Bound Brook Public School District High School PreCalculus Curriculum

2007-2008

Dr. Edward Hoffman, Superintendent

2006-2007 Board of Education Members

Martin Gleason, President

Steve Clouser, Vice – President

Peter Allen – South Bound Brook Representative

Hal Dietrich

Terrence Hoben

Robyn Ann Jeskie

Carol Ann Koupiaris

Robert Murray

Kenneth Sella

Rae Siebel

Carole Deddy, Board Secretary

Administration

Mr. Dan Gallagher, Principal Mr. Mario Bernardo, Vice Principal Mr. Robert Nixon, Vice Principal

Ms. Dianne Ianniello, Director of Pupil Services

Curriculum Revision By:

Richard R. Selander, Mathematics Teacher DISTRICT EDUCATIONAL PHILOSOPHY MISSION STATEMENT Bound Brook High School is a supportive multicultural community that provides an innovative and academically challenging educational program while offering a variety of extra-curricular and social opportunities that encourage life-long learning and citizenship. VISION STATEMENT

The vision of the Bound Brook Public School community is to provide a comprehensive educational environment that will:

• Develop tolerant citizens • Prepare graduates for their educational and vocational choices in life • Develop life long learners • Allow students to be users of technology

• Develop finders and users of data • Provide educational opportunities both within and outside the classroom • Challenge students educationally • Provide a positive learning environment • Make students aware of their strengths and weaknesses • Recognize student successes.

BELIEFS We believe that the Bound Brook community will provide a supportive environment for academic and personal growth that will:

• Foster independence, self-reliance, and self-worth

• Prepare students for a diverse and ever-changing society. • Encourage the development of programs that promote good character in the school community.

• Enable everyone to feel physically, emotionally, and intellectually safe (free to verbally express opinions and ideas). • Value all for their unique qualities.

• Encourage all to pursue their individual goals in a challenging, supportive, and safe environment. • Provide a positive learning environment where mutual respect and opportunity exist for the exchange of ideas among teachers,

students, parents, and community members. • Deliver an instructional program that encompasses a variety of learning styles, interests, and levels of readiness for all students

in all disciplines • Demonstrate honesty, integrity, and trustworthiness in academic pursuits and social interactions.

• Respect all people and cultures • Encourage participation in one’s community as a social, civic, and personal responsibility.

• Promote learning as a life-long process.

ACADEMIC GOALS/EXPECTATION LEARNING GOALS

1. Students are able to use basic communication and mathematics skills for purposes and situations they will encounter throughout their lives. 2. Students shall develop their abilities to apply core concepts and principles from mathematics, the sciences, the arts, the humanities, social studies, practical living studies, and vocational studies to what they will encounter throughout their lives. 3. Students shall develop their abilities to become self-sufficient individuals. 4. Students shall develop their abilities to become responsible members of a family, work group, or community, including demonstrating effectiveness in community service. 5. Students shall develop their abilities to think and solve problems in school situations and in a variety of situations they will encounter in life. 6. Students shall develop their abilities to connect and integrate experiences and new knowledge from all subject matter fields with what they have previously learned and build on past learning experiences to acquire new information through various media sources.

Academic Expectations

• Students will use reference tools such as dictionaries, almanacs, encyclopedias, and computer reference programs and research tools such as interviews and surveys to find the information they need to meet specific demands, explore interests, or solve specific problems.

• Students will make sense of the variety of materials they read, observe, and hear.

• Students will use mathematical concepts and procedures to communicate, reason, and solve problems. • Students will organize and classify information through an understanding of terms defined in this course

• Students will use appropriate conventions and styles in their written work to communicate ideas and information to different

audiences and for different purposes. • Students’ oral communication will incorporate appropriate forms, conventions, and styles to communicate ideas and

information to different audiences and different purposes.

• Students will use of technology to collect, organize, and communicate information and ideas. • Students will understand scientific ways of thinking and working and use those methods to solve real-life problems.

• Students will identify, analyze, and use patterns such as cycles and trends to understand past and present events and predict

possible future events. • Students will identify and analyze systems and understand how their components work together or affect each other.

• Students will use and scientific models and scales to explain the organization and functioning of living and non-living entities

and predict other characteristics that might be observed.

• Students will understand that under certain conditions nature tends to remain the same or move toward a balance.

• Students will understand how living and nonliving things change over time and the factors that influence the changes.

• Students will understand number concepts and use numbers appropriately and accurately.

• Students will understand various mathematical procedures and use them appropriately and accurately.

• Students will understand space and dimensionality concepts and use them appropriately and accurately.

• Students will understand measurement concepts and use measurement appropriately and accurately.

• Students will understand mathematical change concepts and use them appropriately and accurately. • Students will understand mathematical structure concepts including the properties and logic of various mathematical systems.

• Students will understand probability and use statistics appropriately.

• Students will understand the democratic principles of justice, equality, responsibility, and freedom and apply them to real-life

situations.

• Students will accurately describe various forms of government and analyze issues that relate to the rights and responsibilities

of citizens in a democracy.

• Students will observe, analyze, and interpret human behaviors, social groupings, and institutions to better understand people and the relationships among individuals and among groups.

• Students will interact effectively and work cooperatively with the many ethnic and cultural groups of our nation and world.

• Students will understand economic principles and are able to make economic decisions that have consequences in daily living.

• Students will understand, analyze, and interpret historical events, conditions, trends, and issues to develop historical

perspective. • Students will recognize and understand the relationship between people and geography and apply their knowledge in real-life

situations.

