Download Honors Algebra 2 - Berkeley Heights Public Schools

BERKELEY HEIGHTS PUBLIC SCHOOLS
BERKELEY HEIGHTS, NEW JERSEY
GOVERNOR LIVINGSTON H. S.
MATHEMATICS DEPARTMENT
ALGEBRA 2/ALGEBRA 2 HONORS/ALGEBRA 2 CONCEPTS
#MAY1110/#MAY1120/#MAY1100
Curriculum Guide
October 2013
REVISED
Mrs. Judith Rattner, Superintendent
Mrs. Patricia Qualshie, Assistant Superintendent
Dr. Mary Ann Kjetsaa, District Supervisor
Developed by: William Halleran
Nicole Manganelli
This curriculum may be modified through varying techniques,
strategies, and materials, as per an individual student’s
Individualized Educational Plan (IEP)
Approved by the Berkeley Heights Board of Education
at the regular meeting held on
11/14/13 .
TABLE OF CONTENTS
Page
Vision Statement ..................................................................................................................1
Mission Statement ................................................................................................................2
Course Proficiencies.............................................................................................................3
Course Objectives ....................................................................................................3
Student Proficiencies ...............................................................................................5
Methods of Evaluation.............................................................................................8
Course Outline/Student Objectives ....................................................................................9
Resources/Activities Guide..................................................................................................15
Suggested Audio Visual/Computer Aids............................................................................16
Suggested Materials .............................................................................................................17
Resources for Students ............................................................................................17
Resources for Teacher .............................................................................................17
VISION STATEMENT
Algebra 2 is intended for college bound students and will be offered at three levels. The course is
designed to reinforce and build upon the student’s arithmetic, algebraic, and geometric
foundations while developing the student’s ability to think in a logical, analytical, and creative
way. The objectives of the course are:
· To develop mastery of all algebraic skills.
· To apply these skills to solve real life problems.
· To develop an appreciation for the value of those skills.
· To prepare the students for advanced mathematical studies.
Effective communication, using the language of mathematics, is essential for all math courses
and will be emphasized throughout this course. The development of mathematical definitions,
notation, terminology, syntax, and logic will be imbedded in the course studies. Students will be
required to explain their solutions using multiple representations in both a written and oral
format.
Berkeley Heights Public Schools
1
MISSION STATEMENT
This course provides an opportunity for students to expand their knowledge of concepts learned
in Algebra 1 and develop more advanced algebraic concepts. Curriculum topics covered in the
course include systems of equations, functions, powers, roots, logarithms, exponents, sequences,
series, probability, complex numbers, and parabolic functions. An extension of topics including
conic sections and matrices will also be covered at the honors level. Through the scope of this
course, the students will become familiar with a variety of problem-solving strategies and
develop an understanding of the applications of algebra in other fields. The students will also
learn to use mathematical language to communicate ideas through the use of models, diagrams,
and symbols. The student will be able to build mathematical models to represent specific
information provided in real world situations. Technology will be integrated throughout the
instruction of the course and will be used to expand the problem-solving capabilities of the
students. The students will be held responsible for individual work while also being expected to
function productively in a cooperative learning environment.
Five (5.0) credits will be earned for successful completion of this full year course. National and
state standards are integrated throughout the curriculum.
