S+Hollingsworth+Tracey

** E-mail: ** tracey.hollingsworth@maine.edu
 * Teacher:** Tracey Hollingsworth
 * Office:** M284
 * Office Phone:** 207.385.5284
 * Office Hours:** 2:00-3:00 M-F, by appointment, or when my door is open

=Summary of Unit= This unit provides students with an in-depth study of right triangles and trigonometry. The unit will begin with the Pythagorean Theorem of which students will think deeply and use their previous knowledge to prove the theorem. They will learn how to use the Pythagorean Theorem and its converse which is will serve as an introduction to the relationships among angles, lengths, and sides of right triangles. These concepts are then applied to 45°-45°-90° and 30°-60°-90° triangles. A major emphasis of the unit is on using the sine, cosine, and tangent ratios to solve problems. Students will examine trigonometric ratios in a multitude of ways which will lead to students understanding how trigonometry is used in real world applications such as aviation, architecture, navigation, technology, and other sciences.

=Establish Goals= 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.

= = =Students will understand that= • there are relationships among angles, lengths, and sides of right triangles. • there are properties of triangles allow us to solve right triangles. • trigonometry has real world applications

= = =Essential Questions= • How are angles, lengths, and sides of right triangles used to determine information about right triangles? • How do the properties of "special" triangles affect trigonometric ratios? • Why is trigonometry important in real life?

= = =Students will know= • 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.

= = =Students will be able to= • prove and apply the Pythagorean Theorem. • solve a right triangle based on the "special" properties of 45°-45°-90° and 30°-60°-90° triangles. • b. Use trigonometry to solve for missing lengths in right triangles. • compare the different trigonometric ratios. • represent real world problems geometrically. • relate the sides of a triangle to its' hypotenuse by using trigonometric functions. • describe where trigonometry is used, other than in a classroom.

**Performance Task Overview** You are a pilot who successfully navigated an emergency landing. You were awarded by the National Safety Council for saving the lives of all the passengers; however, in the air, you had a disagreement with air traffic control about which city to land in. When you informed air traffic control that you needed to perform an emergency landing, you were flying at an altitude of 25,000 feet. You had looked out your window and found that the angle of depression to a city on the horizon was 24°. Air traffic control had calculated your angle of decent to be 28° and told you to land 500 miles from the city that you spotted. Now you have to prove to the FAA why your city was the best choice. You will create a digital comic to depict what happened while you were flying, showing why you landed in the city that you did. You and your co-pilot will use mathematical reasoning and show proof mathematically either in the comic or during your oral presentation to the FAA.

= = =Expectations=
 * Students are expected to give respect to myself and their classmates.
 * Students will be expected to come to class on time; tardiness will not be accepted. It is inconsiderate to the teacher and classmates, not to mention it results in a loss of valuable learning time.
 * Students are expected to come to class prepared and ready to learn every day; this includes but is not limited to bringing: pencil(s), notebook, textbook, homework/assignments, and USB drive.
 * Students are expected to ask any questions they may have; feel free to stop by before or after school.
 * Students and parents are expected to communicate any issues that arise that may impact their learning; communication is key for success. Students and/or parents may contact me by stopping by before or after class, by email, or by voicemail.
 * Students are responsible for completing any work missed due to absence. Any work assigned the day they are absent will be due the next class, unless an extension has been granted.
 * Academic misconduct will **__NOT__** be accepted. Academic misconduct will include, but is not limited to:
 * **Plagiarism**: The adoption or reproduction of ideas or words or statements of another person without due acknowledgment.
 * **Fabrication**: The falsification of data, information, or citations in any formal academic exercise.
 * **Deception**: Providing false information to an instructor concerning a formal academic exercise—//e.g.,// giving a false excuse for missing a deadline or falsely claiming to have submitted work.
 * **Cheating**: Any attempt to give or obtain assistance in a formal academic exercise (like an examination) without due acknowledgment.
 * **Sabotage**: Acting to prevent others from completing their work. This includes, but is not limited to, willfully disrupting the experiments of others.

=Benchmarks= >>
 * **Class attendance and participation - 200 points**
 * Class attendance and participation is mandatory. To earn all 200 points, students must **attend class everyday** and contribute to class discussions and class learning.
 * Many classes will involve working in pairs or groups; each student will have a role. Teacher reserves the right to deduct points for lack of cooperation and collaboration.
 * **Quizzes - 100 points**
 * Quizzes will be given at the beginning of each class after any questions have been answered. Supplemental questions will be given in the event that a student does not perform well and will receive half credit for each question.
 * The lowest quiz grade will be dropped.
 * **Homework - 100 points**
 * Homework will be given during every class; it will be checked and reviewed at the beginning of every class.
 * **Blogs - 100 points**
 * Throughout the unit students will be prompted to reflect on their learning experiences in their class blogs and give constructive criticism to classmates' blogs.
 * Constructive criticism is  defined as "criticism  kindly meant that has a goal of improving some area of another person’s life or work. Often  constructive criticism  refers specifically to the critique of someone’s written or artistic work...that would allow that person to further improve the work or to improve their approach to future endeavors".
 * Blogs will be monitored and students are expected to be respectful to others. Disrespect will result in loss of credit.
 * **Projects/assessments - 1000 points**
 * **Pythagorean Theorem *100 points*:** Create a digital compilation of right triangle pictures, flowchart, and geometric representation of the Pythagorean Theorem proof.
 * **Special Triangles *50 points*:** Interactive discussion about "special" right triangles via VoiceThread.
 * **Sine & Cosine Ratios *75 points*:** Create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function.
 * **Tangent Ratio *50 points*:** Interactive discussion about "tangent ratios" of right triangles via VoiceThread.
 * **Investigation *100 points*:** 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.
 * **Life Applications *75 points*:** Students will create a wordle that will be embedded on the class wiki with at least 20 words they think of when they hear the words "right triangle" and "trigonometry".
 * **UNIT PROJECT *200*: ** (see Performance Task)
 * **UNIT EXAM *300 points* **

= = = = = = =Grading Scale= A (95 -100), A- (90 - 94), 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).