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WOODLAND HILLS HIGH SCHOOL LESSON PLAN SAS and Understanding By Design Template Name Melissa Broadwater Date 10/01/14 Calculus Length of Lesson 29 days Content Area Intro to STAGE I – DESIRED RESULTS LESSON TOPIC: Trigonometry BIG IDEAS: UNDERSTANDING GOALS (CONCEPTS): Students will understand how to use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. Measure and compare angles in degrees and radians Demonstrate mathematical solutions to problems (e.g., in the physical sciences). Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Present mathematical procedures and results clearly, systematically, succinctly and correctly. Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. Represent functional relationships in tables, charts and graphs Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Model situations geometrically to formulate and solve problems. Use graphing calculators to display periodic and circular functions; describe properties of the graphs. Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. ESSENTIAL QUESTIONS: How do you cChange from radian to degree measures and vice versa. What is meant by coterminal angles? In what ways can the unit circle be used? How do you determine the domain, range, and period of the sine and cosine functions using the unit circle? How do you sketch a graph of a sin, cos, tan, cot, sec, or csc? . M11.A.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, exponents and scientific notation). M11.A.2.1 Apply ratio and/or proportion in problem-solving situations. M11.A.2.2 Use exponents, roots and/or absolute value to solve problems. M11.B.2.1 Use and/or compare measurements of angles. M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals. M11.C.1.3 Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three- dimensional figures M11.C.1.4 Solve problems involving right triangles using the Pythagorean Theorem. M11.D.1.1 Analyze and/or use patterns or relations. VOCABULARY: arc length, coterminal angles, radian, unit circle, odd function, even function, trigonometric identities STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES): Students will be able to: 1 Change from radian to degree measures and vice versa. 2. Sketch and find coterminal angles. 3. Find arc length with degree and radian measures. 4. Use the unit circle to evaluate the 6 trig functions and their inverses. 5. Determine the domain, range, and period of the sine and cosine functions using the unit circle. 6. Define odd and even functions and relate them to trig functions (using unit circle). 7. Define the six trig functions using right triangle trig. Evaluate trig functions of special angles without a calculator. Evaluate trig functions using a calculator. 8. Understand and apply trig identities to solve problems. 9. Find the trig function of any angle using definitions, reference angles, trig identities and calculators. 10. Construct basic sin and cos curves. 11. Identify period, amplitude, shifts, and translations from a sin or cos equation. Use identified information to graph functions. 12. Determine an equation of a function given its graph. 13. Sketch basic tan, cot, sec, and csc curves. 14. Define, evaluate and sketch inverse trig functions. 15. Apply trig functions to solve problems.How do you use operations involving logarithms? STAGE II – ASSESSMENT EVIDENCE PERFORMANCE TASK: Students will actively participate in class examples, discussion, and group work. Formative Assessments and OTHER EVIDENCE: Students will actively participate in class examples, discussion, class work, whiteboards, open ended assessments, graphic organizers, exit tickets, daily warm ups, homework, unit tests, quizzes, and other formative assessments. STAGE III: LEARNING PLAN INSTRUCTIONAL PROCEDURES: MATERIALS AND RESOURCES: DO NOW: DO NOW will include a spiraling review of prior knowledge as well as the upcoming lesson. We will use Collins writing 1 and 2 daily Chapter 4 (Precalculus text and supplementals) Mini Lesson: Mini lessons will vary daily based upon student needs and informal assessments. We will use Active Engagement and Scaffolding within each lesson. Examples: Radian and Degree Measures Coterminal Angles The Unit Circle Right Triangle Trigonometry Trigonometric Functions Graphs of Sin, Cos, Tan Warm ups (daily) Homework (daily) worksheets/ activities Unit Test Additional materials as needed (rulers, compass, grid paper, etc) INTERVENTIONS: Think Through Mass Peer Tutoring A+ Math (if available) Math Lab Online Self Check Quizzes and Tests ASSIGNMENTS: Note: Assignments may be altered based on student need for practice and drill. Complete Chapter 4 Note Sheets Text Problems Pg. 367: 1-14 Pg. 367: 15-61 eoo Pg. 367: 71-81 odd Pg. 377: 1-16 Pg. 377: 17-30 Pg. 378: 25-53 odd Pg. 387: 1-21 odd Pg. 388: 23-55 odd Pg. 389: 57-67 odd Pg. 399: 1-21 odd Pg. 400: 43-67 odd Pg. 401: 75-80 Review Test Applications of Trig Curves Inverse Trig Functions Guided Practice: Note Taking, Modeling, Whole Class Response, Partnering, Higher Level Thinking Skills Guided Notes, Chunking, Build on prior Knowledge, Teacher Prompting, Visual Support Independence Practice: Check for understanding using practice pages and text as well as school/SAS developed activities. Summative/Formative Assessments: Quizzes as needed for understanding. Unit test is summative as well as cumulative for constant knowledge retention. Students will actively participate in class examples, discussion, class work, whiteboards, open ended assessments, graphic organizers, exit tickets, daily warm ups, homework, Study Island and, unit tests, quizzes, and other formative assessments. Reflections: Check for understanding using do now, homework, or formative assessment questioning to determine whether to continue as needed or do interventions as needed. (Model, spiral scaffolding, instruct/reteach as needed) Teacher reflection: