L4+McKeown,+Sarah

COLLEGE OF EDUCATION, HEALTH AND REHABILITATION LESSON PLAN FORMAT**
 * UNIVERSITY OF MAINE AT FARMINGTON


 * Teacher’s Name:** **Ms. Sarah C. McKeown Date of Lesson:** Lesson #4: Perspective
 * Grade Level:** 10th or 11th grade **Topic:** Right Triangles

__**Objectives**__

 * Student will understand that** there exist useful relationship between angles and sides of right triangles.
 * Student will know** how to interpret given information to determine missing lengths/angles of triangles and be able to solve for those values
 * Student will be able to** analyze given information to determine missing lengths/angles of triangles and how to solve for those values

__**Maine Learning Results Alignment**__
Maine Learning Result: Mathematics - C. Geometry Geometric Figures Grades 9 - Diploma 3. c) Students will be able to use inverse trigonometric functions to find missing angles in right triangles

This lesson builds off of the previous three in a way which will enable students to use trigonometric functions to represent the relationship between angles and sides and also use the inverse trigonometric functions to find the measure of angle that relates to two given sides.
 * Rationale:**

__**Assessment**__
The formative assessment that couples with this lesson is a standard, un-graded quiz to review comprehension of concepts. On this quiz, students will be asked a series of questions where they must use inverse trigonometric functions to find the measure of various angles. After working silently on this quiz for approximately 10 minutes, students will be given 5 minutes to go around the room and "cheat" off of any other student who is willing to share their answers. This is a chance for students to compare their method of solving to the methods employed by others as well as a time for students to check their work in relation to other students. At the end of the 15 minutes, the quizzes will be collected and then corrected and handed back the following class. No numerical grade will be recorded for this assignment, however students will receive 10 participation points for doing the activity.
 * Formative (Assessment for Learning)**

Students are to participate in a discussion on the class wiki where they recognize and assess the benefits of triangles in the real world. This is the time for students to connect with their peers and discuss the practical applications of triangles. They will be graded on how analytical their contributions are and their ability to //discuss//, not merely //post//. In their posting, students need to include an example of a right triangle they encounter in their everyday life, the sides of which they have measured and have calculated the measure of all three included angles. For this assignment, students may use triangles identified in past assignments.
 * Summative (Assessment of Learning)**

__**Integration**__

 * Technology**: Students will be asked to participate in a discussion on the class wikipage.


 * English**: This assignment will require students to use a wide range of literary tactics to sucessfully convey an analysis of their example of a triangle. Students will also have to employ their skills as effective communicators in order to carry out an effective, interactive discussion.

__Groupings__
For this lesson, students will be able to pick their own groups of four. The only requirement is that students pick individuals that they know they can communicate well with. At the end of the lesson, students will be asked to reflect upon their experience in this group as opposed to previous groupings and give feedback as to which was more effective for their learning process.

__**Differentiated Instruction**__

 * Strategies**
 * Verbal Linguistic**: for students who are linguistic, as always, I will present my lesson in both written and spoken word. Also, I will introduce the popular acronym Soh Cah Toa for the trigonometric functions.
 * Mathematical Logical**: for students who gravitate towards math, I will present a step by step analysis of the problem solving method.
 * Visual Spacial**: for students who are visually inclined, I will include pictures with my examples to help relate the shape to the functions that warp the shape.
 * Bodily Kinesthetic**: during the initial "hook" part of the class, bodily kinesthetic students will be urged to get up and act out their own personal slide that they picked.
 * Musical Rhythmic:** for my musical students, I will play the video of the "Trig Rap" found on YouTube.
 * Intrapersonal**: for the intrapersonal students, time will be provided for them to reflect on what they have learned before the quiz is administered.
 * Interpersonal**: during the "hook" of the class, students will be encouraged to work with others as a means of making connections to the material.
 * Naturalistic:** for my naturalistic students, I plan on creating some kind of lose example like the one that follows. In nature, there are specific ratios that animals follow. For example, there can only be one queen be for every hive (a 1 queen : 1 hive ratio). The trig functions are not much different. For example, let's pretend the queen bee is the trig function "tangent". For the one queen bee, she can only use the two sides of the hive closest to her nest. If the workers were the "sine" function, they would only be able to use one of the queens walls (in a triangle that would be the side opposite the adjudicated angle) and the third one that she wasn't using.


 * Modifications/Accommodations**

//**I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.**//

If student knows that he or she will be absent, they are required to follow the school's planned absence policy and retrieve all work (this includes the lecture notes and the Garden Gate graphic organizer) from me prior to the absence. Any student encountering an unexpected absence must see me as soon as possible (preferably prior to the next class with me) to get the missed work. Students in both situations will have the opportunity to talk with me about the material if they have any questions, although it will be mandatory.

