algebra 2 honors - edison€¦ · unit 1: prerequisites for algebra 2 9 unit ... algebra 2 honors...

PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION

ALGEBRA 2 HONORS Length of Course: Term Elective/Required: Elective School: High Schools Student Eligibility: Grades 9 -10 Credit Value: 5 Credits Date Approved: 11/22/10

Algebra 2 Honors

THE PUBLIC SCHOOLS OF EDISON TOWNSHIP

MISSION STATEMENT

The Public Schools of Edison Township ensure that all students achieve at the highest level of academic success through the New Jersey Core Curriculum Content Standards and in partnership with the community, through a safe, supportive learning environment. This promotes self-worth and encourages productive contributions to a diverse, technological and constantly evolving global society. The district will maintain a staff of professional educators who support the New Jersey Core Curriculum Content Standards and the New Jersey Standards for Professional

Development.

Algebra 2 Honors

TABLE OF CONTENTS Statement of Purpose 3 Introduction 4 Course Objectives 6 Forward 7 Suggested Time Schedule 8

Unit 1: Prerequisites for Algebra 2 9 Unit 2: Equations and Inequalities 12 Unit 3: Functions and Their Graphs 15 Unit 4: Polynomial Functions 18 Unit 5: Sequences, Series and Probability 21 Unit 6: Systems of Equations and Inequalities 24 Unit 7: Matrices and Determinants 27 Unit 8: Rational Functions and Conics 29 Unit 9: Exponential and Logarithmic Functions 32 Unit 10: Introduction to Trigonometry 34 Unit 11: Analytic Trigonometry 37 Unit 12: Additional Topics in Trigonometry 38

Basic Text / References 39 Course Requirements 40 Essential Instructional Behavior (Draft 12) 42 Career Lessons 44 Modifications will be made to accommodate IEP mandates for classified students.

Algebra 2 Honors 3

STATEMENT OF PURPOSE

This course of study has been designed for all students who have satisfactorily completed Algebra 1 Honors and are in or completed Geometry Honors and were recommended for this course by their teacher. The content was selected to challenge the students and to extend student understanding of Algebra in preparation for further study in advanced mathematics. Topics also include review for HSPA and college entrance exams. This curriculum guide was revised / updated by: Lynn Harris - Edison High School Mary Anne Baldessari - John P. Stevens High School Coordinated by: Don Jobbins, Supervisor of Mathematics Vincent Ciraulo, Supervisor of Mathematics

Algebra 2 Honors 4

Introduction The most precious resource teachers have is time. Regardless of how much time a course is scheduled for, it is never enough to accomplish all that one would like. Therefore, it is imperative that teachers utilize the time they have wisely in order to maximize the potential for all students to achieve the desired learning. High quality educational programs are characterized by clearly stated goals for student learning, teachers who are well-informed and skilled in enabling students to reach those goals, program designs that allow for continuous growth over the span of years of instruction, and ways of measuring whether students are achieving program goals. The Edison Township School District Curriculum Template The Edison Township School District has embraced the backward-design model as the foundation for all curriculum development for the educational program. When reviewing curriculum documents and the Edison Township curriculum template, aspects of the backward-design model will be found in the stated enduring understandings/essential questions, unit assessments, and instructional activities. Familiarization with backward-design is critical to working effectively with Edison‟s curriculum guides. Guiding Principles: What is Backward Design? What is Understanding by Design?

“Backward design” is an increasingly common approach to planning curriculum and instruction. As its name implies, “backward design” is based on defining clear goals, providing acceptable evidence of having achieved those goals, and then working „backward‟ to identify what actions need to be taken that will ensure that the gap between the current status and the desired status is closed.

Building on the concept of backward design, Grant Wiggins and Jay McTighe (2005) have developed a structured approach to planning programs, curriculum, and instructional units. Their model asks educators to state goals; identify deep understandings, pose essential questions, and specify clear evidence that goals, understandings, and core learning have been achieved.

Program based on backward design use desired results to drive decisions. With this design, there are questions to consider, such as: What should students understand, know, and be able to do? What does it look like to meet those goals? What kind of program will result in the outcomes stated? How will we know students have achieved that result? What other kinds of evidence will tell us that we have a quality program? These questions apply regardless of whether they are goals in program planning or classroom instruction.

Algebra 2 Honors 5

The backward design process involves three interrelated stages for developing an entire curriculum or a single unit of instruction. The relationship from planning to curriculum design, development, and implementation hinges upon the integration of the following three stages.

Stage I: Identifying Desired Results: Enduring understandings, essential questions, knowledge and skills need to be woven into curriculum publications, documents, standards, and scope and sequence materials. Enduring understandings identify the “big ideas” that students will grapple with during the course of the unit. Essential questions provide a unifying focus for the unit and students should be able to answer more deeply and fully these questions as they proceed through the unit. Knowledge and skills are the “stuff” upon which the understandings are built.

Stage II: Determining Acceptable Evidence: Varied types of evidence are specified to ensure that students demonstrate attainment of desired results. While discrete knowledge assessments (e.g.: multiple choice, fill-in-the-blank, short answer, etc…) will be utilized during an instructional unit, the overall unit assessment is performance-based and asks students to demonstrate that they have mastered the desired understandings. These culminating (summative) assessments are authentic tasks that students would likely encounter in the real-world after they leave school. They allow students to demonstrate all that they have learned and can do. To demonstrate their understandings students can explain, interpret, apply, provide critical and insightful points of view, show empathy and/or evidence self-knowledge. Models of student performance and clearly defined criteria (i.e.: rubrics) are provided to all students in advance of starting work on the unit task.

Stage III: Designing Learning Activities: Instructional tasks, activities, and experiences are aligned with stages one and two so that the desired results are obtained based on the identified evidence or assessment tasks. Instructional activities and strategies are considered only once stages one and two have been clearly explicated. Therefore, congruence among all three stages can be ensured and teachers can make wise instructional choices.

