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NEPTUNE TOWNSHIP SCHOOL DISTRICT
Pre-Calculus Curriculum
(College Prep and Honors) Grades 10-12
NEPTUNE TOWNSHIP SCHOOL DISTRICT
Office of the Superintendent
60 Neptune Blvd.
Neptune, NJ 07753-4836
August 23, 2017 Document C1#1
NEPTUNE TOWNSHIP BOARD OF EDUCATION
Laura G. Granelli, President
Monica Kowalski-Lodato, Vice President
Brady M. Connaughton Dorothea L. Fernandez
Nicole M. Green Chanta L. Jackson
Jason A. Jones Michelle A. Moss
Donna L. Puryear
SCHOOL DISTRICT ADMINISTRATION
Tami R. Crader, Ed.D.
Superintendent of Schools
Matthew Gristina, Ed.D.
Assistant Superintendent of Schools
Peter J. Leonard
Business Administrator/Board Secretary
Peter I. Bartlett
Assistant Business Administrator/Assistant Board Secretary
Kathleen M. Skelton
Director of Special Services
Shawanda Beale
Supervisor of School Counseling Services
Cheryl L. Romano
Supervisor for Curriculum, Instruction & Assessment
Kathleen M. Thomsen
Supervisor of Early Childhood Education
Nicholas Pizzulli
Interim Administrator for Athletic & Co-Curricular Activities
ELEMENTARY SCHOOL ADMINISTRATION
Principals
Mark K. Alfone, Ed.D., Midtown Community
Lori B. Burns, Ed.D., Early Childhood Center
Lakeda D. Demery, Shark River Hills
Sally A. Millaway, Ed.D., Gables
James M. Nulle, Green Grove
Jerard L. Terrell, Ed.D., Summerfield
MIDDLE SCHOOL ADMINISTRATION
Arlene M. Rogo, Ed.D., Principal
Thomas Decker, Vice Principal
Michael V. Smurro, Vice Principal
HIGH SCHOOL ADMINISTRATION
Jennifer C. Joseph, Principal
Titania M. Hawkins, Ed.D., Vice Principal
James H. Whitson, Vice Principal
POSEIDON ADMINISTRATION
Richard W. Allen, Principal
DEPARTMENT CHAIRPERSONS
Kelly Baldino
Robert J. Hamm
Charles M. Kolinofsky
Joshua Loveland
Dawn Reinhardt
Nicole Sanyigo
Tara Stephenson
Karen Watt
Hillary L. Wilkins
NEPTUNE TOWNSHIP SCHOOL DISTRICT
Office of the Superintendent
60 Neptune Blvd.
Neptune, NJ 07753
An Affirmative Action Equal Opportunity Employer
2017
NEPTUNE TOWNSHIP SCHOOL DISTRICT
PRE-CALCULUS
CURRICULUM
Table of Contents
Acknowledgements ............................................................................................................i
District Mission Statement ............................................................................................... ii
District Educational Outcome Goals .............................................................................. iii
Course Description........................................................................................................... iv
Curriculum
Unit Title Page
Functions ........................................................................................................................... 1
Exponential and Logarithmic Functions ........................................................................... 8
Trigonometric Functions ................................................................................................. 13
Analytical Trigonometry ................................................................................................. 18
Applications of Trigonometry Using Vectors................................................................. 23
Systems and Matrices ..................................................................................................... 28
Conics ............................................................................................................................. 33
Sequences, Series, and Limits ......................................................................................... 38
Pacing Guide College-Prep Level ................................................................................... 43
Pacing Guide Honors Level ............................................................................................ 46
NEPTUNE TOWNSHIP SCHOOL DISTRICT
Pre-Calculus
Acknowledgements
The Pre-Calculus Curriculum guide was developed for Neptune High School through the efforts
of Erin Seneca, Neptune High School mathematics teacher, in cooperation with Tara Stephenson,
Department Chairperson, and under the guidance of Cheryl Romano, Supervisor for Curriculum,
Instruction and Assessment.
The teacher is to be commended for her dedication in creating this curriculum and formatting it
into UbD and her expertise in the area of mathematics. This curriculum guide prepares students to
topics in calculus. It is our hope that this guide will serve as a valuable resource for the staff
members who teach this course and that they will feel free to make recommendations for its
continued improvement.
The Pre-calculus Curriculum guide was written with related pacing guide in alignment to the 2016
New Jersey Student Learning Standards for Mathematics.
i
NEPTUNE TOWNSHIP SCHOOL DISTRICT
DISTRICT MISSION STATEMENT
The primary mission of the Neptune Township School District is to prepare all students for life
in the twenty-first century by encouraging them to recognize that learning is a continuing
process. It is with high expectations that our schools foster:
• A strong foundation in academic areas, modern technologies, life skills and the arts.
• A positive and varied approach to teaching and learning.
• An emphasis on critical thinking skills and problem-solving techniques.
• A respect for and an appreciation of our world, its resources, and its peoples.
• A sense of responsibility, good citizenship, and accountability.
• An involvement by the parents and the community in the learning process.
ii
Neptune Township School District
Educational Outcome Goals
The students in the Neptune Township schools will become life-long learners and will:
Become fluent readers, writers, speakers, listeners, and viewers with comprehension and
critical thinking skills.
