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Model Mathematics Curriculum Unit Implementation Plan UNIT COVER SHEET Name: Matthew Blair Grade Level: Hs Geometery Unit Title: Math 2 Unit 7 Right Triangles and Trigonometry Dates of Instruction: November Timeframe (Add days as needed) Unit Timeframe: 2-3weeks Day 1: Using Pythagorean Theorem Lesson/task/assessment Day 2: Triangle Similarity and Trig Ratios Lesson/task/assessment Lesson/task Day 3: A complements B Lesson/task/assessment: Assessment Lesson Day 4: Getting Triggy with It(Day1) Lesson/task/assessment:Lesson Day 5: Getting Triggy with It(Day 2) Lesson/task/assessment:Lesson/task Standards Alignment Content Standards: G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle, leading to definitions of ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Standards for Mathematical Practice: -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Model Mathematics Curriculum Unit Implementation Plan UNIT: Math 2 Unit 7 DAY: 1 DAILY LESSON PLAN Objectives Students will self assess Students will use similarity to discover sine, cosine, and tangent. Content Standards G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle, leading to definitions of trigonometric ratios for acute angles. Mathematical Practices -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Materials Using Pythagorean theorem worksheet Preparation Worksheet needs to be in the hands of the students for homework the night before so need copies Lesson Activities This a preassessment so students will be given to students the night before,We go over it as a class discussing where common pitfalls may have been if there were any. Assessments This is a preassessment for this unit In what ways will you intentionally emphasize the development of student mathematical practices through this lesson?To intentionally emphasize the development of the student I will review Pythagoreans theorem and discuss finding missing angles in the triangle this is super important to understand these basic components to understand the rest of the unit. Model Mathematics Curriculum Unit Implementation Plan UNIT: Math 2 Unit 7 DAY: 2 DAILY LESSON PLAN Objectives Content Standards Mathematical Practices Students will -Recognize the ratios of the sides of right triangles are functions of the acute angles. -Determine that the sine of an acute angle in a right triangle is equal to the cosine of that angle’s complement. -Use trigonometric ratios to solve for unknowns in right triangles. G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Materials Triangle Similarities and Trig Ratios Worksheets Preparation -Making pairs or triads before class, Run off worksheets, Gather up posters and markers for “DANG” Posters Lesson Activities -Teacher should start by talking about the fact that up to this point we have been able to find angles given angles, and side lengths given side lengths. Then, present to the students if they think it is possible to go from knowing angles to knowing side lengths, or from side lengths to angles. After the discussion, hand out the “Triangle Similarities and Trig Ratios,” have the students work in pairs or triads to complete the guided sheet to get to the ratios of sine, cosine, and tangent. - After students have completed the “Triangle Similarities and Trig Ratios,” have them check their answers and fill in the self-assessment rubric to see where their deficiencies are and then have the students find someone in the class that had gotten what they got wrong and have them explain it to them. If there are concepts that everyone missed, then teacher should go over it as a class. -Assign each pair or triad a new problem and have them make a “DANG” poster to display to the class Assessments “Dang” Poster -Self assessment of worksheet Triangle similarities and Trig Ratio In what ways will you intentionally emphasize the development of student mathematical practices through this lesson? It will be super important to relate find missing angles and missing sides in the pre assessment to the Trig ratios. Also, we need to emphasize the angle we are referring to really matters when finding sin, cos, tangent. Model Mathematics Curriculum Unit Implementation Plan UNIT: Math 2 Unit 7 DAY: 3 DAILY LESSON PLAN Objectives Students will explain and use the relationship between the sine and cosine of complementary angles. Content Standards G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Materials A complements B Worksheet Preparation Run of worksheet, set up groups Lesson Activities -Hand out a Complements B assessment, and ask students to complete Exercises 1 and 2 individually. Walk around and monitor student work (check to make sure students are calculating trigonometric ratios correctly). - Pair students, and ask them to discuss Exercises 3 through 5. Monitor discussion between students. - Ask students to share their findings as a class. Then, discuss Exercise 6. - Have students complete Exercise 7 individually for independent practice. Assessments Observation, and homework problem from number seven on worksheet In what ways will you intentionally emphasize the development of student mathematical practices through this lesson? It is super important to realize how these ratios relate, to make sure of this I will have students discuss these ratios in small groups, and then have a class discussion discussing how they relate and why. Model Mathematics Curriculum Unit Implementation Plan UNIT: Math 2 Unit 7 DAY: 4 DAILY LESSON PLAN Objectives -Students should be able to find missing side lengths or missing angles using trigonometric ratios. Content Standards G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle, leading to definitions of trigonometric ratios for acute angles. Mathematical Practices G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Materials Getting triggy with it worksheet and activity Preparation -Run off worksheet part one(finding third side of triangle) -Discussion questions Lesson Activities -As an introductory exercise, ask students to find a missing side of a right triangle with two given sides. Students should use the Pythagorean Theorem. - Discuss what would happen if only one side was given. What other information would need to be known in order to find the length of a missing side? Remind students of the trigonometric ratios. - Present the following problem to students. 12 x 49° Assessments - Discuss which sides are given with respect to the given angle. Ask students what trigonometric ratio involves these sides. Demonstrate solving for the missing side using sine. - Repeat examples using cosine and tangent to find a missing side of a right triangle.(Work in groups) -Each group present a problem -observation -Group presentations and discussion In what ways will you intentionally emphasize the development of student mathematical practices through this lesson? Very rarely in math do we see a triangle given where each with all the information given. I really want to show and convey to students you have to refer to what information is given and how it relates whether through Pythagorean Theorem or trig ratios. Because deciding what is given makes the problems do able. As the teacher I will hammer home you have to digest what you are given before starting. Model Mathematics Curriculum Unit Implementation Plan UNIT: Math 2 Unit 7 DAY: 5 DAILY LESSON PLAN Objectives - Use trigonometric ratios to solve for unknowns in right triangles. Content Standards G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angle in the triangle, leading to definitions of ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices -Makes sense of problems and persevere -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with Mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning Materials Getting triggy with it worksheet and posterboard for presentation Preparation Run of worksheets and decide on how to group Lesson Activities 1. - Present the following right triangle to students. 15 x° 8 Ask students what is the different here. They should recognize that the angle is the unknown this time. Explain that if two sides are known, then the angle may be found using trigonometric ratios and their inverses. Ask what trigonometric ratio could be written for this unknown angle. Demonstrate solving for the missing angle. Explain the inverse trigonometric ratio used to find the solution. - Discuss definitions of angle of elevation and angle of depression. 2. - Complete the following word problems requiring students to apply trigonometric ratios to real life situations: a. A flagpole creates a 16 foot shadow on the ground. The angle of elevation from the tip of the shadow to the sun is 67°. To the nearest foot, how tall is the flagpole? An airplane traveling 25,000 feet above the ground begins a landing. The pilot spots his landing zone on the ground at an angle of depression of 4°. How far will the airplane travel to arrive at his landing zone? Assessments - Hand out Getting Triggy With It(part 2) assessment. Monitor students as they complete exercises. Getting triggy with it assessment and observation In what ways will you intentionally emphasize the development of student mathematical practices through this lesson? To solve any of these elevation or depression problems you have to draw the problems and refer to the picture which will be required. Secondly we will discuss how angles of elevation and depression relate and what is which but I think to understand and make the relation to previous material students must and I mean must draw a picture to solve.