L3+Hollingsworth+Tracey

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

Teacher’s Name:** Ms. Hollingsworth
 * Date of Lesson:** TBA
 * Grade Level:** 9-12
 * Topic:** Triangular Trigonometry - Sine & Cosine Ratios

__**Objectives**__

 * Student will understand that** //and use basic ideas of trigonometry.// They will understand what trigonometry and trigonometric ratios are. Students will understand that when the sides and angles of a triangle are known, trigonometric relationships can be used to find unknown parts of a triangle.

• Definitions: trigonometry, trigonometric ratio, cosine, sine, angle of elevation/depression, hypsometer, trigonometric identities, SOHCAHTOA, "father of trigonometry". • Critical Details: The relationships between angles, lengths, and sides of triangles by use of the Pythagorean Theorem and trigonometric ratios. • Theorems and Properties: Trigonometric Identities.
 * Student will know**


 * Student will be able to** relate the sides of a triangle to its' hypotenuse by using trigonometric functions. They will create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function.

__**Maine Learning Results Alignment**__
Maine Learning Results - Mathematics - C. Geometry Geometric Figures: 3. Students understand and use basic ideas of trigonometry. b. Use trigonometry to solve for missing lengths in right triangles.


 * Rationale:** Learning the sine and cosine trigonometric ratios of triangles will allow students to solve problems involving measurements and ratios of right triangles. Furthermore, this lesson will prepare the students to make connections in our next lesson between these concepts and other trigonometric ratios.

__**Assessment**__
Students will use a graphic organizer to organize and visualize the sine and cosine trigonometric ratios. Students will individually explore sine and cosine using [|virtual manipulatives]. Then they will work on the "Investigate Trigonometry" handout. Although students are working individually, they may quietly collaborate with the person sitting next to them. Once completed, there will be a class discussion to compare and converse about the results and feedback will be given. Students will have clarification from their peers and/or myself. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments.
 * Formative Assessment for Learning:**

Students will relate the sides of a triangle to its' hypotenuse by using trigonometric functions. Students will research sine and cosine and create a creative PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric ratio. Students will be graded on their understanding of the material based on the criteria of the given rubric.
 * Summative Assessment of Learning:**

__**Integration**__

 * Technology:**
 * Students will use calculators.
 * Students will use PowerPoint software to create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function.
 * Students will use their blogger account to reflect on the lesson and discuss any further questions. Students will comment on the blogs of whom they did not work with throughout the lesson.
 * Students will embed their PowerPoint online and link it to the class wiki.


 * Other Content:**
 * History
 * Students will learn about the father of trigonometry.
 * English
 * Students will be writing in their blogs and present an oral and/or written explanation of the sine and cosine trigonometric ratios.

__Groupings__
Students will individually explore sine and cosine using [|virtual manipulatives]. Then they will work on the "Investigate Trigonometry" handout. Although students are working individually, they may quietly collaborate with the person sitting next to them. Once completed, there will be a class discussion to compare and converse about the results. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments.

__**Differentiated Instruction**__

 * Strategies:**
 * **Verbal:** Students will be involved in team, and class discussions.
 * **Logical:** Students will use a step-by-step process of solving a right triangle.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the trigonometric ratios. The trigonometric ratios will be displayed geometrically and algebraically.
 * **Naturalist:** Students will work on part of the "In the Park" handout which portrays some of the right triangles that are found outdoors.
 * **Interpersonal:** Students will be involved in group work.
 * **Intrapersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** Classical music will be played while students are in groups.


 * Modifications/Accomodations:**

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

In the event that a student must miss class, it is their responsibility to make up any missed work. On the class wiki, every class will have a descriptive overview of the lesson that was presented that day including any relevant notes, graphic organizers, and or/study guides. Students will have full access to the class wiki and will be able to keep up with any missed work. However, students should also communicate with me and/or a fellow classmate to get a full understanding of the missed material. Any missed assignments will be due within the following two classes. If an assignment was due the day that the student was absent, that assignment will be due at the beginning of the following class.


 * Extensions**

Students will use calculators when needed to solve problems. Students will use PowerPoint software to create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function. Students will use their blogger account to reflect on the lesson and discuss any further questions. Students will comment on the blogs of whom they did not work with throughout the lesson. Students will embed their PowerPoint online and link it to the class wiki.