In this lesson, students will be integrating technology in a Type II way through use of wikispaces. Students will be required to go online and participate in a discussion with other students over the course of a week. This enables students to communicate with each other about classroom content while employing their 21st century skills. This also allows me to provide feedback in a timely manner and to lead students in guided exploration of the digital resources at their fingertips.
 * Extensions**

__**Materials, Resources and Technology**__
Print out of the "Garden Gate" graphic organizer. Handout Formative Assessment Quiz. Whiteboard and markers. Students will need computer access to contribute to the class wiki discussion.

__Source for Lesson Plan and Research__
The first section of this page refers to the three trigonometric functions we will cover in this lesosn. How inverse trigonometric functions work and how they can help solve for an angle. Link to website that the class wikipage will be on. The "Trig Rap".

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** Throughout this lesson, students will be given options to work either individually or in pairs as they do their work and will be encouraged to explore the problems using their own methods as well as the ones provided by the instructor (beach ball). As always, a class agenda will be outlined at the beginning of the class to give direction to the 80-minute period and all problems will be done out in a sequential order (clipboard). Students will be asked to perform an in depth analysis of the importance of these triangles and their measures in their own life. This will require students to look at their own experiences and consider a number of influences on their lives that are caused by triangles (microscope). As always, I intend to make myself available in close proximity to the students in order to speak one on one if need be so that I can establish a personal relationship with my students and thus make them feel that my classroom is a safe zone (puppy).
 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//

Rationale:** In this lesson, students will be able to analyze triangles, find the right triangles within those triangles, and use the given information to solve for all of the angles and sides of the shape. This lesson is a "perspective" lesson because it requires students to employ what they know about one triangle and apply it to another to collectively solve for both. Through this lesson, students will be able to master triangles and have the ability to solve for any missing measure of them.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:**
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Verbal Linguistic**: for students who are linguistic, as always, I will present my lesson in both written and spoken word. Also, I will introduce the popular acronym Soh Cah Toa for the trigonometric functions.
 * Mathematical Logical**: for students who gravitate towards math, I will present a step by step analysis of the problem solving method.
 * Visual Spacial**: for students who are visually inclined, I will include pictures with my examples to help relate the shape to the functions that warp the shape.
 * Bodily Kinesthetic**: during the initial "hook" part of the class, bodily kinesthetic students will be urged to get up and act out their own personal slide that they picked.
 * Musical Rhythmic:** for my musical students, I will play the video of the "Trig Rap" found on YouTube.
 * Intrapersonal**: for the intrapersonal students, time will be provided for them to reflect on what they have learned before the quiz is administered.
 * Interpersonal**: during the "hook" of the class, students will be encouraged to work with others as a means of making connections to the material.
 * Naturalistic:** for my naturalistic students, I plan on creating some kind of lose example like the one that follows. In nature, there are specific ratios that animals follow. For example, there can only be one queen be for every hive (a 1 queen : 1 hive ratio). The trig functions are not much different. For example, let's pretend the queen bee is the trig function "tangent". For the one queen bee, she can only use the two sides of the hive closest to her nest. If the workers were the "sine" function, they would only be able to use one of the queens walls (in a triangle that would be the side opposite the adjudicated angle) and the third one that she wasn't using.

In this lesson, students will be integrating technology in a Type II way through use of wikispaces. Students will be required to go online and participate in a discussion with other students over the course of a week. This enables students to communicate with each other about classroom content while employing their 21st century skills. This also allows me to provide feedback in a timely manner and to lead students in guided exploration of the digital resources at their fingertips.

Rationale:** The formative assessment that couples with this lesson is a standard, un-graded quiz to review comprehension of concepts. On this quiz, students will be asked a series of questions where they must use inverse trigonometric functions to find the measure of various angles. After working silently on this quiz for approximately 10 minutes, students will be given 5 minutes to go around the room and "cheat" off of any other student who is willing to share their answers. This is a chance for students to compare their method of solving to the methods employed by others as well as a time for students to check their work in relation to other students. At the end of the 15 minutes, the quizzes will be collected and then corrected and handed back the following class. No numerical grade will be recorded for this assignment, however students will receive 10 participation points for doing the activity. Students are to participate in a discussion on the class wiki where they recognize and assess the benefits of triangles in the real world. This is the time for students to connect with their peers and discuss the practical applications of triangles. They will be graded on how analytical their contributions are and their ability to //discuss//, not merely //post//. In their posting, students need to include an example of a right triangle they encounter in their everyday life, the sides of which they have measured and have calculated the measure of all three included angles. For this assignment, students may use triangles identified in past assignments.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//

