Plumsted Township Public Schools
PHILOSOPHY
“To compete in today’s global, information-based economy, students must be able to solve real problems, reason effectively, and
make logical connections.”1 The mathematics department of the Plumsted Township School District believes that math is an essential
part of society. Our math program offers a variety of experiences, which correlate to authentic situations that exist in our community
and beyond. The mathematics curriculum supports all students’ academic needs and provides a meaningful, thorough, and efficient
education through the development of critical thinking and problem solving skills. Content provided in our program is congruent to
the National (NCTM) and State Core Content Curriculum Standards (NJCCCS). In addition, our courses are designed to be flexible in
addressing multiple assessments and cross content curriculum integration.
DEPARTMENT OBJECTIVES:
The learner will be able to:
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Devise strategies to solve meaningful problems that relate to authentic situations in society
Understand and use mathematical processes to solve problems
Use technology to address tasks within the mathematics domain
Foster logical reasoning skills
Develop conclusions using problem solving skills
Use critical thinking skills to construct theories based on real life applications
Identify the importance of mathematics and its benefits within human, physical, environmental, and social systems
Model problems to find solutions within the mathematics domain
Plumsted Township Public Schools
Plumsted Township Public Schools
Mission Statement
The educational program of the New Egypt Schools shall foster high expectations, in academics and behavior, giving attention to all
students’ individual needs. Children will be provided a variety of activities and experiences that allow them to mature into lifelong
learners, who are critical thinkers, and who cooperate with others as they grow and learn in our democratic society.
Plumsted Township Board of Education
Mrs. Joanne Barlow, President
Mr. Herbert Marinari, Vice President
Mrs. Karen Amburgey,
Mr. Lawrence Downs
Mr. Anthony O’Donnell
District Administration
Dr. Robert Smith, Superintendent
Frank Gripp, Business Administrator
Elizabeth Panella, Principal New Egypt High School
John Blair, Assistant Principal New Egypt High School
Andrea Raniero, Principal New Egypt Middle School
Tom Farrell, Assistant Principal New Egypt Middle School
Jean Morgan, Principal New Egypt Elementary School
Toni Ferry, Principal New Egypt Primary School
Colleen Davidson, Director of Curriculum & Instruction
Richard Carroll, Supervisor of Athletics
*All concepts and objectives are mastery learning objectives aligned to the New Jersey State Core Content Curriculum Standards2008
**Professional staff will differentiate instruction to ensure students achieve the stated objectives.
2
Plumsted Township Public Schools
PreCalculus Curriculum
Scope and Sequence
1. Functions and Graphs
a. Functions and their properties
b. Twelve Basic Functions
c. Building Functions from Functions
d. Parametric Relations and Inverses
e. Graphical Transformations
2. Polynomial, Power, and Rational Functions
a. Linear and Quadratic Functions
b. Power functions and Polynomial functions of
Higher Degree
c. Real Zeros of Polynomial Functions
d. Graphs of Rational Functions
e. Solving Equations in One Variable
f. Solving Inequalities in One Variable
3. Exponential, Logistic, and Logarithmic Functions
a. Exponential and Logistic Functions
b. Exponential and Logistic Modeling
c. Logarithmic Functions and Their Graphs
d. Properties of Logarithmic Functions
e. Equation Solving and Modeling
f. Mathematics of Finance
*
4.
Trigonometric Functions
a. Angles and Their Measures
b. Trigonometric Functions of Acute Angles
c. Trigonometry Extended: The Circular Functions
d. Graphs of Sine and Cosine: Sinusoids
e. Graphs of Tangent, Cotangent, Secant, and
Cosecant
f. Inverse Trigonometric Functions
5. Analytic Trigonometry
a. Fundamental Identities
b. Proving Trigonometric Identities
c. Sum and Difference Identities
d. Multiple-Angle Identities
e. The Law of Sines
f. The Law of Cosines
6. Analytic Geometry in Two Dimensions
a. Conic Sections and Parabolas
b. Ellipses
c. Hyperbolas
Plumsted Township Public Schools
Curriculum
Unit Topic: Functions and Graphs
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
a.
Functions and
Their Properties
Why do some rational
functions have breaks in the
domain?
Why do some square root
functions have domains that
are not all real numbers?
How do you determine the
domain and range of a
function by looking at the
graph?
How do you determine what
type of asymptotes a function
has?
What is the connection
between asymptotes and
domain?
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?

Represent functions
numerically, algebraically,
and graphically, determine
the domain and range for
functions, and analyze
function characteristics such
as extreme values,
symmetry, asymptotes, and
end behavior.
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Provide guided notes on
functions, functional notation,
and domain. As a class, do
several examples of finding
domain.
o Solve domain
algebraically, then
support graphically.
o Solve range
graphically
Individually, students will
complete Pg 102 #1-19 odd.
Discuss concepts of continuity,
symmetry, increasing &
decreasing behavior, and
extrema.
In groups, students will
complete Pg 98 #65-67
o 1.2 Group Activity
Worksheet
Introduce various types of
asymptotes with example
problems to follow each type.
Group Activity
o Pg 104 #79-81
Assessment
How will you
know they have
learned it?
Assignment
Domain and Range
Homework Ditto
Group Work
Circulate the room
to correct any
group
misunderstandings.
Observe
discussions within
each group.
Assignment
Pg 102-103 #10-16
even, 26, 28, 48-54
even
Journal Entry
Create a function
that has a vertical
asymptote at x = 3,
4, -1 and a
horizontal
asymptote at y=0.
Assignment
Pg 103 #56, 60-66
Chapter 1 Quiz 1
*
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
Graphing
Calculator
Graph functions
to determine
domain, range,
and intervals of
increasing,
decreasing, and
constant behavior.
NJCCCS
(CPI’s)
4.3.B.2
Plumsted Township Public Schools
Curriculum
b. Twelve Basic
Functions

From a data table, how can
you determine if a function
has an asympotote?

Recognize graphs of twelve
basic functions, determine
domains of functions related
to the twelve basic functions
and combine the twelve
basic functions in various
ways to create new
functions.
Analyze data tables and
create functions that
represent the data.
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c. Building Functions
from Functions
Why must you consider the
original domain of a function
before you can determine the
domain of a combined or
composed function?
*
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Build new functions from
old functions in several
ways: by adding, subtracting,
multiplying, dividing, and
composing functions.
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Students will put 12 basic
functions into their notebooks to
be memorized.
Graph and analyze piecewise
defined functions
Individually, students will
complete pg 105 #31-35 odd.
Provide instructions for putting
data into a list and making a
statistical plot of the data in a
graphing calculator.
In groups of 4, students will
enter data into their calculator
and determine the family of
functions to which the data
belongs. If possible, they will
come up the with equation for
the function.
Discussion
Students will
display results
from class work
and provide
analysis of fellow
classmates’
conclusions.
Provide guided notes on
combining functions
algebraically and composition
of functions.
Individually, students will
complete 1.4 Practice
Worksheet
Assignment
Pg 122 – 124
#2-20 even
Assignment
Pg 113-114 #2-28
even, 46-52 even
Data Table
Homework Ditto
Journal Entry
Create a Data
Table for
variations of 4
different basic
functions.
Graphing
Calculator
Use STAT PLOT
feature to
determine
equations of
graphs.
4.3.B.2
Plumsted Township Public Schools
Curriculum
d. Inverse Functions

How is a function and its
inverse related?

