Algebra 2 Syllabus Certificated Teacher: Date: 2012-13 Desired Results Course Title/Grade Level: Algebra 2 A and B Credit: one semester (.5) x two semesters (1) Estimate of hours per week engaged in learning activities 5 hours of class work per week. Prerequisites and/or recommended preparation: Completion of Algebra 1 and Geometry Instructional Materials: All learning activity resources and folders are contained within the student online course. Online course is accessed via login and password assigned by student s school (web account) or emailed directly to student upon enrollment, with the login website address. This course requires a MathXL account that you will receive from your virtual learning teacher. Graphing calculator recommended ( not required) Ti-83 Plus; Ti-84 Plus, Ti-84 Plus Silver Course Overview: This course is designed to prepare students for success in their future. Emphasis will be given to equip students with skills and understandings required for success for higher level math courses. At the same time, this course will focus on the keys to the implementation of math in everyday living. Enduring Understandings for Course: We can use a variety of mathematical tools to describe our world and help solve daily problems. First Semester (2A) Unit 1 Transformations of Models Students will identify and apply transformations both algebraically and graphically to the family of functions previously explored in Algebra 1. Students will continue to studying transformations throughout this course as they extend their understanding of Unit 2 Extending Linear Models Students will extend their understanding of linear functions from Algebra 1 to include linear programming and linear equations in three dimensions. Unit 3 - Extending Exponential Models Students will extend their understanding of exponential functions from Algebra 1 to include the use of logarithms. Unit 4 Extending Quadratic Models Students will complete their study of the complex number system by extending their understanding of quadratic functions from Algebra 1 to include non-real solutions. The vertex form of a quadratic function is used to help students analyze quadratic functions and their graphs. Second Semester (2B) Unit 5 Higher Order Polynomial Functions Students will extend their understanding of functions and their zeros to include higher degree polynomial Equivalence of polynomial expressions will be explored by using factor and remainder theorems. Unit 6 Rational Expressions and Functions A central theme of this unit is that the arithmetic operations on rational expressions are governed by the same rules as the arithmetic operations on rational numbers. Students will apply the concept of equivalence to simplify rational expressions and solve rational equations. The exploration of the zeros of rational functions provides an introduction to the asymptotic behavior of
Unit 7 Extending Trigonometric Models Students will extend their understanding of trigonometry as ratios from Geometry to include trigonometric In addition to becoming fluent with the unit circle and the Pythagorean identity, students will graph and transform trigonometric functions to model and solve problems. Unit 8 Probability and Statistics Students will extend their understanding of probability and statistics. Establish Goals: (Grade Level Expectations) A2.1. Core Content: Solving problems A2.2. Core Content: Numbers, expressions, and operations A2.3. Core Content: Quadratic functions and equations A2.4. Core Content: Exponential and logarithmic functions and equations A2.5. Core Content: Additional functions and equations A2.6. Core Content: Probability, data, and distributions A2.7. Additional Key Content A2.8. Core Processes: Reasoning, problem solving, and communication Understandings: Unit 1 Students will: 1. understand and identify transformation(s) when given a function. 2. understand and identify transformation(s) when given a table. 3. understand and identify transformation(s) when given a graph. 4. understand and apply transformation(s) to graphs. 5. Understand and apply transformation(s) to (quadratic, exponential, absolute value, and piecewise functions). Unit 2 Students will: 1. create and interpret constraint equations and their graphs. 2. understand how to optimize an objective function given a set of constraints. 3. understand how to write a system of equations in three dimensions. 4. understand how to create and interpret matrix equations for linear equations in three dimensions. 5. understand how to use matrices to solve a system of linear equations in three dimensions. 6. understand how to identify the solution of a 3x3 system of equations as intersecting planes, parallel planes, or coplanar figures. Essential Questions: How can linear models be used to solve real world problems and make predictions? How can quadratic models be used to solve real world problems and make predictions? How can polynomial functions be used to solve real world problems and make predictions? How can exponential and logarithmic models be used to solve real world problems and make predictions? How can rational and radical equations be used to model real world problems and make predictions? How can various functions be transformed? How can probability help you decide if an offer is fair? How can sequences and series be used to find different sums or specific term in a certain pattern?
