ŠĻą”±į>ž’ ”–ž’’’’“’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’ģ„Į7 łæŁ%bjbjUU ƒR7|7|®!'’’’’’’lffffŚŚŚ4ģģģhTptcšĪšdT"vvv‘Ž4Sā™ä™ä™ä™ä™ä™ä™$1œ Qž†šŚo‘ooš ffvvš   o^fRvŚvā™ oā™  -$ījˆø"Śę˜vä 0@E¤ĒŽģĶjņ’`ę˜ü3š0cšR“”מ7äמę˜ ffffŁ Algebra 2 Curriculum November 7, 2006 Mathematics Department Table of Contents TOC \f  Syllabus  PAGEREF _Toc148245026 \h 3 Philosophy  PAGEREF _Toc148245027 \h 5 Content Standards  PAGEREF _Toc148245028 \h 6  Syllabus TC "Syllabus" \f C \l "1"  Name of Course: Algebra 2 Grade Levels: 10-12 Department: Mathematics Length & Credit:  FORMDROPDOWN ,  FORMDROPDOWN  credit Prerequisites: Algebra 1 General Description: This course is a review of the properties studied in Algebra 1 and their extension to sets of complex numbers. Topics will include but are not limited to the following: Models and Functions Linear Relationships and Functions Linear Systems Quadratic Equations and Functions Polynomials and Polynomial Functions Exponential and Logarithmic Functions* Rational Functions* School Wide Rubrics Used: Mathematics School-Wide Rubric Recommended Text: Bellman, Allan., et. al., Advanced Algebra. Needham, Massachusetts: Prentice Hall, 1998. Software: Geometer’s Sketchpad, Spreadsheet Course Sequence: Graphical Models (light) Relations and Functions Working with Functions Vertical and Horizontal Translations (light) Linear Equations and Slope Direct Variation Interpreting Linear Functions One-Variable Equations and Inequalities Exploring and Graphing Systems of Equations Solving Systems Algebraically Systems with Three Variables (light) Inverse Matrices and Systems (light) Modeling Data with Quadratic Functions Properties of Parabolas Comparing Vertex and Standard Forms Quadratic Equations Complex Numbers Completing the Square The Quadratic Formula Inverses and Square Root Functions Properties of Exponents Power Functions and Their Inverses Polynomial Functions Polynomials & Linear Factors (exclude Factor Theorem) Solving Polynomial Equations Dividing Polynomials (light) Exploring Exponential Models* Exponential Functions* Logarithmic Functions as Inverse* Properties of Logarithms* Exponential and Logarithmic Equations* Natural Logarithms* Exploring Inverse Variation* Graphing Inverse Variations* Rational Functions and Their Graphs* Rational Expressions* Adding and Subtracting Rational Expressions* Solving Rational Equations* *If time permits Mathematics Education Philosophy TC "Philosophy" \f C \l "1"  The mathematics program at AHS attempts to prepare the student for active participation in a complex and ever-changing society. In order to accomplish this, the Mathematics Department believes that the student must be actively involved in the processes of reasoning, problem solving, communicating, computing, and estimating. Our students will be expected to show proficiency in each of these major areas. The student should be able to: Communicate information to others in the language of mathematics using mathematical models, graphs, pictures, and symbols; Collect, organize, and analyze raw data in order to make predictions, to make inferences, and to draw reasonable conclusions; Use inductive reasoning to formulate mathematical hypotheses and deductive reasoning to justify those hypotheses; Choose appropriate methods for solving numerical, algebraic, and geometric problems; Use the tools of technology to accomplish the above objectives; Demonstrate an understanding of individual rights, roles, and responsibilities in their community; Develop personal goals for further education and/or vocational planning.  TC "Content Standards" \f C \l "1" PROGRAM AREA: Mathematics CONTENT AREA: Algebra 2 Educational experiences in the 10-12 Algebra 2 program will assure that students attain the performance standards and learning outcomes listed below: Basic text resources: Bellman, Allan., et. al., Advanced Algebra. Needham, Massachusetts: Prentice Hall, 1998. PERFORMANCE STANDARDSENDURING UNDERSTANDINGESSENTIAL QUESTIONSASSESSMENT1. Algebraic Reasoning: Patterns and Functions Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.Students should understand, describe, and generalize patterns and functional relationships. (1.1) Students should model real-world situations and make generalizations about mathematical relationships using a variety of patterns and functions.(1.1) Students should represent and analyze linear relationships symbolically and with tables and graphs. (1.2) Students should relate the behavior of functions and relations to specific parameters and determine functions to model real-world situations. (1.2) Students should use operations, properties and algebraic symbols to determine equivalence and solve problems containing equations and inequalities. (1.3) Students should use and extend algebraic concepts to include real and complex numbers, vectors and matrices.What are the properties of linear functions? What is the graph of a given function? What is the equation for a given graph? What are the slope, x-intercept, and y-intercept and what do they mean? What is the algorithm to solving an equation, inequality, linear, quadratic and absolute value? What is the algebraic sentence for the word problem? What are the methods of solving linear systems? What is the simplified form of a given equation/inequality? What is the domain and range of a given relation/function? What are the properties of exponential, polynomial, rational and logarithmic functions? What is the difference between direct and inverse variations? What are the effects of changing the parameters on a graph or function or relation? How can linear, exponential and polynomial functions be evaluated and interpreted? Is the composition of functions commutative? Which of the four main operations are commutative? What functions have inverses? How are the graphs of a function and their inverses related? What two methods can be used to solve exponential equations? Class participation Homework assignments Lesson quizzes Notebooks/Binders Project(s) Tests Time FrameTeachers will review the required material and make appropriate choices as to the time spent on each performance standard and objective. This should be reinforced throughout the year. (24-32 weeks) PROGRAM AREA: Mathematics CONTENT AREA: Algebra 2 Educational experiences in the 10-12 Algebra 2 program will assure that students attain the performance standards and learning outcomes listed below: Basic text resources: Bellman, Allan., et. al., Advanced Algebra. Needham, Massachusetts: Prentice Hall, 1998. PERFORMANCE STANDARDSENDURING UNDERSTANDINGESSENTIAL QUESTIONSASSESSMENT2. Numerical and Proportional Reasoning: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.Students should understand that a variety of numerical representations could be used to describe quantitative relationships. (2.1) Students should extend the understanding of numbers to include integers, rational numbers, real numbers and complex numbers. (2.1) Students should interpret and represent large sets of numbers with the aid of technologies. (2.1) Students should use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. (2.2) Students should develop strategies for computation and estimation using properties of number systems to solve problems. (2.2) Students should solve proportional reasoning problems. (2.2) Students should investigate mathematical properties and operations related to objects that are not numbers. What are real numbers? What are integers? What are rational numbers? What are complex numbers? What is the appropriate form of number to solve practical problems? What is an appropriate method for solving a problem? What is the number in scientific notation? Is this a reasonable estimate for this answer? How could this be solved using dimensional analysis? How can problems be solved using direct or inverse variation? How is the graphing calculator best utilized to organize and analyze large amounts of data? How is the magnitude of results affected by computations with powers and roots? How can expressions with complex numbers and/or logarithms be simplified? Class participation Homework Assignments Lesson quizzes Notebooks/Binders Project(s) Tests Time FrameTeachers will review the required material and make appropriate choices as to the time spent on each performance standard and objective. This should be reinforced throughout the year. 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