Pre-Calculus · HIGH SCHOOL ADMINISTRATION Jennifer C. Joseph, Principal Titania M. Hawkins, Ed.D., ... Sequences, Series, and Limits ... This course contains the background information

NEPTUNE TOWNSHIP SCHOOL DISTRICT

Pre-Calculus Curriculum

(College Prep and Honors) Grades 10-12


Office of the Superintendent

60 Neptune Blvd.

Neptune, NJ 07753-4836

July 31, 2019 Document C1#1

NEPTUNE TOWNSHIP BOARD OF EDUCATION

Dorothea L. Fernandez, President

Laura G. Granelli, Vice President

Brady M. Connaughton Nicole M. Green

Jerome H. Hubbard Jason A. Jones

Mark A. Matson Michelle A. Moss

Donna Puryear Antonio Lopez, Neptune City Rep.

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

Sally A. Millaway, Ed.D.

Director for Curriculum, Instruction & Assessment

Kathleen M. Skelton

Director of Special Services

Lakeda Demery-Alston

Supervisor of Humanities & ESL

Charles Kolinofsky

Supervisor of Data & Information

Kathleen M. Thomsen

Supervisor of Early Childhood Education

ELEMENTARY SCHOOL ADMINISTRATION

Principals

Lori B. Burns, Ed.D., Early Childhood Center

Joshua Loveland, Gables

James M. Nulle, Green Grove

Mark K. Alfone, Ed.D., Midtown Community

Janelle Williams, Shark River Hills

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

Kevin McCarthy, Vice Principal

James H. Whitson, Vice Principal

Richard Arnao, Administrator for Athletic & Co-Curricular Activities

DEPARTMENT CHAIRPERSONS

Kelly Baldino

Juan Beltran

Dawn Reinhardt

Nicole Sanyigo

Tara L. Stephenson

Karen Watt

Hillary L. Wilkins


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 ........................................................................ 10

Trigonometric Functions ................................................................................................ 17

Analytical Trigonometry ................................................................................................ 25

Applications of Trigonometry Using Vectors ................................................................ 32

Systems and Matrices ..................................................................................................... 40

Conics ............................................................................................................................. 48

Sequences, Series, and Limits ........................................................................................ 55

Accommodations ........................................................................................................... 55

Pacing Guide College-Prep Level .................................................................................. 66

Pacing Guide Honors Level ........................................................................................... 69


Pre-Calculus

Acknowledgements

The Neptune Township School District Pre-Calculus Curriculum guide for grades 10-12 was

developed through the efforts of Erin Seneca, teacher of Mathematics, under the guidance of

Dawn Reinhardt, Department Chairperson, Heba Abdo, Ed.D., Supervisor of STEM, and

Sally A. Millaway, Ed.D., Director for Curriculum, Instruction and Assessment.

The teacher is to be commended for her dedication in creating this curriculum, formatting it

into UbD, and her expertise in the area of mathematics. This curriculum guide includes

Algebra and Trigonometry at a level which is designed to prepare students for the study of

Calculus.

This curriculum was written in alignment with the 2016 New Jersey Student Learning

Standards for Mathematics and the increased rigor that those standards bring to the teaching

and learning of mathematics. It is our hope that this curriculum will serve as a valuable

resource for the staff members who teach this course and that they will continue to make

recommendations for improvement to the document.

i


DISTRICT MISSION STATEMENT

The primary mission of the Neptune Township School District is to prepare students for a life-

long learning process in a complex and diverse world. It is with high expectations that our

schools foster:

• A strong foundation in academic and modern technologies.

• 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 people.

• 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 Student Learning Standards (NJSLS).

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.

Prerequisite: Successful completion of Algebra 2.

iv

1

Unit 1

Functions

Suggested Time

Frame

24 Days (Honors) / 26 Days (College Prep)

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

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

New Jersey Student Learning Standards for Mathematics

Established Goals:

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).

2

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.

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.

3

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.

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.

4

Essential Questions:

How do the algebraic properties of a

function relate to its graph?

What is the importance of the domain in

studying a function?

Enduring Understandings:

Students will understand that…

The algebraic properties of a graph,

including the calculation of zeros, can help

us describe the behavior of a function

including its intercepts.

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.