Unit 3 Students will: 1. I can identify the rate of change and initial value of an exponential model. 2. I can model real-world situations with exponential 3. I can use logarithms to solve exponential equations. 4. I can apply transformations to exponential Unit 4 Students will: 1. I can perform the three mathematical operations addition, subtraction and multiplication on non-real numbers. 2. I can solve quadratic equations which have nonreal solutions. 3. I can identify whether the roots of a quadratic function are real or non-real given an equation or a graph. 4. I can write quadratic functions in vertex form. 5. I can graph quadratic functions in vertex form. 6. I can apply transformations to quadratic Unit 5 Students will: 1. understand and use the remainder and factor theorems. 2. understand how to factor higher order polynomials. 3. understand and use arithmetic operations (add, subtract, multiply, divide) on functions to create equivalent forms. 4. determine a function rule for a function when given the graph. 5. determine the number of real and non-real zeros when given a function. 6. apply transformations to higher degree polynomial Unit 6 Students will: 1. I can apply properties of exponents to simplify expressions with rational exponents. 2. I can simplify rational expressions. 3. I can use arithmetic operations (add, subtract, multiply, divide) on rational expressions to create equivalent forms. 4. I can solve rational equations in the form of proportions. 5. I can model problem situations with rational 6. I can identify the domain of a rational function. 7. I can graph rational 8. I can determine the zeros of a rational function. Unit 7 Students will: 1. I can use both radian and degree measure fluently. 2. I can identify trigonometric values of common angles on the unit circle fluently. 3. I can graph the Sine, Cosine, and Tangent 4. I can apply transformations to trigonometric
5. I can use trigonometric functions to solve right triangles. 6. I can use trigonometric functions to solve non-right triangles. Unit 8 Students will: 1. I can solve problem involving the fundamental counting principle. 2. I can solve problems involving permutations and combinations. 3. I can find the theoretical probability of and event. 4. I can find the experimental probability of an event. 5. I can determine whether events are independent or dependent. 6. I can find the probability of independent and dependent events. 7. I can find the probability of mutually exclusive events 8. I can find the probability of inclusive events. Students will know: How to model various situations with many powerful mathematical tools so that they can make predictions and describe pattern in depth and detail. Students will be able to: Apply and use linear models. Apply and use quadratic models. Apply and use exponential and logarithmic Apply and use rational and radical Apply and use polynomial Apply and use piecewise Apply algebraic properties to all Transform Use and understand probability skills. Apply and use sequence and series formulas. Evidence of Assessment What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skill attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] Performance Tasks: Units are arranged so that students work through ALEKS to master the I can statements for each target. Once they have gained the skill through ALEKS they will then complete activities for each target that requires them to apply their skills to real world problems. The unit is then completed with an assessment of both skills and application problems.
Other Evidence (self-assessments, observations, work samples, quizzes, tests and so on): Work in MathXL Quizzes and Assessments in MathXL Videos Activity completion Weekly blogging on a specific topic Types of Learning Activities Learning Activities: What sequence of learning activities and teaching will enable students to perform well at the understandings in Stage 2 and thus display evidence of the desired results in stage one? Possibly use the WHERE acronym to design activities (see below). Each unit follow the same basic pattern: 1. View videos and Take Notes 2. Weekly Blog Entries 3. Complete Assignments and Quizzes in MathXL 4. Unit