At the curricular level, these three stages are best realized as a fusion of research, best practices, shared and sustained inquiry, consensus building, and initiative that involves all stakeholders. In this design, administrators are instructional leaders who enable the alignment between the curriculum and other key initiatives in their district or schools. These leaders demonstrate a clear purpose and direction for the curriculum within their school or district by providing support for implementation, opportunities for revision through sustained and consistent professional development, initiating action research activities, and collecting and evaluating materials to ensure alignment with the desired results. Intrinsic to the success of curriculum is to show how it aligns with the overarching goals of the district, how the document relates to district, state, or national standards, what a high quality educational program looks like, and what excellent teaching and learning looks like. Within education, success of the educational program is realized through this blend of commitment and organizational direction.

Algebra 2 Honors 6

COURSE OBJECTIVES The student will demonstrate proficiency in: 1. Recognizing and using terminology and symbols which relate to Algebra 2. 2. Simplifying algebraic expressions through the set of complex numbers. 3. Solving systems of algebraic equations and inequalities involving the set of

complex numbers. 4. Translating application problems involving systems of linear, quadratic and

exponential equations into algebraic sentences. 5. Graphing linear, quadratic and exponential functions and relations. 6. Deriving and applying algebraic relationships and formulas. 7. Applying algebraic and graphing techniques to the study of trigonometric functions. 8. Developing strategies that solve traditional and non-traditional application

problems. 9. Expressing mathematical concepts and/or solutions in oral or written formats. 10. Techniques of using a calculator (scientific and graphing). 11. Recognizing and using terminology of probability and its applications.

Algebra 2 Honors 7

FORWARD

Topics covered in each unit of the curriculum have been written in terms of instructional objectives strategies and notes to teacher have been included in each unit to give the teacher direction in presentation of the material and to identify additional materials for classroom use. Teachers should realize that this course of study denotes a minimum of topics that are to be covered and that there are numerous other appropriate topics that can be included The career lessons attached reinforce and/or extend the course content. These lessons should be included as course work in appropriate units.

Algebra 2 Honors 8

SUGGESTED TIME TABLE

UNIT

Suggested Number of

Class Periods

1. Prerequisites for Algebra 2 --------------------------------------------

15

2.

Equations and Inequalities --------------------------------------------

23

3.

Functions and Their Graphs -----------------------------------------

20

4.

Polynomial Functions --------------------------------------------------

10

5.

Sequences, Series and Probability ---------------------------------

7

6.

Systems of Equations and Inequalities ----------------------------

10

7.

Matrices and Determinants -------------------------------------------

10

8.

Rational Functions and Conics --------------------------------------

20

9.

Exponential and Logarithmic Functions ----------------------------

10

10.

Introduction to Trigonometry -----------------------------------------

20

11.

Analytic Trigonometry -------------------------------------------------

20

12.

Additional Topics in Trigonometry ----------------------------------

5

Total

170

NOTES: Units 1- 6 Performance Assessments Units 7-12 Final Exam

Algebra 2 Honors 9

UNIT 1: PREREQUISITES FOR ALGEBRA 2 Enduring Understanding: To extend the knowledge of Algebra 1 with additional information on problem solving (1, 10)*

Mastery Objectives

Materials

Strategies

Notes To Teacher

Reference to Standards

The student will be able to: 1. Represent, classify and order real

numbers. 2. Evaluate algebraic expressions. 3. Apply the basic rules and properties

of algebra. 4. Simplify problems involving

exponents and radicals. 5. Add, subtract and multiply

polynomials. 6. Factor polynomials using:

a. common factors b. difference of 2 squares c. perfect square trinomials d. sum/difference of 2 cubes e. grouping

1. Textbook 2. Calculator 3. Graphing Calculator 4. www.math.college.

hmco.com 5. Resource CD

1. Review the set of real numbers; how to write decimals in rational form; rules for operation with real numbers.

2. Do examples to show students that evaluating a formula is the same as evaluating an algebraic expression.

3. Encourage students to use calculators to perform operations with real numbers.

4. Stress the problems in Section P.6 with the S sign to get students to think ahead to calculus.

1. This unit is covered in section P

of the basic text. 2. Section P. 6 should be stressed in

order for students to learn how to avoid common errors in Algebra.

3. The order of operations should be reviewed and how to use with the calculator 4. The website or Resource CD can be used to find expanded versions of prerequisite topics.

5. The problem solving section at the end of each chapter show the topics applied to real life examples. 6. Assessments will be performed at

different points of the chapter. Assessments will be on P.1-P.2, P.1-P.4, P.3-P.5

7. Quarterly test will occur at the end

of the marking period.

4.1.12.A.1 4.1.12.A.2 4.1.12.A.3 4.1.12.B.1 4.1.12.B.2 4.1.12.B.4 4.2.12.C.1 4.2.12.C.3 4.2.12.D.1 4.3.12.D.2 4.3.12.D.3 4.5.A.2 4.5.A.5 4.5.B.1 4.5.B.2 4.5.B.3

*Number in parentheses relate to course objectives

http://www.math.college.hmco.com/

http://www.math.college.hmco.com/

Algebra 2 Honors 10

UNIT 1: PREREQUISITES FOR ALGEBRA 2 (cont.) Enduring Understanding: To extend the knowledge of Algebra 1 with additional information on problem solving

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: (con‟t) 7. Simplify, add, subtract, multiply and divide rational expression. 8. Simplify complex fractions. 9. Learn how to avoid common

algebraic mistakes. 10. Recognize and use algebraic techniques used in calculus. 11. Plot points in the Cartesian place. 12. Recognize and use terms:

a. real numbers b. rational number c. irrational number d. absolute value e. algebraic expression f. variables g. coefficient

5. Emphasis the use of formulas in everyday life by showing formulas related to economics, banking, science, etc. 6. Stress pattern for the sum and difference of cubes. This is new for most students. 7. Emphasize to students the importance of checking factoring by multiplying. 8. Emphasize that factoring must be complete.