Acquire the mathematical skills, understandings, and attitudes that are needed to be
successful in their careers and everyday life.
Understand fundamental scientific principles, develop critical thinking skills, and
demonstrate safe practices, skepticism, and open-mindedness when collecting, analyzing,
and interpreting information.
Become technologically literate.
Demonstrate proficiency in all New Jersey Core Curriculum Content Standards
(NJCCCS), New Jersey Student Learning Standards (NJSLS), and Next Generation
Science Standards (NGSS).
Develop the ability to understand their world and to have an appreciation for the heritage
of America with a high degree of literacy in civics, history, economics and
geography. Develop a respect for different cultures and demonstrate trustworthiness,
responsibility, fairness, caring, and citizenship.
Become culturally literate by being aware of the historical, societal, and multicultural
aspects and implications of the arts.
Demonstrate skills in decision-making, goal setting, and effective communication, with a
focus on character development.
Understand and practice the skills of family living, health, wellness and safety for their
physical, mental, emotional, and social development.
Develop consumer, family, and life skills necessary to be a functioning member of
society.
Develop the ability to be creative, inventive decision-makers with skills in
communicating ideas, thoughts and feelings.
Develop career awareness and essential technical and workplace readiness skills, which
are significant to many aspects of life and work.
iii
PRE-CALCULUS
CURRICULUM
COURSE DESCRIPTION
(5 credits) This course contains the background information that enables students to study advanced
mathematics. In this course the students will be studying extensions of Algebra II along with
advanced trigonometry and analytic geometry. All major areas of Algebra II are covered in greater
depth and application. Students will analyze functions and curve sketching, advanced trigonometry
including radian measures and trigonometric graphing, along with selected topics from discrete
mathematics including sequences, series, and probability models. This course is designed to cover
all topics that are necessary for the student to be successful in a college calculus course.
Appropriate use of technology is integrated throughout the course.
Prerequisites: successful completion of Algebra 2.
iv
1
Unit 1
Functions
Suggested Time
Frame
24 Days (Honors) / 26 Days (CP)
Overview / Rationale
This unit will serve as a review of the various functions that students have studied throughout
Algebra 1 and Algebra 2, as well as offering students an introduction to the various functions that
they will be utilizing throughout their study of Pre-Calculus. Students will study the graphs of
functions, including finding real and complex zeroes. Students will be able to compare the various
types of functions and discuss applications including inverses.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
N-CN.A.1. Know there is a complex number i such that i2 = –1, and every complex number
has the form a + bi with a and b real.
N-CN.A.2. Use the relation i2 = –1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
N-CN.A.3. (+) Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
N-CN.C. Use complex numbers in polynomial identities and equations.
N-CN.C.7. Solve quadratic equations with real coefficients that have complex solutions.
N-CN.C.8. (+) Extend polynomial identities to the complex numbers. For example, rewrite
x2 + 4 as (x + 2i)(x – 2i).
N-CN.C.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials
A-APR.A. Perform arithmetic operations on polynomials
A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely,
they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
A-APR.B. Understand the relationship between zeros and factors of polynomials
2
A-APR.B.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number
a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of
p(x).
A-APR.B.3. Identify zeros of polynomials when suitable factorizations are available, and
use the zeros to construct a rough graph of the function defined by the polynomial.
A-APR.D. Rewrite rational expressions
A-APR.D.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the
form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x)
less than the degree of b(x), using inspection, long division, or, for the more complicated
examples, a computer algebra system.
A-APR.D.7. (+) Understand that rational expressions form a system analogous to the
rational numbers, closed under addition, subtraction, multiplication, and division by a
nonzero rational expression; add, subtract, multiply, and divide rational expressions.
A-REI.D. Represent and solve equations and inequalities graphically
A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations
y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic functions.
F-IF.A. Understand the concept of a function and use function notation
F-IF.A.1. Understand that a function from one set (called the domain) to another set (called
the range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f corresponding to
the input x. The graph of f is the graph of the equation y = f(x).
F-IF.A.2. Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
F-IF.A.3. Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. For example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
F-IF.B. Interpret functions that arise in applications in terms of the context
F-IF.B.4. For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and periodicity.
F-IF.B.5. Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function.
F-IF.B.6. Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a
graph.
F-IF.C. Analyze functions using different representations
3
F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by
hand in simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions
and absolute value functions.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available,
and showing end behavior.
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
F-IF.C.8. Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
Essential Questions: 1. How do the algebraic properties of a
function relate to its graph?
2. What is the importance of the domain
in studying a function?
Enduring Understandings: 1. The algebraic properties of a graph,
including the calculation of zeros, can
help us describe the behavior of a
function including its intercepts.
2. The domain of a function is needed to
determine any extraneous solutions and
to properly study the graph of the
function.
Knowledge: Students will know…
● Methods to determine end behavior of
the graph of polynomial functions.
● How to apply synthetic division to
divide polynomials and find zeros of
the graph of the polynomial.
● Properties of complex numbers.
● Methods for combining functions.
