Pre-Calculus
Course Description and Philosophy
The Pre-Calculus course presented at the high school is intended to serve those students who have successfully
completed the course Algebra 2. The purpose of the course is to continue the study of elementary functions
including topics in algebra, geometry, and especially trigonometry. The course is geared at preparing the student
for their first course in Calculus or other collegiate mathematics courses. In short, Pre-Calculus provides
experiences that encourage and enable students to value mathematics, gain confidence in their own
mathematical ability, become mathematical problem solvers, communicate mathematically, and reason
mathematically. Further, students will use current technology such as the graphing calculator on a day-to-day
basis. This course further reflects the needs of such capable students and recognizes the fact that they will spend
their adult lives in a society increasingly dominated by technology and quantitative methods.
Teacher Resources:
Illustrative Mathematics Content Standards: High School http://www.illustrativemathematics.org/standards/hs
The Teaching Channel (Common Core Math Channel) https://www.teachingchannel.org/videos?page=1&categories=subjects_math,topics_common-core&load=1
The Mathematics Common Core Toolbox (http://ccsstoolbox.agilemind.com/resources_samples.html) has both sample scope and sequence
documents as well grades 4-12 PARRC assessment tasks.
Text Reference:
Brown, Richard G. Advanced Mathematics, 1992 Houghton Mifflin Company, Boston, MA / USA
Revised 2013
1
Unit I: Functions and Models
Essential Question: Why are relations and functions represented in multiple ways?
Objectives: Students will be able to




Represent functions and relations numerically, graphically, and algebraically.
Describe and apply properties of functions and relations.
Perform a variety of operations and geometrical transformations on functions and relations.
Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.
Topic/Content Skills
Represent a piece-wise
function numerically,
algebraically, and
graphically.
Assessment
Tests/Quizzes
Homework
Class Participation
Class Investigations
Resources
Describe the properties
of linear, quadratic,
power, polynomial,
rational, exponential,
logarithmic,
trigonometric, and
inverse trigonometric
functions
Describe the properties
of a piece-wise function.
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Text
Worksheets
2
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.1.PC.8
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.2.PC.3
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.2.PC.4
Topic/Content Skills
Assessment
Resources
Identify and distinguish
between the graphs of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and
inverse trigonometric
functions.
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Describe the effect of
single or multiple
transformations on the
graph of f(x), including
a f(x), f⎛x−h⎞, f(x)+k,
f(ax), f x, and f⎛x⎞,
f(|x|), |f(x)|
Describe the effect of
transformations on a
function with a restricted
domain.
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Interpret and solve
problems involving
piece-wise functions.
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Make predictions using
trigonometric or power
mathematical models
given a set of data.
Tests/Quizzes
Homework
Class Participation
Class Investigations
Text
Worksheets
Instructional Method
3
Tech Infusion
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.2.PC.6
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.3.PC.1
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.3.PC.5
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.4.PC.9
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
Links to “Flipped
Classroom” resources: (e.g.
Khan Academy)
1.4.PC.12
Differentiated Learning Activities
Strategic Learner: Break problems into distinct steps, verbalizing the reasoning process. Encourage the use of the graphing calculator. Students
should refer to Khan tutorials for additional support. Advanced Learner: Pose journal problems. Discuss ill-posed problems. Students may create
their own tutorials to help peers and to demonstrate their own mastery.
Ethical Decision Making/Character Education
Discuss the history of the quintic solution including the issue of plagiarism regarding Ferrari, Cardano, and Tartaglia.
21st Century Skills
Students use graphing calculators, computer algebra systems, or both, to
assist in examining patterns in population growth or decline
of
a particular animal species
using data from the U.S. Fish & Wildlife Service or another source. For example, students might study the changes in
the population of Canada geese by building functions and examining graphs to answer problems regarding long-term trends. Students can share
their findings with a school biology class by developing a lesson on the use of mathematics in examining biological developments.
Unit II: Trigonometric Functions
Essential Question: How do trigonometric and circular functions model real- world problems and their solutions?
Objectives: Students will be able to






Represent functions and relations numerically, graphically, and algebraically.
Describe and apply properties of functions and relations.
Perform a variety of operations and geometrical transformations on functions and relations.
Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.
Analyze two- and three-dimensional figures using tools and technology when appropriate.
Apply geometric properties and relationships to solve problems using tools and technology when appropriate
Topic/Content Skills
Determine the period,
amplitude, phase shift,
and/or vertical shift of a
trigonometric function
represented graphically
or algebraically.
Assessment
Materials
Tests/Quizzes
Text
Homework
Worksheets
Class Participation
Class Investigations
Instructional Method
Lectures
Discussion
Investigations
Activities
4
Tech Infusion
Graphing calculator
SmartBoard
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
NJCCCS/CC
1.1.PC.15
Unit 2
Topic/Content Skills
Describe the properties of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and
inverse trigonometric
functions.
