ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: PRE-CALCULUS – LEVEL 1
GRADE LEVEL: HIGH SCHOOL
CREATION DATE: November 2003
Essential Question, Concept or Theme: A. Polar Coordinates and Complex Numbers
PA Standards: 2.2.11.F; 2.3.11.A, B, C; 2.4.11.E; 2.5.11.A, B; 2.8.11.A, E; 2.10.11.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1: Students will use their
prior graphing skills on a new set of axes,
the polar axes. They will apply what they
have learned in trigonometry to more
complex functions. They will compare and
convert in the rectangular and polar
coordinate systems and the rectangular and
complex polar systems.
Homework checks, board
work, worksheets, teacher
observation, quizzes, test,
graphing calculator
proficiency.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
a) Graph a point given its polar
coordinates.
b) Express rectangular coordinates as polar.
c) Express polar coordinates as rectangular.
d) Graph polar equations.
e) Express complex numbers in polar form.
f) Perform basic operations on complex
numbers in both rectangular and polar
form.
g) Use DeMoivre’s Theorem to find
powers of complex numbers.
h) Use the Nth Root Theorem to find the
roots of an equation.
Pre-Calculus – Level 1
Text Book - Analytic
Trigonometry with
Applications, Barnett/Ziegler,
1995. Text Book - Advanced
Mathematical Concepts,
Glencoe Division, 1994.
Page 1
Approx. Time Allotment:
Instructional Strategies
Teacher will demonstrate graphing
exercises using the graphing
calculator display on the overhead
and sketching by hand using the
polar coordinate system.
Instruction will also include
lecture, demonstration of concepts
and problem solving probing
questions.
-1-
November 2003
Essential Question, Concept or Theme: A. Polar Coordinates and Complex Numbers
PA Standards: 2.2.11.F; 2.3.11.A, B, C; 2.4.11.E; 2.5.11.A, B; 2.8.11.A, E; 2.10.11.A
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Students may wish to
independently research
sailing and astronomy,
where polar diagrams
are used extensively.
Other strategies may
include poster projects,
computer programs,
and Internet
investigations.
Page 2
Remediation Strategies
Remediation strategies may
include after school help, test
corrections, Mu Alpha Theta
tutoring.
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
May include:
Physics – application
problems relating to force and
astronomy.
-2-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.8.11.K; 2.8.11.L; 2.8.11.O; 2.8.11.P; 2.8.11.Q; 2.8.11.R; 2.8.11.S; 2.8.11.T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
B. Linear Relations and Functions
(This chapter will be briefly discussed
since it is review material.)
Benchmark #1: Students will define
relations, functions, composites, and
inverses.
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Homework checks, board
work, worksheets, teacher
observation, quizzes, test,
graphing calculator
proficiency.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
Approx. Time Allotment:
Instructional Strategies
Instruction may include lecture,
demonstration of concepts,
discovery activities with patterns
and problem-solving probing
questions.
Benchmark #2: Students will
determine the equations of lines, find
the distance between two points,
determine the slope of a line, and find
the midpoint of a line segment.
Pre-Calculus – Level 1
Page 3
-3-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: B. 2.8.11.K; 2.8.11.L; 2.8.11.O; 2.8.11.P; 2.8.11.Q; 2.8.11.R; 2.8.11.S; 2.8.11.T
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster
projects, computer
programs, independent
study, Internet
investigations.
Page 4
Remediation Strategies
Remediation strategies
may include after school
help, test corrections, Mu
Alpha Theta tutoring.
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
May include:
Economics – application
problems relating supply vs.
demand, profit functions, and cost
functions.
-4-
November 2003
Essential Question, Concept or Theme: C: Systems of Equations
PA Standards: C. 2.2.11.B, F; 2.5.11.A, B; 2.8.11.D, F, G, H, I, J, K, L; 2.11.11.A; 2.11.11.B
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1: Students will continue work with
equations to include methods for solving systems of
equations graphically and algebraically. After
students learn to evaluate determinants and find
inverses of matrices, they are shown the connections
of using matrices as a tool for solving systems of
equations.
Homework checks, board
work, worksheets, teacher
observation, quizzes, test,
graphing calculator
proficiency.
a) Solve systems of equations graphically and
algebraically and with matrices.
b) Evaluate determinant and inverses of matrices.
c) Graph systems of linear inequalities.
d) Find the maximum or minimum value of a
function defined for a polygonal convex set.