• Students will present works of art convey a point of view. • Students will analyze and reflect on their own and others' artistic products and performances using accepted standards.

• Students will gain knowledge of major works of art, music, and literature and appreciate creativity and the contributions of the

arts and humanities.

• In the products they make and the performances they present, students will show that they understand how time, place, and society influence the Arts and Humanities such as languages, literature, and history.

• Students will demonstrate skills that promote individual well-being and healthy family relationships.

• Students will evaluate consumer products and services and make effective consumer decisions.

• Students will demonstrate the knowledge and skills they need to remain physically healthy and to accept responsibility for their

own physical well-being.

• Students will demonstrate strategies for becoming and remaining mentally and emotionally healthy.

• Students will demonstrate the skills to evaluate and use services and expectation resources available in their community.

• Students will perform physical movement skills effectively in a variety of settings.

• Students will demonstrate knowledge and skills that promote physical activity and involvement in physical activity throughout their lives.

• Students will use strategies for choosing and preparing for a career.

• Students will demonstrate skills and work habits that lead to success in future schooling and work.

• Students will demonstrate skills such as interviewing, writing resumes, and completing applications that are needed to be

accepted into college or other postsecondary training or to get a job.

• Students will use critical thinking skills such as analyzing, prioritizing, categorizing, evaluating, and comparing to solve a variety of problems in real-life situations.

• Students will use creative thinking skills to develop or invent novel, constructive ideas or products.

• Students will organize information to develop or change their understanding of a concept. • Students will use a decision-making process to make informed decisions. • Students will use problem-solving processes to develop solutions to complex problems.

• Students will connect knowledge and experiences from different subject areas.

• Students will use scaffolding to acquire new knowledge, develop new skills, or interpret new experiences. • Students will expand their understanding by making connections to new paradigms, skills, and experiences

PRECALCULUS COURSE DESCRIPTION This course covers all of the necessary topics of a PreCalculus course. Students coming into the course should have completed one year of geometry and two years of algebra. This class is designed for students who are either honors students or are preparing for college, as it will give them a solid foundation and knowledge of what they will study in college mathematics courses. It will also help students prepare for college entrance exams such as the SAT or ACT.

PREREQUISITES Completion of Algebra II or IMP III. OUTCOMES Participation in the district’s mathematics programs will enable students to develop mathematical proficiency. This program is designed to help students gain an ability to use and understand mathematics in a variety of contexts in order to prepare them to succeed both socially and academically. NEW JERSEY CORE CURRICULUM CONTENT STANDARDS AND STRANDS FOR MATHEMATICS There are five standards altogether, each of which has a number of lettered strands. These standards, and their associated strands, are enumerated below: 4.1. Number and Numerical Operations A. Number Sense B. Numerical Operations C. Estimation 4.2. Geometry and Measurement A. Geometric Properties B. Transforming Shapes C. Coordinate Geometry D. Units of Measurement E. Measuring Geometric Objects

4.3. Patterns and Algebra A. Patterns and Relationships B. Functions C. Modeling D. Procedures 4.4. Data Analysis, Probability, and Discrete Mathematics A. Data Analysis (Statistics) B. Probability C. Discrete Mathematics--Systematic Listing and Counting D. Discrete Mathematics--Vertex-Edge Graphs and Algorithms 4.5. Mathematical Processes A. Problem Solving B. Communication C. Connections D. Reasoning E. Representations F. Technology

The first four of these "standards" also serve as what have been called "content clusters" in the current state assessments; the lettered strands replace what have been called "macros" in the directories of test specifications. The fifth standard will continue to provide the "power base" of the assessments. It is anticipated that the expectations presented here will be used as the basis for test specifications for the next version of the statewide assessments.

WRITTEN CURRICULUM Instructional Methods and Strategies This course will be taught using a variety of instructional methods. Students will be taught directly via an auditory and visual approach through lecture and note-taking. Indirect instruction via an auditory and visual approach will be presented through the use of multimedia presentations as well as technological presentations. Teachers will utilize technology and manipulatives to assist students who require a more kinesthetic teaching approach for success. Students will be given homework and projects so they can work at home independently. Students will not only be expected to work individually, but cooperatively as well. Students will be expected to interact with one another and work cooperatively in groups, as well as create their own group multimedia presentations. Group oral/visual representations will also be required of students during the school year. Academic Expectations All students should be able to work both independently and cooperatively to develop their mathematical skills. Students should be able to prepare for standardized tests by focusing on expressing mathematical ideas and concepts clearly. Students should also become mathematically proficient by mastering a variety of problem-solving strategies. Finally, students should be able to present their learnings via the use of oral/visual presentations using classroom technology. Student Assessment Students will be assessed both formally and informally. Informally, teachers will note how students have comprehended the material via classroom and discussions and activities. Teachers will informally assess students orally by asking students questions during lectures, as well as visually by looking over the students’ classwork. Formally, teachers will assess students via homework, quizzes and tests. Homework will be checked regularly, and the homework average will account for 20% of each marking period grade. Quizzes, projects, and oral/visual presentations will be given at different intervals during each chapter of the book, and the quiz/project/presentation average will account for 30% of each marking period grade. Finally, tests will be given at the end of every chapter, and the test average will account for the remaining 50% of each marking period grade. The midterm and final exams will each count for 10% of the final grade for the course.

