Understanding Trigonometric
Functions Using the Unit Circle
High School/ Grades 11 & 12
Trigonometry
Trigonometric Functions; Unit Circle; Graphing
Connor B. Sabia
Mount Blue Regional School District
Mount Blue High School
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.
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 nit 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
4. Use the unit circle to explain symmetry (odd and even) and periodicity
of trigonometric functions.
• The unit circle is universal in mathematics
• The unit circle is applied towards occupational
• The unit circle is helpful when remembering trigonometric values
• 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?
• Terminology: (unit circle, altitude, sin(), cos(), tan(), degrees,
radians, special triangles, soh/cah/toa, trigonometric values, arc
length, Pythagorean Theorem)
• Demonstrate connections between the unit circle and
trigonometric values
• Illustrate different mathematical concepts that are applied
when using the unit circle
• Formulas: (radian/ degree conversion formula (degrees = radians x
180^o/pie, radians = degrees x pie/180^o), Pythagorean Theorem (a^2 • Produce job-related scenarios that use the unit circle's
concepts
+ b^2 = c^2), soh/cah/toa (sine(theta) = opposite/ hypotenuse,
• Analyze the unit circle's properties
cos(theta) = adjacent/ hypotenuse, tan(theta) = opposite/ adjacent),
• Consider ways of using the unit circle in job-related
arc length (theta/ 360^o x (2 x pie x r))
situations
• Critical Thinking: (drawing a unit circle, x and y coordinates,
• Reflect on mathematical methods that are used when
applying special triangles, converting degrees into radians,
making the unit circle
soh/cah/toa, finding sin(), cos(), and tan() of x and y)
Goal: Your task is to create a website on the unit circle for Khan Academy.
Role: You are recruits for Khan Academy's challenge.
Audience: The target audience is Khan Academy's CEOs.
Situation: The challenge involves with creating a 5-7 minute presentation explaining
the website's features including a unit circle lesson and examples.
Product/Presentation: You will create a website that provides a lesson on the unit
circle and examples following the unit circle's lesson
Standards (Criteria from both rubrics - product and presentation): Website:
(Accuracy of Content 35%, Effectiveness 25%, Sequence of Information 15%,
Navigation 15%, Audio 5%, Text 5%), Presentation: (Comprehension 30%,
Preparedness 25%, Enthusiasm 12.5%, Speaks Clearly 12.5%, Posture and Eye
Contact 10%, Stays on Topic 10%)
• ComicLife: 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.
• Glogster: Students will use Glogster to develop interactive posters of the unit circle and how to apply it to
finding trigonometric functions.
• Powerpoint Show: Students will use Powerpoint and share links, videos, and movies that analyze and
explain the unit circle's properties.
• Google Earth: Students will use Google Earth to solve questions on how the unit circle can be used to
create building structures.
• Skype: Students will interview professionals and ask them how they apply the unit circle towards their line
of work.
• iMovie: Students will use iMovie to reflect, develop, and create a visual and literal lesson plan on the unit
circle.
• Pre-Assessment: Questionnaire, short, open-ended questions that ask their previous
knowledge in mathematics
• Checking for Understand: Fist to Five, Circle-Triangle-Square, Flag it, Handprint,
Notebook/ Student Data, Triangular Prism
• Self-Assessment: Students, Peers, and Teachers/ Timely Feedback
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
Trigonometry
Common Core Standards
Content Area: Trigonometry
Domain: Trigonometric Functions
Cluster: Extend the domain of trigonometric functions
using the unit circle
Unit Circle
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!
Google Sites
Presentation
By what criteria will student products/performances be evaluated?