(optional)
e) Use linear programming procedures to solve
word problems involving a system of linear
inequalities. (optional)
Pre-Calculus – Level 1
Page 5
Text Book – Advanced
Mathematical Concepts,
Glencoe Division, 1994.
Graphing calculators
(optional) Instructional
videos
(optional) BoxerMath
Product
Approx. Time Allotment:
Instructional Strategies
Teacher will demonstrate matrix
operations using the graphing
calculator display. Instruction will
also include lecture, demonstration
of concepts and problem solving
probing questions.
-5-
November 2003
Essential Question, Concept or Theme: C. Systems of Equations
PA Standards: 2.2.11.B, F; 2.5.11.A, B; 2.8.11.D, F, G, H, I, J, K, L; 2.11.11.A; 2.11.11.B
Adaptations/Inclusion Techniques
Common adaptations may include the
following: extended time, hands-on
activities, individual/partner/group work,
after school help. Adaptations as stated
in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster projects,
computer programs, independent
study, Internet investigations.
Page 6
Approx. Time Allotment:
Remediation Strategies
Multicultural/Interdisciplinary
Connection
Remediation strategies may
include after school help, test
corrections, Mu Alpha Theta
tutoring.
May include:
Economics – application problems
relating to expenses, revenue,
break even point and sales.
-6-
November 2003
Essential Question, Concept or Theme: D. The Nature of Graphs
PA Standards: 2.1.11.A; 2.2.11.C, E, F; 2.5.11.A, B; 2.8.11.E, K, L, O, P, Q, S, T; 2.11.11.A
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1 Students will graph
relations and functions along with
analyzing families of graphs. Study
will include symmetry, continuity and
transformations of graphs. Students
will be required to find asymptotes,
intercepts and critical points of graphs.
a) Graph polynomial functions and
approximate the real zeros of
functions.
b) Identify symmetrical graphs and
use symmetry to complete a graph.
c) Identify even and odd functions.
d) Determine the inverse of a function
or a relation and graph.
e) Determine vertical, horizontal and
slant asymptotes of rational
functions and graph.
f) Introduce derivatives of a function
and find the slope and the equation
of a line tangent to the graph of a
function at a given point.
g) Find the critical points of a graph.
h) Use 1st and 2nd derivative to
determine maximum, minimum
informational points.
Pre-Calculus – Level 1
Homework checks, board
work, worksheets, teacher
observation, quizzes, test,
graphing calculator
proficiency. Cooperative
learning activity is optional.
Students will team-teach
one of four sections. They will
be responsible for a lesson
plan, practice problems, class
instruction and review of
homework problems.
Page 7
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Graphing calculators
Instructional videos
BoxerMath Product
Approx. Time Allotment:
Instructional Strategies
Teacher will demonstrate graphing
functions and their inverses using
the graphing calculator display on
the overhead. Instruction will also
include lecture, demonstration of
concepts and
-7-
November 2003
Essential Question, Concept or Theme: D. The Nature of Graphs
PA Standards: 2.1.11.A; 2.2.11.C, E, F; 2.5.11.A, B; 2.8.11.E, K, L, O, P, Q, S, T; 2.11.11.A
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster
projects, computer
programs, independent
study, Internet
investigations.
Page 8
Approx. Time Allotment:
Remediation Strategies
Multicultural/Interdisciplinary
Connection
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
May include:
Physics – application problems
relating to astronomy, Boyle’s law,
instantaneous velocity.
-8-
November 2003
Essential Question, Concept or Theme: E. Polynomial and Rational Functions
PA Standards: 2.1.11.A; 2.2.11.A, F; 2.3.11.A,C; 2.5.11.B, C, D; 2.8.11.N, Q, S, T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1: Students will use a
variety of strategies and theorems to
solve polynomial functions of varying
degrees.
a) Solve and graph quadratic
equations and inequalities.
b) Use the discriminant to determine
the nature of the roots.
c) Use the remainder and factor
theorems, rational root theorem,
Descartes’ Rule of Signs and the
location principle to identify the
rational, irrational and imaginary
roots of polynomial functions.
d) Decompose a rational expression
into partial fractions.
e) Solve radical equations and
inequalities.
Pre-Calculus – Level 1
Homework checks, board work,
worksheets, teacher observation,
quizzes, test, graphing calculator
proficiency. Cooperative
learning activity is optional.
