WOODLAND HILLS HIGH SCHOOL LESSON PLAN SAS and Understanding By Design Template Name _Steve Flanders__________ Date 12-13-13 Length of Lesson __1 weeks_____ Content Area Trigonometry_______ Edline was updated this week: x My class website was updated this week: x STAGE I – DESIRED RESULTS LESSON TOPIC: Polynomial and Rational Functions BIG IDEAS: Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. (Content standards, assessment anchors, eligible content) objectives, and skill focus) UNDERSTANDING GOALS (CONCEPTS): Students will understand: *Algebraic properties, processes and representations *Quadratic functions and equations *Polynomial functions and equations Students will understand: 1. 2. 3. Write an equation for a quadratic function in standard form. Graph a quadratic function using the vertex and intercepts. Write an equation for a quadratic function in vertex form by completing the square. 4. Divide polynomials using long division and synthetic division. 5. Apply the remainder and factor theorems. 6. Simplify imaginary and complex numbers. 7. Solve quadratic equations with complex number solutions 8. Find the domain and asymptotes of a rational function 9. Graph rational functions. 10. Solve applications involving quadratic functions. VOCABULARY: *Axis of Symmetry, Vertex, Standard Form *Synthetic Division, Remainder Theorem, Factor Theorem *Imaginary Unit, Complex Number, Complex Conjugates, Principle Square Root *Rational Function, Vertical, Slant & Horizontal Asymptotes 2.8.11.A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically. 2.8.11.E Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas) 2.8.11.N Solve linear, quadratic and exponential equations both symbolically and graphically. 2.8.11.Q Represent functional relationships in tables, charts and graphs. 2.8.11.S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8.11.T Analyze and categorize functions by their characteristics. ESSENTIAL QUESTIONS: How do quadratic equations and their graphs and/or tables help us interpret events that occur in the world around us? How can you extend algebraic properties and processes to quadratic, exponential and polynomial expressions and equations and then apply them to solve real world problems? STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES): Students will be able to: Represent exponential, quadratic, and polynomial functions in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the growth/decay rate of the associated exponential equation to each representation. *Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems. *Represent a quadratic function in multiple ways, including tables, graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated quadratic equation to each representation. STAGE II – ASSESSMENT EVIDENCE PERFORMANCE TASK: Students will demonstrate adequate understanding via a chapter test. FORMATIVE ASSESSMENT: #1 Pre-Assessment #2 Open-Ended Questions #3 Think-Pair-Share STAGE III: LEARNING PLAN INSTRUCTIONAL PROCEDURES: MATERIALS AND RESOURCES: Active Engagement use: #1 Note-Taking #2 Cooperative Education Textbook Notebook Projector/Promethean Board Scaffolding used: #1 Guided Notes #2 Build on prior knowledge MINI LESSON: *Quadratic Functions *Polynomial and Synthetic Division *Complex Numbers *Rational Functions INTERVENTIONS: Limited small group/ flexible grouping will occur. Students will be encouraged to stay for math lab, or find help with a math teacher. ASSIGNMENTS: p. 213-217 p. 239-241 p. 258-259 p. 278-281