6. The problem solving section at the end of each chapter show the topics applied to real life examples.

4.5.B.4 4.5.C.1 4.5.C.6

Algebra 2 Honors 11

UNIT 1: PREREQUISITES FOR ALGEBRA 2 (cont.) Enduring Understanding: To extend the knowledge of Algebra 1 with additional information on problem solving

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 12. Recognize and use terms: (cont.)

h. rules of Algebra i. exponent j. base k. scientific notation l. square root m. principal nth root n. index o. radicand p. radical q. rational exponent r. polynomials s. degree of a polynomial t. conjugate u. rational expression v. complex fraction w. ordered pair x. Distance Formula y. Midpoint Formula

Algebra 2 Honors 12

UNIT 2: EQUATIONS AND INEQUALITIES Enduring Understanding: To extend the knowledge of linear equations and inequalities (1, 3, 4, 5, 6)

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 1. Sketch a graph of an equation. 2. Write the standard form of a circle and

graph. 3. Solve linear equations in one variable. 4. Solve verbal problems. 5. Solve quadratic equations by:

a. factoring b. extracting square roots c. completing the square d. quadratic formula

7. Add, subtract, multiply and divide

complex numbers. 8. Find complex solutions of a quadratic

equation.

1. Textbook 2. Calculator 3. Graphing Calculator

1. Use the table on page 98 to have students understand key words and phrases for word problems. 2. Have the students list key words in order to solve word problems. 3. Do several examples of unit analysis problems. 4. Show the pattern of powers of “i”.

1. This unit is covered in Chapter 1 of the basic text. 2. Stress the importance of checking solutions in the original problem to find extraneous solutions. 3. Encourage students to create a verbal model to solve problems in section 1.3. 4. Stress the leading coefficient of the quadratic equation must be one when completing the square.

4.1.12.A.1 4.1.12.B.1 4.1.12.B.2 4.2.12.B.4 4.1.12.C.3 4.3.12.B.1 4.3.12.D.2 4.3.12.D.3 4.4.12.A.4 4.5.A.1 4.5.A.2 4.5.A.3 4.5.A.4 4.5.A.5 4.5.A.6 4.5.B.2

Algebra 2 Honors 13

UNIT 2: EQUATIONS AND INEQUALITIES (cont.) Enduring Understanding: To extend the knowledge of linear equations and inequalities

Mastery Objectives

Materials

Strategies

Notes To Teacher


8. Solve the following: a. polynomial equations with degree three or greater.

a. equations with radicals b. equations with fractions c. equations with absolute value d. linear inequalities in one variable e. polynomial inequalities f. rational inequalities

9. Recognize and use terms:

a. intercepts b. symmetry c. solution d. extraneous solution e. mathematical modeling f. imaginary number g. pure imaginary number h. complex number i. complex conjugate j. principal square root k. critical numbers

5. Have students explain how adding and subtracting complex numbers compares to real numbers. 6. Compare inequality and interval rotation for the solution set of an inequality. 7. Use a graphing calculator to explain the domain of a function.

5. Use a graphing calculator to show the solution set of absolute value inequality. 6. Stress to students that a radical must be isolated to solve a radical equation 7. Assessments will be performed

at various points of the chapter. Assessments can take place after 1.1, 1.3, 1.4, 1.6, 1.7.

8. Quarterly tests will take place at

the end of the marking period. 9. Performance Assessment will

be done after Chap.1 This will be the first of 4 tasks.

4.5.B.3 4.5.C.2 4.5.C.6

Algebra 2 Honors 14

UNIT 2: EQUATIONS AND INEQUALITIES (cont.) Enduring Understanding: To extend the knowledge of linear equations and inequalities

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 10. Solve real-live problems using:

a. graphs b. linear equations c. mathematical models d. quadratic equations e. inequalities

Algebra 2 Honors 15

UNIT 3: FUNCTIONS AND THEIR GRAPHS Enduring Understanding: To be able to graph different types of functions (1, 3, 5, 10)

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to:

1. Find the slope of a line 2. Write the equation of a line:

a. using the slope and y-intercept b. using the slope and a point c. using two points d. through a point and parallel or

perpendicular to a given equation e. given the intercepts

3. Determine whether two lines are parallel or perpendicular. 4. Graph the following: a. linear function b. squaring functions c. cubic functions d. square root functions e. reciprocal functions f. step functions g. piece-wise functions h. inverse functions


1. Use the graphing calculators once the students have mastered graphing techniques. 2. Use the examples on pg. 190 in the margin to demonstrate punctuation of piecewise functions. 3. Complete an activity using “Geometer sketchpad” to demonstrate to students what makes a graph shift, reflect and stretch. 4. Explain to the students that to find the inverse functions they must interchange x and y, and then solve y.

1. This unit is covered in Chapter 2 of the basic text. 2. Make certain the student knows that every point on the line is a solution and every solution is a point on the line. 3. Stress to students that f (x) is not f times x. 4. Explain to students the domain are possible input values. The range values are the possible outputs for those inputs. 5. Assessments will take place at

various point of the chapter. 6. Quarterly tests will be given at

the end of the marking period. 7. A second and third Performance

Assessment task will be given.

4.1.12.A.1 4.1.12.B.1 4.2.12.C.1 4.3.12.B.1 4.3.12.B.2 4.3.12.B.3 4.3.12.B.4 4.3.12.C.1 4.3.12.C.2 4.3.12.C.3 4.4.12.A.4 4.5.A.1-6 4.5.B.1-4 4.5.C.1 4.5.C.2 4.5.C.6

Algebra 2 Honors 16

UNIT 3: FUNCTIONS AND THEIR GRAPHS (cont.) Enduring Understanding: To be able to graph different types of functions

Mastery Objectives

Materials

Strategies

Notes To Teacher



5. Identify a relation and function. 6. Evaluate functions. 7. Find the domain and range of a function. 8. Find the zeros of a function. 9. Sketch graphs using:

a. vertical shifts b. horizontal shifts c. reflections d. non-rigid transformation