Students will team-teach one of
four sections. They will be
responsible for a lesson plan,
practice problems, class
instruction and review of
homework problems.
Page 9
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
Approx. Time Allotment:
Instructional Strategies
Teacher will demonstrate graphing
polynomials using the graphing
calculator display. Instruction will
also include lecture, demonstration
of concepts and problem solving
probing questions.
-9-
November 2003
Essential Question, Concept or Theme: E. Polynomial and Rational Functions
PA Standards: 2.1.11.A; 2.2.11.A, F; 2.3.11.A,C; 2.5.11.B, C, D; 2.8.11.N, Q, S, T
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster
projects, computer
programs, independent
study, Internet
investigations.
Page 10
Approx. Time Allotment:
Remediation Strategies
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
Multicultural/Interdisciplinary
Connection
May include:
Construction – application
problems relating to construction.
Physics – path of a space
- 10 -
November 2003
Essential Question, Concept or Theme: F. Conic Sections (beginning 2004-2005 school year)
PA Standards: 2.8.11.E; 2.8.11.F; 2.8.11.G; 2.8.11.H; 2.8.11.J; 2.8.11.T; 2.9.11.H; 2.9.11.J
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark #1: Students will learn
the concepts involved with the
development of the four types of
conic sections. Students will be able
to write and identify the equations of
each conic as well as graph each.
Homework checks, board work,
worksheets, teacher observation,
quizzes, test, graphing calculator
proficiency.
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
Approx. Time Allotment:
Instructional Strategies
Instruction may include lecture,
demonstration of concepts,
discovery activities with patterns
and problem-solving probing
questions.
a.) Use the standard and general
forms of the equation of a circle
and graph.
b.) Use the standard and general
forms of the equation of a
parabola and graph.
b.) Use the standard and general
forms of the equation of an ellipse
and graph.
c.) Use the standard and general
forms of the equation of a
hyperbola and graph.
d.) Recognize the conic sections by
their equations and determine
their eccentricity.
e.) Graph and solve systems of
second-degree equations and
inequalities. (optional)
Pre-Calculus – Level 1
Page 11
- 11 -
November 2003
Essential Question, Concept or Theme: F. Conic Sections (beginning 2004-2005 school year)
PA Standards: 2.8.11.E; 2.8.11.F; 2.8.11.G; 2.8.11.H; 2.8.11.J; 2.8.11.T; 2.9.11.H; 2.9.11.J
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster
projects, computer
programs, independent
study, Internet
investigations.
Page 12
Remediation Strategies
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
May include:
Engineering – application
problems in designing car
headlights, satellite dishes, and
theaters.
Astronomy – application
problems involving planetary
orbits, satellite orbits, and solar
system orbits.
- 12 -
November 2003
Essential Question, Concept or Theme: G. Exponential and Logarithmic Functions
PA Standards: 2.1.11.A; 2.2.11.A, B, F; 2.5.11.A, B; 2.8.11.A, B, N, Q, S; 2.11.11.C
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1: Students will graph
exponential functions and learn to use
functions involving the irrational
number e. After deducing the
properties of logarithms from the
properties of exponents, students will
use the properties to evaluate,
simplify and solve equations. The
study of logarithms includes common
logs and natural logs.
Homework checks, board work,
worksheets, teacher observation,
quizzes, test, graphing calculator
proficiency.
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
Approx. Time Allotment:
Instructional Strategies
Teacher will demonstrate graphing
exponential and logarithmic
functions using the graphing
calculator display on the overhead.
Instruction will also include
lecture, demonstration of concepts
and problem solving probing
questions.
a) Use the properties of exponents.
b) Evaluate and simplify expressions
containing rational exponents.
c) Find common logs and natural
logs and use them to solve
equations.
d) Graph exponential and
logarithmic functions.
e) Derive the irrational number e.
f) Determine present value and
future value of annuities.
g) Compare solutions given different
ways of compounding interest.
h) Determine the half-life of an
object. (optional)
Pre-Calculus – Level 1
Page 13
- 13 -
November 2003
Essential Question, Concept or Theme: G. Exponential and Logarithmic Functions
PA Standards: 2.1.11.A; 2.2.11.A, B, F; 2.5.11.A, B; 2.8.11.A, B, N, Q, S; 2.11.11.C
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Remediation Strategies
Students may wish to
further explore finances and
economics using the
formulas studied. Other
strategies may include
poster projects, computer
programs, and Internet
investigations.