• Accuracy of Content 35%
• Effectiveness 25%
• Sequence of Information 15%
• Navigation 15%
• Audio 5%
• Text 5%
• Comprehension 30%
• Preparedness 25%
• Enthusiasm 12.5%
• Speaks Clearly 12.5%
• Posture and Eye Contact 10%
• Stays on Topic 10%
(W) 1.1 Students understand that the unit circle is helpful when remembering trigonometric values (Where), Real Life: The
properties of the unit circle are essential when building, solving, and applying for trigonometric values. (Why), 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. Use the unit circle to explain symmetry (odd and even) and
periodicity of trigonometric functions. (What)
(H) 1.2 The hook will be a general question, "What objects relate to a circle?" Even though this may seem bizarre at first , the
point to this question is to think that circles are everywhere in our everyday life and then tie it all back together by introducing the
unit circle. If executed correctly, students will understand the connections between the unit circle and circles found in everyday
life. (Hook)
(E) 1.3 Students will know the unit circle, sin(), cos(), tan(), degrees, radians, trigonometric values, radian/ degree conversion
formula (degrees = radians x 180^o/pie, radians = degrees x pie/180^o), and soh/cah/toa (sine(theta) = opposite/ hypotenuse,
cos(theta) = adjacent/ hypotenuse, tan(theta) = opposite/ adjacent). (Equip), Students will use the Web Chart to establish key
mathematical properties, uncover their usefulness, understand their formula, and their application towards the unit circle. The
Web Chart help students establish key mathematical properties, uncover their usefulness, understand their formula, and their
application towards the unit circle. It assist students in uncovering the essential uses of the unit circle, the properties required to
make the unit circle, and the property's functions that make up the unit circle's essentials. Students will be split up into Think-PairShare Groups. Students will use this time to examine and share their ideas on their assigned unit circle property that they will
have to present in their Powerpoint presentation. (Explore), Students will use Powerpoint and share links, videos, and movies that
analyze and explain the unit circle's properties. (Experience)
(R) 1.4 Five minutes before the bell rings, students will draw a single handprint on a black sheet of paper. For each finger and
thumb, students will write five ideas, concepts, and understandings before they leave. Before the students leave, they will hand in
their handprint to me. The Handprint activity will not only whether students comprehended the material, but it will also provide
me an assessment on whether my students are understanding my lectures and teaching strategy. (Rethink), Students will use a
checklist to assess their use of the unit circle, it's properties, and the mathematics that make up its properties when forming their
multiple technological presentation. Student's peers will be able to give an assessment of the student's presentation, the
understanding of the content within the presentation, and the amount of research findings the students found when researching the
unit circle's properties. (Rethink/ Revise), The teacher will follow a rubric to assess students' understandings of content,
relatability to the unit circle, and the amount of ideas and information gathered on the unit circle's properties.(Rethink/ Revise)
(E) 1.5 Formative Assessment - Pre-Assessment: Students will be provided with a questionnaire, which will consist of short, open
ended questions that ask the student's previous knowledge in mathematics, specifically algebra II and geometry. Checking for
Understanding: Handprint. Timely Feedback: Student Checklist, Peer Assessment, Teacher Rubric (Evaluate)
(T) 1.6 Tailors
Verbal: The hook will allow students to verbally solve the question "What objects relate to a circle?" For a more general point of
view, hook, my lectures, and students' presentations are areas where students can learn the essentials and relationships about the
unit circle and it's properties.
Logic: The Powerpoint presentations will allow students to logically understand the patterns between the unit circle and it's
properties.
Visual: Students will visually see the relationships between the unit circle, it's properties, and common objects through the hook,
powerpoint presentations, and the Web Chart presented in class
Musical: Students can find or present musical relationships between the unit circle and it's properties for their presentation.
Kinthestic: Students can come up to the board and draw objects and ideas relating to the hook in the beginning of the class.
Intrapersonal: The Handprint activity provides students meditative time to think about the ideas and concepts they comprehended
and well as come up with any questions that might progress their comprehension. Students can ponder the hook's question in the
beginning of the class.
Interpersonal: Students can appropriately socialize and compare thoughts related to the subject, specifically during the hook, the
Web Chart, the Think-Pair- Share Groups, and the powerpoint project.
Naturalist: During the Handprint activity, students do not have to be confined to a handprint. They can use naturalistic ideas such
as a four-leaf clover to explain their understandings. Students can relate naturalistic items when thinking about the hook's
question.