10. Add, subtract, multiply and divide functions. 11. Find composite functions. 12. Find inverse functions.

5. Point out that the graph of an inverse of a function is a reflection of the original function over the line y = x.

Algebra 2 Honors 17

UNIT 3: FUNCTIONS AND THEIR GRAPHS (cont.) Enduring Understanding: To be able to graph functions

Mastery Objectives

Materials

Strategies

Notes To Teacher



13. Recognize and use the following:

a. slope b. parallel lines c. perpendicular lines d. relation e. function f. domain g. range h. independent variable i. dependent variable j. function notation k. piecewise function l. vertical line test m. even function n. odd function o. arithmetic combination p. horizontal line test

Algebra 2 Honors 18

UNIT 4: POLYNOMIAL FUNCTIONS Enduring Understanding: To be able to sketch and find zeros of polynomials (1, 2)

Mastery Objectives

Materials

Strategies

Notes To Teacher



1. Write a quadratic in standard form and graph. 2. Find the vertex and x-intercepts of a parabola. 3. Sketch polynomial functions of higher degree. 4. Use the Leading Coefficient Test to determine end behavior of graphs. 5. Find zeros of a polynomial function by factoring. 6. Use the Intermediate Value Theorem to locate zeros. 7. Divide a polynomial by a polynomial using long division.


1. Use the technology box on page 279 to discuss the Intermediate Value Theorem. 2. Emphasize that arranging the terms in descending order makes the work of dividing a polynomial by another possible. 3. After students are able to find zeros, demonstrate how zeros may be found using a graphing calculator.

1. This unit is covered in Chapter 3 of the basic text. 2. Review completing the square with the students to write a parabola in standard form. 3. Emphasize to students that they do not divide to apply the Remainder and Factor Theorems. 4. Assessments will take place at

various points of the chapter. 5. Quarterly test will be given at the

end of the marking period. 6. A fourth and last Performance

Assessment will be given.

4.1.12.A.1 4.2.12.B.1 4.3.12.B.2 4.3.12.B.3 4.3.12.B.4 4.3.12.C.1 4.5.A.1-6 4.5.B.1-4 4.5.C.2 4.5.C.6

Algebra 2 Honors 19

UNIT 4: POLYNOMIAL FUNCTIONS (cont.) Enduring Understanding: To be able to sketch and find zeros of polynomials

Mastery Objectives

Materials

Strategies

Notes To Teacher



8. Divide a polynomial by a binomial using synthetic division. 9. Apply the Factor and Remainder Theorems. 10. Find the zeros of a polynomial using:

a. Rational Zero Test b. Descartes‟ Rule

Rule of signs 11. Write a mathematical model for the following:

a. direct variation b. inverse variation c. joint variation

Algebra 2 Honors 20

UNIT 4: POLYNOMIAL FUNCTIONS (cont.) Enduring Understanding: To be able to sketch and find zeros of polynomials

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 12. Recognize and use the following:

a. polynomial function b. quadratic function c. parabola d. axis of symmetry e. vertex f. power functions g. multiplicity h. conjugates i. directly proportional j. constant of variation k. inversely proportional l. jointly proportional

Algebra 2 Honors 21

UNIT 5: SEQUENCES, SERIES AND PROBABILITY Enduring Understanding: To extend knowledge to probability and its applications (1, 11)

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 1. Write the terms of a sequence using sequence notation. 2. Evaluate factorial expressions. 3. Find the sum of an infinite series. 4. Solve real-life problems using sequences and series. 5. Calculate binomial coefficients and expand a binomial using: a. the Binomial Theorem b. Pascal‟s Triangle 6. Solve counting problems using:

a. the Fundamental Counting Theorem

b. permutations c. combinations


1. Use the exploration on pg. 844 to have students discover the relationship between nCr and Pascal‟s Triangle. 2. Use the activities in the margin on pg. 866 to generate discussions about probability.

1. This unit is covered in Chapter

11 of the basic text. 2. Sections 11.2, 11.3 and 11.4 are

optional. 3. Objectives #9-12 correspond to the optional sections. 4. Stress the difference between permutations and combinations. 5. Assessments will be taken at

various points in the Chapter.

4.2.12.B.1 4.3.12.A.1 4.3.12.A.3 4.4.12.B.1-6 4.4.12.C.1-4 4.5.A.1-5 4.5.B.1-4 4.5.C.1 4.5.C.2 4.5.C.6

Algebra 2 Honors 22

UNIT 5: SEQUENCES, SERIES AND PROBABILITY (cont.) Enduring Understanding: To extend knowledge to probability and its applications

Mastery Objectives

Materials

Strategies

Notes To Teacher



7. Find the probabilities of:

a. events b. mutually exclusive events c. independent events d. complement of an event 8. Recognize and use the following:

a. infinite sequence b. terms of a sequence c. finite sequence d. factorial e. summation notation f. finite series g. infinite series h. binomial coefficients i. distinguishable permutations j. probability of the union of two events (optional) 9. Recognize and write:

a. arithmetic sequences b. geometric sequences c. nth term of a sequence

Algebra 2 Honors 23

UNIT 5: SEQUENCES, SERIES AND PROBABILITY (cont.) Enduring Understanding: To extend knowledge to probability and its applications

Mastery Objectives

Materials

Strategies

Notes To Teacher



10. Find an nth partial sum of an arithmetic sequence 11. Find the sum of:

a. geometric sequence b. infinite geometric sequence c. powers of integers

12. Find finite differences of a sequence

Algebra 2 Honors 24

UNIT 6: SYSTEMS OF EQUATIONS AND INEQUALITIES Enduring Understanding: To solve and graph linear equations and inequalities (1, 3, 5)

Mastery Objectives

Materials

Strategies

Notes To Teacher



1. Solve systems of linear equations in 2 variables by using the following methods:

a. substitution b. graphing c. elimination d. Gaussian elimination

2. Solve systems of linear equations in 3 variables by using the following methods: a. substitution b. Gaussian elimination 3. Sketch the graphs of inequalities in 2 variables. 4. Solve systems of inequalities

1. Textbook 2. Graphing Calculator

1. Stress that the solution of a system of equation should be checked in each equation of the original system. 2. Use graphing calculators to graph systems once the students have mastered graphing techniques. 3. Use graphing calculators to illustrate consistent and inconsistent systems. 4. Use different colored markers to shade each solution for in a system of inequalities

1. This unit is covered in Chapter 9 of the basic text. 2. Point out the differences between the substitution and elimination methods and the advantages of one over the other. 3. Remind students to graph equations in the form y=mx+b. 4. Stress the importance of the vocabulary on the linear programming section. 5. Assessments will be taken at


end of the marking period.

