L5+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 - Investigate Trigonometric Ratios

__**Objectives**__
• Definitions: radical expression, perfect squares, square root, radical sign, radicand, simplest form, 45°-45°-90° triangle, 30°-60°-90° triangle, trigonometry, trigonometric ratio, cosine, sine, tangent, angle of elevation/depression, hypsometer, 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: Pythagorean Theorem, Pythagorean Theorem Converse, Product/Quotient Property of Square Roots, 45°-45°-90° Triangle Theorem, 30°-60°-90° Triangle Theorem, and 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** represent real world problems geometrically. Students will take a screen shot of the scaled drawings they created on Geometer's Sketchpad, prepare a slide or slides with the necessary mathematical information and pictures of giant sequoias, make a pdf of the slide, and link it to the class wiki.

__**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:**Understanding how trigonometry is used in real world applications will help students realize the importance of mathematics. Furthermore, this lesson will prepare the students to make more real world connections in our next lesson.

__**Assessment**__

 * Formative Assessment for Learning**

Students will use graphic organizers to organize and visualize the multiple relationships within a triangle. They will explore real world trigonometric ratios in 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 "Adjacent" partners to work on the assignment. Students will use a graphic organizer to record their measurements and provide a rough sketch of their final product. Students and I will be able to discuss any misunderstandings prior to creating their final product.


 * Summative Assessment of Learning**

Students will identify right triangles created from three objects on school property. They will use their knowledge of the Pythagorean Theorem, special right triangles, and trigonometric ratios to solve the three triangles. Students will make scaled drawings to show the angle of elevation, distance to the ground, and distance from the object. Students will research indirect measurement and write a paragraph on how indirect measurement was used in ancient times. In all of their work, students will have to describe what actions they are taking and why. Students will take a screen shot of their scaled drawing they created on Geometer's Sketchpad, prepare a slide with the necessary mathematical information, include pictures of the objects they measured, make a pdf of the slide and link it to the class wiki.

__**Integration**__

 * Technology:**
 * Students will use a digital camera (phone, laptop, etc) to take pictures of right triangles in the real world. If they do not have a camera, they can look for pictures online of real world right triangles and site their sources.
 * Students will use calculators when needed.
 * Students will use Inspiration software to create an outline for their final product of this lesson and create a flowchart of their proof of the Pythagorean Theorem.
 * 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 software of their choice to create a creative digital compilation of their work. Software examples include iMovie and PowerPoint.
 * Students will embed their compilation online and link it to the class wiki.


 * Other Content:**
 * History
 * Students will learn historical details about Pythagoras.
 * Art
 * Students will take pictures of real world right triangles.
 * 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] "special" triangles, then will be put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. At the beginning of the year, students will fill out their "Parts of a Triangle" worksheet with their classmate's names. During the cooperative learning activity for this lesson, students will be paired with their "Angle" partners to work on "Dragon" assignment. After the class discussion, students will continue to work on individual assignments.

__**Differentiated Instruction**__
> > >
 * Strategies:**
 * **Verbal:** Students will be reading word problems, participating in group and class discussions, and writing explanations of their mathematical work.
 * **Logical:** Students will derive a geometrical approach to solving word problems.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** Students will d raw a geometric representation of trigono metric word problems.
 * **Naturalist:** Weather permitting, this project will be worked on outside.
 * **Intrapersonal:** Students will be involved in group work.
 * **Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** **--**


 * 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 a digital camera (phone, laptop, etc) to take pictures of right triangles in the real world. If they do not have a camera, they can look for pictures online of real world right triangles and site their sources. Students will use calculators when needed to solve problems. Students will use Inspiration software to create an outline for their final product of this lesson and create a flowchart of their proof of the Pythagorean Theorem. Students will use software of their choice (e.g - iMovie/PowerPoint) to create a creative digital compilation of their work which will be embedded online and linked to the class wiki. 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
 * digital camera (phone,etc)
 * graphic organizers
 * blogger account
 * VoiceThread 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.
 * Special Right Triangle Hook - http://www.teachertube.com/view_video.php?viewkey=9782f54425c4673f5301
 * Graphic Organizer URL's (I have to go back and find these because I didn't save them.)

__**Maine Standards for Initial Teacher Certification and Rationale**__
Rationale:**
 * //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:**
 * //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.//

Rationale:**
 * //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__

 * Content Notes**

(see attachments)


 * Handouts**

(see attachments)