__**Materials, Resources and Technology**__

 * paper
 * pencils/pens
 * laptop/desktop access
 * computer/projector
 * graphic organizers
 * blogger account
 * calculator
 * textbook
 * further study resources

__Source for Lesson Plan and Research__
Special Triangles Lesson created by T.Hollingsworth

Materials used:
 * Brown, R.G. (1994). Advanced mathematics: Precalculus with discrete mathematics and data analysis. Boston: Houghton Mifflin.
 * Coxford, A., DiBianca, R., Highstone, V., Hirschhorn, D., Lewellen, H., Maeir, M., Oppong, N., Usiskin, Z. (2002). Geometry. Upper Saddle River: Prentice-Hall.
 * Cummins, J., Kanold, T., Kenney, M., Malloy, C., Mojica, Y. (2006). Geometry: Concepts and applications. China: R.R. Donnelley.
 * SOHCAHTOA Hook - http://www.teachertube.com/view_video.php?viewkey=cf86981529a0cb6e4f35
 * Virtual Manipulatives - http://catcode.com/trig/index.html

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:** This lesson provides diverse learning opportunities that support intellectual, physical, emotional, social, and cultural development. Students that have a "beach ball" type learning style, a style that requires a variety of resources, adaptive environment, choices of activities, spontaneity, and personal freedom, will be able to create their own slide using PowerPoint. Other students that need organization, structure, visual directions, sequential learning, clear procedures and expectations, such as "clipboards", will use graphic organizers to organize information and create a visual reference for students to use. They will also be describing, step-by-step, how and why they are solving problems on their PowerPoint. The "microscope" type learners, who learn best by discovery learning, analyzing concepts, deep exploration, discussion, and focusing on details, will discover sine and cosine ratios, analyze their properties, and apply their knowledge to solve problems. Students will also participate in one-on-one and class discussions. Students that have a "puppy" type learning style, a style that thrives in a comfortable environment, encouraging atmosphere, supportive grouping, empathic listeners, and sensitive peer, will participate comfortable and respectful one-on-one and class discussions, positive feedback from myself and peers.
 * //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:** This lesson will continue the concept of relationships within triangles by introducing trigonometry and trigonometric ratios. Students will understand //and use basic ideas of trigonometry.// They will understand that there are relationships among angles, lengths, and sides of right triangles as demonstrated by the Pythagorean Theorem. By learning the sine and cosine trigonometric ratios of triangles, students will be able to solve problems involving measurements and ratios of right triangles. Furthermore, this lesson will prepare the students to make connections in our next lesson between these concepts and other trigonometric ratios.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** This lesson on sine and cosine satisfies the Maine Standards for Initial Teacher Certification by using Type I and Type II technology. Students will use their computers to explore right triangles using virtual manipulatives. Students will use calculators when needed to solve problems. They will identify special right triangles, use formulas to find the lengths of the legs and hypotenuse including using the Pythagorean Theorem, and solve practical problems involving special right triangles. Students will have to describe what actions they are taking and why. Students will use PowerPoint software to create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function. Students will embed their PowerPoint online and link it to the class wiki. Students will also have to discuss their classmates results. Students will use their blogger account to reflect on the lesson and discuss any further questions. Students will comment on the blogs of whom they did not work with throughout the lesson. Students will use calculators when needed to solve problems. Technology will also be used to present information to students.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * **Verbal:** Students will be involved in team, and class discussions.
 * **Logical:** Students will use a step-by-step process of solving a right triangle.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the trigonometric ratios. The trigonometric ratios will be displayed geometrically and algebraically.
 * **Naturalist:** Students will work on part of the "In the Park" handout which portrays some of the right triangles that are found outdoors.
 * **Interpersonal:** Students will be involved in group work.
 * **Intrapersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** Classical music will be played while students are in groups.