District Grading Philosophy and Policy The Board of Education recognizes that a system of measuring, recording, and reporting the achievements of individual pupils is important to the continuing process of learning. The Board, therefore directs the instructional program of this school district include a system of grading that measures progress toward the New Jersey Core Curriculum Content Standard and the educational goals of the district. Pupils shall be informed at the outset of any course of study of the behaviors and achievements that are expected of them and shall be kept informed of their progress during the course of study. As a rule, grading should reward pupils for positive efforts and minimize failure, and pupils should be encouraged to evaluate their own achievements. The Superintendent shall develop and continually review in consultation with teaching staff members, parent(s) or legal guardian(s), and pupils, a grading program appropriate to the course of study and maturity of pupils. The final decision on any contested grade will be the responsibility of the Principal. A pupil classified as disabled will be graded in accordance with his/her Individualized Educational Program (IEP) or the Section 504 Plan. Suggested Materials and Textbooks Notebook (to keep notes, homework, quizzes, and tests in) Writing utensil TI-83Plus Graphing Calculator Honors Textbook (Redlin, Lothar, James Stewart, and Saleem Watson. Precalculus: Mathematics for Calculus. 3rd ed. Pacific

Grove, CA: Brooks/Cole Publishing Company, 1998.) CP Textbook (Hostetler, Robert P., and Roland E. Larson. Precalculus. 3rd ed. Lexington, Ma: D.C. Heath and Company, 1993.)

COURSE MAP: PRECALCULUS

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-Curricular Support

Activities/ Experiences

4.1A,. 4.1B, 4.2A, 4.2C, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5A, 4.5C, 4.5D,

4.5E, 4.5F

SWBAT review the topics they covered in

Algebra II. These topics include the following

subjects: sets of numbers, real numbers

and operations, algebraic expressions, properties of numbers, properties of exponents

and radicals, solving equations and

inequalities, writing equations and

inequalities, using equations and

inequalities, graphing equations and

inequalities, testing for symmetry, rational

expressions, scientific notation, using the

graphing calculator, and linear equations. They

will learn to graph a circle, and be able to

write the equation of a circle in standard form.

Students will review what they

covered in Algebra II to

prepare them for the material to

be presented to them in

PreCalculus.

What are the different sets of numbers, and how do

we distinguish among them? How do we add, subtract, multiply, and

divide real numbers, and scientific notation? What are the different numerical properties, and how do we

use them? What are exponents and radicals,

and what are the different rules that apply to them? What are equations and inequalities, how do write them, how do we graph them, and how do we

solve them? How do we use equations to solve

word problems? How do we perform the basic operations on rational

expressions? What is the Cartesian Coordinate

Plane, and how can we use it to graph lines,

curves, and circles? What are the main parts of the

graph of an equation, and how do we test an

1) Summer Assignment on concepts covered in Algebra II. 2) Test on concepts

covered in Summer

Assignment.

1) Science: Scientific

Notation and its uses.

2) Language Arts: Being able

to read and properly interpret a word problem.

3) Physical Education/Health: Using quadratic

functions to model scientific,

physical, or nutritional situations.

equation for symmetry? How can we use a

graphing calculator to view the graphs of equations?

What are the main characteristics of linear

equations?

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.2A, 4.2B, 4.2C, 4.3A, 4.3B, 4.3C, 4.3D, 4.5A, 4.5C, 4.5D,

4.5E, 4.5F

SWBAT learn that a function is a subset of

equations, and that they are treated the same as

equations. They will learn how to graph

functions, be able to define and explain the

terms domain and range, and find the critical points of any graph. They will

continue to see the correlation between a function and the graph

that represents it, and be able to see how changing

one will change the other. Students will revisit the topic of

variation, and be able to apply it to different word problems. Students will

be introduced to the concept of one-to-one

functions, and how one must have a one-to-one function in order to be able to find an inverse

function.

Students will learn how to

logically apply their

mathematical knowledge to

situations involving linear relationships.

What is a function? What are different types of

functions, and how are they used? What are the

domain and range of a function, and what does it stand for? What are the

direct and inverse variation equations, and where are

they used outside the classroom? What happens to a graph when we change its algebraic equation, and vice-versa? How do we

find the extreme values of functions? How are

combinations of functions solved? What are one-to-one functions, and how do

we find and graph their inverses?

1) Quiz on functions, graphs of functions, applied

functions, and transformations

of functions. 2) Quiz on

extreme values of functions, combining

functions, and one-to-one

functions and their inverses.

3) Test on chapter

concepts mentioned

above.

1) Science or Social

Studies: Students will

be able to take any situation

involving a starting point

and a constant

slope (such as spending money or a

increasing or declining

population or growth of

bacteria), and be able to

write a linear equation to represent

that situation.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.2A, 4.2C, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5C, 4.5D, 4.5E,

4.5F

SWBAT continue to learn polynomials and

polynomial operations. They will solve polynomial equations, and be able to find the critical points of

the graph of any polynomial. They will be

able to find the zeroes/roots of a

polynomial not only by using the graphing calculator, but also

algebraically by using a set of different rules and theorems. Students will review complex numbers

and complex number operations, as well as

rational expressions and rational expression

operations. They will also review how to find the

asymptotes of a polynomial, and how they

affect that polynomial's graph.

Students will demonstrate the

mathematical thinking and processes

required of them in the fields of mathematics and science. Students will learn what it means to "do

Algebra" as they learn to isolate and solve for

variables.