● Methods for finding and graphing
inverse functions.
Skills: Students will be able to…
● Graph polynomial functions and
describe end behavior.
● Perform polynomial and synthetic
division given polynomials.
● Perform operations with complex
numbers.
● Find real and complex zeros of
polynomial functions.
● Simplify and evaluate rational
functions
● Perform various combinations of two or
more functions.
● Determine if a function has an inverse
and find the inverse if it exists.
4
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy E CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers E CRP2. Apply appropriate
academic and technical skills.
Money Management CRP3. Attend to personal health
and financial well-being.
Credit and Debt Management ET CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and Investing CRP5. Consider the
environmental, social and economic
impacts of decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility ET CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
E CRP9. Model integrity, ethical
leadership and effective
management.
Career Awareness E CRP10. Plan education and career
paths aligned to personal goals.
Career Exploration ETA CRP11. Use technology to enhance
productivity.
Career Preparation ET CRP12. Work productively in
teams while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
5
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Transformations Project
- Students will create a drawing on the
coordinate plane and use
transformations - translations, and
reflections using function notation to
describe them.
Unit Assessment
- Differentiated for College Prep and
Honors levels
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
6
Suggested
Learning
Activities
Teacher directed lessons
● Course introduction(grading, syllabus, rules)
● Functions and a Library of Parent Functions
● Polynomial Functions of Higher Degree
● Polynomial and Synthetic Division
● Complex Numbers
● Zeros of Polynomial Functions
● Rational Functions
● Combinations of Functions: Composite Functions
● Inverse Functions
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
7
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
8
Unit 2
Exponential and Logarithmic Functions
Suggested Time
Frame
8 Days
Overview / Rationale
This unit will serve as a review of the Exponential and Logarithmic functions that students have
studied throughout Algebra 2, as well as offering students an introduction to using the function to
model real life phenomena that they will be utilizing throughout their study of Pre-Calculus.
Students will be able to compare the exponential and log functions and discuss applications
including inverses.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
F-IF.B. Interpret functions that arise in applications in terms of the context
F-IF.B.4. For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and periodicity.
F-IF.B.5. Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes. For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function.
F-IF.C. Analyze functions using different representations
F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by
hand in simple cases and using technology for more complicated cases.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
F-IF.C.8. Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
9
b. Use the properties of exponents to interpret expressions for exponential functions. For
example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y =
(1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay
Essential Questions: 1. How can exponential and logarithmic
functions be used to model real life
phenomena?
Enduring Understandings: 1. Functions can be used to represent
situations including the study of the
growth or decline of populations and
the maximization of volume for an
object, among other phenomena.
Knowledge: Students will know…
● Properties of logarithmic and
exponential functions.
● Methods of rewriting and evaluating
logarithmic expressions.
● Methods of solving logarithmic and
exponential equations.
Skills: Students will be able to…
● Graph and evaluate exponential and
logarithmic functions.
● Apply the properties of logarithms to
simplify logarithmic expressions.
● Solve exponential and logarithmic
equations.
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy E CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers E CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health
and financial well-being.
Credit and Debt Management ET CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and Investing CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility E CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
CRP9. Model integrity, ethical
leadership and effective
10
management.
X Career Awareness E CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ET CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
11
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Exponential Functions and Their Graphs
● Logarithmic Functions and Their Graphs
● Properties of Logarithms
● Exponential and Logarithmic Equations
● Exponential and Logarithmic Models
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
12
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
13
Unit 3
Trigonometric Functions
Suggested Time
Frame
9 Days (Honors) / 12 Days (CP)
Overview / Rationale
This unit will build on previous studies of trigonometry done in Geometry and Algebra 2.
Students will build on their understanding of the unit circle to evaluate trigonometric functions.
They will expand their understanding to all triangles by using the law of sines and law of cosines
to be able to solve any triangle. Students will explore the graphs of trigonometric functions,
building an understanding of periodicity and amplitude.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
F-TF.A. Extend the domain of trigonometric functions using the unit circle
F-TF.A.1. Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
F-TF.A.2. Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.
F-TF.A.3. (+) Use special triangles to determine geometrically the values of sine, cosine,
tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and
tangent for π-x, π+x, and 2π–x in terms of their values for x, where x is any real number.
F-TF.A.4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
F-TF.B. Model periodic phenomena with trigonometric functions
F-TF.B.5. Choose trigonometric functions to model periodic phenomena with specified
amplitude, frequency, and midline. F-TF.B.6. (+) Understand that restricting a trigonometric function to a domain on which it is
always increasing or always decreasing allows its inverse to be constructed.
F-TF.B.7. (+) Use inverse functions to solve trigonometric equations that arise in modeling
contexts; evaluate the solutions using technology, and interpret them in terms of the context. G-SRT.C. Define trigonometric ratios and solve problems involving right triangles
14
G-SRT.C.6. Understand that by similarity, side ratios in right triangles are properties of the
angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G-SRT.C.7. Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
in applied problems.«
G-SRT.D. Apply trigonometry to general triangles
G-SRT.D.9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing
an auxiliary line from a vertex perpendicular to the opposite side.
