving
by factoring
� using
logic symbolism
� Projects
using graphing calculator
� Journal
writing & Mathematical vocabulary
Learning
Outcomes
As a result of
taking algebra students will:
�
master the art of translating verbal expressions into algebraic
equations.
�
be able to write an equation as a verbal sentence.
�
understand the use of variables to represent unspecified amounts or
numbers.
�
solve algebraic problems using and not using a graphing calculator.
�
understand how algebra can be summoned to solve problems in other
disciplines in the sciences and
the
humanities
Forms of
Assessment
�
Group problem solving
�
Project presentations
�
Class participation in problem solving activities
�
Homework assignments
�
Formal tests.
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Geometry 
General
Description
This mathematics
course focuses on two and threedimensional Geometry.
As students encounter new concepts in geometry, basic concepts in algebra
are reinforced forming an integrated approach. The first term of this
course begins with Euclidean concepts using the compass, straightedge, and
protractor. The course examines theoretical forms as well as shapes and
structures in the real world (The Brooklyn Bridge and a cathedral are
among the field trips we take.) Students learn to use numbers and symbols
to communicate mathematical ideas. Measurement in both British and Metric
units is practiced. Theorems will be learned and applied to problems (e.g.
the oppositeangle and Pythagorean theorems). In the second term of this
course students will learn about conic sections and how to perform
geometric transformations. Realworld applications, handson activities,
and self discovery are the primary methods use in this class to prepare
students for study of Trigonometry and the world around them.
Essential Questions
�
What is geometry?
� How do I
use a compass, straightedge, and protractor to display knowledge of
Euclidean plane
geometry?
� How do I
measure and calculate surface area and volume of theoretical and
realworld objects?
� What are
the important theorems in geometry and how do I use them in proofs and
reasoning?
� What are
conic sections and how do I graph them?
Units of
Study/
Activities & Projects
�
Algebra review
�
points, lines, rays
� congruence
�
angles (use of a protractor and compass), angle theorems
perpendicular, bisecting segments
and
angles
�
triangles: right, isosceles, equilateral, Pythagoras� theorem
�
measuring length
�
calculating perimeter and area
�
quadrilaterals, circles
�
volume
�
solids of the above dimensions: cubes, pyramids, spheres, cones,
conic sections
�
the coordinate plane
�
transformations (Eischer�s mathematically based designs)
Learning
Outcomes
As a result
of Geometry class, students will gain:
�
knowledge of Geometry according to New York State standards (see
attached)
�
knowledge of Euclidean plane geometry
�
increased linguistic knowledge and performance skill. With an
emphasis on communicating
concepts of Geometry in speech and writing.
�
ability to to solve complex problems and tasks in mathematics (in
groups and individually).
Forms
of Assessment
�
completion and competency in group and individual activities
�
glossary and journal responses
�
individual projects; two and threedimensional
�
class participation and group participation
�
performance of skills using tools (i.e. straight edge, compass and
protractor)
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Advanced
Algebra and
Trigonometry

General Description
Advanced algebra and trigonometry is a course covered in two sections. In
the first section the concept of a function is introduced and a variety of
functions are examined and manipulated. In the second section students
begin to explore right angle trigonometry and the functions and laws that
are applied to the six trigonometric identities. Students will also have
the opportunity to problem solve, develop their logical and critical
thinking skills and communicate their ideas.
Essential Questions
�
What is a function?
�
How are functions used in our world?
�
What are the characteristics of different functions?
�
How to graph different functions?
�
What are the different number systems and when/how do you use each?
�
What are the six trigonometric identities? How are they used to
solve problems in the real world?
�
How do we use the Law of Sines and the Law of Cosine?
�
Draw the basic graphs of each of the trigonometric functions. How
do their formulas change when
they are
shifted to the right or left, shortened or lengthened, or stretched
vertically?
�
What are some problem solving strategies used to solve problem?
Units of Study/Activities &Projects
Area
Studies:
�
Multiplying binomials, least common denominator (L.C.D.) real
numbers, right triangles
�
What is a function?, domain and range, factoring, working with
graphs, imaginary and complex numbers and constant and linear functions.
�
Constant functions, linear functions, cubing functions, quadratic
functions and rate of change
�
Polynomial functions, logarithmic functions and exponential
functions
�
Right angle trigonometry
�
Laws of Sines and Cosines
�
Graphing the Trigonometric Functions:
Problem Solving Strategies: Students choose from among many different word
problems which are designed to teach students the various types of
strategies in problem solving. These problems give the students the
opportunity to work collaboratively and think critically about real life
problems. In addition, students will also communicate what they have
learned through writing.
Learning Outcomes
As a result of this class, students will gain
�
Knowledge of algebra and trigonometry that meet state standards
�
Awareness of multiple representations of functions
�
Knowledge of various number systems, both their importance and
derivation
� Increased
linguistic knowledge in the subject that will enable student to
communicate math concepts through oral and written presentations in
class.
And will also gain the ability
�
to work in groups to solve complex problems and to complete
difficult tasks
�
convert radians to degrees and vice versa
�
solve problems using the six identities
�
solve problems using the Laws of Sines and Laws of Cosines
�
graph and describe the six functions and their transformations
�
use different strategies to solve problems
�
communicate mathematically
�
problem solve
Forms of Assessment
�
tests
�
completed group and individual projects & activities
�
graphing book
�
homework
�
problem solving reports
�
journal writing
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PreCalculus 
General
Description
This mathematics class is divided into two sections. In the first section, basic concepts in Algebra, Geometry,
and Trigonometry are reinforced and new, more advanced applications of
these disciplines are explored. This
is done in order to increase and strengthen the mathematical foundation
needed for Calculus. In
addition, the concept of a function is introduced and some basic functions
are examined. In the second
section, higher mathematical functions are examined and manipulated, more
complex number systems are applied, and calculus principles introduced.
Real world applications, handson activities, and selfdiscovery
are the primary tools used in this class to prepare students
mathematically for Calculus and the world.
EssentialQuestions
�
What is Precalculus?
�
What is a function?
�
How are these functions used in our world?
�
What are the characteristics of different functions?
�
How do I graph different functions?
�
What are the different number systems and when/how do I use
each?
�
What is the rate of change?
Units of
Study/Activities & Projects
�
Algebra/Geometry/Trigonometry review
�
Area Studies: working with variables, multiplying binomials,
least common denominator (L.C.D.),
real numbers, right triangles
�
Number game boards, trigonometry angle relationship poster,
L.C.D. game, student step by step
instructions for binomial multiplying, journal entries, native language
& English glossary of words
and definitions
�
Introduction to Functions
�
Area Studies: what is a function?, domain and range,
factoring, working with graphs, imaginary
and complex numbers, & constant and
linear functions.
�
Graph scrapbook of functions, expanded number game board,
creating students' own imaginary
number problems, journal entries, native
language & English glossary of words and definitions
�
Basic Functions
�
Area Studies: constant functions, linear functions, cubing
functions, quadratic functions, & rate of
change
�
Graph scrapbook of variations of these four functions, self
discovery and analysis of movements of
graphs of functions, realworld
applications of these functions and their graphs, journal entries,
native language & English glossary of
words and definitions
�
Advanced Functions & Basic Calculus
�
Area Studies: polynomial functions, logarithmic functions,
exponential functions, basic
calculus
�
graph scrapbook of variations of these complex functions,
realworld applications of these functions
and their graphs, journal entries, native language & English glossary
of words and definitions, & (in
the near future) using graphing calculators
and/or computer software to examine and manipulate
these functions and their graphs.
Learning
Outcomes
As
a result of Precalculus class, students will gain:

knowledge
of precalculus material according to state standards.

awareness
of multiple representations of functions.

knowledge
of various number systems, their importance, and derivation

increased
linguistic knowledge, with emphasis on the ability to communicate math
ideas and to
explain intricate concepts in speech and writing

ability to work in groups to solve complex
problems and to complete difficult tasks
Forms
of Assessment
 group and individual activities completion and
competency
 glossary and journal responses
 quizzes to assess knowledge
 participation and role in group and in class
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Calculus 
General
Description
This math class begins by combining previous
mathematics courses and applying the material learned in the solving of
complex reallife problems. Then
the class begins to analyze functions.
Students examine functions in terms of different limits and
derivatives. Different
methods of differentiation and integration and the concept of continuity
are also studied. All of
these areas can be applied to subjects outside of calculus such as in
physics and economics.
Essential
Questions

What is a limit?

When is a function continuous?

What is a rate of change?

How can we find the rate of change of a nonlinear function?

What are some shortcuts that we can use to find the
derivative?

How can we apply the derivative to our lives?

Does differentiability imply continuity?

How can we find the height, velocity, or acceleration of a free
falling object?

How' is the rate of change
used in economics?

What is integration and how is it applied?
Units
of Study/Projects
Introduction
�
Area studies: PreCalculus review: intervals, inequalities,
inequalities and absolute value, exponents and radicals, operations with
exponents, finding the domain, special product and factorization
techniques, complex fractions, rationalization.
�
"9 types of intervals" activity,
"inequalities" group and individual activity. math in economics
activity, "prove the 7 properties" activity, "find the
domain" activity, " special products and factorization"
poster activity, journal entries.
Functions,
Gral2hs and Limits
�
Area studies: distance formula, nddpoint formula, graphs
of equations, breakeven points, slope, inverse, introduction to limits,
properties of limits, onesided limits, continuity.
�
"Football distance" and "estimating
sales" activities, "economics breakeven point" activity,
"using the slope int he real world" activity, graphs of basic
functions, �properties of limits" and "operations with
limits" activities, continuity reading, "determining
continuity" activity, journal entries and quiz.
Differentiation:
Part One
 Area
studies: derivative and the slope, rate of changesecant line and
tangent line, definition of the slope of a graph, definition of a
derivative, differentiability, continuity, differentiation rules.
 Rate
of change questioning, "slope activity", "definition of
the derivative application", "differentiability and
continuity " reading and questions, "differentiation rules,
proofs and applications", journal entries, quiz.
Differentiation:
Part Two
�
Area studies: average rate of change, instantaneous rate of
change, position functions, velocity functions, more differentiation
rules, marginal cost/revenue/profit.
�
Rate of changevelocity and economics activity. "Create
your own 2 rate of changes", activity, "summary of
differentiation rules" poster activity.
Differentiation:
Part Three
 Area
studies: higher order derivatives, acceleration, implicit
differentiation, related rates.
 "Higher
order derivative " activity, acceleration word problems, related
rates word problems, oral quiz
Learning
Outcomes
As
a result of studying calculus, students will gain:

Knowledge of limits and derivatives and using them to find
rates of change

Increased linguistic knowledge, with emphasis on the ability to
communicate math ideas and
concepts through writing and oral
presentation.

Ability to work in groups to solve more complex mathematical
problems

Knowledge of integration
Forms
of Assessment

Group and individual activities

Journal entries and responses

Written and oral quizzes

Participation and role in group work

Group
discussion panel evaluation
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