5

Integrated Social and Emotional Learning Competencies

The following social and emotional competencies are integrated in this curriculum document:

Self-Awareness

☐ Recognize one’s own feelings and thoughts

☐ Recognize the impact of one’s feelings and thoughts on one’s own behavior

☒ Recognize one’s personal traits, strengths and limitations

☒ Recognize the importance of self-confidence in handling daily tasks and challenges

Self-Management

☐ Understand and practice strategies for managing one’s own emotions, thoughts and

behaviors

☒ Recognize the skills needed to establish and achieve personal and educational goals

☐ Identify and apply ways to persevere or overcome barriers through alternative

methods to achieve one’s goals

Social Awareness

☐ Recognize and identify the thoughts, feelings, and perspectives of others

☐ Demonstrate an awareness of the differences among individuals, groups, and

others’ cultural backgrounds

☒ Demonstrate an understanding of the need for mutual respect when viewpoints

differ

☒ Demonstrate an awareness of the expectations for social interactions in a variety of

setting

Responsible Decision Making

☒ Develop, implement and model effective problem solving and critical thinking

skill

☒ Identify the consequences associated with one’s action in order to make

constructive choices

☐ Evaluate personal, ethical, safety and civic impact of decisions

Relationship Skills

☒ Establish and maintain healthy relationships

☒ Utilize positive communication and social skills to interact effectively with others

☒ Identify ways to resist inappropriate social pressure

☒ Demonstrate the ability to present and resolve interpersonal conflicts in

constructive ways

☒ Identify who, when, where, or how to seek help for oneself or others when needed

6

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.

X 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.

Career Awareness, Exploration, and Preparation

Computer Programmer or Engineer

Engineers: Aerospace, Chemical, Electrical, Environmental, and Industrial

Farmers, Ranchers, and Agricultural Managers

Funeral Directors

Budget Analysts / Insurance Underwriters

7

Interdisciplinary Connections

New Jersey Student Learning Standards - ELA

R.1- Read closely to determine what the text say as explicitly and to make logical inferences

from it; cite specific textual evidence when writing or speaking to support conclusions

drawn from the text.

W.1- Write arguments to support claims in an analysis of substantive topics or texts using

valid reasoning and relevant and sufficient evidence.

W.2- Write informative/explanatory texts to examine and convey complex ideas and

information clearly and accurately through the effective selections organization, and

analysis of content.

Technology Integration

New Jersey Student Learning Standards for Technology

NJSLS 8.1 Educational Technology: All students will use digital tools to access, manage,

evaluate, and synthesize information in order to solve problems individually and collaborate and

to create and communicate knowledge.

Google Suite - Docs, Sheets, Slides, Forms

Microsoft Platform – Word, EXCEL, PowerPoint

NJSLS 8.2 Technology Education, Engineering, Design and Computational Thinking

All students will develop an understanding of the nature and impact of technology, engineering,

technological design, computational thinking and the designed world as they relate to the

individual, global society, and the environment.

Texas Instrument TI-84 Plus and TI-89 Calculators

8

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.

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.

Website: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/

Worksheets: Teacher created worksheets - www.kutasoftware.com

Videos:

Teacher created

www.khanacademy.com

http://patrickjmt.com/

http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/

http://www.kutasoftware.com/

http://www.khanacademy.com/


9

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.

Other Evidence:

Pre-Assessments

Formative Assessments

Exit Slip

Self-Assessment

Informal Observations

Summative Assessments:

Quizzes and Unit Test

Differentiated for College Prep and

Honors levels

Stage 3 – Learning Plan

Suggested

Learning

Activities

● 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

10

Unit 2

Exponential and Logarithmic Functions

Suggested Time

Frame

8 Days


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.











Standards for Mathematical Content

Established Goals:

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.

11

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.

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.


How can exponential and logarithmic

functions be used to model real life

phenomena?



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:


Properties of logarithmic and exponential

functions.

Methods of rewriting and evaluating

logarithmic expressions.

Methods of solving logarithmic and

exponential equations.

Skills:


Graph and evaluate exponential and

logarithmic functions.

Apply the properties of logarithms to

simplify logarithmic expressions.

Solve exponential and logarithmic

equations.

12



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


13



21st Century Themes



● T – taught

● A – assessed


9.1 Personal Financial Literacy E CRP1. Act as a responsible and


Income and Careers E CRP2. Apply appropriate academic








decisions.


innovation.

Civic Financial Responsibility E CRP7. Employ valid and reliable







CRP9. Model integrity, ethical


management.