Rationale:** Students will use a graphic organizer to organize and visualize the sine and cosine trigonometric ratios. Students will individually explore sine and cosine using [|virtual manipulatives]. Then they will work on the "Investigate Trigonometry" handout. Although students are working individually, they may quietly collaborate with the person sitting next to them. Once completed, there will be a class discussion to compare and converse about the results and feedback will be given. Students will have clarification from their peers and/or myself. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//
 * Formative Assessment for Learning:**

Students will relate the sides of a triangle to its' hypotenuse by using trigonometric functions. Students will research sine and cosine and create a creative PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric ratio. Students will be graded on their understanding of the material based on the criteria of the given rubric.
 * Summative Assessment of Learning:**

__Teaching and Learning Sequence__
Total Class Time: 80 minutes


 * Minutes || Activity ||
 * 0 - 10 || Review Lesson 2 Homework ||
 * 10 - 17 || Exploration - Virtual Manipulatives ||
 * 17 - 40 || Graphic Organizers & Sample/Practice Problems ||
 * 40 - 65 || Group Investigation - PowerPoint ||
 * 65 - 73 || Class Discussion/Answer Questions ||
 * 73 - 80 || Start Homework ||

Students will understand that and use basic ideas of trigonometry. They will understand what trigonometry and trigonometric ratios are. Students will understand that when the sides and angles of a triangle are known, trigonometric relationships can be used to find unknown parts of a triangle. Students will watch a video about trigonometric ratios and the acronym "SOHCAHTOA" to increase their interest. Students will learn the definition of trigonometry, trigonometric ratio, cosine, sine, angle of elevation/depression, hypsometer, trigonometric identities, SOHCAHTOA, and "father of trigonometry". Students will be able to relate the sides of a triangle to its' hypotenuse by using trigonometric functions. They will create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function. **//Where; Why; What; Hook;//**

Students will know who the "father of trigonometry" is and understand the meaning of trigonometry. Students will know how trigonometric functions are used to determine information to solve right triangles. Students will know how to use their knowledge of trigonometric ratios to solve right triangles. Students will use a graphic organizer to organize and visualize the multiple relationships within a triangle and trigonometric ratios. The trigonometric ratios will be displayed geometrically and algebraically. To make sure that all students are learning, students will be involved in pair, team, and class discussions. They will work through specific logical steps to solve a problem. Students will work on part of the "In the Park" handout which portrays some of the right triangles that are found outdoors. Students will be involved in individual work and group work. Classical music will be played while students are in groups. Students will be required to reflect on the class activities and there will be a pre/post blogging assignment to allow them to reflect. **//Equip; Tailor;//**

Students will individually explore sine and cosine using virtual manipulatives. Then they will work on the "Investigate Trigonometry" handout. Although students will be working individually, they may quietly collaborate with the person sitting next to them. Once completed, there will be a class discussion to compare and converse about the results. Students will reconsider the importance of trigonometric functions and their relationships within right triangles. Feedback will be given on their investigative handout. Students will use their knowledge about "special" triangle properties to determine the sine and cosine ratios of 45°-45°-90° and 30°-60°-90° triangles. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments. Graphic organizers will be given and include sample problems for the groups to work on individually. The graphic organizers will be collected and I will review their sample problems to get a better idea of the students' understanding. Feedback will be given on the graphic organizers and students will be able to discuss any misunderstandings prior to working on the PowerPoint slides. After the class discussion, students will continue to work on individual assignments. **//Explore; Experience; Revise; Refine; Reflect; Evaluate; Tailor;//**

This lesson will continue the concept of relationships within triangles and introduce the sine and cosine trigonometric ratios. Students will understand and use basic ideas of trigonometry. Students will be able to relate the sides of a triangle to its' hypotenuse by using trigonometric functions. Students will use a graphic organizer to organize and visualize the sine and cosine trigonometric ratios. They will create a PowerPoint slide defining one of the trigonometric functions and graphically show how to solve a right triangle using that specific trigonometric ratio. They will identify special right triangles, use formulas to find the lengths of the legs and hypotenuse including using the Pythagorean Theorem, and solve practical problems involving special right triangles. Students will have to describe what actions they are taking and why. Students will also have to discuss their classmates results. They will be graded on their understanding of the material based on the criteria of the PowerPoint rubric. Furthermore, this lesson will prepare the students to make connections in our next lesson between these concepts and tangent trigonometric ratios. **Evaluate; Organize/Product; Tailor;**

(see attached)
 * Content Notes** - all content notes will be available on the class wiki.

(see attached)
 * Handouts** - all handouts will be accessible from the class wiki.