Berkeley Heights Public Schools
2
COURSE PROFICIENCIES
COURSE OBJECTIVES
1. To perform operations with real numbers. (12.A.SSE.2)
2. To simplify and evaluate algebraic expressions. (12.A.SSE.1.a, 12.A.SSE.1.b)
3. To solve equations, inequalities, and absolute value equations. (12.A.CED.1, 12.A.CED.3,
12.A.SSE.1b)
4. To solve problems involving probability. (12.S.CP.1, 12.S.CP.2, 12.S.CP.3, 12.S.CP.5,
12.S.CP.7, 12.S.CP.9, 12.S.MD.1, 12.S.MD.3, 12.S.MD.4)
5. To identify and graph functions and relations, model real world data, and predict with linear
models. (12.F.IF.4, 12.F.IF.5, 12.F.IF.6, 12.F.IF.9, 12.A.SSE.1.b, 12.A.CED.2)
6. To solve and graph problems involving direct and inverse variation.(12.F.IF.4, 12.A.CED.2 )
7. To solve systems of equations and inequalities. (12.A.CED.3, 12.A.REI.11)
8. To use linear programming to solve maximum and minimum problems. (12.A.CED.3)
9. To use matrices to organize data. (12.N.VM.6)
10. To add, subtract, and multiply matrices. (12.N.VM.7, 12.N.VM.8, 12.N.VM.9, 12.N.VM.10)
11. To graph parabolas, find maximum and minimum values, and translate vertically and
horizontally. (12.F.IF.7.a, 12.F.IF.9, 12.F.BF.3)
,
12. To find the nature of the solutions, of a quadratic equation, using the discriminant and solve
a quadratic equation by factoring, completing the square, and the quadratic formula.
(12.A.SSE.2, 12.A.SSE.3.a, 12.A.SSE.3.b, 12.A.CED.1, 12.A.REI.4.a, 12.A.CED.4.b)
13. To identify and use complex numbers. (12.N.CN.1, 12.N.CN.2, 12.N.CN.4, 12.N.CN.5,
12.N.CN.7)
14. To explore and perform operations on polynomial functions. (12.A.APR.1)
15. To explore the rational root theorem, the Fundamental Theorem of Algebra, Pascal’s
Triangle, and the Binomial Theorem. (12.A.APR.3, 12.A.APR.5, 12.N.CN.8, 12.N.CN.9)
16.
To perform operations on radical expressions, solve and graph radical equations.
(12.A.SSE.2, 12.N.RN.1, 12.N.RN.2, 12.F.IF.7.b ,12.F.BF.3, 12.F.BF.4.b)
Berkeley Heights Public Schools
3
COURSE PROFICIENCIES (continued)
17. To find the composition and inverse of a function. (12.F.BF.1.b, 12.F.BF.3, 12.F.BF.4.a,
12.F.BF.4.b, 12.F.BF.4.c)
18. To simplify expressions with rational exponents. (12.N.RN.1, 12.N.RN.2 )
19. To explore exponential models, properties of exponential functions, and solve exponential
equations. (12.F.LE.1.a, 12.F.LE.1.c, 12.F.LE.3, 12.F.LE.4, 12.F.LE.5)
20. To explore logarithmic models, properties of logarithmic functions, and solve logarithmic
equations. (12.F.BF.5, 12.F.LE.4)
21. To explore natural logarithms. (12.F.BF.5, 12.F.LE.4)
22. To identify properties and perform operations with rational expressions, and graph and solve
rational equations. (12.A.APR.7, 12.A.REI.2)
23.
To graph and write the equations of the conic sections. (12.G.GPE.1, 12.G.GPE.2,
12.G.GPE.3)
24. To identify and generate mathematical patterns, arithmetic sequences, and geometric
sequences. (12.A.CED.4)
25. To write and evaluate an arithmetic series and a finite/infinite geometric series.
(12.A.SSE.4)
Berkeley Heights Public Schools
4
STUDENT PROFICIENCIES
The student will be able:
1. To identify, graph, and order real numbers.
2. To simplify and evaluate algebraic expressions.
3. To solve linear and quadratic equations.
4. To solve problems by writing equations.
5. To solve, graph, and write inequalities.
6. To solve and graph absolute value equations and inequalities.
7. To find experimental, theoretical, and conditional probabilities.
8. To count permutations and combinations.
9. To find the probability of events (A and B) and (A or B).
10. To identify and graph relations, linear functions, quadratic functions, exponential
functions, and logarithmic functions.
11. To solve and graph problems involving direct, inverse, and combined variation.
12. To write linear equations that model real world data and be able to make predictions.
13. To translate absolute value functions and parabolic functions vertically and horizontally.
14. To solve a system of equations by graphing, substitution, elimination, inverse matrices,
and Cramer’s Rule.