Career Exploration ET CRP11. Use technology to enhance

productivity.



competence.


Computer Programmer or Engineer

Engineers: Aerospace, Chemical, Electrical, Environmental, and Industrial

Farmers, Ranchers, and Agricultural Managers

Funeral Directors

Budget Analysts / Insurance Underwriters

14























15

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.

Websites: http://www.larsonprecalculus.com/precalc9e/content/interactive-activities/

Worksheets: Teacher created - www.kutasoftware.com

Videos: Teacher created

www.khanacademy.com






16



Project:

Rubric-based Assessment

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment


Summative Assessments: Differentiated

for College Prep and Honors levels.


Suggested

Learning

Activities

● Exponential Functions and Their Graphs

● Logarithmic Functions and Their Graphs

● Properties of Logarithms

● Exponential and Logarithmic Equations

● Exponential and Logarithmic Models

17

Unit 3

Trigonometric Functions

Suggested Time

Frame



This unit will build on previous studies of trigonometry completed 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.










MP8. Look for and express regularity in repeated reasoning.


Established Goals:

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.

18

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.

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).

19


How can trigonometric functions be

applied to triangles other than right

triangles?

How do trigonometric functions model

real world problems and their solutions?



Trigonometric functions can be used to

find the missing sides and angles for any

triangle and to find the area of any

triangle.

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:


● 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:


● 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.

20



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


21



21st Century Themes



● T – taught

● A – assessed


9.1 Personal Financial Literacy CRP1. Act as a responsible and


Income and Careers CRP2. Apply appropriate academic




Credit and Debt Management ETA CRP4. Communicate clearly and




decisions.


innovation.

Civic Financial Responsibility CRP7. Employ valid and reliable







ET CRP9. Model integrity, ethical


management.

X Career Awareness CRP10. Plan education and career


Career Exploration ET CRP11. Use technology to enhance

productivity.



competence.


Animator

Game Designer

Jet Fighter Pilot

Robotics Engineer

22























23

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






24



Unit Circle Project:

Students will create a unit circle with special

right triangles and complete unit circle

worksheets using their created unit circle.

Exponentials and Logs Scavenger Hunt:

Students complete a problem and find the

card with the correct answer, then complete

the problem on the new card. The students

will complete 20 problems.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment


Summative Assessments: Quizzes and

Unit Test


Suggested

Learning

Activities

● 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

25

Unit 4

Analytical Trigonometry

Suggested Time

Frame

9 Days


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.












Established Goals:

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.

26


How can using a trigonometric identity be

used to verify other identities?

How can methods for solving general

equations be used to solve trigonometric

equations?



Manipulating the fundamental

trigonometric identities can create

equivalent expressions that can verify

other trigonometric identities.

Strategies for solving linear and quadratic

equations can be applied to trigonometric

equations. Vectors represent motion.

Knowledge:


● The fundamental trigonometric identities.

● Strategies for verifying trigonometric

identities.

● How to solve trigonometric equations.

● Sum and difference formulas for


● Multiple-angle and product-to-sum

formulas for trigonometric functions.

Skills:


● Verify trigonometric identities.

● Solve trigonometric equations.

● Use sum-and difference formulas for


● Use multiple-angle and product-to-sum

formulas for trigonometric functions.

27



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


28



21st Century Themes



● T – taught

● A – assessed




Income and Careers CRP2. Apply appropriate academic








decisions.

Becoming a Critical Consumer ET CRP6. Demonstrate creativity and

innovation.










management.



Career Exploration CRP11. Use technology to enhance

productivity.



competence.


Animator

Game Designer

Jet Fighter Pilot

Robotics Engineer

Roller Coaster Designer

Sports Announcer

29























30

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






31



Analytic Trigonometry – This unit does not

have a performance task at this time. The

skills in this section are fundamental to

calculus and the extra time we have is taken

by completing more practice problems as no

two problems are exactly the same and the

process of completing trig identities and

verifying them is of the utmost importance.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment


Summative Assessments: Differentiated

for College Prep and Honors levels.


Suggested

Learning

Activities

● Using Fundamental Identities

● Verifying Trigonometric Identities

● Solving Trigonometric Equations

● Sum and Difference Formulas

● Multiple-Angle and Product-to-Sum Formulas

32

Unit 5

Applications of Trigonometry Using Vectors

Suggested Time

Frame

8 Days


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.