What is the relationship
between the domain and range
of a function, and the domain
and range of the function’s
inverse?
Build new functions by
computing inverses of
functions.
Algebraically and
graphically determine if two
functions are inverses.
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Provide guided notes for
inverses which include:
o Define inverse
functions
o Verify Inverses
o Procedure for finding
the inverse of f(x)
o Finding inverse
graphically
o Domain and Range of
Inverse Functions
o Guaranteeing inverse
to be a function.
Individually students will work
on the following assignment.
o Pg 122-123 #33-47
odd
Discussion
Students will
display results
from class work
and provide
analysis of fellow
classmates’
conclusions.
Journal Entry
Suppose f and g
are inverse
functions and
f(3)=7. Find g(3)
and g(7), if
possible.
Assignment
Pg 122-123 #34-52
even, 57, 58, 61
Chapter 1 Quiz 2
e.
Graphical
Transformations
How is a graph affected if
numbers are added to a
function?
How is a graph affected when
either the entire graph or just
the x is multiplied by a
constant.
If a function has even
symmetry, how does the
equation of the graph relate to
the equation of its reflection
over the y axis?

Algebraically and
graphically represent
translations, reflections,
stretches, and shrinks of
functions and parametric
relations.
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Using a graphing calculator the
students will be guided through
explorations to discover the
rules of transformations.
In groups, students will
complete 1.5 Major Concepts
and 1.5 Group Activity Dittos.
Journal Entry
Students will
complete a ditto on
“Summary of
translation facts.”
Group Work
Circulate the room
to correct any
group
misunderstandings.
Observe
discussions within
each group.
Assignment
Pg 147-148 #1-54
multiples of 3
Chapter 1 Test
*
Graphing
Calculator
Investigating
functions
Plumsted Township Public Schools
Curriculum
Unit Topic: Polynomial, Power, and Rational Functions
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
a.
Linear and
Quadratic
Functions
How is the vertex form of a
quadratic related to
translations of functions?
b. Power Functions
and Polynomial
Functions of Higher
Degree
How does the lead coefficient
of a polynomial affect the end
behavior of the function?
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?
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Analyze quadratic functions.
Using transformations, graph
quadratics from vertex and
intercepts.
Use maximums or
minimums to solve
application problems of
quadratics.

Graph polynomial functions
using transformations.
Identify the zeros and their
multiplities of a polynomial
function.
Analyze the end behavior of
a power function.
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Review finding the equation of
a line and completing the square
in a quadratic.
Given the vertex and a point on
the curve, write the equation of
the quadratic.
In pairs, students will complete
169-170 #1-9 odd, 19-25 odd,
35.
Use graphing calculator to
explore various power
functions. As a class, determine
what causes graphs to be
similar.
Graph polynomial funtions
given their zeros.
Group work – students will
complete Ditto pg 159 #45-49
How does the multiplicity of a
zero affect the graphs
behavior at the x-axis?
c. Real Zeros of
Polynomial
Functions
What does it mean when there
is a remainder of zero?
What are the possibilities of
zeros if there are no rational
roots?
*
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Graph polynomial functions,
predict their end behavior,
and find their real zeros
using an algebraic method.
Find all zeros of polynomials
using the rational zeros
theorem.
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Provide guided notes on
division algorithm, long
division, synthetic division, and
factor theorem.
Individually, students will
complete Pg 223-224 #5-25
odd.
In pairs, students will complete
2.4 Practice Worksheet
Assessment
How will you
know they have
learned it?
Assignment
Pg 169-170 #2-28
even, 36-40 even
Discussion
Students will
display results
from class work
and provide
analysis of fellow
classmates’
conclusions.
Assignment
Pg 209 #1-6, 9-12,
25-28, 33-38, 3942
Assignment
Pg 223-224 #2-32
even
Pg 224 #33-36, 4556
Chapter 2 Quiz 1
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
Graphing
Calculator
Graph quadratics
Graphing
Calculator
Graph power
functions in
various windows.
NJCCCS
(CPI’s)
Plumsted Township Public Schools
Curriculum
d. Graphs of Rational
Functions

How do you find the
asymptotes of a rational
function?
What pieces of information
are necessary to graph a
rational function?

