Name: John Toney Date: 11-17-14 Content Area: Mathematics WOODLAND HILLS SECONDARY LESSON PLANS Length of Lesson: 20 days STAGE I – DESIRED RESULTS Lesson Topic (Modules, if applicable): Big Ideas: Understanding Goals (Concepts): Polynomial and Rational Functions 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. 1. Student Objectives (Competencies/Outcomes): Students will be able to: Essential Questions: Vocabulary: How do quadratic equations and their graphs and/or tables help us interpret events that occur in the world around us? *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 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 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? Write an equation for a quadratic function in standard form. 2. Graph a quadratic function using the vertex and intercepts. 3. 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. representations; relate the solution of the associated quadratic equation to each representation. STAGE II – ASSESSMENT EVIDENCE Performance Task: Formative Assessments: Students will demonstrate adequate understanding via a chapter test. Pre-assessments, open-ended questions, Think-Pair-Share STAGE III – LEARNING PLAN Interventions: Flexible grouping, students will be encouraged to attend Trig Lab Materials and Resources: Textbook, notes Procedures Instructional Procedures*: Monday Date: 11/17 Day: B “Do Now” – N/A “Mini Lesson” – N/A Students will complete a multiple choice assessment on transformations of graphs, compositions of functions, finding inverse functions and their graphs, and applying mathematical models through direct, inverse, and joint variations. Tuesday Date: 11/18 Day: A “Do Now” – N/A “Mini Lesson” – N/A Students will complete an open-ended assessment on transformations of graphs, compositions of functions, finding inverse functions and their graphs, and applying mathematical models through direct, inverse, and joint variations. Wednesday Date: 11/19 Day: B “Do Now” – Write three lines explaining what you know about a quadratic. “Mini Lesson” – Completing the Square of Quadratics Students will work on completing the square examples so they can write quadratics in standard form. Thursday Date: 11/20 Day: A “Do Now” – Complete the square of a quadratic. “Mini Lesson” – Completing the Square of Quadratics Students will work in pairs on completing the square examples so they can write quadratics in standard form. Friday Date: 11/21 Day: B “Do Now” – Solve a quadratic equation for the vertex and intercepts. “Mini Lesson” – Quadratic Functions – Sketching the graph of quadratics Students will practice sketching the graphs of quadratics, write quadratics in standard form, and use the completing the square method to write a quadratic in standard form. Assignments Continue studying for the Chapter 1.5-1.7 Open-Ended Assessment Read over Section 2.1 Complete the square problems from worksheet Finish the completing the square worksheet. *Include Do Now, Mini Lesson, Guided Practice, Independent Practice, Summations/Formative Assessments, Reflections Textbook – Page 213 #1-12 all (only parts a and b)