What are polynomials, and how are they graphed? How

do we add, subtract, multiply, and divide

polynomials? How do we factor polynomials? How do

we solve an equation by factoring, and can you solve word problems that involve

solving equations by factoring? What are the

critical points of the graph of a polynomial, and how do

we find them? What are the zeroes/roots of a polynomial,

and how do we find them algebraically and

graphically? What are complex numbers, and how do we perform the four basic

operations on this set of numbers? What is a rational expression, and how do we simplify one? How do we

add, subtract, multiply, and divide rational expressions? What are the asymptotes of an equation, and what do

they represent?

1) Quiz on polynomial functions, graphs of

polynomial functions, and real zeros of

polynomials. 2) Quiz on

complex numbers, complex

roots, The Fundamental Theorem of Algebra, and

rational functions. 3) Test on

chapter concepts

mentioned above.

1) Social Studies:

Finding the constant of variation or

finding different

values given different

populational or

economical situations that

involve variation.

2) Science: Being able to isolate and solve for a variable in different scientific formulas.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.1C, 4.2A, 4.2B, 4.2C, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5A, 4.5C, 4.5D, 4.5E,

4.5F

SWBAT learn about exponential equations and how to graph them. They will also learn about the

natural exponential equation, how to graph it,

and how it is used to determine compound

interest and exponential growth of populations. Students will also be

introduced to logarithmic equations, how to graph

them, and the three basic laws of logarithms. They

will also be able to see the relationship between

exponential and logarithmic equations, and

be able to take an equation in one form and rewrite it using the other. This will enable them to solve for a variable in

different equations. They will also be able to use the fact that exponential and logarithmic functions are inverses in order to solve more difficult equations. Students will also apply

the rules of transformations of graphs

Students will learn different ways to invest

their money, and how to become more financially

responsible.

What are exponential functions, and how are they

graphed? What is the natural exponential function, how is it graphed, and where

is it applied outside of the classroom? What are

logarithmic functions, how are they solved, and how

are they graphed? What are the different laws that

govern logarithmic functions? How are

exponential and logarithmic functions related to one

another? How do we solve exponential and logarithmic

equations?

1) Quiz on exponential functions, the natural exponential

function, and logarithmic functions. 2) Quiz on

laws of logarithms, exponential equations, logarithmic equations,

and applications

of exponential

and logarithmic functions. 3) Test on

chapter concepts

mentioned above.

1) Social Studies/

Economics: Computing the interest

gained using different

investment strategies. 2) Science: Finding the

half-life given a rate of

decay for any substance.

on both exponential and logarithmic graphs and

equations.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.1C, 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5E, 4.5F

SWBAT review trigonometric functions in terms of the unit circle.

Students will learn different identities and

relationships among the trigonometric functions.

They will also learn how to graph trigonometric functions and their

transformations, and find the distinctive points and behavior of each type of

function. Students will be able to use the graphing

calculator to evaluate and graph these functions.

Given a situation involving

trigonometric relationships,

students will be able to create an

equation or formula to match

the situation.

What is the unit circle, and how do we find the

trigonometric functions for an angle in the unit circle?

What is the domain and range of the basic

trigonometric functions? What are some properties

and fundamental identities of trigonometric functions?

How can we find trigonometric function values using a graphing calculator?

How do we graph trigonometric functions and their transformations? What

are some relationships among the trigonometric

functions?

1) Quiz on the Unit

Circle and trigonometric functions of

real numbers. 2) Quiz on

trigonometric graphs.

3) Test on chapter

concepts mentioned

above.

1) Science: Using

trigonometry to solve

problems in physics involving

finding the distance

between two objects given the distance between one of the objects

and a third object, and the angle

from one of the objects to

the third.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.1C, 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5A, 4.5C, 4.5D, 4.5E, 4.5F

SWBAT see the relationship between

degrees and radians, and be able to convert

between the two. They will be able to take

information about the measure of an interior

angle of a circle and be able to find certain pieces of information regarding the section of the circle

that interior angle creates. They will explore

trigonometric functions in terms of right triangles.

Students will learn different identities and

relationships among the trigonometric functions.

They will also learn about the Law of Sines and Law of Cosines, and be able to use this information to find the side lengths and area

of any triangle.

Students will be able to apply a

given or created trigonometric equation or

formula in order to make

discoveries.

How do we convert from degrees to radians? How do

we find the length of a circular arc and the area of a circular sector? How do we

find the trigonometric functions for an angle of a right triangle? Given an

acute angle measure of a right triangle, how can we

find the lengths of the sides of that triangle? What are some of the fundamental trigonometric identities?

What are the Law of Sines and Law of Cosines and

how can they help us find the dimensions of any

triangle?

1) Quiz on angle

measure, trigonometry

of right triangles,

and trigonometric functions of

angles. 2) Quiz on

Law of Sines and Law of Cosines.

3) Test on chapter

concepts mentioned

above.

1) Science: Using

trigonometry to solve

problems in physics that

involve vectors, such

as motion and force.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-Curricular

Support Activities/

Experiences

4.1A, 4.1B, 4.1C, 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.3A, 4.3B, 4.3C, 4.3D,

4.5E, 4.5F

SWBAT further explore trigonometric identities, relationships, and laws.

Students will learn to simplify trigonometric

identities. They will learn to prove identities, step-by-step, from beginning

to end. Students will also review inverse

trigonometric functions and how to graph them.

They will continue learning how to solve

equations that mix both algebraic and

trigonometric concepts. Students will learn to solve trigonometric

equations. They will be able to write a complex

number using trigonometric notation, use this new form to

perform the four basic operations and further investigate complex

numbers. Students will be introduced to the

concept of vectors, how to manipulate them, and

why they are an important mathematical concept.