4.1.12.A.1 4.1.12.B.1 4.3.12.B.2 4.3.12.D.2 4.5.A.1-6 4.5.B.1-4 4.5.C.2 4.5.C.6

Algebra 2 Honors 25

UNIT 6: SYSTEMS OF EQUATIONS AND INEQUALITIES (cont.) Enduring Understanding: To solve and graph linear equations and inequalities

Mastery Objectives

Materials

Strategies

Notes To Teacher



5. Solve linear programming problems. 6. Use the following to model and solve real life problems:

a. systems of equations in two variables

b. systems of equations in three or more variables

c. systems of inequalities in 2 variables

d. linear programming 7. Recognize and use the following:

a. system of equations b. solution of a system of equations c. point of intersection d. equivalent systems e. consistent system f. inconsistent system

Algebra 2 Honors 26

UNIT 6: SYSTEMS OF EQUATIONS AND INEQUALITIES (cont.) Enduring Understanding: To solve and graph linear equations and inequalities

Mastery Objectives

Materials

Strategies

Notes To Teacher



7. Recognize and use the following:

g. row-echelon form h. ordered triple i. row operations j. nonsquare system of equations k. solution of an inequality l. graph of an inequality m. linear inequalities n. solution of a system of

inequalities o. optimization p. linear programming q. objective function r. constraints s. feasible solutions

Algebra 2 Honors 27

UNIT 7: MATRICES AND DETERMINANTS Enduring Understanding: To understand matrices and determinants and their applications (1, 3, 5)

Mastery Objectives

Materials

Strategies

Notes To Teacher



1. Recognize and use the following terms:

a. scalar multiplication b. identify matrix c. inverse matrix d. determinant of a matrix e. Cramer‟s Rule

2. Add, subtract and multiply matrices. 3. Use matrix operations to model and solve real-life problems. 4. Verify that two matrices are inverses of each other. 5. Find inverses of 2x2 matrix. 6. Use inverse matrices to solve systems of linear equations.


1. Students should also learn the “basketweave” method of finding determinants as a alternative. 2. Remind students to use the matrix that references co-factors.

1. This unit is covered in Chapter 10 Section 2-4 and Section 5 Example 1-3 2. Sample problems for Cramer‟s Rule and matrices can be found in Algebra 2 with Trigonometry (Prentice Hall) p. 233-238. 3. Problem Solving section on p. 798-9 may be used as Supplemental Activity. 4. Assessments will take place at



4.1.12.A.1 4.1.12.B.1 4.1.12.B.3 4.3.12.C.1 4.3.12.C.3 4.5.A.1-6 4.5.B.1-4 4.5.C.2 4.5.C.6

Algebra 2 Honors 28

UNIT 7: MATRICES AND DETERMINANTS (cont.) Enduring Understanding: To understand matrices and determinants and their applications

Mastery Objectives

Materials

Strategies

Notes To Teacher



7. Find the determinants of matrix by minors. 8. Use Cramer‟s Rule to solve systems of linear equations. 9. Use determinants to find the area of triangles.

Algebra 2 Honors 29

UNIT 8: RATIONAL FUNCTIONS AND CONIC SECTIONS Enduring Understanding: Be able to identify the graphs of the conic sections from their equations and to write their equations from their graphs or other given information. (1, 5, 6)

Mastery Objectives

Materials

Strategies

Notes To Teacher




a. rational function b. vertical asymptote c. horizontal asymptote d. slant asymptote e. conic section f. degenerate conic g. parabola h. directrix i. focus j. standard form of the equation of a

parabola k. ellipse l. foci m. vertices n. major axis o. center p. minor axis q. standard form of the equation of

an ellipse

1. Textbook 2. Scientific Calculator 3. Teacher- prepared Worksheet 4. Graphing Calculator

1. Stress the domain of the function. 2. Show the general as well as the standard form of the equations of the conic sections. 3. Stress the locations of the foci in an ellipse, parabola and hyperbola 4. Review completing the square.

1. This unit is covered in Chapter 4 Section 1, 2, 4, 5. Do not cover Section 4.3. 2. Outline steps to graph rational functions. 3. Use a cone to show how each conic is a cross section of a cone. 4. Problem Solving Section on p. 386-387 can be used a Supplementary Activities. 5. Scientific applications of the ellipse could be discussed at this time. 6. Assessments will be given at



4.1.12.A.1 4.2.12.A.1 4.2.12.B.1 4.3.12.B.2 4.3.12.D.3 4.5.A.1-6 4.5.B.1-4 4.5.C.2 4.5.C.6

Algebra 2 Honors 30

UNIT 8: RATIONAL FUNCTIONS AND CONIC SECTIONS (cont.) Enduring Understanding: Be able to identify the graphs of the conic sections from their equations and to write their equations from their graphs or other given information.

Mastery Objectives

Materials

Strategies

Notes To Teacher



Recognize and use the following terms: (con‟t)

r. hyperbola s. branches t. transverse axis u. standard form of the equation of a

hyperbola v. conjugate axis w. asymptotes of a hyperbola

2. Find the domains of rational functions.

3. Find the horizontal and vertical asymptotes of graphs of rational functions.

4. Use a rational expressions to model and solve real-life problems.

5. Analyze and sketch graphs of rational function with or without slant asymptotes.

6. Recognize the four conics, (circle, parabola, ellipse and hyperbola) and sketch each.

Algebra 2 Honors 31

UNIT 8: RATIONAL FUNCTIONS AND CONIC SECTIONS (cont.) Enduring Understanding: Be able to identify the graphs of the conic sections from their equations and to write their equations from their graphs or other given information.

