L1+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:** High School
 * Topic:** Triangular Trigonometry

__**Objectives**__

 * Student 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. Understanding the Pythagorean Theorem is the basis for understanding trigonometric ratios in right triangles**.**


 * Student will know** historical details about Pythagoras, the Pythagorean Theorem, multiple ways to prove the Pythagorean Theorem, and the relationship between the sides, lengths, and angles of a triangle.


 * Student will be able to** relate the sides of a triangle to its' hypotenuse. They will be able to create a digital compilation of right triangle pictures, flowchart, and geometric representation of the Pythagorean Theorem proof.

__**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:** This lesson will introduce the concept of relationships among sides, lengths, and angles of a triangle through the demonstration of the Pythagorean Theorem.

__**Assessment**__
Students will use graphic organizers to list key facts about Pythagoras' life. They will be given a handout with different visual representations of the Pythagorean Theorem proof. Each group will have a different representation to prove and present it 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. The graphic organizers will also include sample problems for the groups to work on. The graphic organizers will be collected and I will review their explanation of the proof and 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 starting their flowchart and lesson project.
 * Formative Assessment for Learning:**

Students will research Pythagoras and the Pythagorean Theorem. They will take their findings and create a creative digital compilation of the history of Pythagoras, real life right triangle pictures and examples, a flowchart of their mathematical step-by-step proof of the Pythagorean Theorem using Inspiration software, and visual geometric representation of the Pythagorean Theorem proof. 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 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 listen to the Pythagoras Rap individually, then 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 "Hypotenuse" partners to hypothesize the Pythagorean Theorem proof. When the teams have finished collaborating, there will be a class discussion reviewing what they learned. Students will be able to review their information and edit it. After the class discussion, students will continue to work on individual assignments.

__**Differentiated Instruction**__

 * Strategies:**
 * **Verbal:** Students will be involved in individual, team, and class discussions.
 * **Logical:** Students will derive the proof of the Pythagorean Theorem and apply the theorem to solve relevant problems.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the Pythagorean Theorem proof. The Pythagorean Theorem will be displayed geometrically and algebraically.
 * **Naturalist:** Homework will include finding right triangles outside the classroom. Right triangles can be found in nature or indoors.
 * **Intrapersonal:** Students will be involved in group work to derive the proof of the Pythagorean Theorem and present their proof to the class.
 * **Interpersonal:** Students will work individually on solving problems, their final product, and will be required to reflect on the class activities.
 * **Musical:** Students will listen to a rap about Pythagoras as the hook for this lesson.


 * 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.

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.
 * Extensions**

__**Materials, Resources and Technology**__

 * paper
 * pencils/pens
 * laptop/desktop access
 * computer/projector
 * digital camera (phone,etc)
 * graphic organizers
 * blogger account
 * calculator
 * textbook
 * further study resources

__Source for Lesson Plan and Research__
Pythagorean Theorem 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.
 * Pythagoras Rap - http://www.youtube.com/watch?v=K3RvkV_OYE8
 * 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:** 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 have a choice on what software they will use for this lesson's product. Students will also see multiple ways to present the proof of the Pythagorean Theorem. 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 create flowcharts for their proof and final project for which the expectations will be clearly defined in the rubric. The "microscope" type learners, who learn best by discovery learning, analyzing concepts, deep exploration, discussion, and focusing on details, will discover the proof of the Pythagorean Theorem, analyze the theorem, and apply it 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 introduce the concept of relationships within triangles. 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. Being able to relate the sides of a triangle to its' hypotenuse and understanding the Pythagorean Theorem is the basis for understanding trigonometric ratios in right triangles.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** This lesson on the Pythagorean Theorem satisfies the Maine Standards for Initial Teacher Certification by using Type I and Type II 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 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. 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 pair, team, and class discussions.
 * **Logical:** Students will derive the proof of the Pythagorean Theorem.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the Pythagorean Theorem proof. The Pythagorean Theorem will be displayed geometrically and algebraically.
 * **Naturalist:** Homework will include finding right triangles outside the classroom.
 * **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:** Students will listen to a rap about Pythagoras as the hook for this lesson.