15. To solve a system of inequalities by graphing.
16. To use linear programming to solve maximum and minimum problems
17. To use matrices to organize data.
18. To add, subtract, and multiply matrices.
19. To find the determinant of 2x2 and 3x3 matrices.
20. To find the inverse of 2x2 matrices.
Berkeley Heights Public Schools
5
STUDENT PROFICIENCIES (continued)
21. To find the inverse of 3x3 matrices using TI-84
22. To solve matrix equations by using inverse matrices, Cramer’s Rule, and augmented
matrices.
23. To convert the standard form of a parabola to vertex form, find maximum and minimum
values, and identify the axis of symmetry.
24. To find the nature of the solutions of a quadratic equation using the discriminant and
solve a quadratic equation by factoring, completing the square, and the quadratic
formula.
25. To identify and use complex numbers.
26. To classify polynomials and model data using polynomials.
27. To divide polynomials using long division and synthetic division.
28. To solve polynomial equations by graphing and factoring.
29. To use the rational root theorem, the Fundamental Theorem of Algebra, Pascal’s
Triangle, and the Binomial Theorem.
30. To add, subtract, multiply, divide, and simplify radical expressions.
31. To solve and graph radical equations.
32. To simplify expressions with rational exponents.
33. To solve problems involving exponential growth and decay.
34. To use the properties of exponential and logarithmic functions.
35. To solve exponential and logarithmic equations.
36. To use natural logarithms and e as a base.
37. To identify the properties of rational equations and use the properties to graph.
38. To add, subtract, multiply, divide, and simplify rational expressions.
39. To simplify complex fractions.
Berkeley Heights Public Schools
6
STUDENT PROFICIENCIES (continued)
40. To solve rational equations and use rational equations in problem solving.
41. To identify and graph conic sections.
42. To write the equations of circles, ellipses, and hyperbolas.
43. To use the characteristics of circles, ellipses, and hyperbolas to graph.
44. To use the equation of the conics to perform vertical and horizontal shifts.
45. To identify mathematical patterns and use formulas to generate terms of a pattern.
46. To identify and generate arithmetic sequences and geometric sequences.
47. To write and evaluate an arithmetic series and a finite/infinite geometric series
48. To use summation notation.
Berkeley Heights Public Schools
7
METHODS OF EVALUATION
1. Homework and class work.
2. Class participation / Board work.
3. Tests and quizzes.
4. Projects.
5. Notebooks (Optional).
6. Cooperative learning assignments.
7. Mid-term and final examinations.
Berkeley Heights Public Schools
8
SCOPE AND SEQUENCE
COURSE OUTLINE/STUDENT OBJECTIVES
The student will be able to:
CCSS
Standard
Category.
Domain
Course Outline/Student Objectives
12.A.SSE
1.a
I.
Tools Of Algebra ( 3 weeks)
1.b
A. Properties of Real Numbers
2
1. Graph and order real numbers
2. Identify and use properties of real numbers
12.A.CED
1
B. Algebraic Expressions
3
1. Evaluate algebraic expressions
4
2. Simplify algebraic expressions
C. Solving Equations
12.A.REI
1
1. Solve equations
3
2. Solve problems by writing equations
D. Solving Inequalities
12.N.RN
3
1. Solve and graph inequalities
2. Solve and write compound inequalities
E. [Absolute Value Equations and Inequalities]
1. Solve absolute value equations
2. Solve absolute value inequalities
12.S.CP
1
II.