(O) 1.7 Students will be able to analyze the unit circle's properties. (Perspective) Product: Powerpoint Show, Type II Technology
(The Powerpoint Show will include videos, diagrams, and picture.), Number of Days: 2-3 days, (Organize)
(W) 2.1 Students will understand that the unit circle is universal in mathematics. (Where), Real Life: Students will
comprehend the importance of applying their previous knowledge in geometry and algebra to future mathematical
functions. (Why), Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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. 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. Use
the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (What)
(H) 2.2 The hook that I will use in this lesson is a trivia race. In the beginning of the class, students will be split up into
groups of five or six (depending on the size of the class). One student will race up to the whiteboard and I will ask them to
demonstrate a mathematical formula and an example of the formula. The mathematical formulas will eventually be related
to the unit circle. If a student does not know it, he or she can return to his or her group and another student within the
group can come up to the board and answer the question. Once the student answers the question correctly, he or she can
return to the group and a different student who has not answered can come to the board and answer another mathematical
trivia question. Once a group has finished answering the questions correctly, the game is over and that group won. (Hook)
(E) 2.3 Students will know the essentials of drawing a unit circle and x and y coordinates, applying special triangles,
converting degrees into radians, soh/cah/toa, finding sin(), cos(), and tan() of x and y, arc length, and Pythagorean
Theorem. (Equip), Students will use the Tree Chart to label essential mathematical concepts and uncover their usefulness
when creating and solving an unit circle. Students will be asked to Mix-Pair-Share; an activity that allows students to
randomly walk around the classroom, have a student pair up with another person closes to him or her, and share there
results between one another. (Explore), Students will use Glogster to develop interactive posters of the unit circle, it's
mathematical properties that make up or assist the unit circle, and how to apply the unit circle to finding trigonometric
functions. (Experience)
(R) 2.4 In the beginning of the semester, I will require students to record notes from my lectures and student presentations
and place them in a notebook. At the end of this lesson, I will have students share and explain their notes while focusing on
three important questions: 1. What have we discussed in class? 2. What have I learned in class? / What areas do I fell
comfortable with knowing and areas that I feel that I am struggling to understanding? 3. How will I expand/ improve my
understandings within the class? (Rethink), Students will follow a checklist that describes the project's principles when
making their Glogster posters on the use of the unit circle, it's properties, and the mathematics that make up its properties.
(Rethink, Revise), The teacher will follow a rubric to assess students' understandings of content, relatability to the unit
circle, and the amount of ideas and information gathered on the unit circle. (Rethink/ Revise)
(E) 2.5 Formative Assessment - Checking for Understanding: Notebook/ Student Notes. Timely Feedback: Student
Checklist, Teacher Rubric (Evaluate)
(T) 2.6 Tailors
Verbal: Students can verbally learn the essentials and relationships about the unit circle and it's properties through my
lectures and students' presentations.
Logic: The Trivia Race will allow students to logically test their knowledge
Visual: The Powerpoint presentations and the Tree Chart will allow students to visually understand the patterns between
the unit circle and it's properties.
Kinthestic: The Trivia Race will allow students to actively participate in the classroom by running to and from the
whiteboard answering mathematics questions. Mix-Pair-Share will actively allow students to randomly walk around the
room and share their ideas with another individual.
Intrapersonal: Student's notes and notebook provides students time to ponder about the knowledge they acquired.
Interpersonal: Mix-Pair-Share provides students the ability to socially interact and share ideas with their colleagues.
Naturalist: The Tree Chart provides a understandable concept that can be easily obtained for naturalistic students.
(O) 2.7 Students will be able to illustrate different mathematical concepts that are applied when using the unit circle.
(Interpretation) Product: Glogster, Type II Technology, Number of Days: 2-3 days, (Organize)
-
(W) 3.1 Students will understand that the unit circle is helpful when remembering trigonometric values. (Where), Real Life:
Students will comprehend the relatability of the unit circle to trigonometric values and reminisce the importance of it's easy
accessibility to trigonometric values. (Why), 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. 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. (What)
(H) 3.2 The hook that I will use is called the trig spinner. First, I will place a huge circle that has an x and y axis and a
moveable radius equaling to one. Next, I will then pass out sheets of paper that have trig values organized by sin, cos, tan,
sec, csc, cot, radians, and degrees. Then, I will have one of the students spin the radius around the circle until it stops. We
will then measure the angle from the positive x-axis to the radius and have the students find the trigonometric value of that
angle first with the unit circle. If the student cannot solve the problem with using the unit circle, they can refer back to the
trigonometric functions sheet. (Hook)
(E) 3.3 Students will know the unit circle, sin(), cos(), tan(), degrees, radians, radian/ degree conversion formula, special
triangles, soh/cah/toa, trigonometric values. (Equip), Students will use the KWL chart to label, reflect, and gather
information that they previously know, want to know, and will know about relationship between the unit circle and
trigonometric values. Students will use the exercise Give One, Get One to answer multiple mathematical examples. It will
also allow students to compare answers will other students within the classroom and see the mathematics that brought them
to that answer. (Explore), 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. They can apply the information gathered from
previous presentations for this project. (Experience)
(R) 3.4 Although I will provide a system that will physically display whether students understand my presentations and the
content, Triangular Prism visually displays a level of student comfortableness on the unit circle. (Rethink), Students will
follow a checklist that describes the project's standards when making their ComicLife Project on the relationship between
the unit circle and trigonometric values. (Rethink, Revise), The teacher will follow a rubric to assess students'
understandings of the content and relatability of the unit circle to trigonometric values. (Rethink/ Revise)
(E) 3.5 Formative Assessment - Checking For Understanding: Triangular Prism. Timely Feedback: Student Checklist,
Teacher Rubric (Evaluate)
(T) 3.6 Tailors
Verbal: My lectures and students' presentations are areas where students can verbally learn the essentials and
relationships about the unit circle and it's properties.