Analyze graphs of rational
functions.
o Find vertical,
horizontal, and slant
asymptotes and x
and y intercepts.
o Describe end
behavior at
asymptotes.
Graph rational functions
without the assistance of a
graphing device.
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As a class, complete several
examples on graphing
transformations of the
reciprocal function. Analyze
each function for its asymptotes
and end behavior.
Graph rational functions using
the zeros, asymptotes, and a
sign chart.
In groups, students will
complete Pg 236 #25-33 odd.
Assignment
Pg 245-246 #3-42
multiples of 3
Group Work
Circulate the room
to correct any
group
misunderstandings.
Observe
discussions within
each group.
Group Quiz
e. Solving Equations
in One Variable
How are extraneous solutions
of a function related to the
graph of the function?


Use various methods to solve
rational equations, while
being mindful of extraneous
solutions.
Find minimum or maximum
perimeter of a rectangle.

Use algebraic and graphical
methods to determine zero,
positive, and negative values
of a function.
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

Why must we look for
extraneous solutions in a
rational function?
f. Solving Inequalities
in One Variable
How can you use the graph of
a function to determine when
the function is zero, positive,
or negative?



Provide guided notes on solving
rational equations with
extraneous solutions.
As a class, solve a minimum
perimeter problem.
Individually, students will
complete 2.7 Practice
Worksheet.
Assignment
Pg 253-255 #3-30
multiples of 3, 34,
35, 40
As a class, graph a polynomial
and discuss the behavior of its
graph. Use a sign chart to
algebraically justify this
behavior.
Complete several examples
which include fractions,
radicals, and absolute values.
In groups, students will
complete 2.8 Practice
Worksheet.
Group Work
Circulate the room
to correct any
group
misunderstandings.
Observe
discussions within
each group.
Discussion
Students will
display results
from class work
and provide
analysis of fellow
classmates’
conclusions.
Assignment
Pg 264-265 #6, 9,
21-54 mult. of 3
Chapter 2 Test
*
Graphing
Calculator
Graph functions
to determine when
they are zero,
positive, or
negative.
Plumsted Township Public Schools
Curriculum
Unit Topic: Exponential, Logistic, and Logarithmic Functions
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
a. Exponential and
Logistic Functions
b. Exponential and
Logistic Modeling
c. Logarithmic
Functions and Their
Graphs
*
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?
Assessment
How will you
know they have
learned it?
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
NJCCCS
(CPI’s)
Plumsted Township Public Schools
Curriculum
d. Properties of
Logarithmic
Functions
e. Equation Solving
and Modeling
f. Mathematics of
Finance
Unit Topic: Trigonometric Functions
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
*
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?
Assessment
How will you
know they have
learned it?
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
NJCCCS
(CPI’s)
Plumsted Township Public Schools
Curriculum
a. Angles and Their
Measures
b. Trigonometric
Functions of Acute
Angles
c. Trigonometry
Extended: The
Circular Functions
d. Graphs of Sine and
Cosine: Sinusoids
*
Plumsted Township Public Schools
Curriculum
e. Graphs of Tangent,
Cotangent, Secant,
and Cosecant
f. Inverse
Trigonometric
Functions
Unit Topic: Analytic Trigonometry
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
*
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?
Assessment
How will you
know they have
learned it?
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
NJCCCS
(CPI’s)
Plumsted Township Public Schools
Curriculum
a. Fundamental
Identities
b. Proving
Trigonometric
Identities
c. Sum and Difference
Identities
d. Multiple-Angle
Identities
*
Plumsted Township Public Schools
Curriculum
e. The Law of Sines
f. The Law of Cosines
Unit Topic: Analytic Geometry in Two Dimensions
Topic/Essential
Question
What are the most important
concepts to be learned during
this unit?
a. Conic Sections and
Parabolas
*
Objectives
Core Activities
What will students know and be
able to do?
What Activities Will help them learn
or know?
Assessment
How will you
know they have
learned it?
Technology
Literacy
What technology
skills are being
introduced,
developed,
mastered?
NJCCCS
(CPI’s)
Plumsted Township Public Schools
Curriculum
b. Ellipses
c. Hyperbolas
*