Established Goals:

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.

33

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.

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).

34


How can vectors be used to represent real

life phenomena?



Vectors represent motion involving both

speed and direction which models real life

events.

Knowledge:


● How to draw vectors in the coordinate

plane.

● How to perform operations vectors.

● How to write the trigonometric form of a

complex number.

Skills:


● 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.

35



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


36



21st Century Themes



● T – taught

● A – assessed




Income and Careers ETA CRP2. Apply appropriate academic








decisions.


innovation.










management.



X Career Exploration ETA CRP11. Use technology to enhance

productivity.

X Career Preparation ET CRP12. Work productively in teams


competence.


Statistician

Survey Quality Engineer

Analog Image Sensor Characterization Engineer

Electrical Engineer

Air Warfare Simulations Engineer

Robotics Software Engineer

37






W.1- Write arguments to support claims in an analysis of substantive topics or texts using valid

reasoning and relevant and sufficient evidence.
















38

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






39



Apps of Trig/Vectors – There is no project

for this unit at this time. This chapter focuses

on the basics of vectors and trig in the polar

plane.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment



Unit Test - differentiated for College Prep

and Honors levels.


Suggested

Learning

Activities

● Vectors in the Plane

● Vectors and Dot Products

● Modeling with Vectors

● Trigonometric Form of a Complex Number

40

Unit 6

Systems and Matrices

Suggested Time

Frame

6 Days


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.



Established Goals:










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.

41

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.

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.

42


How can matrices be used to solve

systems of linear equations?

How can systems of equations be used to

represent real life situations?



Matrices can be created from a linear

system and reduced to find the solution to

the system.

Systems of equations can represent many

real life situations, such as finance and

chemistry, which require multiple

variables.

Knowledge:


● 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:


● 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).

43



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


44



21st Century Themes



● T – taught

● A – assessed




Income and Careers ET CRP2. Apply appropriate academic








decisions.


innovation.










management.



X Career Exploration ET CRP11. Use technology to enhance

productivity.



competence.


Human Resources Analyst

Statistician

Engineer: Aerospace, Electrical, Nuclear, Environmental, Chemical

Forest Conservationist

Computer Operator

Funeral Director

45



R.1 Read closely to determine what the text say as explicitly and to make logical inferences



W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid


W.2 Write informative/explanatory texts to examine and convey complex ideas and















46

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






47



Systems and Matrices – No performance

task is done for this unit as it is a review unit

from Algebra I and Algebra II. This unit is

typically just a quick review unit in order for

students to be comfortable with the next 2

units.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment



Unit Test - Differentiated for College Prep

and Honors levels.


Instructional

Strategies

Descriptions

Suggested

Learning

Activities

● 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.

48

Unit 7

Conics

Suggested Time

Frame

5 Days


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.












Established Goals:

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.

49


How can various conic sections be created

from the same figure?



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:


● The various conic shapes that can be

created.

● The standard equations of each of the

conic sections.

● How to write an equation in standard form

for each conic section.

Skills:


● Write the equation of a circle given its

center and radius.

● 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.

50



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


51



21st Century Themes



● T – taught

● A – assessed




Income and Careers ET CRP2. Apply appropriate academic








decisions.


innovation.







Exploration,

and Preparation



management.

X Career Awareness ET CRP10. Plan education and career



productivity.



competence.


Astronomer

Chemist

Physicist

Statistician

Cryptologist

52























53

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






54



Conic Sections Project

Students will create a picture using a

minimum of 4 conic sections using a

graphing application, Desmos.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment



Unit Test- Differentiated for College Prep

and Honors levels.


Instructional

Strategies

Descriptions

Suggested

Learning

Activities

● Graphs of Equations (Circles)

● Introduction to Conics: Parabolas

● Ellipses

● Hyperbolas

55

Unit 8

Sequences, Series, and Limits

Suggested Time

Frame



In this culminating unit, students will explore the concepts of sequences and series. Students will

learn about various concepts that will be needed to move forward into Calculus. Students in the

Honors class will also explore the concept of limits.












Established Goals:

Standards to be covered…

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).

56

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.


How can sequences and series be used to

model real life phenomena?

How do limits help us to study

mathematical functions? (Honors Only)



How sequences and series are used to

model and explain real life phenomena.

How limits help us to study mathematical

functions. (Honors Only)

Knowledge:


● 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:


● 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).