Mastery Objectives

Materials

Strategies

Notes To Teacher


The student will be able to: 7. Determine:

a. the relationship among the center, radius and the equation of a circle. b. the relationship among the focus, directrix and vertex and the equation of a parabola. c. the relationship among the center, foci, vertices and endpoints of the axis and the equation of an ellipse.

d. the relationship among the center, foci, vertices and endpoints of the axes and the equation of a hyperbola.

Algebra 2 Honors 32

UNIT 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS Enduring Understanding: Identify, solve and simplify expressions or equations involving logarithms (1, 2, 4, 5)

Mastery Objectives

Materials

Strategies

Notes To Teacher




a. exponential function b. natural base c. natural exponential function d. continuously compounded

interest e. logarithmic function f. common logarithmic function g. natural logarithmic function h. change of base i. properties of logs j. exponential equation k. logarithmic equation l. exponential growth m. exponential decay

2. Recognize, evaluate and graph exponential functions with base a.


1. Stress that the logarithm is defined only for positive real numbers. 2. Stress that the log of a number, y, is the exponent that the base must be “raised to” in order to get the number y.

1. This unit is covered in Chapter 5. 2. Problem Solving Section on p.

450-1 may be used as Supplemental Activity.

3. Assessments will be given at



4.1.12.A.1 4.1.12.B.1 4.3.12.B.4 4.3.12.C.1 4.3.12.C.2 4.3.12.C.3 4.3.12.D.2 4.5.A.1-6 4.5.B.1-4 4.5.C.1 4.5.C.3 4.5.C.4 4.5.C.6

Algebra 2 Honors 33

UNIT 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS (cont.) Enduring Understanding: Identify, solve and simplify expressions or equations involving logarithms

Mastery Objectives

Materials

Strategies

Notes To Teacher



3. Recognize and evaluate exponential functions with base e. 4. Use exponential functions to solve real-life applications. 5. Recognize and evaluate and graph logarithmic functions. 6. Recognize, evaluate natural logarithmic functions. 7. Use logarithmic functions to solve real-life applications. 8. Use Change of Base Formula 9. Use properties of logarithms to evaluate, rewrite, expand or condense logarithmic expressions. 10. Solve exponential and logarithmic equations. 11. Use exponential growth and decay to solve real-life problems.

Algebra 2 Honors 34

UNIT 10: INTRODUCTION TO TRIGONOMETRY Enduring Understanding: To build a basic understanding of the trigonometric functions and their graphs (1, 7)

Mastery Objectives

Materials

Strategies

Notes To Teacher




a. trigonometry b. angle c. initial side of angle d. terminal side of angle e. vertex f. standard position g. co terminal angles h. degree i. radian j. linear speed k. angular speed l. sine m. cosine n. tangent o. cosecant p. secant q. cotangent r. angle of elevation s. angle of depression t. unit circle u. reference angles v. period w. amplitude

1. Textbook 2. Scientific Calculator 3. Graphing Calculator

1. Students have to be comfortable with the degree and radian mode. 2. Teacher-prepared transparencies will help students understand the changes that occur in the graph that occur in the graph of a function when coefficients in the standard equation are changed. 3. Stress the relationship between the graphs of the sine and co secant functions, as well a cosine and secant functions.

1. This unit is covered in Chapter 5. 2. Problem Solving Section on p.

450-1 may be used as Supplemental Activity.

3. Assessments will be given at



4.1.12.A.1 4.1.12.B.1 4.2.12.A.3 4.2.12.C.3 4.3.12.B.1 4.3.12.B.4 4.3.12.C.1 4.3.12.C.2 4.3.12.D.2 4.5.A.1-6 4.5.B.1-4 4.5.C.1 4.5.C.2 4.5.C.4 4.5.C.6

Algebra 2 Honors 35

UNIT 10: INTRODUCTION TO TRIGONOMETRY (cont.) Enduring Understanding: To build a basic understanding of the trigonometric functions and their graphs

Mastery Objectives

Materials

Strategies

Notes To Teacher



1. Recognize and use the following terms: (con‟t)

x. phase shift x. inverse sine function y. inverse cosine function z. inverse tangent function

2. Use degree and radian measure. 3. Convert between degree and radian measure. 4. Evaluate trigonometric functions. 5. Use reference angles to evaluate trig functions. 6. Graph the six trigonometric functions. 7. Graph the six trigonometric functions using amplitude, period, pause shift and vertical shift. 8. Evaluate inverse trigonometric functions.

Algebra 2 Honors 36

UNIT 10: INTRODUCTION TO TRIGONOMETRY (cont.) Enduring Understanding: To build a basic understanding of the trigonometric functions and their graphs

Mastery Objectives

Materials

Strategies

Notes To Teacher


9. Evaluate the composition of trigonometric functions. 10. Apply to real-life problems. 11. Solve real-life problems involving right triangle and directional bearings.

Algebra 2 Honors 37

UNIT 11: ANALYTIC TRIGONOMETRY Enduring Understanding: To understand identities, solve equations and apply formulas (1, 7)

Mastery Objectives

Materials

Strategies

Notes To Teacher




a. Sum and Difference Formulas b. Double Angle Formulas c. Half-Angle Formulas

2. Recognize and write the fundamental trigonometric identities. 3. Use the trigonometric identities to evaluate trigonometric functions, simplify and rewrite trigonometric functions. 4. Verify trigonometric identities. 5. Solve trigonometric equations. 6. Use inverse trigonometric functions to solve trigonometric equations. 7. Use sum and difference formulas to evaluate trigonometric functions, verify identities and solve questions.