Logic: The KWL chart will have the students think about their previous knowledge of the subject of trigonometric values
with information that they will want to learn and will learn.
Visual: By demonstrating the hook in the beginning of the class, the students will visually understand the simplicity of using
the unit circle.
Musical: The ComicLife project can be about a musical interaction with the content.
Kinthestic: Give One, Get One will actively allow students to randomly walk around the room and share their answers with
other students.
Intrapersonal: The KWL chart will have the students think about their previous knowledge of trigonometric values with
information that they will want to learn and will learn. Give One, Get One will have the students reflect on the content's
questions and solve them.
Interpersonal: The cooperative learning activity Give One, Get One will have the students time to interact with students on
the content's questions and discuss the answers with them.
Naturalist: I can have naturalistic students imply the ComicLife Project towards ways that can be related to nature.
(O) 3.7 Students will be able to demonstrate connections between the unit circle and trigonometric values. (Explanation)
Product: ComicLife, Type II Technology, Number of Days: 2-3 days, (Organize)
(W) 4.1 Students will understand that the unit circle is applied towards occupational jobs. (Where), Real Life:
These exercises provide a basic and broad explanation of situations that could arise for certain future
occupations. (Why), 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. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (What)
(H) 4.2 The hook for the class is measuring the trigonometric values of pacman's mouth and body by literally
using the unit circle. The main idea for this hook is for students to relate the unit circle to occasions that may
require the use of the unit circle. (Hook)
(E) 4.3 Students will know the essentials to drawing a unit circle, applying special triangles, Pythagorean
Theorem (a^2 + b^2 = c^2), soh/cah/toa (sine(theta) = opposite/ hypotenuse, cos(theta) = adjacent/ hypotenuse,
tan(theta) = opposite/ adjacent), and arc length (theta/ 360^o x (2 x pie x r)
converting degrees into radians (degrees = radians x 180^o/pie, radians = degrees x pie/180^o). (Equip), Students
will use the KWS Chart to establish what they know about unit circles in job-related situations, seek out what they
want to further their knowledge in for unit circles, and list the possible resources that they can obtain that
information including Google Earth and the related questions I that will provide them. Before the group activity
Pair Checks begins, I will present and teach my students Google Earth and provide examples that relates the unit
circle to specific structures and obstacles. Pair Checks allow students to listen, teach, and compare answers on
Google Earth related problems that relate to the unit circle. (Explore), Students will use Google Earth to solve
questions on how the unit circle can be used to create building structures. (Experience)
(R) 4.4 Although I will provide a system that will visually display whether students understand my presentations
and the content, Fist to Five physically displays a level of student comfortableness on the unit circle. (Rethink),
Students will be put into peer assessment groups where the students can assess each others findings. (Rethink,
Revise), The teacher will follow a checklist and have a short classroom discussion to assess whether the students
understood the question and its relatability of the unit circle to trigonometric values, the problems' solutions, and
the usefulness of Google Earth and it's relatability to the content. (Rethink/ Revise)
(E) 4.5 Formative Assessment - Checking for Understanding: Fist to Five. Timely Feedback: Peer Assessment,
Teacher Checklist/ Discussion
(T) 4.6 Tailors
Logic: Google Earth provides the students with a logical relationship between the unit circle and real-life
scenarios. KWS Chart assist students in thinking about their previous knowledge of trigonometric values and their
relationships to real-life, places that have trigonometric values that have not been explored, and possible
resources that can provide that information. The hook provides a pattern that connects related objects to the unit
circle.
Visual: Google Earth provides a visual look to solving trigonometric values using the unit circle. The hook
provides a visual aspect when relating the unit circle to related ideas.
Kinthestic: Fist to Five participates students in the classroom by having them physically state their level of content
understanding.
