L4+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 - Tangent Ratio

__**Objectives**__
• Definitions: tangent, angle of elevation/depression, hypsometer, and trigonometric identities. • 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 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.
 * Student will know**
 * Student will be able to** compare the different trigonometric ratios and have an interactive discussion about "tangent ratios" of right triangles via VoiceThread.

__**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 graphic organizers to organize and visualize the multiple relationships within a triangle. Students will individually explore tangent using virtual manipulatives and then they will finish their "In the Park" handout. 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. Students will have clarification from their peers and/or myself. 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 students 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 participating in a VoiceThread discussion.
 * Formative Assessment for Learning**

Students will be prompted to have a discussion about special right triangles via VoiceThread. They will identify special right triangles, use formulas to find the lengths of the legs and hypotenuse including using the tangent ratio, and solve practical problems involving right triangles. Students will have to describe what actions they are taking and why. Students will also have to discuss their classmates results. Students will be graded on their understanding of the material based on the criteria of the VoiceThread rubric.
 * Summative Assessment of Learning**

__**Integration**__

 * Technology:**


 * Students will use calculators when needed.
 * Students will use online virtual manipulatives to explore the tangent ratio of right triangles.
 * Students will use VoiceThread to show their understanding of the tangent ratio.
 * 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.


 * Other Content:**


 * Art
 * Students will be representing problems visually.
 * English
 * Students will be writing in their blogs and present an oral and/or written explanation of the Pythagorean Theorem.

__Groupings__
Students will individually explore tangent using virtual manipulatives, then they will finish their "In the Park" handout. 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. Students will have clarification from their peers and/or myself. Graphic organizers will be given and include sample problems for the students to work on. 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: --
 * 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 participate in a class discussion.
 * Intrapersonal: Students will work individually and will be required to reflect on the class activities.
 * Musical: Students will have the option of using music in their VoiceThread.


 * Modifications/Accommodations:

//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 their computers to explore right triangles using virtual manipulatives. Students will use their VoiceThread account to have a discussion about the tangent trigonometric ratio. They will identify right triangles, use formulas to find the lengths of the legs and hypotenuse including using the Pythagorean Theorem, and solve practical problems involving the tangent ratio of right triangles. Students will use calculators when needed. Students will have to describe what actions they are taking and why. 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.

__**Materials, Resources and Technology**__

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

__Source for Lesson Plan and Research__
Special Right 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.
 * Tangent Ratio Hook - http://www.teachertube.com/view_video.php?viewkey=d9420816bfec5edd6c2b
 * Tangent Virtual Manipulatives - http://www.education.uoit.ca/lordec/ID_LORDEC/tangent_ratio/hussein_tangent_ratio.swf

__**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 in their VoiceThread. The "microscope" type learners, who learn best by discovery learning, analyzing concepts, deep exploration, discussion, and focusing on details, will discover tangent 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. 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.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** This lesson on Tangent Ratios 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 their VoiceThread account to have a discussion about the tangent trigonometric ratio. They will identify right triangles, use formulas to find the lengths of the legs and hypotenuse including using the Pythagorean Theorem, and solve practical problems involving the tangent ratio of right triangles. Students will use calculators when needed. Students will have to describe what actions they are taking and why. 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.
 * //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: --
 * 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 participate in a class discussion.
 * Intrapersonal: Students will work individually and will be required to reflect on the class activities.
 * Musical: Students will have the option of using music in their VoiceThread.

Rationale:** Students will use graphic organizers to organize and visualize the multiple relationships within a triangle. Students will individually explore tangent using virtual manipulatives and then they will finish their "In the Park" handout. 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. Students will have clarification from their peers and/or myself. 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 students 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 participating in a VoiceThread discussion.
 * //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 be prompted to have a discussion about special right triangles via VoiceThread. They will identify special right triangles, use formulas to find the lengths of the legs and hypotenuse including using the tangent ratio, and solve practical problems involving right triangles. Students will have to describe what actions they are taking and why. Students will also have to discuss their classmates results. Students will be graded on their understanding of the material based on the criteria of the VoiceThread rubric.
 * Summative Assessment of Learning**