Students will demonstrate the

mathematical thinking and processes

required of them in the fields of mathematics and science.

What are some more fundamental trigonometric

identities, and how can they help us find trigonometric function values? How do we simplify trigonometric expressions? How do we

prove trigonometric identities? What are the trigonometric functions of

sums and differences, and what identities describe

them? What are the double-angle and half-angle

identities and product-to-sum and sum-to-product formulas, and how do we

use them? How do we find the inverse of a

trigonometric function, and how do we graph it? How do we solve trigonometric equations? How can we

algebraically manipulate an equation that contains

trigonometric functions? How do we write complex

numbers using trigonometric notation?

How can we now multiply, divide, and apply powers to

complex numbers? How can we find the roots of

1) Quiz on trigonometric

identities, addition and subtraction formulas, double-

angle, half-angle, and

product-sum formulas. 2) Quiz on

inverse trigonometric

functions, trigonometric

equations, trigonometric

form of complex numbers,

DeMoivre’s Theorem,

and vectors. 3) Test on

chapter concepts

mentioned above.

1) Science: Using different trigonometric identities and

relationships to simplify scientific

problems that involve angles and vectors.

2) Social Studies/

Technology: Research a

famous mathematician,

and then prepare and

present a PowerPoint

presentation to the class.

complex numbers? What are vectors, and where are they applied outside of the

classroom?

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.1C, 4.2A, 4.2C, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5C, 4.5D,

4.5E, 4.5F

SWBAT review what they learned in Algebra II of

systems of equations and inequalities. They will be introduced to the concept of matrices, and how they can help solve a system of equations. They will further explore matrices algebraically. Students

will also learn how to take one large fraction and split it up into rational

factors known as partial fractions.

Given a situation involving

mathematical relationships,

students will be able to create an

equation, inequality, or

formula to match the situation,

and then apply that equation, inequality, or

formula to make discoveries.

What is a system of equations/inequalities, and

how do we solve them graphically and

algebraically? What kinds of system of equations are

there? How does a graphing calculator work,

and can you use it to solve a system of equations? What are matrices, and how can

we use them to solve a system of equations? What

is the algebra behind matrices? How can we find

the inverse of a matrix? How can we solve matrix equations? What is the

determinant of a matrix, and how can we use it to find the

solution of a system of equations? How can we split a single fraction into

partial fractions?

1) Quiz on systems of equations,

pairs of lines, and systems

of linear equations. 2) Quiz on the algebra of matrices, inverses of matrices,

matrix equations,

determinants, Cramer’s

Rule, systems of inequalities, and partial fractions. 3) Test on

chapter concepts

mentioned above.

1) Social Studies/

Economics/ Technology:

Using a graphing

calculator or computer software,

students will be able to

take a situation involving selling

multiple items at the same time (with

restrictions on the total number of items that

can be sold), and be able to determine

the best number of

each item to sell to make the biggest

profit. Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.3A, 4.3B, 4.3C, 4.3D, 4.4A, 4.5C, 4.5E, 4.5F

SWBAT learn about these conic sections: parabolas, ellipses, and hyperbolas.

They will learn how to recognize the equation of a conic, how to graph it,

and what the major points of each graph are. They

will also learn to transform the graph of a conic.

Students will learn about polar coordinates, how to graph them, and how they

are used in equations. They will learn how to write polar equations. They will learn about

parametric equations, how to graph them, and how they are used to rewrite

polar equations.

Students will also continue to

explore the relationship

between Algebra and Geometry. Students will

also be able to see how

different objects that are circular and elliptical in

shape are created by

understanding their equations.

What is a parabola, and what are its major points?

What is an ellipse, and what are its major points? What

is a hyperbola, and what are its major points? How do we shift and transform the graph of a conic? What are polar coordinates, and how are

they related to trigonometry? How do we graph polar coordinates and polar

equations on paper and on the graphing calculator?

How do we write the equation for a conic using polar coordinates? What are parametric equations,

how do we graph them, and how are they used? How do

we put polar equations in parametric form?

1) Quiz on parabolas, ellipses,

hyperbolas, and shifted

conics. 2) Quiz on rotation of axes, polar

coordinates, polar

equations of conics, and parametric equations. 3) Test on

chapter concepts

mentioned above.

1) Science: Using

second-degree

equations to model

different scientific

situations. Also, using a

graphing calculator or

computer software,

students will be able to

take multiple different scientific situations

involving the same number

of scientific variables, and find

when each situation has

an equal amount of

each variable.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-

Curricular Support

Activities/ Experiences

4.1A, 4.1B, 4.1C, 4.3A, 4.3B, 4.3D, 4.4A, 4.4C, 4.5A, 4.5C, 4.5D, 4.5E,

4.5F

SWBAT build and recognize arithmetic and

geometric sequences. They will be able to find

different sums of a series through the use of

summation notation. Students will be introduced to the

important investment strategy of annuities, how they work, and how they grow and are calculated over time. An important buying strategy they will

be introduced to is that of installment buying, where students will learn how to

calculate monthly payments. Students will

learn about how to attempt proving an identity

through the use of induction. They will also

be introduced to both Pascal's Triangle and the Binomial Theorem, and how they are related to

each other.

Students will become more

adept in finding patterns given a set of data, and

be apply to apply those patterns to

make future predictions.

