Strategies in Action Debrief
Managing Response Rates & Using Verbal and Nonverbal Behaviors that Indicate
Affection for Students (Grades 9-12)
Standard(s): CCSS.Math.912.G-­‐SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CCSS.Math.912.G-­‐SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles. CCSS.Math.912.G-­‐SRT.C.8: Use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems. Note: The wording or portions of the standards in gray are not the focus of this video, but are included in the scale below. Learning Target: Use inverse tangent, sine, and cosine ratios to solve a right triangle Lesson Summary: The teacher leads the class through several problems that use inverse tangent, sine, and cosine ratios to solve right triangles. Scale: 4.0 3.0 2.0 Students will be able to: • Generate a real-­‐world problem utilizing trigonometric functions and the Pythagorean theorem Students will be able to: • Solve real-­‐world application or applied problems using trigonometric ratios and the Pythagorean theorem • Understand and explain that by similarity, side ratios in right triangles are properties of the angles in the triangle that leads to definitions of trigonometric ratios for acute angles • Explain the relationship between the sine and cosine of complementary angles Students will recognize and recall specific vocabulary, including: • Trigonometric Ratio, tangent, sine, cosine, angle of elevation, angle of depression, solve a right triangle, inverse tangent, inverse sine, inverse cosine, Pythagorean theorem 1.0 Students will be able to: • Use similarity to define trigonometric ratios (tangent, sine, and cosine) for acute angles in right triangles • Use inverse tangent, sine, and cosine ratios to solve a right triangle • Express the Pythagorean theorem as a2 + b2 = c2 and use it to find the unknown length of a right triangle side • Use the relationship between sine and cosine of complementary angles to solve problems • Determine cosine and sine rations for acute angles in right triangles given the lengths of two sides • Construct a diagram to illustrate the relationship between sine and cosine With help, partial success at 2.0 and 3.0 level content © 2016 Learning Sciences International
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Element(s) and Developmental Scale Level(s): Multiple elements could be present. However, only dominant elements are scored. Element Managing Response Rates Using Verbal and Nonverbal Behaviors that Indicate Affection for Students Developmental Scale Level Applying Applying Rationale: Managing Response Rates – The teacher uses multiple response rate techniques to maintain student engagement through questioning processes. He uses Popsicle sticks to call on students, replacing the sticks in his pocket so all students have the expectation of being called on at any time. Additionally, students are often required to respond to each other’s answers using Agree/Disagree cards. These techniques serve to maintain engagement in the content for a majority of the students, resulting in a score of Applying. Using Verbal and Nonverbal Behaviors that Indicate Affection for Students – The teacher uses humor, and smiles and nods to the students when appropriate. He compliments their academic accomplishments and jokes with them. As a result, the students appear to feel part of the classroom community and are not afraid to share their answers and ideas. At the end of the lesson, one student said she felt much more confident in her ability to solve the problems. We can see that the desired effect of the students’ perceptions of acceptance and sense of community are enhanced in the majority of the students, leading to a score of Applying in this element. Feedback and Guiding Questions for the Teacher: When using the Agree/Disagree cards, try asking several students to explain why they agree or disagree to further facilitate their processing, and monitor their understanding. When using the Popsicle sticks, how could you increase student engagement? Possibly by asking the question first, then drawing the name and waiting for an answer? This will ensure that all students are listening to the question. © 2016 Learning Sciences International
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