Syllabus For The Unit Circle
Teacher: Mr. Sabia
Office Location: 221b
Office Hours: Monday - Thursday: 7:00AM 8:00AM, 3:00PM - 4:30PM, Friday: 7:00AM 8:00AM
E-mail: connor.sabia@maine.edu
Summary of Unit
Most students dislike mathematics because educators simply teach the subject, the uses
for it, and the methods of performing it out. Teachers rarely apply mathematics to
everyday life, other subjects, student’s interests, and technology. As a future mathematics
teacher, I will make it my number one goal to incorporate how certain mathematics is
applied to specific usages in everyday life. I will integrate technology into my arithmetic
lessons in order for students to broaden, apply, and learn their understandings of math. As
a future educator, I would also want my students to feel comfortable with the
terminology, formulas, and critical thinking aspect within mathematics. The unit that I
will be teaching is on the unit circle and it’s techniques to finding trigonometric values. I
will provide multiple lessons that focus on three essential ideas: the unit circle is
universal in mathematics, the unit circle is applied towards occupational jobs, and the
unit circle is helpful when remembering trigonometric values. In order for students to
fully absorb the lesson’s information, there understandings will be verified through
multiple mathematical projects, presentations, and classroom work with augmentative,
modified, and redefined technological devices. At the conclusion of my unit lesson,
students will not only fully understand the prerequisites of the unit circle, but also
recognize the connections between the unit circle and mathematics, realistic scenarios,
and technology.
Establish Goals
Common Core State Standards
Content Area: Trigonometry
Grade Level: High School
Domain: Trigonometric Functions
Cluster: Extend the domain of trigonometric functions using the unit circle
Standards:
1. Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
2. Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.
3. Use special triangles to determine geometrically the values of sine, cosine, tangent for
pie/3, pie/4, and pie/6 and use the unit circle to express the values of sine, cosine, and
tangent for pie-x, pie+x, 2(pie)-x in terms of their values for x, where x is any real
number.
4. Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
Students Will Understand That
• the unit circle is universal in mathematics
• the unit circle is applied towards occupational jobs
• the unit circle is helpful when remembering trigonometric values
Essential Questions
• Why is the unit circle universal in mathematics?
• How is the unit circle applied towards areas of
occupation?
• How is the unit circle helpful when remembering
trigonometric values?
Students Will Know
• Terminology: (unit circle, altitude, sin(), cos(), tan(), degrees, radians, special triangles,
soh/cah/toa, trigonometric values, arc length, Pythagorean Theorem)
• Formulas: (radian/ degree conversion formula (degrees = radians x 180^o/pie, radians =
degrees x pie/180^o), Pythagorean Theorem (a^2 + b^2 = c^2), soh/cah/toa (sine(theta) =
opposite/ hypotenuse, cos(theta) = adjacent/ hypotenuse, tan(theta) = opposite/ adjacent),
arc length (theta/ 360^o x (2 x pie x r))
• Critical Thinking: (drawing a unit circle, x and y coordinates, applying special triangles,
converting degrees into radians, soh/cah/toa, finding sin(), cos(), and tan() of x and y)
Students Will Be Able To
• demonstrate connections between the unit circle and trigonometric values
• illustrate different mathematical concepts that are applied when using the unit circle
• produce job-related scenarios that use the unit circle's concepts
• analyze the unit circle's properties
• consider ways of using the unit circle in job-related situations
• reflect on mathematical methods that are used when making the unit circle
Performance Task Overview
In an attempt to motivate adolescents in learning and understanding mathematics, Khan
Academy has launched a new and engaging activity that requires students from schools
around the United States to create a website that demonstrates their knowledge of
mathematics. Khan Academy executives, especially Khan Academy's CEO Salman
Khan, are on the hunt for new and creative websites that provide students, teachers, and
mathematicians with an easy, engaging, and understanding access to mathematics. The
Khan Academy team has come to you all and asked for groups of students to create a
mathematical website on the current mathematics lesson you are studying on (unit
circles), and present that website and its features in a 5-7 minute presentation at the next
TED Talk Conference in Vancouver, Canada in front of Khan Academy's CEOs and
Salman Khan. When presenting to Salman Khan, please dress professionally, be ready
and prepared to present, and enthusiastic when presenting. Good luck!
