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Name: Andrea Sisk Date: February 23, 2015 WOODLAND HILLS SECONDARY LESSON PLANS Content Area: Geometry Length of Lesson: 10 days STAGE I – DESIRED RESULTS Lesson Topic (Modules, if applicable): Right Triangles and Trigonometry Big Ideas: CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios. CC.2.3.HS.A.7 Apply trigonometric ratiosto solve problems involving righttriangles CC.2.3.8.A.3 Understand and apply the Pythagorean theorem to solve problems. CC.2.3.HS.A.3 Verify and apply geometric theorems asthey relate to geometric figures. Understanding Goals (Concepts): Use of geometric mean to solve problems involving side length. How the Pythagorean Theorem and its converse are used to solve problems. Trigonometric ratios, their definitions, and how to use them to solve right triangle problems. Student Objectives (Competencies/Outcomes): 1Simplify, multiply, add, subtract, and divide radicals 2.Find the geometric mean between two numbers. Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. 3. Use the Pythagorean Theorem and its converse. -90 6.Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios. 7.Solve problems involving angles of elevation and depression. Essential Questions: How can you use coordinates and algebraic techniques to represent, interpret, and verify geometric relationships? How can patterns be used to describe relationships in mathematical situations? How can recognizing repetition or regularity assist in solving problems more efficiently? How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems? How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving? How can geometric properties and theorems be used to describe, model and analyze situations? Vocabulary: Radical, simplified radical form, geometric mean, Pythagorean triple, trigonometry, trigonometric ratio, sine, cosine, tangent, angle of depression, angle of elevation, STAGE II – ASSESSMENT EVIDENCE Performance Task: Students will actively participate in mini-lessons, guided and independent practice, activities (including authentic problem-solving tasks and vocabulary), and group work. Also, students will demonstrate adequate understanding via various quizzes, a writing assignment, and an end-of-chapter test. STAGE III – LEARNING PLAN Interventions: Flexible grouping, students will be encouraged to attend Math Lab and College and Career Access Center tutoring. Materials and Resources: Textbook and notes Procedures Instructional Procedures*: Monday Date: 2/23 Day: B “Do Now” – N/A “Mini Lesson” – Review Sections 7.2-7.4 “Guided Practice” – Problems from 7.2-7.4 Worksheets “Independent Practice” – Students will use the 7.2, 7.3, and 7.4 Worksheets to review Chapter 7 “Formative Assessment” - Observe students during “Guided Practice” and “Independent Practice” Formative Assessments: Pre-assessments, open-ended higher-order-thinking questions, think-pairshare, graphic organizers, do nows, observation of guided and independent practice, brief in-class writing prompts Tuesday Date: 2/24 Day: A “Do Now” – Collins 2. Define elevation and depression in 3 lines. “Mini Lesson” – Angles of Elevation and Depression Section 7.5 Day 1 “Guided Practice” – Solve problems involving angles of elevation and depression “Independent Practice” – Students will use angles of elevation and angles of depression to find missing sides of a triangle. “Formative Assessment” - Observe students during “Do Now”, “Guided Practice” and “Independent Practice” Wednesday Date: 2/25 Day: B “Do Now”- Find missing sides of a triangle using angles of elevation “Mini Lesson” – Angles of Elevation and Depression Section 7.5 Day 2 “Guided Practice” – Solve problems involving angles of elevation and depression “Independent Practice” Students will use indirect measurement to find distances. “Formative Assessment” - Observe students during “Independent Practice” Thursday Date: 2/26 Day: A “Do Now” – Find a distance using indirect measurement “Mini Lesson” – Angles of Elevation and Depression Section 7.5 Day 3 “Guided Practice” – N/A “Independent Practice” – Students will use angles of elevation and depression to find missing sides of a triangle. Students will use indirect measurement to find distances. “Formative Assessment” - Observe students during “Do Now” and “Independent Practice” Friday Date: 2/27 Day: B “Do Now” – N/A “Mini Lesson” – Angles of Elevation and Depression Section 7.5 Project “Guided Practice” – N/A “Independent Practice” – Students will create an authentic situation, illustrate and solve using angles of elevation or depression. “Formative Assessment” - Observe students during “Independent Practice” Assignments 7.5 Problems in packet 7.5 Day 2 p. 374 #9-25 odd 7.5 Worksheet *Include Do Now, Mini Lesson, Guided Practice, Independent Practice, Summations/Formative Assessments, Reflections Finish Project