G-SRT.D.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G-SRT.D.11. (+) Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems, resultant
forces).
Essential Questions: 1. How can trigonometric functions be
applied to triangles other than right
triangles?
2. How do trigonometric functions model
real world problems and their
solutions?
Enduring Understandings: 1. Trigonometric functions can be used to
find the missing sides and angles for
any triangle and to find the area of any
triangle.
2. Trigonometric functions can model real
world problems through their use in
finding various hard to find
measurements and through modeling of
phenomena such as sound waves.
Knowledge: Students will know…
● How the unit circle can be used to find
trigonometric values.
● Properties of special right triangles.
● How to graph a trigonometric function
using technology.
● How to describe a trigonometric graph
using its equation.
● Use the laws of sines and cosines to
solve triangles.
Skills: Students will be able to…
● Use the unit circle to find trigonometric
values.
● Solve special right triangles using their
properties.
● Graph a trigonometric function using
technology.
● Describe the graph of a trigonometric
function using its period and amplitude.
● Solve triangles using the law of sines
and law of cosines.
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
15
Income and Careers CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health and
financial well-being.
Credit and Debt Management ETA CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and Investing CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
ET CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ET CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
16
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Circle Project
- Students will create a unit circle with
special right triangles and complete unit
circle worksheets using their created
unit circle.
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Radian and Degree Measure
● Trigonometric Functions: The Unit Circle
● Right Triangle Trigonometry
● Trigonometric Functions of Any Angle
● Graphs of Sine and Cosine Functions
● Graphs of Other Trigonometric Functions
● Inverse Trigonometric Functions
● Applications and Models
● Law of Sines
● Law of Cosines
17
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
18
Unit 4
Analytical Trigonometry
Suggested Time
Frame
9 Days
Overview / Rationale
Students will further explore trigonometric functions throughout this unit. Students will study
trigonometric identities and use the identities to verify that the identities are true. Students will
then make connections between their understanding of trig identities and strategies for solving
equations to solve trigonometric equations and use various related trigonometric formulas.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
F-TF.B. Model periodic phenomena with trigonometric functions.
F-TF.B.7. (+) Use inverse functions to solve trigonometric equations that arise in modeling
contexts; evaluate the solutions using technology, and interpret them in terms of the context.
F-TF.C. Prove and apply trigonometric identities
F-TF.C.8. Prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1 and use it to find sin(θ),
cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
F-TF.C.9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and
use them to solve problems.
Essential Questions: 1. How can using a trigonometric identity
be used to verify other identities?
2. How can methods for solving general
equations be used to solve
trigonometric equations?
Enduring Understandings: 1. Manipulating the fundamental
trigonometric identities can create
equivalent expressions that can verify
other trigonometric identities.
2. Strategies for solving linear and
quadratic equations can be applied to
trigonometric equations. Vectors
represent motion
Knowledge: Students will know…
Skills: Students will be able to…
19
● The fundamental trigonometric
identities.
● Strategies for verifying trigonometric
identities.
● How to solve trigonometric equations.
● Sum and difference formulas for
trigonometric functions.
● Multiple-angle and product-to-sum
formulas for trigonometric functions.
● Verify trigonometric identities.
● Solve trigonometric equations.
● Use sum-and difference formulas for
trigonometric functions.
● Use multiple-angle and product-to-sum
formulas for trigonometric functions.
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health and
financial well-being.
Credit and Debt Management ETA CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and
Investing
CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical
Consumer
ET CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility ET CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness,
Exploration, and
Preparation
E CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
20
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
21
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Using Fundamental Identities
● Verifying Trigonometric Identities
● Solving Trigonometric Equations
● Sum and Difference Formulas
● Multiple-Angle and Product-to-Sum Formulas
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students:
22
● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
23
Unit 5
Applications of Trigonometry Using Vectors
Suggested Time
Frame
8 Days
Overview / Rationale
Students will be introduced to vectors which will tie back to their previous study of complex
numbers. They will use the vectors to model problems of motion. Students will be introduced
to polar coordinates which will lead to new and interesting graphs. At the end of the unit
students will use polar coordinates in the context of complex numbers to explore De-Moive’s
Theorem.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
N-CN.B. Represent complex numbers and their operations on the complex plane.
N-CN.B.4. (+) Represent complex numbers on the complex plane in rectangular and polar
form (including real and imaginary numbers), and explain why the rectangular and polar
forms of a given complex number represent the same number.
N-CN.B.5. (+) Represent addition, subtraction, multiplication, and conjugation of complex
numbers geometrically on the complex plane; use properties of this representation for
computation. For example, (-1 + √3i)3 = 8 because (-1+ √3i) has modulus 2 and argument
120°.
N-CN.B.6. (+) Calculate the distance between numbers in the complex plane as the modulus
of the difference, and the midpoint of a segment as the average of the numbers at its
endpoints.
N-VM.A. Represent and model with vector quantities.
N-VM.A.1. (+) Recognize vector quantities as having both magnitude and direction.
Represent vector quantities by directed line segments, and use appropriate symbols for
vectors and their magnitudes (e.g., v, |v|, ||v||, v).