__Teaching and Learning Sequence__
Break into groups - 3 minutes Introduction/Hook - 7 minutes Lecture/Examples/Individual Discussion - 50 minutes Introduce homework - 5 minutes Quiz - 10 minutes "Cheat" - 5 minutes

Desks will be arranged in groups of four to allow for optimum discussion. From this lesson, student will understand that there exist useful relationship between angles and sides of right triangles because being able to look at small problems to solve the larger ones is a life long skill that will help students be better problem solvers through out their lives. This lesson will meet the MLR Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 3. c. Students will be able to use inverse trigonometric functions to find missing angles in right triangles. To start off this lesson, students will be given a taste of what they will be able to accomplish by the end of the lesson. To hook and engage my students in a real life application, I am going to ask the class to close their eyes and think of their favorite slide as a kid. Which of these categories does that slide fall in (the two categories being one that looks like a right triangle and one that is not).? I will then remind the class of how the material we covered prior to this lesson would in fact enable us to find the length of the slide (if we were given enough information), so it would only be fair if we learned how to solve for the length of the other slide as well! **Where, Why, What, Hook, Visual, Intrapersonal, Logical, Interpersonal.**

For this lesson, students will need to know the three basic trigonometric functions (sine, cosine and tangent) and their inverses (arcsine, arccosine and arctangent). Because this lesson is heavy on content, the majority of the lesson will be done in a presentation format however, students will be encouraged to interact with their group to work on the numerous problems presented. Understanding will be checked through a quiz at the end of class. **Equip, Logical, Interpersonal, Verbal, Visual.**

To review previous information, students will fill out the "garden gate" graphic organizer. As an active part of class, students will be asked to share with a partner their answer to the day's "hook" question. During this time, students will also be asked to brainstorm other examples of non-right triangles and share them with the class. We will use these examples in class when computing angles using the trigonometric functions. In this lesson, students will be able to analyze triangles, find the right triangles within those triangles, and use the given information to solve for all of the angles and sides of the shape. This lesson is a "perspective" lesson because it requires students to employ what they know about one triangle and apply it to another to collectively solve for both. Through this lesson, students will be able to master triangles and have the ability to solve for any missing measure of them. Students will be able to pick their own groups of four in which to sit. The only requirement is that students pick individuals that they know they can communicate well with. At the end of the lesson, students will be asked to reflect upon their experience in this group as opposed to previous groupings and give feedback as to which was more effective for their learning process. Once again, students will demonstrate their learning through a short quiz at the end of class. Because of the level of difficulty of this content, students will actually have a chance to "cheat" off of members at their group after an allotted 10 minutes during which they will be required to work alone. To take a different perspective on the trigonometric functions, students will be asked to find similarities between them instead of the differences. With this new found facet to trig functions, what can be concluded? How will they help us find the "length of the slide"?. If students still seem unclear about the concept of trigonometric functions, the pace of the class should be handled accordingly and perhaps a more hands-on or real-example approach would be helpful. **Explore/Experience, Rethink, Revise, Refine, Verbal, Interpersonal, Visual, Logical,**

The formative assessment that couples with this lesson is a standard, un-graded quiz to review comprehension of concepts. On this quiz, students will be asked a series of questions where they must use inverse trigonometric functions to find the measure of various angles. After working silently on this quiz for approximately 10 minutes, students will be given 5 minutes to go around the room and "cheat" off of any other student who is willing to share their answers. This is a chance for students to compare their method of solving to the methods employed by others as well as a time for students to check their work in relation to other students. At the end of the 15 minutes, the quizzes will be collected and then corrected and handed back the following class. Upon receiving them the following class, students will be able to gauge their own learning. Note, no numerical grade will be recorded for this assignment, however students will receive 10 participation points for doing the activity. This lesson gives students the tools necessary to measure any triangle and calculate the angles contained within it (a problem they will actually have to do for homework). **Logical, Intrapersonal, Interpersonal.**

- Sin (x) = opposite/hypotenuse - Cos (x) = adjacent/hypotenuse - Tan (x) = opposite/adjacent - All of the trigonometric functions can be undone by their "arc" functions. Sin (x) can be solved for "x" by performing the operation arcsin (x) to both sides of an equation, Cos (x) can be solved for "x" by performing the operation arccos (x) to both sides of an equation and Tan (x) can be solved for "x" by performing the operation arctan (x) to both sides of an equation. - To find the measure of an angle, use the arc function associated with the equation (this is solved on the TI calculators by pressing 2nd then sin, cos or tan depending on which function you are trying to undo). - We can draw line segments to create right triangles within other triangles.
 * Content Notes**

- Garden Gate graphic organizer. - Formative assessment quiz.
 * Handouts**