1. Students may use a study aid to reinforce the trigonometric identities. The study may be an index card or worksheet.

1. This unit is covered in Chapter 7. 2. Problem Solving Section on p. 594-595 may be used as Supplemental Activity. 3. In Chapter 7 Section 5 only Double Angle and Half-Angle Formulas are used. 4. Assessments will be given at


end of the marking period. 6. Final exam will be given at the

end of the course.

4.1.12.A.1 4.1.12.B.1 4.2.12.A.3 4.2.12.C.3 4.3.12.B.1 4.3.12.B.4 4.3.12.C.1 4.3.12.C.2 4.3.12.D.2 4.5.A.1-6 4.5.B.1-4 4.5.C.1 4.5.C.2 4.5.C.4 4.5.C.6

Algebra 2 Honors 38

UNIT 12: ADDITIONAL TOPICS IN TRIGONOMETRY

Enduring Understanding: To apply and use Law of Cosines and Law of Sines (1, 7)

Mastery Objectives

Materials

Strategies

Notes To Teacher




a. Law of Sines b. Ambiguous Case c. Area of Oblique Triangle d. Law of Cosines e. Heron‟s Area Formula

2. Use Law of Sines to solve oblique triangles (AAS or ASA)

3. Use Law of Sines to solve triangles using the Ambiguous Case (SSA)

4. Find area of triangles.

5. Use Law of Cosines to solve oblique triangles. (SSS or SAS) 6. Use Law of Sines and Law of Cosines to solve real-life problems.

7. Use Heron‟s Area Formula to find area of triangle.


1. This unit is covered in Chapter 8, Section 1 & 2. 2. Problem Solving Section on p. 660-1 may be used as Supplemental Activity.

4.1

4.2

4.3

4.4

4.5

Algebra 2 Honors 39

BASIC TEXT

Larson, R., Hostetler, R. et al. Algebra and Trigonometry, Houghton Mifflin Company, New York, NY 2004

REFERENCES

Hall, B. et al. Algebra 2 with Trigonometry, Prentice Hall, Englewood Cliffs, NJ 1997. Hall, B. et al. Using the Graphics Calculator Book 2, Prentice Hall, Englewood Cliffs, NJ, 1996. Benson, J., et al. Algebra 2 and Trigonometry, McDougal, Little and Company, Evanston, IL, 1991.

Algebra 2 Honors 40

PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION

COURSE REQUIREMENTS

ALGEBRA II HONORS

GRADES: 9-10 LENGTH OF COURSE: TERM

I. COURSE CONTENT – This course will consist of the following units of study: A. Problem Solving: Introduction to problem solving, graphic solutions, modeling, finding and using patterns B. The Language of Algebra: Expressions, solving equations, solving inequalities, graphing, matrices, probability, exponents, radicals C. Linear Relationships: Graphing linear equations, systems of linear equations, graphing inequalities, functions and direct variation, compound functions D. Quadratic Functions: Definition of quadratics, factoring, graphing quadratic functions, solving quadratic equations, completing the square, applications of quadratic function E. Functions: Definitions of functions and relations, inverse functions, operations with functions, discrete functions, measures of central tendency, inverse variation F. Rational Expressions, Equations and Functions: Operations with rational expressions, rational equations and inequalities, complex fractions G. Extending the Real Number System: Rational exponents, solving radical expressions, rational equations and inequalities, complex fractions H. Polynomials and Polynomial Functions: Remainder and factor theorems, rational-zeros theorem, binomial theorem, synthetic theorem I. Graphing: Plotting points, translating graphs, reflections and symmetry, asymptotes, graphing conic sections J. Exponential and Logarithmic Functions: Definitions and graphs of exponential and logarithmic functions, properties of logarithms, solving exponential and logarithmic equations, applications K. Introduction to Trigonometry: Unit circle, circular functions, coordinate definitions, inverse trigonometric functions, right triangles, radian measure, trigonometric relationships, basic trigonometric identities, solving trigonometric equations L. Trigonometric Graphs and Applications: Law of sines, law of cosines, graphing the sine function, other trigonometric graphs

(Additionally, career-related topics and information will be presented/reviewed.)

Course Requirements – Algebra 2 Honors (page 2)

Algebra 2 Honors 41

II. COURSE REQUIREMENTS - To complete this course successfully, students will be required to demonstrate a satisfactory (or higher) level of proficiency in: A. Recognizing and using terminology and symbols which relate to Algebra II B. Simplifying algebraic expressions through the set of complex numbers C. Solving systems of algebraic equations and inequalities involving the set of complex numbers D. Translating application problems involving systems of linear, quadratic and exponential equations into algebraic sentences E. Graphing linear, quadratic and exponential functions and relations F. Deriving and applying algebraic relationships and formulas G. Applying algebraic and graphing techniques to the study of trigonometric functions H. Developing strategies that solve traditional and non-traditional application problems I. Expressing mathematical concepts and/or solutions in oral and written formats

III. EVALUATION PROCESS - Throughout the length of this course, students will be evaluated on the bases of: A. Tests/quizzes B. Homework assignments C. Class participation D. Notebook E. Mid-term and final examinations shall be administered. The academic value of the examination grade shall be 20% of the final grade. Mid-term grade is determined by Performance Assessment tasks.

Rev. 7/05

Algebra 2 Honors 42

Public Schools of Edison Township Divisions of Curriculum and Instruction

Draft 14

Essential Instructional Behaviors

Edison’s Essential Instructional Behaviors are a collaboratively developed statement of effective teaching from pre-school through Grade 12. This statement of instructional expectations is intended as a framework and overall guide for teachers, supervisors, and administrators; its use as an observation checklist is inappropriate.

1. Planning which Sets the Stage for Learning and Assessment

Does the planning show evidence of: a. units and lessons directly related to learner needs, the written curriculum, the New Jersey Core Content

Curriculum Standards (NJCCCS), and the Cumulative Progress Indicators (CPI)? b. measurable objectives that are based on diagnosis of learner needs and readiness levels and reflective of

the written curriculum, the NJCCCS, and the CPI? c. lesson design sequenced to make meaningful connections to overarching concepts and essential

questions? d. provision for effective use of available materials, technology and outside resources? e. accurate knowledge of subject matter? f. multiple means of formative and summative assessment, including performance assessment, that are

authentic in nature and realistically measure learner understanding? g. differentiation of instructional content, processes and/or products reflecting differences in learner

interests, readiness levels, and learning styles? h. provision for classroom furniture and physical resources to be arranged in a way that supports student

interaction, lesson objectives, and learning activities?