Probability (2.5 weeks)
2
A. Probability (Section 1-6)
3
1. Find experimental probabilities
5
2. Find theoretical probabilities
6
B. Permutations and Combinations (Section 6-7)
7
1. Count permutations
8
2. Count combinations
9
C. Probability of Multiple Events (Section 9-7)
1. Find the probability of events (A and B)
12.S.MD
1
2. Find the probability of events (A or B)
3
D. Probability Distributions (Section 12-1)
4
1. To make a probability distribution
2. To use a probability distribution in a simulation
E. [Conditional Probability (Section 12-2)]
1. Find conditional probabilities using a formula
2. Find conditional probabilities using a tree diagram
12.F.IF
1
III. Functions, Equations, And Graphs (2.5 weeks)
2
A. Relations and Functions
4
1. Graph relations
5
2. Identify functions
6
B. Linear Equations
7
Berkeley Heights Public Schools
9
12.F.IF
9
12.F.BF
3
12.A.CED
2
12.A.SSE
1.b
12.N.Q
1
12.A.REI
10
12
12.F.LE
1.a
2
5
12.S.ID
6.a
6.c
7
8
12.A.CED
3
12.A.REI
5
6
11
12
9.1/12/A
1
12.N.VM
6
7
8
9
10
12
Berkeley Heights Public Schools
III.
IV.
V.
Functions, Equations, And Graphs (continued)
1. Graph linear equations
2. Write equations of lines
3. Write and graph piecewise functions
C. Direct Variation
1. Write direct variation equations
2. Interpret these equations and use them to solve for a
missing value
D. Using Linear Models
1. Write linear equations that model real world data
2. Make predictions from linear models
3. [Finding the line of best fit]
E. [Absolute Value Functions and Graphs]
1. Graph absolute value functions
2. Identify parts of an absolute value graph
F. [Vertical and Horizontal Translations]
1. Analyze vertical and horizontal translations
2. Write equations of a function given the vertical and
horizontal translations
G. [Two Variable Inequalities]
1. Graph linear inequalities
2. Graph absolute value inequalities
Linear Systems (3 weeks)
A. Solve System of Equations by Graphing
B. Solving Systems Algebraically
1. Solve a system by substitution
2. Solve a system by elimination
C. Solve Systems of Linear Inequalities
D. [Linear Programming]
1. Find maximum and minimum values
2. Solve problems with linear programming
E. Graphs in Three Dimensions (Honors Optional)
1. Graph points in three dimensions
2. Graph an equation in three dimensions
F. Systems With Three Variables (Honors)
1. Solve systems in three variables by elimination
method
2. Solve systems in three variables by substitution
method
Matrices (Honors) (2.5 weeks)
A. Organizing Data Into Matrices
1. Identify matrices and their elements
2. Organizing data into matrices
B. Adding and Subtracting Matrices
1. Add and subtract matrices
2. Solve certain matrix equations
10
12.A.REI
8
9
12.F.IF
7.a
8
9
12.F.BF
3
12.A.SSE
2
3.a
3.b
12.A.CED
1
12.A.REI
4.a
4.b
12.N.CN
1
2
4
5
7
Berkeley Heights Public Schools
V.