Describe the inverse
relationship between
trigonometric and inverse
trigonometric functions,
numerically,
algebraically, and
graphically.
Identify and distinguish
between the graphs of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and
inverse trigonometric
functions
Describe the effect of
transformations on the
graphs of trigonometric
functions.
Interpret and solve
problems involving
trigonometric functions.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
5
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.2.PC.3
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
1.2.PC.5
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
1.2.PC.6
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
1.3.PC.4
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
1.4.PC.10
Unit 2
Topic/Content Skills
Make predictions using
trigonometric or power
mathematical models
given a set of data..
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Write the value of an
inverse trigonometric
expression in radians
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Determine the angular
and linear velocities of an
object moving at a
constant speed on a
circular path
Evaluate a trigonometric
expression using radian
measure.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Describe and apply the
relationship between the
trigonometry of the right
triangle and the unit
circle.
Describe and apply the
relationship between the
radian measure of a
central angle of a circle
and its intercepted arc.
Define and graph the six
circular functions.
6
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.4.PC.12
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.1.PC.4
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.1.PC.5
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.1.PC.8
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.2.PC.1
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.2.PC.4
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.2.PC.5
Unit 2
Topic/Content Skills
Convert degree measure
to radian measure.
Measure indirectly using
trigonometric
relationships.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
2.2.PC.6
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
2.2.PC.7
Links to “Flipped Classroom”
resources: (e.g. Khan Academy)
Differentiated Instruction:
Strategic Learner: Use visual models and manipulatives. Use graphing calculator and SmartBoard. Advanced Learner: Emphasize proof and
foundations.
Ethical Decision Making/Character Education
Review Honor Code and its implication for Midterm exams. Discuss/review policy on group work vs. individual.
21st Century Skills
Working in teams, students study examples of Kolams from Southern India
or Sona from Angola and the Congo
and explore the mathematics
in these complex geometric art forms. They will explore Kolam designs based on Fibonacci numbers (http://vindhiya.com/Naranan/FibonacciKolams/ ) and examine how an array of dots can give rise to a one-line sona (www.beloit.edu/computerscience/faculty/chavey/sona/). Using the
concepts they have learned, students try to create their own Kolams or Sona.
7
Unit III: Trigonometric Identities
Essential Question: How are the six trigonometric and circular functions related to each other?
Objectives: Students will be able to



Represent functions and relations numerically, graphically, and algebraically.
Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.
Apply geometric properties and relationships to solve problems using tools and technology when appropriate.
Topic/Content Skills
Apply the fundamental
trigonometric identities.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Interpret and solve
problems involving
trigonometric functions.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Evaluate a trigonometric
expression using radian
measure.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Measure indirectly using
trigonometric
relationships.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Solve trigonometric
equations.
8
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.1.PC.17
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.5
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.10
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.2.PC.5
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.2.PC.7
Differentiated Learning Activities
Use the graphic calculator and smartboard to explore various graphs and manipulations of the graphs.
21st Century Skills
Students explore knot theory
and its role in genetics (www.oglethorpe.edu/faculty/~j_nardo/knots/history.htm ). They learn how the DNA in
every cell of our bodies is made up of long, coiled strands that get mathematically knotted in ways that lead to chemical changes
in the DNA.
Using string, rope, or even tangled audio headphone chords, students create several types of knots, such as those shown at
www.mathedpage.org/pcmi/knot-theory.pdf . Then students examine each other’s knots and identify them by type: unknot, trefoil, figure eight,
five-star, one of the six’s, etc. Students photograph and label the knots and display them by creating a poster or posting them to a photo gallery on
a class website.
Unit IV: Rational Functions
Essential Question: How do rational functions model real-world problems and their solutions?
Objectives: Students will be able to
 Represent functions and relations numerically, graphically, and algebraically.
 Describe and apply properties of functions and relations.
 Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems
Topic/Content Skills
Write a rational function
or expression in an
equivalent form,
including partial
fractions.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Resources
Text
Worksheets
Graph rational functions
and describe their
properties.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
9
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.1.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.11
Topic/Content Skills
Graph rational functions
and describe their
properties, including
limit theory as it applies
to determining their
asymptotes & removable
discontinuities.
Describe the properties
of rational functions,
including domain, range,
continuity, end behavior,
horizontal and vertical
asymptotes.
Describe oblique
asymptotes of rational
functions.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Resources
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Identify and distinguish
between the graphs of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and
inverse trigonometric
functions.
