Understanding by Design Template (Shawn Turner / H Trigonometry)
Stage 1 - Desired Results
Established Goals:
Students will be able to model graphs of sine and cosine on a coordinate plane using the degrees,
radians, and trigonometric values of the unit circle in order to visualize the wave-like qualities of a
sinusoidal graph.
Students will be able to identify dilation, translation, and reflection of a sinusoidal transformation using
the A-, B-, C-, and D-values in order to graph transformation of the basic graphs of sine and cosine.
Standards:
F-TF.3: Extend the domain of trigonometric functions using the unit circle. Use special triangles to
determine geometrically the values of sine, cosine, tangent for pi/3, pi/4, and pi/6, and use the unit
circle to express the values of sine, cosine, and tangent for in terms of their values for “pi minus x,” “pi
plus x,” “two times pi minus x,” where is any real number.
F-TF.4: Extend the domain of trigonometric functions using the unit circle. Use the unit circle to explain
symmetric (odd and even) and periodicity of trigonometric functions.
1.1 Enduring Understandings 1.2 Essential Questions
Students will understand that . . . . 1. Why do we study trigonometric functions?
1. Graphing sine and cosine acts as a concrete 2. Why do we memorize the unit circle?
way to visualize some of the key features 3. Why do we graph?
we saw regarding the trigonometric values 4. How do special right triangles inform
on the unit circle. graphs of trigonometric functions?
2. The repetition of trigonometric values on 5. What is does it mean to transform?
the unit circle, dependent on the quadrant
translates to the wave-like appearance of
the sine and cosine graphs.
3. Sinusoidal functions all derive from the
graph of sine and that the graph of cosine is
simply a horizontal translation of the graph
of sine.
1.3 Acquisition of Knowledge and Skills
Students will know . . . . Students will be able to . . .
1. The degrees and radians and their 1. Translate unit-circle knowledge to identify
corresponding trigonometric values on the trigonometric values form the y-axis for the
unit circle. coordinate plane.
2. The sketch of the graphs of sine and cosine 2. Convert degrees to radians to form the
on a coordinate plane using a period of 2pi values on the x-axis for the coordinate
3. The transformation language generated by plane.
the asin(bx+c)+d and acos(bx+c)+d forms.. 3. Graph sine and cosine on the coordinate
plane.
4. Extend SOHCAHTOA knowledge to predict
what graphs of other trigonometric
functions would look like (tangent,
Adapted from Understanding by Design (p. 22), by G. Wiggins and J. McTighe, 2005, Upper Saddle River, NJ: Pearson
Education, Inc. Copyright 2005 by ASCD.
cosecant, secant, and cotangent).
5. Identify the dilation, translation, and
reflection using the transformation
language form for sine and cosine.
6. Graph transformations of sine and cosine
functions using the transformation
language form for sine and cosine.
Stage 2 - Assessment Evidence
Performance Tasks: Other Evidence:
1. Take a homework quizzes on the graph of 1. Observation of students’ understandings,
sine and cosine.. questions, misconceptions, and frustrations
2. Participate in a Snake-Method activities to 2. Feedback (oral) from whole-group
list the trigonometric values for sine and discussion
cosine. 3. Quick-check question and answer session
3. Work on the white board at the beginning of class
4. Classwork Assignment 4. Feedback (written and oral) from classwork
5. Peer-conversation about the graphs of and homework assignment.
transformations of sine and cosine
6. Homework Assignment
Stage 3 - Learning Plan
Learning Activities:
(Day 1)
1. Welcome, Prayer, and Attendance
2. Presentation of Goals
3. Definition and Terminology
a. Sinusoid
b. Period
4. Connection to the Past
a. Snake-Method Activity
b. Whole-Group Discussion
5. New Content
a. Graphing Sine on a Coordinate Plane
b. Viewing Desmos Graph of Sine
6. Present Homework → Homework Quiz on the Graph of Sine
(Day 2)
1. Welcome, Prayer, and Attendance
2. Homework Quiz - Graph of Sine
3. Review Homework Quiz
4. Review Concepts from Previous Lesson
5. Presentation of Goals
6. Connection to the Past
a. Snake-Method Activity
b. Whole-Group Discussion
7. New Content
a. Graphing Cosine on a Coordinate Plane
b. Viewing Desmos Graph of Cosine
Adapted from Understanding by Design (p. 22), by G. Wiggins and J. McTighe, 2005, Upper Saddle River, NJ: Pearson
Education, Inc. Copyright 2005 by ASCD.
8. Present Homework → Homework Quiz on the Graph of Cosine
(Day 3)
1. Welcome, Prayer, and Attendance
2. Presentation of Goals
3. Definition and Terminology
a. Transformation
b. Dilation
c. Translation
d. Reflection
4. Connection to the Past
a. Algebra II transformation language
5. New Content
a. Transformation language form for sine and cosine
i. Amplitude
ii. Reflection
iii. Period
iv. Frequency
v. Phase Shift
vi. Vertical Shift
b. Board Work to identify components of transformation language
c. Handout
6. Present Homework → Finish Classwork Handout on identifying components of transformation
language
(Day 4)
1. Welcome, Prayer, and Attendance
2. Review of Concepts from Previous Lesson
3. Presentation of Goals
4. Connections to the Past
5. New Content
a. Modeling Graphs with Desmos
b. Group/Peer Conversations about the Graphs
6. Present Homework → Handout on graphing transformations of sine and cosine
Adapted from Understanding by Design (p. 22), by G. Wiggins and J. McTighe, 2005, Upper Saddle River, NJ: Pearson
Education, Inc. Copyright 2005 by ASCD.
