S+McKeown,+Sarah

Office: Education Center - Room 543 Office Phone: (207) 123-456 Office Hours:** 3-4PM and by appointment ** E-mail: ** sarah.mckeown@maine.edu
 * Teacher: Ms. Sarah McKeown

=Summary of Unit:= This unit will begin uncovering the wonder of triangles by exploring fascinating, unique properties of right triangles. The unit begins by identifying and labeling the anatomy of a right triangle and acquainting the students with the Pythagorean Theorem The second lesson expands on the knowledge from the previous class by analyzing different situations in which the Pythagorean Theorem can be utilized. Lesson three delves into special cases of right triangles (such as the infamous 45/45/90 and 30/60/90 triangles) and introduces the relationship between angles and sides of triangles. The following lesson will review the established angle and side relationships and introduce the ever-helpful trigonometric functions. In the same day, students will learn how to apply these functions to situations where an angle or a side of a triangle is missing, thus evolving their understanding of angle and side relationships. In the fifth lesson, the class will review all that has been covered in the unit and then begin to bridge concepts by locating triangles within other shapes. Leading up to the ultimate lesson, students will have compiled this plethora of information and will now be ready to do some real application. In this lesson, students are will reflect upon what they have learned about triangles thus far, then relate the properties and formulas listed in the reflection to properties and formulas of other shapes. Students will come away from this unit with a solid understanding of the special properties the right triangle possesses and will be equipped with the necessary tools to succeed in future lessons involving other geometric shapes.

=Establish Goals= Maine Learning Results: Mathematics - C. Geometry Geometric Figures Grades 9 - Diploma 1. Students justify statements about polygons and solve problems. a) Use properties of triangles to prove theorems about figures and relationships among figures. 3. Students understand and use basic ideas of trigonometry.

= = =Students will understand that=
 * there exist useful relationship between angles and sides of right triangles.
 * the unique properties of right triangles can be used to solve other geometric problems.
 * the Pythagorean Theorem can only be used in certain conditions and will be able to determine when it is appropriate to use.

= = =Essential Questions=

• How is the Pythagorean Theorem used? • Why do the properties unique to right triangles help solve other geometric problems? • How can trigonometry be used to find missing angles and/or sides of triangles?

= = =Students will know= •Vocabulary: angle, leg, "right" angle, "right" triangle, hypotenuse, sine, cosine and tangent. •Formulas: Pythagorean Theorem, Law of Sines, Law of Cosines, Inverse trigonometric functions, the 45, 45, 90 triangle, the 30, 60, 90 triangles. •Critical Details: Relationship between angles of a triangle.

= = =Students will be able to=

•Describe the Pythagorean Theorem. •Evaluate the proper situation in which to use the Pythagorean Theorem. •Apply prior knowledge of triangles to new shapes. •Analyze given information to determine missing lengths/angles of triangles and how to solve for those values. •Relate properties and formulas of triangles to properties and formulas of triangles. •Recognize relationships between angles and sides.

**Performance Task Overview**

You and your colleges are doctors of Visual Media and Mathematics, fresh out of college and ready to make your break into show business. You have just received word that the popular television station QFZ has just recently partnered with the Department of Education's Mathematics division to create the new TV station, the EDQ. For their first order of business, the EDQ has done a study on television shows within the last 20 years and the results are devastating. There is enough math in modern broadcasting! The EDQ has decided to make a new show "Timmy the Talented Triangle" that discretely integrates triangles into television and they're opening up a contest for math doctors like YOU to direct the pilot episode! In order to prove your skills in the visual media field, you must create a five to ten minute film based on a pre-existing television show and parody the show while integrating right triangles in an entertaining manner. The judges are looking for a film that can include properties of the 45/45/90 triangle, the 30/60/90 triangle, and use the Pythagorean Theorem and Trigonometric Functions. In all, the judges will only select one team of mathematicians to be the directors so put your calculators down and put your directors' hats on... it's time to make your big break into show biz!

=Expectations=
 * Students are expected to respect other students, the classroom and myself at all times to keep a positive learning environment.
 * Students are expected to arrive to class on time and be prepared with the necessary materials (book, binder, pencil and homework). If a situation should arise where a student knows that he or she will be tardy or will be missing one of the materials, he or she should contact me in advance, either by phone or e-mail.
 * Students are expected to attend class and actively participate as it is a part of the learning process. If a student knows that he or she will not be able to attend class, notify me as soon as possible (either by phone or e-mail) so that we may set up a time to compensate for the lost class time.
 * Students are expected to adhere to the school's plagiarism policy. There is __**zero tolerance**__ for any plagiarism or cheating.