Solve rational equations
numerically, graphically,
or algebraically.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Solve rational
inequalities using a
numeric method.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
10
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS/CC
1.1.PC.12
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.2.PC.1
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.2.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.2.PC.6
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.3
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.4
Differentiated Learning Activities
Strategic Learner: Break problems into distinct steps, verbalizing the reasoning process. Encourage the use of the graphing calculator. Students
should refer to Khan tutorials for additional support. Advanced Learner: Pose journal problems. Discuss ill-posed problems. Students may create
their own tutorials to help peers and to demonstrate their own mastery.
21st Century Skills
Students work in groups to investigate the history of a topic within the class’s current field of study, using websites such as the MacTutor History
of Mathematics (http://www-history.mcs.st-and.ac.uk/ ). For example, if the class is studying algebra, each group explores the history of an
algebra topic, such as quadratic equations, group theory, or set theory. Each group creates a wiki entry based on its findings.
Unit V: Exponential and Logarithmic Functions
Essential Question: How do exponential functions model real-world problems and their solutions?
Objectives: Students will be able to





Represent functions and relations numerically, graphically, and algebraically.
Describe and apply properties of functions and relations.
Perform a variety of operations and geometrical transformations on functions and relations.
Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.
Estimate and compute using mental strategies, paper and pencil, and technology.
Topic/Content Skills
Write an exponential
function or expression in
an equivalent form using
laws of exponents.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
11
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
NJCCCS/CC
1.1.PC.3
Topic/Content Skills
Describe the properties of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and inverse
trigonometric functions.
Identify and distinguish
between the graphs of
linear, quadratic, power,
polynomial, rational,
exponential, logarithmic,
trigonometric, and inverse
trigonometric functions.
Describe the effect of
transformations on graphs
of exponential functions, f
(x)= a(b)cx.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Describe the effect of
transformations on graphs
of logarithmic functions.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Solve exponential
equations, including base
e, using various methods
including laws of
logarithms.
Solve logarithmic
equations, including base
e, using laws of
logarithms and exponents.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
12
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS
1.2.PC.3
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.2.PC.6
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.3.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.3.PC.3
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.1
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.2
Topic/Content Skills
Interpret and solve
problems involving
exponential functions.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Interpret and solve
problems involving
logarithmic functions.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Evaluate a logarithm using Tests/Quizzes
the change of base rule.
Homework
Class Participation
Investigations
Text
Worksheets
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS
1.4.PC.7
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.8
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
4.2.PC.5
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Differentiated Learning Activities
Collaborate with a science class and watch cell division.
Ethical Decision Making/Character Education
Discuss the concepts of loans and interest in banking and investments.
21st Century Skills: Problem-Based Assignment
Students review the algebraic formula for exponential growth and use the formula to solve a basic problem involving the spread of a viral
disease: If 100 people are currently infected, and the number of people infected doubles every twelve hours, how many people will be infected
after one week? The class discusses the exponential spread of infections
and identifies other relevant
examples of exponential growth, such
as: bacteria growth; human population growth; the growth of atmospheric carbon dioxide; and in finance, the compounding of interest. Then
students work in groups: each group poses a question involving exponential growth and gives it to another group to answer. Each group shares its
results with the class.
13
Unit VI: Vectors, Parametrics, and Polars
Essential Question: Why are functions and relations represented by parametric equations?
Objectives: Students will be able to






Represent functions and relations numerically, graphically, and algebraically.
Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.
Analyze two- and three-dimensional figures using tools and technology when appropriate.
Apply geometric properties and relationships to solve problems using tools and technology when appropriate.
Describe and represent numbers and their relationships.
Estimate and compute using mental strategies, paper and pencil, and technology
Topic/Content Skills
Write equivalent forms for
rectangular and polar
equations.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Write equivalent equations
for functions and relations
in parametric and
rectangular form.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Write a vector equation of
a line in 2-space.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Write an equation of a line
or plane in 3-space.
Graph polar equations and
describe their properties.
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Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
NJCCCS
1.1.PC.4
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.5
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.6
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.7
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.13
Topic/Content Skills
Graph a point, line, or
plane in 3-space.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Interpret and solve
problems involving
parametric functions and
relations.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Write equivalent
rectangular and polar
forms of points on the
coordinate plane.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Represent a vector in 2space by its magnitude
and direction, its initial
and terminal point, and its
component form.
Represent a vector in 3space by its magnitude
and direction, its initial
and terminal point, and its
component form.
Determine multiple polar
form representations of a
point.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Solve systems of
equations in polar form.
15
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
NJCCCS
1.1.PC.14
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.6
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.4.PC.11
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.1.PC.1
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.1.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.1.PC.3
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.1.PC.6
Topic/Content Skills
Identify the pole and the
polar axis, and plot points
given in polar form.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Determine the distance
from a point to a line in 2space.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Write equivalent
rectangular and polar
forms for complex
numbers.