N-VM.A.2. (+) Find the components of a vector by subtracting the coordinates of an initial
point from the coordinates of a terminal point.
N-VM.A.3. (+) Solve problems involving velocity and other quantities that can be
represented by vectors.
24
N-VM.B. Perform operations on vectors.
N-VM.B.4. (+) Add and subtract vectors.
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that
the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form, determine the magnitude and
direction of their sum.
c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w,
with the same magnitude as w and pointing in the opposite direction. Represent vector
subtraction graphically by connecting the tips in the appropriate order, and perform vector
subtraction component-wise.
N-VM.B.5. (+) Multiply a vector by a scalar.
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their
direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of
cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v
(for c < 0).
Essential Questions: 1. How can vectors be used to represent
real life phenomena?
Enduring Understandings: 1. Vectors represent motion involving
both speed and direction which models
real life events.
Knowledge: Students will know…
● How to draw vectors in the coordinate
plane.
● How to perform operations vectors.
● How to write the trigonometric form of
a complex number.
Skills: Students will be able to…
● Draw vectors in a coordinate plane.
● Find the dot product of two vectors.
● Determine the magnitude of a vector.
● Find the angle between two vectors.
● Write the trigonometric form of a
complex number.
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers ETA CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health and
financial well-being.
Credit and Debt Management ET CRP4. Communicate clearly and
effectively and with reason.
25
Planning, Saving, and Investing CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility ET CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
E CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ETA CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets:
26
Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Vectors in the Plane
● Vectors and Dot Products
● Modeling with Vectors
● Trigonometric Form of a Complex Number
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
27
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
28
Unit 6
Systems and Matrices
Suggested Time
Frame
6 Days
Overview / Rationale
Students will review strategies for solving systems of equations and inequalities and expand their
understanding to nonlinear systems. Students will work with systems with more than two variables
to compare how the methods they use are similar to those used with two variables. Students will
then develop skills for performing operations on matrices and to see how they can be applied to
solve systems of equations, including the use of technology.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
A-REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in
two variables algebraically and graphically. For example, find the points of intersection
between the line y = –3x and the circle x 2 + y 2 = 3.
A-REI.8. (+) Represent a system of linear equations as a single matrix equation in a vector
variable.
A-REI.9. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear
equations (using technology for matrices of dimension 3 × 3 or greater). Represent and solve
equations and inequalities graphically
A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y
= f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic functions.
N-VM. Perform operations on matrices and use matrices in applications.
N-VM.6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or
incidence relationships in a network.
29
N-VM.7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the
payoffs in a game are doubled.
N-VM.8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
N-VM.9. (+) Understand that, unlike multiplication of numbers, matrix multiplication for
square 16 matrices is not a commutative operation, but still satisfies the associative and
distributive properties.
N-VM.10. (+) Understand that the zero and identity matrices play a role in matrix addition
and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse.
N-VM.11. (+) Multiply a vector (regarded as a matrix with one column) by a matrix of
suitable dimensions to produce another vector. Work with matrices as transformations of
vectors.
N-VM.12. (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the
absolute value of the determinant in terms of area.
Essential Questions: 1. How can matrices be used to solve
systems of linear equations?
2. How can systems of equations be used
to represent real life situations?
Enduring Understandings: 1. Matrices can be created from a linear
system and reduced to find the solution
to the system.
2. Systems of equations can represent
many real life situations, such as
finance and chemistry, which require
multiple variables.
Knowledge: Students will know…
● Methods for solving linear systems of
two or more variables algebraically.
● Methods for solving non-linear systems
of two variables algebraically.
● How to write and solve a linear system
using a matrix and technology.
● How to find the inverse of a square
matrix.
● How to calculate the determinant of a
square matrix.
● Applications of the determinant of a
square matrix.
Skills: Students will be able to…
● Solve systems of linear and nonlinear
equations algebraically.
● Perform operations on a matrix.
● Use a matrix to solve a system of
equations.
● Find the inverse of a square matrix
(using technology for a 3x3 or above.)
● Calculate the determinant of a square
matrix (using technology for a 3x3 or
above).
● Use the determinant of a matrix in real
life situations (including finding the
area of a triangle).
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
30
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers ET CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health and
financial well-being.
Credit and Debt Management ETA CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and Investing CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility E CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
E CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ET CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
31
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Linear and Nonlinear Systems of Equations
● Two-Variable Linear Systems
● Multivariable Linear Systems
● Systems of Inequalities
● Matrices and Systems of Equations
● Operations with Matrices
● The Inverse of a Square Matrix
● The Determinant of a Square Matrix
● Applications of Matrices and Determinants.
32
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
33
Unit 7
Conics
Suggested Time
Frame
5 Days
Overview / Rationale
In this unit, students will explore the different conic sections in mathematics. Students will build
on what they have learned previously about quadratic equations to understand parabolas. Students
will be introduced to ellipses and hyperbolas and discuss the various properties of each conic
section.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
G-GPE. Translate between the geometric description and the equation for a
conic section
G-GPE.1. Derive the equation of a circle of given center and radius using the Pythagorean
Theorem; complete the square to find the center and radius of a circle given by an equation.