=Benchmarks=


 * Attendance 5,000 points**: You are expected to attend all classes and arrive on time, as it is crucial to learning this material. In order to receive all 1,000 points, you must be present at every class. If you give me notice in advance of an absence, the missed day will not count against you, however it will not count for you either (that day will remain as an empty box in the grade book). Even though it is not a large part of your grade, you are advised to take attendance seriously, as class time is the best and easiest way to learn the material.

Assignment: Make a short epic that applies the Pythagorean Theorem to real life. This project will demonstrate your initial understanding of the Pythagorean Theorem in a way that allows you to utilize the media. Be sure to include at least two ways in which Pythagorean Man (or whatever you choose to name your character) can use the Pythagorean Theorem to save the day! You will be graded on your comprehension of the Theorem and the validity of your examples.
 * Comic Life - 7,000 points:**

Assignment: Create a wikispace that includes what you have learned about the 45/45/90 and 30/60/90 triangles as well as the Pythagorean Theorem. Make sure to include a digital artifact for each fact you list. The artifact can be something you found yourself, or something found from another source. IF the artifact came from another source, proper citation is expected to be present on the bottom of the page. Even though this is a one time assignment, you are encouraged to continue adding to it as the unit progresses so that you have a digital list of all the material that was covered. You will be graded on the thouroughness of your explanations and the practicality of your artifacts (for example, you want artifacts of things that exist in real life and that are beneficial to real people. A bad idea would be taking a picture of a triangle and to say that knowing the Pythagorean Theorem was beneficial because you could solve the lengths of that triangle. Be more creative).
 * Wikispace - 10,00 points:**

Assignment: Create a brochure using Microsoft to advertise the "appeals" (properties) of right triangles with your target audience being another shape. This project will synthesize all you have learned about right triangles throughout the unit and also demonstrate your understanding of how those properties relate to other shapes. Be sure to appeal to at least two other shapes that the triangle can be applied to. You will be graded on the accuracy of your representation of the relationships (something you would NOT want to do is tell me how a triangle can help solve the surface area of an ink blotch). Focus on the shapes discussed in class.
 * Brochure - 15,000 points:**

Assignment: Participate in a discussion on the class wiki where students recognize and assess the benefits of right triangles in the real world. This assignment is worth a lot! This is your time to connect with your peers and discuss the practical applications of triangles. You will be graded on how analytical your contributions are and your ability to //discuss//, not merely //post//.
 * Class Wiki - 17,000 points:**

Assignment: Find several examples of right triangles either online or in your every day life the post a blog reflecting on your discoveries. Were you surprised on the number of examples you found? Why or why not? This is your chance to get involved with the material, not simply analyze and apply. Take this assignment as an opportunity to really explore the geometric properties of the objects around you and begin to accept geometry as an integrated part of your every day life. You will be graded on the thoughtfullness of your reflection and the variety of examples you found (proper citations are expected at the bottom of the page for examples you did not personally capture).
 * Blog - 7,500 points:**

Assignment: Take the quiz at "@http://www.funtrivia.com/playquiz/quiz14712910d9bc0.html" record your findings and list three things you could do to change your score were you to take it again. This quiz supplies questions about right triangles and their properties, and taking it will enable you to gauge your own personal comprehension. Either on paper or on your blog (the blog would be preferred), post the findings and personal suggestions. This assignment will not be graded critically, it is an "all or nothing" assignment.
 * Journal - 5,000 points:**

Assignment: (refer to the Performance Task Overview above). You will be graded in two areas; their mastery of the content and their ability to convey the information in the format required (an iMovie). You will be graded using two rubrics (one for each concentration). The content rubric will assess your content mastery, your ability to stay on task, your ability to parody, your citation of external work (note, //anything// **not** mentioned in class **//is an outside source//** that **__needs to be cited__**!). The technical rubric will assess your ability to collaborate with peers, your ability to create a film that parrallels a self-constructed story board, your ability to speak clearly, the flow of your film, your ability to stay within a given time limit and your use of digital transitions between scenes.
 * End of the unit project: 24,932 points:**

__**Total number of points possible: 91, 432**__

=Grading Scale=


 * A** (93 -100), **A-** (90 - 92), **B+** (87 - 89), **B** (83 - 86), **B-** (80 - 82), **C+**(77 - 79), **C** (73-76),
 * C-** (70 - 72), **D+**(67 - 69), **D** (63 - 66), **D-** (60 - 62), **F** (0 - 59).