57



Self-Awareness





Self-Management


behaviors




Social Awareness





differ


setting



skill




Relationship Skills





constructive ways


58



21st Century Themes



● T – taught

● A – assessed




Income and Careers ETA CRP2. Apply appropriate academic








decisions.


innovation.

Civic Financial Responsibility CRP7. Employ valid and reliable






Exploration,

and Preparation

ET CRP9. Model integrity, ethical


management.




productivity.



competence.


Biomedical Engineer

Nuclear Engineer

Computer Software Engineer

Farmers, Ranchers, and Agricultural Manager

Financial Manager

Budget Analyst

59























60

Student Resources

Primary Source

Readings




Teacher Resources

Texts:








2014. Print.



Videos:

Teacher created

www.khanacademy.com






61



Sequences, Series and Limits – Typically by

the end of this unit there is not enough time

for a performance task. In the honors section

especially since we go over limits in

preparation for calculus. We currently do not

have a performance task for this unit as we

have never had time for one.

Other Evidence:

Pre-Assessments


Exit Slip

Self-Assessment



Unit Test- Differentiated for College Prep

and Honors levels.


Suggested

Learning

Activities

● 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)

62

Accommodations and Modifications

Below please find a list of suggestions for accommodations and modifications to meet the

diverse needs of our students. Teachers should consider this a resource and understand that

they are not limited to the recommendations included below.

An accommodation changes HOW a student learns; the change needed does not alter the

grade-level standard. A modification changes WHAT a student learns; the change alters the

grade-level expectation.

Special Education and 504 Plans All modifications and accommodations must be specific to each individual child’s IEP

(Individualized Educational Plan) or 504 Plan.

Pre-teach or preview vocabulary

Repeat or reword directions

Have students repeat directions

Use of small group instruction

Pair visual prompts with verbal presentations

Ask students to restate information, directions, and assignments

Repetition and time for additional practice

Model skills/techniques to be mastered

Extended time to complete task/assignment/work

Provide a copy of class notes

Strategic seating (with a purpose - eg. less distraction)

Flexible seating

Repetition and additional practice

Use of manipulatives

Use of assistive technology (as appropriate)

Assign a peer buddy

Emphasize key words or critical information by highlighting

Use of graphic organizers

Scaffold with prompts for sentence starters

Check for understanding with more frequency

Provide oral reminders and check student work during independent practice

Chunk the assignment - broken up into smaller units, work submitted in phases

Encourage student to proofread assignments and tests

Provide regular home/school communication

Teacher checks student planner

Provide student with clear expectations in writing and grading criteria for assignments

(rubrics)

Testing Accommodations:

Students should receive all testing accommodations for Benchmark assessments that they

receive for State testing.

63

Setting: Alternate setting for assessments, small groups, screens to block distractions

Presentation: large print, test readers, use of audio, fewer questions on each page

Response: answer verbally, use large block answer sheet, speech-to-text dictation,

accept short answers

Allow for retakes

Provide study guides

Use of reference aids such as glossary, multiplication tables, calculator

Choice of test format (multiple-choice, essay, true-false)

Alternate ways to evaluate (projects or oral presentations instead of written tests)

Open-book or open-note tests

English Language Learners: All modifications and accommodations should be specific to each individual child’s LEP level

as determined by the WIDA screening or ACCESS, utilizing the WIDA Can Do Descriptors.

Pre-teach or preview vocabulary

Repeat or reword directions

Have students repeat directions

Use of small group instruction

Scaffold language based on their Can Do Descriptors

Alter materials and requirements according to Can Do Descriptors

Adjust number of paragraphs or length of writing according to their Can Do Descriptor

TPR (Total Physical Response-Sheltered Instruction strategy) Demonstrate concepts

through multi-sensory forms such as with body language, intonation


Repetition and additional practice

Model skills and techniques to be mastered

Native Language translation (peer, assistive technology, bilingual dictionary)

Emphasize key words or critical information by highlighting

Use of graphic organizers

Scaffold with prompts for sentence starters

Check for understanding with more frequency

Use of self-assessment rubrics

Increase one-on-one conferencing; frequent check ins

Use study guide to organize materials

Make vocabulary words available in a student created vocabulary notebook, vocabulary

bank, Word Wall, or vocabulary ring

Extended time

Select text complexity and tiered vocabulary according to Can Do Descriptors

Projects completed individually or with partners

Use online dictionary that includes images for words:

http://visual.merriamwebster.com/.