__Teaching and Learning Sequence__
Total Class Time: 80 minutes  Students will understand the relationships between angles, lengths, and sides of triangles. They will learn the difference between a 45°-45°-90° triangle and a 30°-60°-90° triangle and understand the theorems of these special triangles. Students will be able to identify and solve a right triangle based on the "special" properties of 45°-45°-90° and 30°-60°-90° triangles. They will also be able to have an interactive discussion about "special" right triangles via VoiceThread. Students will understand that certain triangles possess specific "special" properties that allow us to find information about a triangle. Understanding special right triangles will allow students to perform calculations easier. MLR - //Students understand and use basic ideas of trigonometry.// Students will [|explore] certain triangles to learn why they are considered "special" and how they make calculations easier. During this lesson, students will individually [|explore] "special" triangles, then will be put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. During the cooperative learning activity for this lesson, students will be paired with their "Angle" partners to work on "Dragon" assignment. //**Where; Why; What; Hook;**//
 * = **Minutes** ||= **Activity** ||
 * = 0-10 || Review Lesson 1 Homework ||
 * = 10-15 || Exploration - Virtual Manipulatives ||
 * = 15-35 || Graphic Organizers & Sample/Practice Problems ||
 * = 35-65 || Investigate - "Dragon" Assignment ||
 * = 65-75 || Class Discussion - Reviewing "Dragon" ||
 * = 75-80 || Start HW/Lesson Project ||

Students will know how to use their knowledge of "special" right triangles to solve right triangles. Students will use a graphic organizer to organize and visualize the multiple relationships within a triangle and trigonometric ratios. 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 be grouped for part of this lesson. However, students will also work individually on their interactive discussions via VoiceThreads and will be required to reflect on the class activities.  After the lesson, students will take a short quiz to measure their general understanding and there will be a pre/post blogging assignment to allow them to reflect. **Equip;** **//Tailor;//**

Students will individually [|explore] "special" triangles, then will be put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. During the cooperative learning activity for this lesson, students will be paired with their "Angle" partners to work on "Dragon" assignment. Students will use graphic organizers to organize and visualize the multiple relationships within a triangle. Each group will present part of the handout to the class for evaluation. Peers will examine each groups' work and discuss possible errors. Students will have clarification from their peers and/or myself. 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 participating in a VoiceThread discussion. After the class discussion, students will continue to work on individual assignments. //**Explore; Experience; Revise; Refine; Reflect; Evaluate; Tailor;**//

Students will be prompted to have a discussion about special right triangles via VoiceThread. 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. Students will be graded on their understanding of the material based on the criteria of the VoiceThread rubric. This lesson will continue the concept of relationships within triangles and introduce the 45°-45°-90° Triangle Theorem and 30°-60°-90° Triangle Theorem. 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 ratios of the sides for some special angle triangles, namely the 45-45-90 and 30-60-90 triangles, students can apply their knowledge to solve problems involving special right triangles. Furthermore, this lesson will prepare the students to make connections in our next lesson between these concepts and trigonometric ratios. //**Evaluate; Organize/Product; Tailor;**//


 * Content Notes**

(see attachments)


 * Handouts**

(see attachments)


 * 22.** **Where:** Students will understand that there are trigonometric functions that can be used to determine information about right triangles. **Why:** When sides and angles of a triangle are known, trigonometric relationships can be used to find unknown parts. **What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 23. Hook:** Students will see a quick demonstration of how the [|tangent] function is used in the real world.
 * 24. Equip:** Students will know how trigonometric functions are used to determine information to solve right triangles. **Explore:** Students will add to their "Sine and Cosine" graphic organizer to organize and visualize the tangent trigonometric ratio. **Experience:** Students will individually explore tangent using [|virtual manipulatives], then they will finish their "In the Park" handout. 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.
 * 25.** **Rethink:** Students will rethink slope (rise/run) and relate it to the tangent ratio. **Revise/Refine:** Feedback will be given on their practice problems. **Rehearse:** Students will write a rule or mnemonic device to remember trigonometric ratios.
 * 26.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 27. Tailor:**
 * **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: --**
 * **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.
 * **Intrapersonal:** Students will participate in a class discussion.
 * **Interpersonal:** Students will work individually and will be required to reflect on the class activities.
 * **Musical: --**
 * 28. (O)** **Organize** Students will be able to compare the different trigonometric ratios. **Product:** Interactive discussion about "tangent ratios" of right triangles via VoiceThread.