Rationale:** Students will use graphic organizers to list key facts about Pythagoras' life. They will be given a handout with different visual representations of the Pythagorean Theorem proof. Each group will have a different representation to prove and present it 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. The graphic organizers will also include sample problems for the groups to work on. The graphic organizers will be collected and I will review their explanation of the proof and 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 starting their flowchart and lesson project.
 * //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 research Pythagoras and the Pythagorean Theorem. They will take their findings and create a creative digital compilation of the history of Pythagoras, real life right triangle pictures and examples, a flowchart of their mathematical step-by-step proof of the Pythagorean Theorem using Inspiration software, and visual geometric representation of the Pythagorean Theorem proof. 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 The classroom will be arranged with desks in groups of 4 based on their "Parts of a Triangle" handout which will minimize transition times within the lesson. Students will understand that there are relationships among angles, lengths, and sides of right triangles. They will realize that understanding the Pythagorean Theorem is the basis for understanding trigonometric ratios in right triangles. Students will understand and use basic ideas of trigonometry. To get students interested in this lesson they will watch and listen to a Pythagoras Rap which will set a foundation for proving the Pythagorean Theorem. //**Where, Why, What; Hook; Equip,**//
 * = **Minutes** ||= **Activity** ||
 * = 0-5 || Introduction to Pythagoras ||
 * = 5-10 || Introduction to the Pythagorean Theorem & Converse ||
 * = 10-20 || Graphic Organizers & Sample Problems ||
 * = 20-45 || Group Investigation - Proving the Pythagorean Theorem ||
 * = 45-55 || Class Discussion - Reviewing Proofs ||
 * = 55-60 || Introduce Lesson Project ||
 * = 60-80 || Work on Lesson Project ||

Students will know historical details about Pythagoras, the Pythagorean Theorem, multiple ways to prove the Pythagorean Theorem, and the relationship between the sides, lengths, and angles of a triangle. Students will use a graphic organizer to summarize the Pythagoras rap. They will also use the Pythagorean Theorem graphic organizers. Students will be learning in a staged (solo-team-class-pair-solo) environment. Students will listen to the rap individually, then move into teams grouped using a lottery to discuss the key elements of Pythagoras' life. When teams have finished collaborating, there will be a class discussion reviewing what they learned. Students will be able to review their information and edit it. After the class discussion, students will split into pairs to hypothesize and propose a proof for the Pythagorean Theorem. Feedback will be given on the graphic organizers, proof, and outline. Students will use Inspiration software to create an outline for their project and create a flow chart of their proof of the Pythagorean Theorem. //**Tailor; Explore; Rehearse; Revise/Refine;**//

There will be a pre/post blogging assignment to reflect. Students will use graphic organizers to list key facts about Pythagoras' life. They will be given a handout with different visual representations of the Pythagorean Theorem proof. Each group will have a different representation to prove and present it 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. The graphic organizers will also include sample problems for the groups to work on. The graphic organizers will be collected and I will review their explanation of the proof and 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 starting their flowchart and lesson project. Students will research Pythagoras and the Pythagorean Theorem. They will take their findings and create a creative digital compilation of the history of Pythagoras, real life right triangle pictures and examples, a flowchart of their mathematical step-by-step proof of the Pythagorean Theorem using Inspiration software, and visual geometric representation of the Pythagorean Theorem proof. Students will be graded on their understanding of the material based on the criteria of the given rubric. //**Evaluate; Organize/Product; Tailor;**//

(see attached) Animated Proofs - http://www.takayaiwamoto.com/Pythagorean_Theorem/Pythagorean_Theorem.html
 * Content Notes** - all content notes will be available on the class wiki.

(see attached) Math Glossary (if needed) "Breaking In" (if needed) Pythagorean Proof #1 Pythagorean Proof #2 Pythagorean Proof #3 Basic Concept - www.mathmax.com/basicmath/chapter/ch_ep/ch8s7.pdf Real World Application - hpms.hpisd.org/LinkClick.aspx?fileticket=9jeEjiyGbTs%3D&tabid=817 Lesson Product Rubric
 * Handouts** - all handouts will be accessible from the class wiki.