Use online translator to assist students with pronunciation:

http://visual.merriamwebster.com/

64

http://www.reverso.net/text_translation.aspx?lang=EN.

Students at Risk of Failure:

Use of self-assessment rubrics for check-in


Ask students to restate information and/or directions

Opportunity for repetition and additional practice

Model skills/techniques to be mastered

Extended time

Provide copy of class notes

Strategic seating with a purpose

Provide students opportunity to make corrections and/or explain their answers

Support organizational skills

Check daily planner

Encourage student to proofread work

Assign a peer buddy

Build on students’ strengths based on Multiple Intelligences: Linguistic (verbal); Logical

(reasoning); Musical/Rhythmic; Intrapersonal Intelligence (understanding of self); Visual

Spatial Intelligence; Interpersonal Intelligence (the ability to interact with others

effectively); Kinesthetic (bodily); Naturalist Intelligence; and Learning Styles: Visual;

Auditory; Tactile; Kinesthetic; Verbal

High Achieving:

Extension Activities

Allow for student choice from a menu of differentiated outcomes; choices grouped by

complexity of thinking skills; variety of options enable students to work in the mode that

most interests them

Allow students to pursue independent projects based on their individual interests

Provide enrichment activities that include more complex material

Allow opportunities for peer collaboration and team-teaching

Set individual goals

Conduct research and provide presentation of appropriate topics

Provide students opportunity to design surveys to generate and analyze data to be used in

discussion

Allow students to move through the assignment at their own pace (as appropriate)

Strategies to Differentiate to Meet the Needs of a Diverse Learning Population

Vocabulary Sorts-students engage with the vocabulary word by sorting into groups of

similar/different rather than memorizing definitions

Provide “Realia” (real life objects to relate to the five senses) and ask questions relating

to the senses

http://www.reverso.net/text_translation.aspx?lang=EN

65

Role Play-students create or participate in role playing situations or Reader’s Theater

Moving Circle-an inside and outside circle partner and discuss, circles moves to new

partner (Refer to Kagan Differentiated Strategies)

Brainstorm Carousel-Large Post Its around the room, group moves in a carousel to

music. Group discusses topic and responses on paper. Groups rotate twice to see

comments of others. (Refer to Kagan Differentiated Strategies)

Gallery Walk-Objects, books, or student work is displayed. Students examine artifacts

and rotate.

Chunking-chunk reading, tests, questions, homework, etc to focus on particular elements.

Think Pair Share Write

Think Talk Write

Think Pair Share

Note-taking -can be done through words, pictures, phrases, and sentences depending on

level

KWL (Know, Want to Know, Learned)/KWHL(Know, What to Know, How Will I

Learn, learned)/KWLS (Know, Want to Know, Learned, Still Want to Know) /KWLQ

(Know, What to Know, Learned, Questions I Still Have) Charts

Corners Cooperative Learning Strategy:

http://cooperativelearningstrategies.pbworks.com/w/page/28234420/Corners.

Circle Map strategy- place the main topic in a small circle and add student ideas in a

bigger circle around the topic. Students may use their native language with peers to

brainstorm.

Flexible grouping -as a whole class, a small group, or with a partner, temporary groups

are created: http://www.teachhub.com/flexible-grouping-differentiated-instruction-

strategy.

Jigsaw Activities -cooperative learning in a group, each group member is responsible for

becoming an "expert" on one section of the assigned material and then "teaching" it to

the other members of the team: http://www.adlit.org/strategies/22371/.

http://cooperativelearningstrategies.pbworks.com/w/page/28234420/Corners

http://www.teachhub.com/flexible-grouping-differentiated-instruction-strategy

http://www.teachhub.com/flexible-grouping-differentiated-instruction-strategy

http://www.adlit.org/strategies/22371/

66

College-Prep Pre-Calculus 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


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

67

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

68

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


44 MIDTERM EXAMS

89 FINAL EXAMS

45 90

69

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


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

70

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

71

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



44 MIDTERM EXAMS

89 FINAL EXAMS

45 90


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Documents

Pre-Calculus · HIGH SCHOOL ADMINISTRATION Jennifer C. Joseph, Principal Titania M. Hawkins, Ed.D., ... Sequences, Series, and Limits ... This course contains the background information