What a sequence? How can we find the sum of a certain number of terms of a given sequence? What is sigma

notation, and how is it used? What is the difference

between arithmetic and geometric sequences, and

how are they used? How do we find the partial sums of

these sequences, as well as the sum of an infinite

geometric series? What is an annuity, and how do we

find the amount of an annuity? What is installment

buying, and how can you calculate monthly

payments? What is the Principle of Mathematical Induction, and how does it

help us prove mathematical conjectures? What is the Binomial Theorem, how does it relate to Pascal's

Triangle, and how do we use it to expand a binomial?

1) Quiz on sequences, summation notation, arithmetic

sequences, and

geometric sequences. 2) Quiz on

annuities and installment

buying, mathematical

induction, and the Binomial Theorem. 3) Test on

chapter concepts

mentioned above.

1) Social Studies: Using

patterns among sets

of economical or

populational data to make predictions about future

results. 2) Science: Finding a pattern or sequence

among sets of biological, chemical, or physical data

in order to make

predictions about future

results.

Unit Reflections:

NJCCCS/Content Content Topics/Key Skills

Enduring Understandings Essential Questions Assessment

Connected Co-Curricular

Support Activities/

Experiences

4.1A, 4.1B, 4.1C, 4.4B, 4.5A, 4.5F

SWBAT refresh their probability skills. They

will find the probability of individual as well as

multiple events, through use of the Fundamental

Counting Principle, permutations,

combinations, and factorials. Students will

also learn about expected value, and its applications in the world

of games.

Students will become more

adept at solving logical problems

that involves discovering and utilizing patterns, such as games and the stock

market.

What is the Fundamental Counting Principle, and

how is it used in probability situations? How do we

perform permutations and combinations? How do we

find the probability of a single event or multiple

events? What is expected value, and how is it used in

probability situations?

1) Quiz on counting

principles, permutations,

and combinations.

2) Quiz on probability and

expected value.

3) Test on chapter

concepts mentioned

above. 4) PowerPoint presentation

on the life of a famous

mathematician.

1) Social Studies: Using historical data to predict the possibility of

history repeating itself

or the probability of

an event happening. 2) Science: Using past

scientific data to predict the probability of

an event occurring. 3) Social Studies/

Technology: PowerPoint presentation

on the life of a famous

mathematician.

Unit Reflections:

Subject: PRECALCULUS

National & State

Standards Guiding Program

Essential Question Skills Assessment

Unit 1: Numbers, Equations, and

Graphing (Days to complete: 16

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.2A - Geometric Properties 4.2C - Coordinate Geometry 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5A - Problem Solving 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F - Technology

What are the different sets of numbers, and how do we distinguish among them? How do we add, subtract, multiply, and divide real numbers, and scientific notation? What are the different numerical properties, and how do we use them? What are exponents and radicals, and what are the different rules that apply to them? What are equations and inequalities, how do write them, how do we graph them, and how do we solve them? How do we use equations to solve word problems? How do we perform the basic operations on rational expressions? What is the Cartesian Coordinate Plane, and how can we use it to graph lines, curves, and circles? What are the main parts of the graph of an equation, and how do we test an equation for symmetry? How can we use a graphing calculator to view the graphs of equations? What are the main characteristics of linear equations?

SWBAT review the topics they covered in Algebra II. These topics include the following subjects: sets of numbers, real numbers and operations, algebraic expressions, properties of numbers, properties of exponents and radicals, solving equations and inequalities, writing equations and inequalities, using equations and inequalities, graphing equations and inequalities, testing for symmetry, rational expressions, scientific notation, using the graphing calculator, and linear equations. They will learn to graph a circle, and be able to write the equation of a circle in standard form.

1) Summer Assignment on

concepts covered in Algebra II. 2) Test on concepts

covered in Summer

Assignment.

Unit 2: Functions and Graphs (Days to complete: 21

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.5A - Problem Solving 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F - Technology

What is a function? What are different types of functions, and how are they used? What are the domain and range of a function, and what does it stand for? What are the direct and inverse variation equations, and where are they used outside the classroom? What happens to a graph when we change its algebraic equation, and vice-versa? How do we find the extreme values of functions? How are combinations of functions solved? What are one-to-one functions, and how do we find and graph their inverses?

SWBAT learn that a function is a subset of equations, and that they are treated the same as equations. They will learn how to graph functions, be able to define and explain the terms domain and range, and find the critical points of any graph. They will continue to see the correlation between a function and the graph that represents it, and be able to see how changing one will change the other. Students will revisit the topic of variation, and be able to apply it to different word problems. Students will be introduced to the concept of one-to-one functions, and how one must have a one-to-one function in order to be able to find an inverse function.

1) Quiz on functions, graphs of functions, applied

functions, and transformations

of functions. 2) Quiz on

extreme values of functions, combining

functions, and one-to-one

functions and their inverses.

3) Test on chapter

concepts mentioned

above.

Unit 3: Polynomials and

Rational Functions (Days to complete: 27

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.2A - Geometric Properties 4.2C - Coordinate Geometry 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F - Technology

What are polynomials, and how are they graphed? How do we add, subtract, multiply, and divide polynomials? How do we factor polynomials? How do we solve an equation by factoring, and can you solve word problems that involve solving equations by factoring? What are the critical points of the graph of a polynomial, and how do we find them? What are the zeroes/roots of a polynomial, and how do we find them algebraically and graphically? What are complex numbers, and how do we perform the four basic operations on this set of numbers? What is a rational expression, and how do we simplify one? How do we add, subtract, multiply, and divide rational expressions? What are the asymptotes of an equation, and what do they represent?