G-GPE.2. Derive the equation of a parabola given a focus and directrix.
G-GPE.3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact
that the sum or difference of distances from the foci is constant.
Essential Questions: 1. How can various conic sections be
created from the same figure?
Enduring Understandings: 1. The different ways that a plane can
intersect a double-napped cone will
create different conic sections based on
the nature of the intersection, each with
its own properties.
Knowledge: Students will know…
● The various conic shapes that can be
created.
Skills: Students will be able to…
● Write the equation of a circle given its
center and radius.
34
● The standard equations of each of the
conic sections.
● How to write an equation in standard
form for each conic section.
● Write the equation of a parabola in
standard form given is focus and
directrix.
● Write the equations of an ellipse given
its foci, vertices and axes.
● Write the equation of a hyperbola given
its foci, vertices, and axes.
● Classify a conic from its general
equation.
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers ET CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health and
financial well-being.
Credit and Debt Management ET CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and
Investing
CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility E CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness,
Exploration,
and Preparation
E CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness ET CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ET CRP11. Use technology to enhance
productivity.
35
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Conic Sections Project
- Students will create a picture using a
minimum of 4 conic sections using a
graphing application, desmos.
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
36
Homework assignments
Lesson Quizzes
Closure activities/exit slips
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Graphs of Equations (Circles)
● Introduction to Conics: Parabolas
● Ellipses
● Hyperbolas
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
37
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
38
Unit 8
Sequences, Series, and Limits
Suggested Time
Frame
12 Days (Honors) / 7 Days (CP)
Overview / Rationale
In this culminating unit, students will explore the concepts of sequences, series, and limits (Limits
are Honors Only). Students will learn about various concepts that will be needed to move forward
into Calculus.
Stage 1 – Desired Results
2016 New Jersey Student Learning Standards
Standards for Mathematical Practice
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content
A-SSE.B. Write expressions in equivalent forms to solve problems
A-SSE.B.4. Derive and/or explain the formula for the sum of a finite geometric series (when
the common ratio is not 1), and use the formula to solve problems. For example, calculate
mortgage payments.
F-BF.A. Build a function that models a relationship between two quantities
F-BF.A.1. Write a function that describes a relationship between two quantities.
F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation
from a context.
F-BF.A.2. Write arithmetic and geometric sequences both recursively and with an explicit
formula, use them to model situations, and translate between the two forms.
F-LE.A.2. Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs (include
reading these from a table).
A-APR.C.5. (+) Know and apply the Binomial Theorem for the expansion of (x + y) n in
powers of x and y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle.
Essential Questions: 1. How can sequences and series be used
to model real life phenomena?
2. How do limits help us to study
mathematical functions? (Honors Only)
Enduring Understandings: 1. How can sequences and series be used
to model real life phenomena?
2. How do limits help us to study
mathematical functions? (Honors Only)
39
Knowledge: Students will know…
● How to evaluate arithmetic and
geometric series.
● How to raise a binomial to a power by
using the Binomial Theorem.
● How to evaluate a limit. (Honors Only).
Skills: Students will be able to…
● Evaluate an arithmetic sequence.
● Evaluate a geometric sequence.
● Use the Binomial Theorem to raise a
binomial expression to a given power.
● Evaluate a limit for a given function.
(Honors Only).
In this unit plan, the following 21st Century Life and Careers skills are addressed:
Check ALL that apply –
21st Century Themes
Indicate whether these skills are:
● E – encouraged
● T – taught
● A – assessed
Career Ready Practices
9.1 Personal Financial Literacy CRP1. Act as a responsible and
contributing citizen and employee.
Income and Careers ETA CRP2. Apply appropriate academic
and technical skills.
Money Management CRP3. Attend to personal health
and financial well-being.
Credit and Debt Management ET CRP4. Communicate clearly and
effectively and with reason.
Planning, Saving, and Investing CRP5. Consider the environmental,
social and economic impacts of
decisions.
Becoming a Critical Consumer E CRP6. Demonstrate creativity and
innovation.
Civic Financial Responsibility CRP7. Employ valid and reliable
research strategies.
Insuring and Protecting ETA CRP8. Utilize critical thinking to
make sense of problems and
persevere in solving them.
9.2 Career Awareness, Exploration,
and Preparation
ET CRP9. Model integrity, ethical
leadership and effective
management.
X Career Awareness E CRP10. Plan education and career
paths aligned to personal goals.
X Career Exploration ET CRP11. Use technology to enhance
productivity.
X Career Preparation ET CRP12. Work productively in teams
while using cultural global
competence.
40
Student Resources
Primary Source
Readings
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel
Kennedy, and David E. Bock. Precalculus: graphical, numerical,
algebraic. Boston: Pearson, 2015. Print.
Secondary Source
Readings
Supporting Text pages
Teacher Resources
Texts:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley, Daniel Kennedy, and David E. Bock.
Precalculus: graphical, numerical, algebraic. Boston: Pearson, 2015. Print.
Larson, Ron, Robert P. Hostetler, and David C. Falvo. Precalculus with Limits. Boston,
Masachusets: Houghton Mifflin Co., 2007. Print.