Matrices (Honors) (continued)
C. Matrix Multiplication
1. Multiply a matrix by a scalar
2. Multiply two matrices
D. Geometric Transformations with Matrices (Optional)
1. Represent translations and dilations with matrices
2. Represent reflections and rotations with matrices
E. 2 x 2 Matrices, Determinants and Inverses
1. Evaluate determinants of a 2 x 2 matrix
2. Find inverse matrices
3. Use inverse matrices to solve matrix equations
F. 3 x 3 Matrices, Determinants and Inverses
1. Evaluate determinants of a 3 x 3 matrix
2. Use inverse matrices to solve matrix equations
G. Solve System Using Inverse Matrices
H. Augmented Matrices and Systems
1. Solve a system of equations using Cramer’s Rule
2. Solve a system using augmented matrices
VI. Quadratic Equations And Functions (3 weeks)
A. Modeling Data with Quadratic Functions
1. Identify quadratic functions and graphs
2. Model data with quadratic functions
B. Properties of Parabolas
1. Graph quadratic functions
2. Find maximum and minimum values
C. Translating Parabolas in the Vertex Form
D. Factoring Quadratic Expressions
1. Find common and binomial factors
2. Factor special cases
E. Quadratic Equations
1. Solve equations by factoring and finding square roots
2. Solve equations by graphing (Optional Regular)
F. [Complex Numbers]
1. Identify and graph complex numbers
2. Add, subtract, and multiply with complex numbers
G. [Completing the Square] (Optional Regular)
1. Solve quadratic equations by completing the square
2. Rewrite functions by completing the square
H. The Quadratic Formula
1. Solve quadratic equations by using the Quadratic
Formula
2. Use the discriminant to determine the types of
solutions
11
12.A.APR
1
2
3
5
6
12.N.CN
3
8
9
12.A.SSE
2
12.F.IF
4
7.b
12.A.SSE
2
3.a
3.b
12.N.RN
1
2
12.F.IF
7.b
12.F.BF
1.b
3
4.a
4.b
4.c
4.d
12.A.REI
12.F.LE
2
1.a
1.c
3
Berkeley Heights Public Schools
VII. Polynomials And Polynomial Functions (2 weeks)
A. Polynomial Functions
1. Classify polynomials
2. To model data using polynomial functions
B. Polynomials and Linear Factors
1. Analyze the factored form of a polynomial
2. Write a polynomial function from its zeros
C. Dividing Polynomials
1. To divide polynomials using long division
2. To divide polynomials using synthetic division
D. [Solving Polynomial Equations]
1. Solve polynomial functions by factoring
2. Solve polynomial functions by graphing
E. [Theorems About Roots of Polynomial Equations]
(Regular if Time Allows)
1. Solve equations using the rational root theorem
2. Solve equations using the irrational and
imaginary root theorems
F. [The Fundamental Theorem of Algebra]
1. Identify and Understand the Fundamental Theorem of
Algebra
2. Apply the Fundamental Theorem of Algebra
G. The Binomial Theorem
(Honors)(Regular if Time Allows)
1. Use Pascal’s Triangle
2. Use the binomial theorem
VIII. Radical Functions And Rational Exponents (2 weeks)
A. Simplify nth Roots and Radical Expressions
B. Multiply and Divide Radical Expressions
1. To multiply radical expressions
2. To divide radical expressions
C. Binomial Radical Expressions
1. Add and subtract radical expressions
2. Multiply and divide binomial radical expressions
D. Simplifying Expressions with Rational Exponents
E. Solving Radical Equations
F. Function Operations
1. To add, subtract, multiply, and divide functions
2. Find the composite of two functions
G. Finding Inverse Relations and Functions
H. [Graphing Radical Functions] (Regular if Time
Allows)
IX.
Exponential And Logarithmic Functions (2 weeks)
A. Exploring Exponential Models
1. To model exponential growth
12
4
5
12.F.BF
3
5
12.F.IF
7.e
12.A.APR
7
12.A.REI
2
12.F.IF
7.d
12.G.GPE
1
2
3
Berkeley Heights Public Schools
X.
XI.