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
Page 14
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
May include:
Economics – application problems
relating to present value annuity,
future value annuity, mortgages,
IRAs. Biology – population
growth. Chemistry – pH, half-life.
Geology – richter scale number.
- 14 -
November 2003
Essential Question, Concept or Theme: H. Sequences and Series
PA Standards: 2.1.11.A; 2.4.11.A, B, C; 2.7.11.B, C, D; 2.8.11.A, C; 2.11.11.D
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark # 1: Students will review
arithmetic and geometric sequences and
series and infinite series. They will
determine whether a series is convergent
or divergent and express a series using
sigma notation. Pascal’s triangle is
reviewed and applied to the expansion of
binomial expressions. The binomial
theorem is introduced. Students will
examine the work of Fibonacci and Euler
to learn about special series and
sequences. They will use mathematical
induction to prove the validity of
formulas.
Independent study will
include a take-home portion
of a test involving defining
vocabulary, plotting graphs
and problem solving.
Students will also be
responsible for a multiplechoice and open-ended
assessment given in class.
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
Instructional Strategies
Instruction may include lecture,
demonstration of concepts,
discovery activities with patterns
and problem-solving probing
questions.
a) Find the nth term, sum, first term,
difference and common ratio for
arithmetic sequences and series.
b) Find the limits of infinite series.
c) Determine convergence or
divergence.
d) Use sigma notation.
e) Expand binomials using Pascal’s
triangle and the Binomial Theorem.
f) Use the Binomial Theorem to
calculate binomial probabilities.
g) Prove the validity of formulas using
mathematical induction.
Pre-Calculus – Level 1
Page 15
- 15 -
November 2003
Essential Question, Concept or Theme: H. Sequences and Series
PA Standards: 2.1.11.A; 2.4.11.A, B, C; 2.7.11.B, C, D; 2.8.11.A, C; 2.11.11.D
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Research reports, poster
projects, computer
programs, independent
study, Internet
investigations.
Page 16
Approx. Time Allotment:
Remediation Strategies
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
Multicultural/Interdisciplinary
Connection
Probability.
- 16 -
November 2003
Essential Question, Concept or Theme: I. Statistics and Data Analysis (for 2003-2004 school year only)
PA Standards: 2.2.11.D, E, F; 2.3.11.A, C; 2.6.11.C, F, G, I; 2.7.11.C; 2.8.11.M
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark # 1: Students will make and
use graphs and plots to analyze data. They
analyze data using measures of central
tendency and variability. Students will
organize data into frequency distributions
and use the normal curve. They build on
their knowledge to find the standard error of
the mean and predict the population mean
for a sample set of data within a given level
of confidence. They will also draw scatter
plots and regression lines along with bar
graphs, frequency polygons and box-andwhisker plots.
Homework checks, board
work, worksheets, teacher
observations, quizzes,
tests, graphing calculator
proficiency.
Text Book – Advanced
Mathematical Concepts, Glencoe
Division, 1994.
Approx. Time Allotment:
Instructional Strategies
Teacher will be available for
general questions while students
learn this section independently.
Graphing calculators
Instructional videos (optional)
BoxerMath Product (optional)
a) Draw, analyze and use bar graphs and
histograms.
b) Organize data into a frequency
distribution table.
c) Find the mean, median and mode of a
set of data.
d) Find the mean deviation, semi-inter
quartile range and standard deviation of
a set of data.
e) Organize and compare data using box
and whisker plots.
f) Use the normal distribution curve.
g) Find the standard error of the mean.
h) Draw scatter plots and regression lines.
Pre-Calculus – Level 1
Page 17
- 17 -
November 2003
Essential Question, Concept or Theme: I. Statistics and Data Analysis (for 2003-2004 school year only)
PA Standards: 2.2.11.D, E, F; 2.3.11.A, C; 2.6.11.C, F, G, I; 2.7.11.C; 2.8.11.M
Adaptations/Inclusion Techniques
Common adaptations may include the following:
extended time, hands-on activities,
individual/partner/group work, after school help.
Adaptations as stated in a student’s IEP.
Pre-Calculus – Level 1
Enrichment Strategies
Independent study unit.
Page 18
Remediation Strategies
Remediation strategies may
include after school help,
test corrections, Mu Alpha
Theta tutoring.
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
Statistics – application problems
relating to research, advertisement,
demographics, sports and business.
- 18 -
November 2003