Carter, John A. Glencoe Precalculus. Bothall, WA: McGraw-Hill Education, 2014. Print.
Supplemental Workbooks: Carter, John A. Glencoe Precalculus Workbook. Bothall, WA: McGraw-Hill Education, 2014.
Print.
Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/
Worksheets: Teacher created worksheets
www.kutasoftware.com
Videos: Teacher created videos
www.khanacademy.com
http://patrickjmt.com/
Stage 2 – Assessment Evidence
Performance Task(s):
Unit Assessment
- Differentiated for College Prep and
Honors levels.
Other Evidence:
Do Now/Anticipatory assignments
Class Notes
Teacher Observations
Participation in class discussions
Peer/Self Assessments.
Guided practice individually, in pairs and in
group
Classroom assignments
Homework assignments
Lesson Quizzes
Closure activities/exit slips
41
Stage 3 – Learning Plan
Instructional
Strategies
Descriptions
Suggested
Learning
Activities
Teacher directed lessons
● Sequences and Series
● Arithmetic Sequences and Partial Sums
● Geometric Sequences and Series
● The Binomial Theorem
● Introduction to Limits (Honors Only)
● Techniques for Evaluating Limits (Honors Only)
Modifications Special Education Students: (These are just suggested ideas to modify
instruction. All modifications and accommodations should be specific to
each individual child’s IEP) ● Multi-sensory instruction.
● Differentiated instruction.
● Additional Vocabulary Activities.
● Provide hands-on manipulatives with format skeletons to groups of
students.
● Draw and label diagrams to represent the data for visual learners.
● Provide time for revision of work when students show need.
● Facilitate group discussions to assess understanding among varying
ability levels of students.
● Scaffolding content.
● Graphic organizers.
English Language Learners:
● Identify key phrases or new vocabulary to pre-teach.
● Additional Vocabulary Activities: to support the ELL students to
build mathematical understanding
● Draw and label diagrams to represent the data for visual learners.
● Provide visual cues.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Encourage students to offer bilingual assistance to each other.
Students at Risk of Failure:
● Reteach to Build Understanding: for struggling learners to revisit
and practice the lesson concept or skill modeling.
● Provide time for revision of work when students show need.
● Scaffolding content.
● Graphic organizers.
● Mneumonics.
Gifted Students: ● Enrichment Activities: to challenge the advanced-proficient student.
42
● Provide extension assignments and activities.
● Projects in multiple tasks.
● Grouping.
● Honors-level courses should feature activities and assessments
that challenge students beyond the general education class
requirements.
43
College-Prep Precalculus Pacing Guide
Day Unit Topic Chapter Day Unit Topic Chapter
1
Intro to class, syllabus, rules,
etc. Algebra 2 Review P 46 3 Inverse Trig Functions 4
2 Algebra 2 Review P 47 3
Solving Problems with Trig
Functions 4
3 Algebra 2 Review P 48 3 Graphs of Sine and Cosine 4
4 Algebra 2 Review P 49 3
Graphs of Tangent,
Cotangent, Secant and
Cosecant 4
5 1
Functions; Domain and
Range; Increasing and
Decreasing 1 50 3 Unit 3B Test 4
6 1 Extrema and End Behavior 1 51 4 Fundamental Trig Identities 5
7 1 Parent Functions 1 52 4 Fundamental Trig Identities 5
8 1 Transformations 1 53 4 Proving Trig Identities 5
9 1 Transformation Project 1 54 4
Sum and Difference
Identities 5
10 1 Transformation Project 1 55 4 Multiple Angle Identities 5
11 1
Function Combinations and
Compositions 1 56 4 Law of Sines 5
12 1 Inverse Relations 1 57 4 Law of Cosines 5
13 1 Unit 1A Review 1 58 4 Unit 4 Review 5
14 1 Unit 1A Test 1 59 4 Unit 4 Test 5
15 1
Polynomial Functions and
Rate of Change 2 60 5
Vector Operations; Unit
Vectors; Direction Angles 6
16 1 Quadratic Functions 2 61 5
Dot Product; Angle Between
Vectors; Vector Projections 6
17 1 Power Functions 2 62 5 Vector Projections and Work 6
44
18 1
Graphs of Polynomial
Functions; End Behavior;
Zeros 2 63 5 Parametric Equations 6
19 1
Polynomial Division;
Remainder and Factor
Theorems 2 64 5 Polar Coordinates 6