SWBAT continue to learn polynomials and polynomial operations. They will solve polynomial equations, and be able to find the critical points of the graph of any polynomial. They will be able to find the zeroes/roots of a polynomial not only by using the graphing calculator, but also algebraically by using a set of different rules and theorems. Students will review complex numbers and complex number operations, as well as rational expressions and rational expression operations. They will also review how to find the asymptotes of a polynomial, and how they affect that polynomial's graph.

1) Quiz on polynomial functions, graphs of

polynomial functions, and real zeros of polynomials. 2) Quiz on

complex numbers,

complex roots, The

Fundamental Theorem of

Algebra, and rational

functions. 3) Test on

chapter concepts

mentioned above.

Unit 4: Exponential and

Logarithmic Functions (Days to complete: 23

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5A - Problem Solving 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F - Technology

What are exponential functions, and how are they graphed? What is the natural exponential function, how is it graphed, and where is it applied outside of the classroom? What are logarithmic functions, how are they solved, and how are they graphed? What are the different laws that govern logarithmic functions? How are exponential and logarithmic functions related to one another? How do we solve exponential and logarithmic equations?

SWBAT learn about exponential equations and how to graph them. They will also learn about the natural exponential equation, how to graph it, and how it is used to determine compound interest and exponential growth of populations. Students will also be introduced to logarithmic equations, how to graph them, and the three basic laws of logarithms. They will also be able to see the relationship between exponential and logarithmic equations, and be able to take an equation in one form and rewrite it using the other. This will enable them to solve for a variable in different equations. They will also be able to use the fact that exponential and logarithmic functions are inverses in order to solve more difficult equations. Students will also apply the rules of transformations of graphs on both exponential and logarithmic graphs and equations.

1) Quiz on exponential

functions, the natural

exponential function, and logarithmic functions.

2) Quiz on laws of logarithms, exponential equations, logarithmic

equations, and applications of

exponential and logarithmic

functions. 3) Test on

chapter concepts

mentioned above.

Unit 5: Trigonometric Functions

of Real Numbers (Days to complete: 9

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.2D - Units of Measurement 4.2E - Measuring Geometric Objects 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5E - Representations 4.5F - Technology

What is the unit circle, and how do we find the trigonometric functions for an angle in the unit circle? What is the domain and range of the basic trigonometric functions? What are some properties and fundamental identities of trigonometric functions? How can we find trigonometric function values using a graphing calculator? How do we graph trigonometric functions and their transformations? What are some relationships among the trigonometric functions?

SWBAT review trigonometric functions in terms of the unit circle. Students will learn different identities and relationships among the trigonometric functions. They will also learn how to graph trigonometric functions and their transformations, and find the distinctive points and behavior of each type of function. Students will be able to use the graphing calculator to evaluate and graph these functions.

1) Quiz on the Unit Circle and trigonometric functions of

real numbers. 2) Quiz on

trigonometric graphs.

3) Test on chapter

concepts mentioned

above.

Unit 6: Trigonometric Functions

of Angles (Days to complete: 10

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.2D - Units of Measurement 4.2E - Measuring Geometric Objects 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5A - Problem Solving 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F - Technology

How do we convert from degrees to radians? How do we find the length of a circular arc and the area of a circular sector? How do we find the trigonometric functions for an angle of a right triangle? Given an acute angle measure of a right triangle, how can we find the lengths of the sides of that triangle? What are some of the fundamental trigonometric identities? What are the Law of Sines and Law of Cosines and how can they help us find the dimensions of any triangle?

SWBAT see the relationship between degrees and radians, and be able to convert between the two. They will be able to take information about the measure of an interior angle of a circle and be able to find certain pieces of information regarding the section of the circle that interior angle creates. They will explore trigonometric functions in terms of right triangles. Students will learn different identities and relationships among the trigonometric functions. They will also learn about the Law of Sines and Law of Cosines, and be able to use this information to find the side lengths and area of any triangle.

1) Quiz on angle measure, trigonometry of right triangles,

and trigonometric functions of

angles. 2) Quiz on Law

of Sines and Law of

Cosines. 3) Test on

chapter concepts

mentioned above.

Unit 7: Analytic Trigonometry (Days to complete: 15

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.2D - Units of Measurement 4.2E - Measuring Geometric Objects 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.5E - Representations 4.5F - Technology

What are some more fundamental trigonometric identities, and how can they help us find trigonometric function values? How do we simplify trigonometric expressions? How do we prove trigonometric identities? What are the trigonometric functions of sums and differences, and what identities describe them? What are the double-angle and half-angle identities and product-to-sum and sum-to-product formulas, and how do we use them? How do we find the inverse of a trigonometric function, and how do we graph it? How do we solve trigonometric equations? How can we algebraically manipulate an equation that contains trigonometric functions? How do we write complex numbers using trigonometric notation? How can we now multiply, divide, and apply powers to complex numbers? How can we find the roots of complex numbers? What are vectors, and where are they applied outside of the classroom?

SWBAT further explore trigonometric identities, relationships, and laws. Students will learn to simplify trigonometric identities. They will learn to prove identities, step-by-step, from beginning to end. Students will also review inverse trigonometric functions and how to graph them. They will continue learning how to solve equations that mix both algebraic and trigonometric concepts. Students will learn to solve trigonometric equations. They will be able to write a complex number using trigonometric notation, use this new form to perform the four basic operations and further investigate complex numbers. Students will be introduced to the concept of vectors, how to manipulate them, and why they are an important mathematical concept.

