Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
WOODLAND HILLS HIGH SCHOOL LESSON PLAN SAS and Understanding By Design Template Name Melissa Broadwater Date 1/28/13 Edline was updated this week: Length of Lesson 29 days Content Area Intro to Calculus My Class website was updated this week: STAGE I – DESIRED RESULTS LESSON TOPIC: Trigonometry BIG IDEAS: (Content standards, assessment anchors, eligible content) objectives, and skill focus) 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. UNDERSTANDING GOALS (CONCEPTS): Students will understand: 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? 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: #1. Exit Tickets #2. Pre-Assessment #3. Graphic Organizers Others: Summarizing Main Idea STAGE III: LEARNING PLAN INSTRUCTIONAL PROCEDURES: MATERIALS AND RESOURCES: Active Engagements used: #1. Note-Taking #2. Compare Contrast Others: Graphic Organziers, Summarizing, Cooperative Education, Partnering Chapter 3 (Precalculus text and supplementals) Describe usage: See below for Compare/Contrast, Graphic Organizers, Cooperative Education, Partnering, NoteTaking. Check for understanding and summarizing using warm up, homework, formative assessment questioning or exit tickets to determine whether to continue lesson or do interventions as needed. (model, spiral scaffolding, instruct/ reteach as needed) Warm ups (daily) Homework (daily) worksheets/ activities Unit Test Additional materials as needed (rulers, compass, grid paper, etc) CONTENT AREA READING: Guided Notes INTERVENTIONS: ASSIGNMENTS: Struggling students will be referred to RTII Small group/flexible grouping will occur. Various computer programs. •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 Scaffolding used: #1. Guided Notes #2 . Build on Prior Knowledge Others: Graphic Organizers, Build Vocabulary Describe usage: Warm up to include spiraling review of prior knowledge to include upcoming lesson. All notes are guided notes to build vocabulary, interspersed with group activities. Graphic organizers utilized when appropriate to compare/contrast vocabulary. Other techniques used: MINI LESSON: Based on daily assessments (formative and summative), additional modeling, instruction, homework, review, interventions, group work, computer or teacher guided practice will be done.