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Montgomery Township School District

Algebra II

Grades 9 - 12

Prepared by: Frances C. Ross

Reviewed by: Dr. Christine Burton

Recommended by:

Board Approval:

Members of the Board of Education:

Mr. R. David Petit, Board President

Mr. Charles F. Jacey, Jr., Board Vice-President

Ms. Shalini Bhargava

Ms. Andrea Bradley

Mr. Humberto Goldoni

Ms. Adelle B. Kirk

Mr. Arun Rimal

Montgomery Township School District

1014 Route 601, Skillman, New Jersey 08558

I. OVERVIEW

Algebra II is the third course in the regular college preparatory program in mathematics. The course reviews basic terminology, concepts, skills, and applications of Algebra I by means of a critical examination of the real number system. Algebra II furthers the development of working with absolute value, inequalities, linear equations, and systems of equations and inequalities by building on Algebra I skills. Major topics are then covered which expand the students’ knowledge of Algebra and prepare them for higher level mathematics courses and include: simplifying and solving rational expressions and equations; solving and graphing polynomial functions; working with powers, roots, and radicals; and graphing second degree equations, working with exponential and logarithmic functions, utilizing the fundamental counting principal in conjunction with permutations and combinations, performing operations on matrices and application of matrices, and organizing and representing statistical data, and representing sequences and series in algebraic symbols.

Throughout the course, students will use scientific and graphing calculators as a tool for processing data, performing calculations, and exploring.

Successful completion of Algebra I and/or Geometry with a 70% or higher is a prerequisite for Algebra II

II. RATIONALE

Algebra is the language in which most of mathematics is communicated and as a result is a fundamental lifetime skill. Algebra I provides the transition from the specifics of arithmetic to the generalizations of higher mathematics. Algebra II extends the development of these generalizations and thereby continues the preparation for post-secondary mathematics study. In addition to preparing students for further study there is a continual emphasis on developing problem solving skills, reasoning skills, and communication skills. Finally, the language of Algebra II along with the appropriate use of calculators, computers, and software included with the textbook will facilitate the acquisition of skills needed in math related careers.

III. STANDARDS

The Montgomery Township Mathematics Program is aligned to the NJ Core Curriculum Mathematics Content Standards. The standards are listed below.

4.1 All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

A. Number Sense

B. Numerical Operations

C. Estimation

4.2 All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

A. Geometric Properties

B. Transforming Shapes

C. Coordinate Geometry

D. Units of Measurement

E. Measuring Geometric Objects

4.3 All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

A. Patterns and Relationships

B. Functions

C. Modeling

D. Procedures

4.4 All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

A. Data Analysis (Statistics)

B. Probability

C. Discrete Mathematics—Systematic Listing and Counting

D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms

4.5 All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

A. Problem Solving

B. Communication

C. Connections

D. Reasoning

E. Representation

IV. STUDENT OUTCOMES

Operations on Numbers and Expressions

Students will be able to perform operations with rational, real, and complex numbers, using both numeric and algebraic expressions, including expressions involving exponents and roots.

Equations and Inequalities

Students will be able to solve and graph the solution sets of equations and inequalities and systems of linear equations and inequalities. The types of equations and inequalities are to include linear, linear absolute value, quadratic, exponential, rational, radical, and higher order polynomials.

Polynomial and Rational Functions

Students will be able to use tables, graphs, verbal statements and symbols to represent and analyze quadratic, rational, and higher order polynomial functions. They will be able to recognize and solve problems than can be modeled using these functions.

Exponential Functions

Students will be able to use tables, graphs, verbal statements and symbols to represent, analyze, mode interpret graphs of exponential functions and have some facility with the properties of logarithms.

Function Operation and Inverses

Students will be able to perform function operations of addition, subtraction, multiplication, division and composition and to combine several functions defined over restricted domains to form a piecewise-defined function. They will be able to determine, graph and analyze the inverse of a function and use composition to determine whether two functions are inverses.

Data and Statistics

Students will be able to analyze, interpret, compare, and compute with summary statistics for sets of data. Analysis of bivariate data includes the determination and interpretation of regression lines and correlation coefficients.

Probability

Students will be able to quantify the likelihood that an event will occur through permutations, combinations and the fundamental counting principle.

Logarithmic Functions

Students will be able to define, represent, and model using logarithmic functions. Students will also be able to recognize the relationship between logarithmic and exponential functions, apply the laws of logarithms, solve logarithmic equations, and use logarithms to solve exponential equations.

Matrices

Students will be able to compute with and use matrices to organize information, solve systems of equations.

Sequences and Series

Students will be expected to find the nth term of sequence or series, the nth partial sum of a finite series and the infinite sum of a geometric series when it exists. General iterative relationships and recursive models are applied to patterns and problems.

V. STRATEGIES

The development of problem solving skills and utilization of algebraic representation for mathematical situations are the central foci for Algebra II. As a result, opportunities will be provided throughout the course for students to see algebra as a tool for problem solving, a way to understand and explain the world around them as well as achieving success in the manipulation of algebraic expressions. Emphasis will be made on real-life applications where applicable, allowing students to connect algebra with other math topics and disciplines.

The steps in using algebra as a tool for representing and solving problems that were introduced in Algebra I are reinforced in Algebra II.

♣ Define a variable or variables to represent the unknowns;

♣ Where appropriate, draw a diagram or create a table/chart

♣ Write an equation or inequality to represent the problem

♣ Solve the equation or inequality

♣ Check the solution of the equation or inequality for reasonableness within the scope of the problem

To further facilitate the interpretation, translation, and solution of problems, the following strategies may be used:

♣ Guess and check

♣ Work backwards to an answer

♣ Make models or use simulations

♣ Look for patterns

♣ Exploration on a graphing calculator

♣ Data collection and analysis with Calculator Based Laboratory and Calculator Based Rangers

Activities involving the graphing calculators and computers will be used to enable students to not only eliminate lengthy computations but also to investigate and develop concepts that previously were not accessible.

The focus of all strategies and methods will be to foster the development of the student’s ability to think logically and communicate clearly. Appropriate classroom time will be given to allow students to:

♣ Work independently, work in pairs and work in cooperative groups;

♣ Use the language and symbols of mathematics to communicate and discuss solutions verbally and in writing.

♣ Present original work to other students and receive critiques of their work; to critique the work of other students.

Since most students in this course will be taking the mandatory HSPA as well as the optional PSAT/SAT during the year, strategies for dealing with the types of questions given on such standardized tests will be studied and practiced when appropriate.

VI. EVALUATION

Students will be evaluated by multiple criteria, which may include:

♣ Chapter/Unit Tests & Quizzes; these will consist of recall questions, short

constructed response questions and open-ended questions requiring students to explain their thinking in arriving at their solution/conclusion.

♣ Notebooks; specific criteria will be determined by the teacher and will include note taking and homework.

♣ Out of class graded assignments such as enrichment problems.

♣ Research and/or enrichment projects.

♣ Oral presentations.

o Informal – participation in class discussions

o Formal – presentation of special assignments/projects.

The marking period grades for the course will be determined as follows:

♣ Formal assessment (tests/quizzes) 80%

♣ Homework (method determined by teacher) 10%

♣ Other – notebook, project, class participation, 10%

Special graded assignments (as determined by teacher)

The number and frequency of tests/quizzes and other assessments will be determined by the teacher.

The final grade for Algebra II will be determined by the following:

Four Quarter Grades each 20% 80%

One Midterm Exam 10%

One Final Exam 10%

Midterm and final exams are departmental tests and will consist of multiple choice, short

constructed response, and open-ended questions.

VII. REQUIRED RESOURCES

• Algebra and Trigonometry: Structure and Method BOOK 2,

McDougal Littell-Houghton Mifflin, Evanston IL 2000, 2011

• Other primary resources

Common Core State Standards, New Jersey State Department of Education, DRAFT, 2009

Teachers Resources Package, Algebra and Trig, McDougal Littell-Houghton Mifflin, Evanston IL 2000. 2011.

Teacher-created resource binder. (Contains resources created and used by Algebra 2 teachers.)

NJ Mathematics Curriculum Framework, NJ Department of

Education, 1996.

Achieve ADP Algebra II End-of-Course Content Standards, Core and Optional Modules, January 2010.

Calculators:

TI-30XA or TI-30XIIS

TI-82/83/84 Plus Graphing Calculator

Software: Packaged software included with the textbook for students and teachers.

SCOPE AND SEQUENCE

TIME

1. PREREQUISTE: ALGEBRA 1 REVIEW 6 days

(Chapter 1) Basic Concepts of Algebra

Teachers will reinforce the concepts learned in chapter 1, sections 1 through 9: Including properties an operations of real numbers, equation solving, and word phrases to Algebraic expressions.

Chapter 1 Assessment

2. INEQUALITIES 8 days

(Chapter 2)

2.1 Solving Inequalities in One Variable

2.2 Solving Combined Inequalities

2.3 Problem Solving Using Inequalities

2.4 Absolute Value in Open Sentences

2.5 Solving Absolute Value Sentences Graphically

3. LINEAR EQUATIONS AND FUNCTIONS 15 days

(Chapter 3 AND 9.9)

3.1 Open Sentences in Two Variables

3.2 Graphs of Linear Equations in Two Variables

3.3 The Slope of a Line

3.4 Finding the Equation of a Line

3.5 Systems of Linear Equations in Two Variables

3.6 Problem Solving: Using Systems

9.9 Systems of Linear Equations in Three Variables

3.7 Linear Inequalities in Two Variables

3.8 Functions

3.9 Linear Functions

3.10 Relations

4. PRODUCTS AND FACTORS OF POLYNOMIALS 16 days

(Chapter 4)

4.1 Polynomials

4.2 Using Laws of Exponents

4.3 Multiplying Plynomials

4.4 Using Prime Factorization

4.5 Factoring Polynomials

4.6 Factoring Quadratic Polynomials

4.7 Solving Polynomial Equations

4.8 Problem Solving Using Polynomial Equations

4.9 Solving Polynomial Inequalities

5. RATIONAL EXPRESSIONS 18 days

(Chapter 5)

5.1 Quotients of Monomials

5.2 Zero and Negative Exponents

5.3 Scientific Notation and Significant Digits

5.4 Rational Algebraic Expressions

5.5 Products and Quotients of Rational Expressions

5.6 Sums and Differences of Rational Expressions

5.7 Complex Fractions

5.8 Fractional Coefficients

5.9 Fractional Equations

Application: Electrical Circuits

6. IRRATIONAL AND COMPLEX NUMBERS 18 days

(Chapter 6)

6.1 Roots of Real Numbers

6.2 Properties of Radicals

6.3 Sums of Radical

6.4 Binomials Containing Radicals

6.5 Equations Containing Radicals

6.6 Rational and Irrational Numbers

6.7 The Imaginary Number i

6.8 The Complex Numbers

←midterm exam (tentative)

7. QUADRATIC EQUATIONS AND FUNCTIONS 14 days

(Chapter 7)

7.1 Completing the Square

7.2 The Quadratic Formula

7.3 The Discriminant

7.4 Equations in Quadratic Form

7.5 Graphing [pic]

7.6 Quadratic Functions

8. VARIATIONS AND POLYNOMIAL EQUATIONS 14 days

(Chapter 8)

8.1 Direct Variation and Proportion

8.2 Inverse and Joint Variation

8.3 Dividing Polynomials

8.4 Synthetic Division

8.5 The Remainder and Factor Theorems

8.6 Some Useful Theorems

8.7 Finding Rational Roots

9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS 20 days

(Chapter 10)

10.1 Rational Exponents

10.2 Real Number Exponents; (Include Extra Practice, ex. [pic])

10.3 Composition and Inverse of Functions

10.4 Definition of Logarithms

10.5 Laws of Logarithms

10.6 Applications of Logarithms

10.7 Problem Solving: Exponential Growth and Decay

10.8 The Natural Logarithm Function

10. SEQUENCES AND SERIES 10 days

(Chapter 11)

11.1 Types of Sequences

11.2 Arithmetic Sequences

11.3 Geometric Sequences

11.4 Series and Sigma Notation

11.5 Sums of Arithmetic Sequences

11.6 Infinite Geometric

11. STATISTICS AND PROBABILITY 9 days

(Chapter 15)

15.1 Presenting Statistical Data

15.2 Analyzing Statistical Data

15.5 Fundamental Counting Principles

15.6 Permutations

15.7 Combinations

15.9 Probability

12. MATRICES AND DETERMINANTS 12 days

(Chapter 16)

16.1 Definition of Terms

16.2 Addition and Scalar Multiplication

16.3 Matrix Multiplication

16.5 Determinants

16.7 Expansion of Determinants by Minors

16.9 Cramer’s Rule

Midterms, Finals, Testing Days, Special Schedules 20 days

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