2. Observed Learner Behavior that Leads to Student Achievement

Does the lesson show evidence of: a. learners actively engaged throughout the lesson in on-task learning activities? b. learners engaged in authentic learning activities that support reading such as read alouds, guided

reading, and independent reading utilizing active reading strategies to deepen comprehension (for example inferencing, predicting, analyzing, and critiquing)?

c. learners engaged in authentic learning activities that promote writing such as journals, learning logs, creative pieces, letters, charts, notes, graphic organizers and research reports that connect to and extend learning in the content area?

d. learners engaged in authentic learning activities that promote listening, speaking, viewing skills and strategies to understand and interpret audio and visual media?

e. learners engaged in a variety of grouping strategies including individual conferences with the teacher, learning partners, cooperative learning structures, and whole-class discussion?

f. learners actively processing the lesson content through closure activities throughout the lesson? g. learners connecting lesson content to their prior knowledge, interests, and personal lives? h. learners demonstrating increasingly complex levels of understanding as evidenced through their growing

perspective, empathy, and self-knowledge as they relate to the academic content? i. learners developing their own voice and increasing independence and responsibility for their learning? j. learners receiving appropriate modifications and accommodations to support their learning?

Algebra 2 Honors 43

3. Reflective Teaching which Informs Instruction and Lesson Design

Does the instruction show evidence of: a. differentiation to meet the needs of all learners, including those with Individualized Education Plans? b. modification of content, strategies, materials and assessment based on the interest and immediate needs

of students during the lesson? c. formative assessment of the learning before, during, and after the lesson, to provide timely feedback to

learners and adjust instruction accordingly? d. the use of formative assessment by both teacher and student to make decisions about what actions to

take to promote further learning? e. use of strategies for concept building including inductive learning, discovery-learning and inquiry

activities? f. use of prior knowledge to build background information through such strategies as anticipatory set,

K-W-L, and prediction brainstorms? g. deliberate teacher modeling of effective thinking and learning strategies during the lesson? h. understanding of current research on how the brain takes in and processes information and how that

information can be used to enhance instruction? i. awareness of the preferred informational processing strategies of learners who are technologically

sophisticated and the use of appropriate strategies to engage them and assist their learning? j. activities that address the visual, auditory, and kinesthetic learning modalities of learners? k. use of questioning strategies that promote discussion, problem solving, and higher levels of thinking? l. use of graphic organizers and hands-on manipulatives? m. creation of an environment which is learner-centered, content rich, and reflective of learner efforts in

which children feel free to take risks and learn by trial and error? n. development of a climate of mutual respect in the classroom, one that is considerate of and addresses

differences in culture, race, gender, and readiness levels? o. transmission of proactive rules and routines which students have internalized and effective use of

relationship-preserving desists when students break rules or fail to follow procedures?

4. Responsibilities and Characteristics which Help Define the Profession

Does the teacher show evidence of: a. continuing the pursuit of knowledge of subject matter and current research on effective practices in

teaching and learning, particularly as they tie into changes in culture and technology? b. maintaining accurate records and completing forms/reports in a timely manner? c. communicating with parents about their child‟s progress and the instructional process? d. treating learners with care, fairness, and respect? e. working collaboratively and cooperatively with colleagues and other school personnel? f. presenting a professional demeanor?

MQ/jlm

7/2009

Algebra 2 Honors 44

CAREER LESSONS

These career lessons utilize Algebra 2 and Trigonometry by Benson, J., et al., McDougal, Little and Company, 1991.

1. Have students read page 433 in basic text. They are then to write out a series of questions they will use to interview a teacher. They may interview a teacher in any discipline and ask them how they use mathematics in their subject and in their grading. They may interview a teacher they presently have or one that they had previously. The teacher could even be a family member or a former teacher who is now in another field. Grade students on their written interview.

2. Have students read page 652 to learn the correlation between trigonometric function graphs and the graph of an EKG. Have the students research the history of the EKG and write a short paper on their findings. You might suggest the use of the Internet for information.

3. Have students read page 232 “Exponentials and Statistics in Banking”. Have students work in small groups to consider the following situation. You have just finished school and are looking for work. You are currently interviewing with a filming company named Code Act. Mr. Poler Ride is the manager of the company and seems to like your resume. He has offered you a job and indicated that the average employee in the company makes $37,500 annually. You like this figure and agree to work. After the first month you discover on your paycheck that you are paid a rate of $15,000 annually and are unhappy.

The data is as follows: Mr. Ride $100,000 Assistant 50,000 Worker 1 30,000 Worker 2 30,000 Worker 3 30,000 Worker 4 30,000 Worker Assistant 15,000 Worker Assistant 15,000

Should you have accepted the average salary as an estimate for your wages? Would the median salary have been any better? How about the mode? Are any of these statistics useful in this situation?

4. Have students read page 560 “Statistics and the Public Mind”. Have students work in small

groups. They are to come up with appropriate questions to poll at least 50 peers. Questions should be “for” or “against” and approved by the teacher. Groups will present the results to the class. All questions must have written results. All written work must have:

a. Cover Sheet: Names of Students in Group b. Handwritten in ink or printed c. Be Neat: No cross-overs, cross-outs or white-outs d. Written on one side of paper

Oral presentations will be 5-10 minutes. Everyone must participate. Students should be able to

answer questions from the class regarding the results of the surveys. A group grade may be given. Some appropriate topics: Gun control, Class rank, Smoking in public buildings

Algebra 2 Honors 45

Algebra 2 Honors 46

Algebra 2 Honors 47

Algebra 2 Honors 48

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