Expectations
Absences: All students taking my class are required to arrive to class prepared with the
appropriate materials and ready to learn. If a student is absent from class, I will assign a
reliable student to deliver the absent student the proper materials for studying his notes
and work, the current homework assignments, and the newest class projects. I will also email the absent student an update on the information we covered in class as well as a set
time and date so we can work out on a plan for turning the absent student's coursework
in.
Plagiarism: All works must be cited. Any works that are clearly cited incorrectly will
receive a zero for an overall grade and a written referral, which will be sent to the
principal and dean of students. The students will eventually learn about proper copyright
and fair use citations for their upcoming projects. Any questions about citation format, I
will gladly be able to help.
Assignments: All assignments must be turned in on time. If there is an issue with
turning in assignments on the day they are due, the students should at least give me a
days notice with a reasonable explanation. The student and I will develop a new plan of
submitting the assignment. If an assignment is not turned in on time, I will ask the
students for a proper reason for its lateness. If a reasonable explanation is given, the
student and I will develop a new plan of resubmitting the assignment. If an unreasonable
excuse is given, I will have no choice but to deduct 20% of the assignments point value.
The student and I will then develop a new plan of resubmitting the assignment.
Classroom Expectations: Classroom rules and expectations will be set by the teacher
and the students. Nonetheless, all students in the classroom are to give everyone the
utmost respect. My number one rule that I want any student that enters into my classroom
to follow is "treat others the way you want to be treated." Humor is allowed within the
classroom; however, it should not be humor that is hurtful, judgmental, or spiteful.
Benchmarks (1000 Points)
• Powerpoint Show (125 Points):
Students will use Powerpoint to share links, videos, and
movies that analyze and explain the unit circle's properties.
Students will be split up into a certain amount of groups,
and each group will receive a mathematical property that
relates to the unit circle. The students are required to
research their mathematical property, methods that assist
in understanding the property, and ways that relate the property and the unit circle. The
students will gather all of their data and present it on Microsoft Powerpoint.
• Glogster (125 Points):
Students will use Glogster to develop interactive posters of the unit circle and how to
apply it to finding trigonometric functions. After the students comprehend the basic
understandings of the unit circle and its properties from the Powerpoint Presentations,
each student will individually develop a Glogster poster on the unit circle. Students
should be able to describe the unit circle and its properties through visual, verbal, and
logical text, pictures, and videos. Part of the class will be discussing about copyrighting.
• ComicLife (125 Points):
Students will use ComicLife to develop a comic strip that has two students debate on the
similarities and differences of the unit circle and trigonometric values. Students will be
partnered up to create a comic about similarities and differences of the unit circle.
Students will use their data and knowledge gathered from the Glogster poster and
Powerpoint Presentation to develop a story on the relationship between unit circles and
trigonometric values.
• Google Earth (125 Points):
Students will use Google Earth to solve questions on how the unit circle can be used to
create building structures. Students will be assigned trigonometric problems, which
requires the use of the unit circle and trigonometric values that involves the use of the
Google Earth. Student will use Google Earth to visually see the real-life example and
apply the unit circle to solve the trigonometric values.
• Skype (125 Points):
Students will interview professionals and ask them how they apply the unit circle towards
their line of work. Students will use interview individuals they know or are related to
them using Skype in order to find whether the interviewee applies the unit circle in his or
her profession. The students are required to record their question and answer and write a
one to two page summary on their evidence. The students will bring their evidence to
class and informally present their evidence.
• iMovie (125 Points):
Students will use iMovie to reflect, develop, and create a visual and literal lesson plan on
the unit circle. Students will create an iMovie that reflects on their understandings of the
unit circle and trigonometric values. The students' movies can use different genres,
themes, or appearances; however, the final outcome should look presentable,
professionally, and logical.
Performance Task (250 Points): Listed Above
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).