2. To model exponential decay
B. Properties of Exponential Functions
1. Identify the role of constants in y = abcx
2. Use e as a base
C. [Logarithmic Functions as Inverses]
1. Write and evaluate logarithmic expressions
2. Graph logarithmic functions (Regular)
D. [Properties of Logarithms]
1. Identify properties of logarithms
2. Use properties to expand, contract, and simplify
logarithmic expressions
E. [Exponential and Logarithmic Equations]
1. To solve exponential equations
2. To solve logarithmic equations
F. [Natural Logarithms]
1. To evaluate natural logarithmic expressions
2. To solve equations using natural logarithms
Rational Functions (2 weeks)
A. Inverse Variation
1. Use inverse variation
2. Use combined variation
B. Graphing Inverse Variations (Honors)
1. Identify an inverse variation or translation of inverse
variation
2. Graph an inverse variation or its translation
C. Rational Functions and Their Graphs (Honors)
1. Identify properties of rational functions
2. Graph rational functions
D. Multiplying, Dividing, and Simplifying Rational
Expressions
E. Adding and Subtracting Rational Expressions
1. Add and subtract rational expressions
2. Simplify complex fractions
F. Solving Rational Equations
1. Solve rational equations
2. Use rational equations in problem solving
Quadratic Relations (Honors) (2.5 weeks)
A. Exploring Conic Sections
1. Identify a conic section by graph or equation
2. Graph a conic section
B. Parabolas
1. Write the equation of a parabola
2. Graph the parabola
C. Circles
13
12.A.CED
4
12.A.SSE
4
1. Write the equation of a circle and graph
2. Use the center and radius of a circle to graph
D. Ellipses
1. Write the equation of an ellipse and graph
2. Use the foci of an ellipse to graph
XI. Quadratic Relations (continued)
E. Hyperbolas
1. Graph hyperbolas
2. Find and use the foci of a hyperbola
F. Translating Conic Sections
1. Write the equation of a translated conic section
2. Identify the equation of a translated conic section
XII. Sequences And Series (If Time Permits) (1.5 weeks)
A. Mathematical Patterns
1. Identify mathematical patterns
2. Use a formula to find a term of a sequence
B. Arithmetic Sequences
1. Identify an arithmetic sequence and its common
difference
2. Write a recursive and/or explicit formula to generate
an arithmetic sequence
C. Geometric Sequences
1. Identify a geometric sequence and its common ratio
2. Write a recursive and/or explicit formula to generate a
geometric sequence
D. Arithmetic Series
1. Write and evaluate arithmetic series
2. Use summation notation
E. Geometric Series
1. Evaluate a finite geometric series
2. Evaluate an infinite geometric series
Topics listed in brackets throughout the scope and sequence should be omitted from the Algebra 2
Concepts course requirements
Topics covered only in Honors are noted as such: (Honors)
Berkeley Heights Public Schools
14
RESOURCES/ACTIVITES GUIDE
Text:
Bellman, Allan E., et. al. Algebra 2. Upper Saddle River, NJ: Prentice Hall, 2004.
Prentice Hall Teacher Online Access Pack
Featuring Interactive Textbook
Prentice Hall Algebra 2 Workbooks
Practice Workbook
Hands-On Activities
Technology Activities
Teaching Resources Kit
Grab & Go Chapter Support Files
Cumulative Assessment
Solution Key
Teacher Express CD-ROM
Prentice Hall Assessment System
Computer Test Generator-Workbook and CD-ROM
Assessment Resources
Content Diagnostic Tests
Skills and Concepts Review
Test Preparation
Test-Taking Strategies with Transparencies
Presentation Assistant Plus!
Prentice Hall Presentation Pro, CD-ROM
Daily Skills Check and Lesson Quiz transparencies
Resource Pro with Planning Express, CD-ROM
Berkeley Heights Public Schools
15
SUGGESTED AUDIO VISUAL/COMPUTER AIDS
Texas Instruments TI-84 Plus Graphing Calculators
Texas Instruments TI-SmartView Emulator Software for the TI-84 Plus Family
Graphing Calculator View Screen for Overhead Projector
Internet Access to:
www.PHSchool.com
www.algebrahelp.com
http://mathforum.org/dr.math
www.terragon.com/tkobrien/algebra/
Students can access a help desk, graph functions, and chat with others regarding Algebra 2
topics.
Manipulatives
Overhead Projector and transparencies
Berkeley Heights Public Schools
16
SUGGESTED MATERIALS
Resources for Students
Bellman, Allan E., et. al. Algebra 2. Upper Saddle River, NJ: Prentice Hall, 2004.
Prentice Hall Algebra 2 Practice Workbook
Prentice Hall Algebra 2 Hands-On Activities
Resources for Teacher
Bellman, Allan E., et. al. Algebra 2. Upper Saddle River, NJ: Prentice Hall, 2004.
Transparencies
Manipulatives
Teacher’s Guide, Test Preparation
Berkeley Heights Public Schools
17