Represent complex
numbers in polar form
numerically and
graphically.
Tests/Quizzes
Homework
Class Participation
Investigations
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
Determine the product or
quotient of two complex
numbers in polar form.
Determine a power or the
roots of a complex number
using DeMoivre’s
theorem.
Determine the sum,
difference, scalar product,
and dot product of vectors
in 2-space.
Determine the sum,
difference, scalar product,
dot product & cross
product of vectors in 3space.
Tests/Quizzes
Homework
Class Participation
Tests/Quizzes
Homework
Class Participation
Investigations
Tests/Quizzes
Homework
Class Participation
Investigations
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Lectures
Discussion
Activities
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
4.2.PC.1
Graphing calculator
SmartBoard
4.2.PC.2
Text
Worksheets
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
4.2.PC.3
Text
Worksheets
Lectures
Discussion
Activities
Graphing calculator
SmartBoard
4.2.PC.4
Text
Worksheets
Text
Worksheets
16
NJCCCS
2.1.PC.7
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
2.2.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
4.1.PC.1
Links to “Flipped
4.1.PC.2
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Differentiated Learning Activities
Strategic Learner: Break problems into distinct steps, verbalizing the reasoning process. Encourage the use of the graphing calculator. Students
should refer to Khan tutorials for additional support. Advanced Learner: Pose journal problems. Discuss ill-posed problems. Students may create
their own tutorials to help peers and to demonstrate their own mastery.
21st Century Skills: Problem-Based Assignment
Students explore the mathematics of the popular puzzle video
game Angry Birds
(http://forum.davidson.edu/mathmovement/2011/11/13/algebra-of-angry- birds/ ).Working in teams, students build a hands- on version of the
game. They create targets by stacking blocks or other lightweight objects and they construct a toy catapult or slingshot to aim at the target (or
toss a beanbag). After experimenting by trying to knock down the target from various starting points, students come up with different equations
for parabolas to see which will work to knock down the structure from a given distance.
Unit VII: Discrete Math
Essential Question: How do sequences and series model real-world problems and their solutions?
Objectives: Students will be able to
•
•
Represent functions and relations numerically, graphically, and algebraically
Estimate compute using mental strategies, paper and pencil, and technology
Topic/Content Skills
Represent a series using
summation notation.
Determine the sum, if it
exists, of an infinite
geometric series.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
17
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS
1.1.PC.10
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
1.1.PC.16
Topic/Content Skills
Expand and evaluate a
series written in
summation notation.
Assessment
Tests/Quizzes
Homework
Class Participation
Investigations
Materials/Resources
Text
Worksheets
Expand powers of
binomials applying the
binomial theorem,
factorials &
combinatorics.
Tests/Quizzes
Homework
Class Participation
Investigations
Text
Worksheets
Instructional Method
Lectures
Discussion
Investigations
Activities
Tech Infusion
Graphing calculator
SmartBoard
Lectures
Discussion
Investigations
Activities
Graphing calculator
SmartBoard
NJCCCS
1.1.PC.18
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
4.2.PC.6
Links to “Flipped
Classroom” resources:
(e.g. Khan Academy)
Differentiated Learning Activities
Discuss the role of sequences in chaos theory, Julia Sets, etc. Cross-curricular study physics.
21st Century Skills: Problem-Based Assignment
Students form teams to engage in a modeling project similar to problems presented in the Mathematical Contest in Modeling run each year by
COMAP. For example, the following problem is adapted from the 2009 competition:
Many cities and communities have traffic circles. Some traffic circles are large and have many lanes, such as at the Arc de Triomphe in Paris, and the Victory
Monument in Bangkok. Some have only one or two lanes in the circle. Some traffic circles position a stop sign or a yield sign on every incoming road that gives
priority to traffic already in the circle. Others post yield signs in the circle at each incoming road to give priority to incoming traffic. Still others have a traffic
light where each incoming road meets the circle (with no right turn allowed on a red light). Other designs may also be possible.
Students form teams and each team develops a model for creating a traffic circle in their own community or in a nearby city (or modifying an
existing traffic circle). Here are the directions:
 First, team members discuss how many lanes should be in the circle and the rate of traffic flow. If feasible, they may collect actual traffic
data. Team members outline alternatives for the placement of stop signs or yield signs and other design factors. Then they work together to
determine how to best control traffic flow in, around, and out of the circle.
 Team members determine the best alternatives and explain what factors influenced their decision, such as the effect on traffic flow and
safety.
 Team members refine their model. For example, if traffic lights are recommended, students develop a method for determining how many
seconds each light should remain green, which may vary according to the time of day and other factors.
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