20 1 Complex Zeros 2 65 5
Polar Form of Complex
Numbers 6
21 1 Graphs of Rational Functions 2 66 5 Unit 5 Review 6
22 1 Graphs of Rational Functions 2 67 5 Unit 5 Test 6
23 1 Solving Rational Equations 2 68 6
Solving Systems of
Equations 7
24 1 Solving Rational Equations 2 69 6 Matrix Algebra 7
25 1 Unit 1B Review 2 70 6 Matrix Algebra 7
26 1 Unit 1B Test 2 71 6 Systems of Inequalities 7
27 2 Exponential and Log Graphs 3 72 6 Unit 6 Review 7
28 2 Growth and Decay Models 3 73 6 Unit 6 Test 7
29 2
Exp. Inverses; Properties of
Logs 3 74 7
Intro to Conic Sections;
Parabolas 8
30 2
Properties of Logs/ Solving
Exponentials 3 75 7 Circles and Ellipses 8
31 2 Solving Log Equations 3 76 7 Hyperbolas 8
32 2 Compound Interest 3 77 7 Unit 7 Review 8
33 2 Unit 2 Review 3 78 7 Unit 7 Test 8
34 2 Unit 2 Test 3 79 8
Intro to Sequences and
Series 9
35 3
Degrees and Radians; Arc
Length; Angular and Linear
Motion 4 80 8
Arithmetic Sequences and
Series 9
36 3 Unit Circle 4 81 8
Geometric Sequences and
Series 9
37 3 Unit Circle Project 4 82 8 Pascal's Triangle 9
45
38 3 Unit Circle Project 4 83 8 Binomial Theorem 9
39 3 Right Traingle Trig 4 84 8 Unit 8 Review 9
40 3 Trig Functions of Any Angle 4 85 8 Unit 8 Test 9
41 3 Trig Functions of Any Angle 4 86 Final Review
42 Midterm Review 87 Final Review
43 Midterm Review 88 Final Review
44 MIDTERM EXAMS
89 FINAL EXAMS
45 90
46
Honors Pre-Calculus Pacing Guide
Day Unit Topic Chapter Day Unit Topic Chapter
1
Intro to class, syllabus, rules,
etc. Algebra 2 Review P 46 4
Fundamental Trig
Identities 5
2 Algebra 2 Review P 47 4
Fundamental Trig
Identities 5
3 Algebra 2 Review P 48 4 Proving Trig Identities 5
4 1
Functions; Domain and
Range; Increasing and
Decreasing 1 49 4
Sum and Difference
Identities 5
5 1 Extrema and End Behavior 1 50 4 Multiple Angle Identities 5
6 1 Parent Functions 1 51 4 Law of Sines 5
7 1 Transformations 1 52 4 Law of Cosines 5
8 1 Transformation Project 1 53 4 Unit 4 Review 5
9 1 Transformation Project 1 54 4 Unit 4 Test 5
10 1
Function Combinations and
Compositions 1 55 5
Vector Operations; Unit
Vectors; Direction
Angles 6
11 1 Inverse Relations 1 56 5
Dot Product; Angle
Between Vectors; Vector
Projections 6
12 1 Unit 1A Review 1 57 5
Vector Projections and
Work 6
13 1 Unit 1A Test 1 58 5 Parametric Equations 6
14 1
Polynomial Functions and
Rate of Change 2 59 5 Polar Coordinates 6
15 1 Quadratic Functions 2 60 5
Polar Form of Complex
Numbers 6
16 1 Power Functions 2 61 5 Unit 5 Review 6
47
17 1
Graphs of Polynomial
Functions; End Behavior;
Zeros 2 62 5 Unit 5 Test 6
18 1
Polynomial Division;
Remainder and Factor
Theorems 2 63 6
Solving Systems of
Equations 7
19 1 Complex Zeros 2 64 6 Matrix Algebra 7
20 1 Graphs of Rational Functions 2 65 6 Matrix Algebra 7
21 1 Graphs of Rational Functions 2 66 6 Systems of Inequalities 7
22 1 Solving Rational Equations 2 67 6 Unit 6 Review 7
23 1 Unit 1B Review 2 68 6 Unit 6 Test 7
24 1 Unit 1B Test 2 69 7
Intro to Conic Sections;
Parabolas 8
25 2 Exponential and Log Graphs 3 70 7 Circles and Ellipses 8
26 2 Growth and Decay Models 3 71 7 Hyperbolas 8
27 2
Exp. Inverses; Properties of
Logs 3 72 7 Unit 7 Review 8
28 2
Properties of Logs/ Solving
Exponentials 3 73 7 Unit 7 Test 8
29 2 Solving Log Equations 3 74 8
Intro to Sequences and
Series 9
30 2 Compound Interest 3 75 8
Arithmetic Sequences
and Series 9
31 2 Unit 2 Review 3 76 8
Geometric Sequences and
Series 9
32 2 Unit 2 Test 3 77 8 Pascal's Triangle 9
33 3
Degrees and Radians; Arc
Length; Angular and Linear
Motion 4 78 8 Binomial Theorem 9
34 3 Unit Circle 4 79 8 Unit 8A Review 9
35 3 Unit Circle Project 4 80 8 Unit 8A Test 9
36 3 Right Traingle Trig 4 81 8 Introduction to Limits 11
48
37 3 Trig Functions of Any Angle 4 82 8 Limits Graphically 11
38 3 Inverse Trig Functions 4 83 8 Limits Algebraically 11
39 3
Solving Problems with Trig
Functions 4 84 8 Limits Review 11
40 3 Graphs of Sine and Cosine 4 85 8 Limits Test 11
41 3
Graphs of Tangent,
Cotangent, Secant and
Cosecant 4 86 Final Review
42 Midterm Review 87 Final Review
43 Midterm Review 88 Final Review
44 MIDTERM EXAMS
89 FINAL EXAMS
45 90