Intrapersonal: Students can individually solve the Google Earth problems before going into Pair Check groups
Interpersonal: Pair Check groups let students teach and assist other students in solving the Google Earth
equations.
Naturalist: Certain Google Earth problems can be naturalistic situations.
(O) 4.7 Students will be able to consider ways of using the unit circle in job-related situations. (Empathy)
Product: Google Earth, Type II Technology, Number of Days: 1-2 days, (Organize)
(W) 5.1 Students will understand that the unit circle is applied towards occupational jobs. (Where), Real Life:
These exercises prepare students to encounter basic and broad situations about unit circles that could arise for
certain future occupations. (Why), 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. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions. (What)
(H) 5.2 Students will understand that the unit circle can be applied to any occupation even the culinary art. I will
bring in cupcakes with the unit circle drawn on top of the cupcakes with icing. (Hook)
(E) 5.3 Students will know the essentials to drawing a unit circle, applying special triangles, Pythagorean
Theorem (a^2 + b^2 = c^2), soh/cah/toa (sine(theta) = opposite/ hypotenuse, cos(theta) = adjacent/ hypotenuse,
tan(theta) = opposite/ adjacent), and arc length (theta/ 360^o x (2 x pie x r)
converting degrees into radians (degrees = radians x 180^o/pie, radians = degrees x pie/180^o). (Equip), Students
will use the Inverted Triangle Chart. This will allow students to narrow down a focus on relating the unit circle
with job-related scenarios. Stand up, Hand up, and Pair Up tactic allows students to work together on coming up
with scenarios that provide the use of the unit circle. (Explore) Students will interview professionals through
Skype and ask them how they apply the unit circle towards their line of work. (Experience)
(R) 5.4 The Circle, Triangle, and Square tactic allows students to ponder, question, and relate ideas towards the
unit circle, trigonometric values, and real-life events. The activity gives the students a chance to actually learn and
think like processional mathematicians. (Rethink), Students will be put into peer assessment groups where the
students can assess each others findings. (Rethink, Revise), The teacher will follow a checklist and have a short
classroom discussion to assess on students' findings on the information they found when they interviewed someone
on the uses of the unit circles. (Rethink/ Revise)
(E) 5.5 Formative Assessment - Checking for Understanding: Circle, Triangle, Square Timely Feedback: Peer
Assessment, Teacher Checklist/ Discussion
(T) 5.6 Tailors
Verbal: Students can verbally learn through the conversations they have with professional mathematicians or
people that use the unit circle in their occupation.
Logic: Creating job-related scenarios through the Stand up, Hand up, and Pair up tactic can assist students in
logically relating the unit circle with real-life settings.
Visual: The Inverted Triangle can visually assist students in describing and creating situations that use the unit
circle.
Musical: Students with musical talents can relate the unit circle to musical situations. Students can ask musician
about whether they know the unit circle and can relate to it with their occupation.
Kinthestic: Students can ask athletic individuals about whether they know the unit circle and can relate to it with
their occupation.
Intrapersonal: Students can ponder whether they understand, question, and agree with certain ideas about the
unit circle and it's properties through the Circle, Triangle, and Square tactic.
Interpersonal: Students' interactions with people through Skype on the unit circle and it's properties can promote
their understands on the subject.
Naturalist: Students can ask naturalistic individuals about whether they know the unit circle and can relate to it
with their occupation.