Assessment in MathXL Indicate from the table below all applicable learning strategies that may be used in the course. Direct Instruction Indirect Instruction Experiential Learning Independent Study Interactive Instruction _x Structured Overview _x Mini presentatio n x Drill & Practice _x Demonstrations Other (List) x Problem-based _Case Studies x Inquiry x Reflective Practice Project Paper Concept Mapping Other (List) Virt. Field Trip Experiments x Simulations _x _Games Field Observ. _Role-playing x Model Bldg. Surveys Other (List) Essays _x Selfpaced computer Journals Learning Logs Reports Directed Study Research Projects Other (List) _x _Discussion Debates _Role Playing Panels Peer Partner Learning Project team Laboratory Groups x Think, Pair, Share Cooperative Learning Tutorial Groups Interviewing Conferencing Other (List)
Learning Activities Algebra 2 Through Modeling Course Learning Targets Algebraic Equivalence Multiple Representations First Semester I. Extending Our Understanding of Functions Unit 1 Transformations of Models A. Understanding how to identify Transformation s. B. Applications of Transformations. C. Connections Apply transformations to the family of functions (linear, quadratic, exponential, square root, absolute value, and piecewise functions) to model real world situations and general graphs. D. Communication Unit 2 Extending Linear Models A. Understanding the use of linear programming in solving problems. B. Understanding linear equations in three dimensions. C. Connections Model real world situations D. Communication Unit 3 Extending Exponential Models A. Understanding the application of exponential models to real world situations. B. Understanding the application of logarithms to solve exponential equations. C. Connections Model real world situations Extend systems to include any combination of 2 linear, exponential. D. Communication Unit 4 Extending Quadratic Models A. Understanding the complex number system. B Understanding complex solutions to quadratic equations. C. Understanding vertex form of a quadratic function. D. Connections Model real world situations Extend systems to include linear & quadratic or 2 quadratic E. Communication
Second Semester II. Extending Our Family of Functions III. Trigonometric Functions IV. Inferences and Conclusions from Data Unit 5 Higher Degree Polynomial Functions Unit 6 Rational Expressions and Functions Unit 7 Extending Trigonometric Models Unit 8 Probability and Statistics A. Understanding the equivalence of polynomial expressions. B. Understanding the relationship between zeros and the analytical or graphical representations of polynomial C. Connections Model real world situations D. Communication A. Understanding the equivalence of rational expressions. B. Understanding the relationship between zeros & vertical asymptotes and the analytical and graphical representations of polynomial C. Connections Rational numbers and rational expressions Model real world situations D. Communication A. Understanding the unit circle (radian and degree measure, common angles, and the Pythagorean identity) B. Understanding trigonometric C. Understanding the application of trigonometric D. Connections Apply transformations to trigonometric Model real world situations. E. Communication A. Understand independence and conditional probability and use them to interpret data. B. Understand and use the rules of probability to compute probabilities of compound events in a uniform probability model. D. Connections Model real world situations E. Communication 1 st Semester Algebra 2A Learning Activities Week 1 Getting Started Get Logged into Blackboard Check Announcements Go Through Start Here Set up MathXL account Find a Proctor Week 2 Start Unit 1 Transformation Models Unit 1 Target 1A Task #1 Exploring Transformations Task #2 Parent Functions Task #3 Target 1A Quiz Week 3 Continue Unit 1 Transformation Models
Unit 1 Target 1B Task #1 Transforming Linear Function (Notes Only) Task #2 Transforming Quadratic Functions (Notes Only) Task #3 Transforming Exponential Functions Task #4 Transforming Piece-wise Functions (Notes Only) Transforming Functions MathXL Assignment Week 4 Complete Unit 1 Transformation Models Unit 1 Target 1B Task #5 Target 1B Quiz Unit 1 Assessment Week 5 Start Unit 2 Extending Linear Models Unit 2 Target 2A Task #1 Linear Inequalities Task #2 Systems of Linear Inequalities Task #3 Linear Programming Week 6 Continue Unit 2 Extending Linear Models Unit 2 Target 2A Task #1 Target 2A Quiz Unit 2 Target 2B Task #1 Linear Functions in Three Dimensions Task #2 Solving Systems Using Matrices Week 7 Complete Unit 2 Extending Linear Models Unit 2 Target 2B Task #3 Target 2B Quiz Unit 2 Assessment Week 8 Start Unit 3 Extending Exponential Models Unit 3 Target 3A Task #1 Exponential Functions Growth and Decay Task #2 Curve Fitting with Exponential Models Task #3 Target 3A Quiz Week 9 Continue Unit 3 Extending Exponential Models Unit 3 Target 3B Task #1 Logarithmic Functions Task #2 Properties of Logarithms Task #3 Exponential and Logarithmic Equations Week 10 Continue Unit 3 Extending Exponential Models Unit 3 Target 3B Task #4 The Natural Base, e Task #5 Target 3B Quiz Week 11 Complete Unit 3 Benchmark #1 Unit 3 Assessment Benchmark #1
Week 12 Start Unit 4 Extending Quadratic Models Unit 4 Target 4A Task #1 Complex Numbers and Roots Task #2 Operations with Complex Numbers Task #3 Target 4A Quiz Week 13 Continue Unit 4 Extending Quadratic Models Unit 4 Target 4B Task #1 The Quadratic Formula Task #2 Target 4B Quiz Week 14 Continue Unit 4 Extending Quadratic Models Unit 4 Target 4C Task #1 Graphing Quadratic Equations in Vertex Form Task #2 Writing Quadratic Functions in Vertex Form Week 15 Continue Unit 4 Extending Quadratic Models Unit 4 Target 4c Task #3 Graphing Quadratics Using Transformations Task #4 Target 4C Quiz Week 16 Complete Unit 4 Extending Quadratic Models Notebook Check Unit 4 Assessment Notebook Check Week 17 Finish up any needed work 2 nd Semester Algebra 2B Learning Activities Week 1 Getting Started Get Logged into Blackboard Check Announcements Go Through Start Here Set up MathXL account Find a Proctor Week 2 Start Unit 5 Higher Degree Polynomials Unit 5 Target 5A Task #1 Polynomials Task #2 Multiplying Polynomials Task #3 Dividing Polynomials Week 3 Continue Unit 5 Higher Degree Polynomials Unit 5 Target 5A
Task #4 Factoring Polynomials Task #5 Finding Root of Polynomial Functions Task #6 Target 5A Quiz Week 4 Complete Unit 5 Higher Degree Polynomials Unit 5 Target 5B Task #1 Writing Polynomials Functions Given a Graph Task #2 Investigating Graphs of Polynomial Functions Week 5 Complete Unit 5 Higher Degree Polynomials Unit 5 Target 5B Task #3 Transforming Polynomial Functions Task #4 Target 5B Quiz Unit 5 Assessment Week 6 Start Unit 6 Rational Expressions and Functions Benchmark #2 Benchmark #2 Unit 6 Target 6A Task #1 Radical Expressions and Rational Exponents Task #2 Multiplying and Dividing Rational Expressions Week 7 Continue Unit 6 Rational Expressions and Functions Unit 6 Target 6A Task #3 Adding and Subtracting Rational Expressions Task #4 Solving Rational Expressions Task #5 Target 6A Quiz Week 8 Continued Unit 6 Rational Expression and Functions Unit 6 Target 6B Task #1 Rational Functions Task #2 Finding the Zeros of Rational Functions Task #3 Target 6B Quiz Week 9 Complete Unit 6 Start Unit 7 Extending Trigonometric Models Unit 6 Assessment Unit 7 Target 7A Task #1 Angles of Rotation Task #2 The Unit Circle Task #3 Target 7A Quiz Week 10 Continue Unit 7 Extending Trigonometric Models Unit 7 Target 7B Task #1 Graphs of Sine and Cosine Task #2 Target 7B Quiz Week 11 Continue Unit 7 Extending Trigonometric Models Unit 7 Target 7C Task #1 Right Triangle Trigonometry
Task #2 Law of Sines Task #3 Law of Cosines Week 12 Continue Unit 7 Extending Trigonometric Models Unit 7 Target 7C Task #4 Target 7C Quiz Unit 7 Assessment Week 13 Start Unit 8 Probability Benchmark #3 Benchmark Assessment Unit 8 Target 8A Task #1 Permutations and Combinations Week 14 Continue Unit 8 Probability Unit 8 Target 8A Task #2 Theoretical and Experimental Probability Task #3 Target 8A Quiz Week 15 Continue Unit 8 Probability Unit 8 Target 8B Task #1 Independent and Dependent Probability Task #2 Compound Events Task #3 Target 8B Quiz Week 16 Complete Unit 8 Probability Notebook Check Week 17 Unit 8 Assessment Notebook Check Finish up any needed work