1) Quiz on trigonometric

identities, addition and subtraction formulas,

double-angle, half-angle, and product-sum

formulas. 2) Quiz on

inverse trigonometric

functions, trigonometric

equations, trigonometric

form of complex numbers,

DeMoivre’s Theorem, and

vectors. 3) Test on

chapter concepts

mentioned above.

Unit 8: Systems of Equations, Systems of Inequalities (Days to complete: 15

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.2A - Geometric Properties 4.2C - Coordinate Geometry 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F – Technology

What is a system of equations/inequalities, and how do we solve them graphically and algebraically? What kinds of system of equations are there? How does a graphing calculator work, and can you use it to solve a system of equations? What are matrices, and how can we use them to solve a system of equations? What is the algebra behind matrices? How can we find the inverse of a matrix? How can we solve matrix equations? What is the determinant of a matrix, and how can we use it to find the solution of a system of equations? How can we split a single fraction into partial fractions?

SWBAT review what they learned in Algebra II of systems of equations and inequalities. They will be introduced to the concept of matrices, and how they can help solve a system of equations. They will further explore matrices algebraically. Students will also learn how to take one large fraction and split it up into rational factors known as partial fractions.

1) Quiz on systems of equations,

pairs of lines, and systems of

linear equations.

2) Quiz on the algebra of matrices,

inverses of matrices,

matrix equations,

determinants, Cramer’s Rule,

systems of inequalities, and partial fractions. 3) Test on

chapter concepts

mentioned above.

Unit 9: Topics in Analytic

Geometry (Days to complete: 14

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.2A - Geometric Properties 4.2B - Transforming Shapes 4.2C - Coordinate Geometry 4.2D - Units of Measurement 4.2E - Measuring Geometric Objects 4.3A - Patterns and Relationships 4.3B - Functions 4.3C - Modeling 4.3D - Procedures 4.4A - Data Analysis 4.5C - Connections 4.5E - Representations 4.5F – Technology

What is a parabola, and what is its major points? What is an ellipse, and what is its major points? What is a hyperbola, and what is its major points? How do we shift and transform the graph of a conic? What are polar coordinates, and how are they related to trigonometry? How do we graph polar coordinates and polar equations on paper and on the graphing calculator? How do we write the equation for a conic using polar coordinates? What are parametric equations, how do we graph them, and how are they used? How do we put polar equations in parametric form?

SWBAT learn about these conic sections: parabolas, ellipses, and hyperbolas. They will learn how to recognize the equation of a conic, how to graph it, and what the major points of each graph are. They will also learn to transform the graph of a conic. Students will learn about polar coordinates, how to graph them, and how they are used in equations. They will learn how to write polar equations. They will learn about parametric equations, how to graph them, and how they are used to rewrite polar equations.

1) Quiz on parabolas, ellipses,

hyperbolas, and shifted

conics. 2) Quiz on rotation of axes, polar

coordinates, polar equations of conics, and

parametric equations. 3) Test on

chapter concepts

mentioned above.

Unit 10: Sequences and Series (Days to complete: 14

Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.3A - Patterns and Relationships 4.3B - Functions 4.3D - Procedures 4.4A - Data Analysis 4.4C - Discrete Mathematics - Systematic Listing and Counting 4.5A - Problem Solving 4.5C - Connections 4.5D - Reasoning 4.5E - Representations 4.5F – Technology

What a sequence? How can we find the sum of a certain number of terms of a given sequence? What is sigma notation, and how is it used? What is the difference between arithmetic and geometric sequences, and how are they used? How do we find the partial sums of these sequences, as well as the sum of an infinite geometric series? What is an annuity, and how do we find the amount of an annuity? What is installment buying, and how can you calculate monthly payments? What is the Principle of Mathematical Induction, and how does it help us prove mathematical conjectures? What is the Binomial Theorem, how does it relate to Pascal's Triangle, and how do we use it to expand a binomial?

SWBAT build and recognize arithmetic and geometric sequences. They will be able to find different sums of a series through the use of summation notation. Students will be introduced to the important investment strategy of annuities, how they work, and how they grow and are calculated over time. An important buying strategy they will be introduced to is that of installment buying, where students will learn how to calculate monthly payments. Students will learn about how to attempt proving an identity through the use of induction. They will also be introduced to both Pascal's Triangle and the Binomial Theorem, and how they are related to each other.

1) Quiz on sequences, summation notation, arithmetic

sequences, and geometric

sequences. 2) Quiz on

annuities and installment

buying, mathematical induction, and the Binomial

Theorem. 3) Test on

chapter concepts

mentioned above.

Unit 11: Counting and Probability

(Days to complete: 8 Days)

4.1A - Number Sense 4.1B - Numerical Operations 4.1C - Estimation 4.4B - Probability 4.5A - Problem Solving 4.5F – Technology

What is the Fundamental Counting Principle, and how is it used in probability situations? How do we perform permutations and combinations? How do we find the probability of a single event or multiple events? What is expected value, and how is it used in probability situations?

SWBAT refresh their probability skills. They will find the probability of individual as well as multiple events, through use of the Fundamental Counting Principle, permutations, combinations, and factorials. Students will also learn about expected value, and its applications in the world of games.

1) Quiz on counting

principles, permutations,

and combinations.

2) Quiz on probability and

expected value.

3) Test on chapter

concepts mentioned

above. 4) PowerPoint

presentation on the life of a

famous

mathematician.