(O) 5.7 Students will be able to produce job-related scenarios that use the unit circle's concepts. (Application)
Product: Skype, Type II Technology, Number of Days: 1-2 days, (Organize)
(W) 6.1 Students will understand that the unit circle is universal in mathematics. (Where), Real Life: It is important for
students to realize their understands the reasons of the unit circle in order for them to relate it later during the math
course. (Why), Understand radian measure of an angle as the length of the arc on the unit circle subtended by the
angle. 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. 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. (What)
(H) 6.2 In the beginning of the class, I will present the Unit Circle Song. The Unit Circle Song provides a musical tone
that might encourage students to easily memorize and relate the unit circle. The Unit Circle Song will be a segue into
one of the final projects they will have to perform, the iMovie project. (Hook)
(E) 6.3 Students will know the essentials to drawing a unit circle, x and y coordinates, applying special triangles,
trigonometric values, arc length, and Pythagorean Theorem, converting degrees into radians, knowing the essentials to
soh/cah/toa, finding sin(), cos(), and tan() of x and y. (Equip) Students will use the Step-by-Step Chart. The Step-by-Step
Chart allows students to record and reflect each approach when solving trigonometric values using the unit circle. This
chart can also be useful to the students for writing their script about their unit circle lessons when making their iMovie
Project. Students will be engaged in a Simultaneous Round Robin. This activity will give the chance for every student to
write and share his or her answer to the student's fellow classmates. This activity will hopefully make students share
different ideas, methods, and interpretations of solving a mathematical question related to the unit circle. (Explore)
Students will use iMovie to reflect, develop, and create a visual and literal lesson plan on the unit circle. (Experience)
(R) 6.4 In order for students to think about the key steps and concepts of using the unit circle to solve for trigonometric
values, students will use the Flag It technique. Flag It has students think about cerian ideas that are essential for
remembering and understanding about the unit circle,
write them on sticky notes, and "flag" them to the whiteboard. (Rethink), Students will follow a rubric that reflects on
mathematical methods that are used when making the unit circle. Students will be put into peer assessment groups
where the students can assess each others projects. (Rethink/Revise), The teacher will have an interview with each
group to assess on the their comprehension, understanding of the content, the movie's overall performance, and public
speaking. (Revise/Refine)
(E) 6.5 Formative Assessment - Checking for Understanding: Flag it. Timely Feedback: Student Rubric, Peer
Assessment, Teacher Interview
(T) 6.6 Tailors
Verbal: Students can verbally learn through the unit circle song's lyrics and the student's iMovie presentations.
Logic: The Step-By-Step Chart helps students understand the unit circle's patterns through the methods and concepts it
uses.
Visual: Students can visually learn through the unit circle song and the student's iMovie presentations
Musical: The unit circle song provides a rhythm and beat that can be easily picked up and understood for students with
musical learning skills.
Kinthestic: Flag It method provides students to actively participate by writing down their important ideas that relate to
the unit circle and have them post them on the whiteboard.
Intrapersonal: The Step-By-Step Chart, Flag It, and Simultaneous Round Robin allow students to individually think
about important concepts, techniques, and properties that make up, assist, and help create the unit circle.
Interpersonal: The Step-By-Step Chart, Flag It, and Simultaneous Round Robin allow students to socially interact with
their classmates about important concepts, techniques, and properties that make up, assist, and help create the unit
circle.
(O) 6.7 Students will be able to reflect on mathematical methods that are used when making the unit circle. (SelfKnowledge) Product: iMovie, Type II Technology, Number of Days: 3-5 days, (Organize)
83.1 Unit Circle’s Reliability (W);
3.2 Trig Spinner (H); 3.3 KWL
Chart, Give One, Get One (E); 3.4
Checklist, Rubric (R); 3.5
Triangle Prism, (E-2); 3.7
Explanation, 2-3 days
Lesson 3
Presentation
5.1 Encountering Unit Circle
Occupational Exercises (W); 5.2 Unit
Circle Cupcakes (H); 5.3 Inverted
Triangle Chart, Stand Up, Hand Up, and
Pair Up (E); 5.4 Peer Assessment,
Checklist/ Discussion (R); 5.5 Circle,
Triangle, Square, (E-2); 5.7
Application, 1-2 days
Lesson 5
2.1 Applying Previous Knowledge
(W); 2.2 Trivia Race (H); 2.3 Tree
Chart, Mix-Pair-Share (E); 2.4
Checklist, Rubric (R); 2.5
Notebook/ Student Notes,(E-2);
2.7 Interpretation, 2-3 days
Lesson 2
Work
4.1 Unit Circle Occupational
Exercises (W); 4.2 Pacman (H);
4.3 KWS Chart, Pair Checks (E);
4.4 Peer Assessment, Checklist/
Discussion (R); 4.5 Fist to Five,
(E-2); 4.7 Empathy, 1-2 days
Lesson 4
1.1 Unit Circle Properties (W); 1.2
“What Relates to a Circle?” (H);
1.3 Think-Pair-Share, Web Chart
(E); 1.4 Checklist, Peer
Assessment, Rubric (R); 1.5
Handprint, Questionnaire (E-2);
1.7 Perspective, 2-3 days
Lesson 1
6.1 Realize Unit Circle’s
Understandings (W); 6.2 Unit Circle
Song (H); 6.3 Step-By-Step Chart,
Simultaneous Round Robin (E); 6.4
Rubric, Peer Assessment, Interview
(R); 6.5 Flag It, (E-2); 6.7 SelfKnowledge, 3-5 days
Lesson 6