Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 46422
Rotation Debate: Radians vs Degrees
In this lesson, students will be able to answer the question why radians are the preferred measure of an angle. This lesson nominally takes two days
to teach.
Day 1: Bell Ringer-Day 1, Lesson Notes, Activity 1
Day 2: Day 1 Review and Wrap-up, Bell Ringer-Day 2, Activity 2
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Graphing Calculators,
Computer for Presenter, Internet Connection, LCD
Projector, Speakers/Headphones, Adobe Flash Player,
Microsoft Office, Computer Media Player
Instructional Time: 1 Hour(s) 40 Minute(s)
Freely Available: Yes
Keywords: radian, degree, coterminal, arc length, unit circle
Instructional Design Framework(s): Direct Instruction, Guided Inquiry (Level 3), Cooperative Learning
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students should be able to
Convert radians to degrees and degrees to radians using the conversion formulas.
Find the arc length of a circle with the given central angle
Find one negative and one positive angle for each given angle
Use radian measure in real-world applications
Prior Knowledge: What prior knowledge should students have for this lesson?
Right Triangle Trigonometry
Definitions of complementary & Supplementary Angles
Arc Length of a Circle
Definition of a Central Angle
Guiding Questions: What are the guiding questions for this lesson?
1. How many degrees are in a circle?
2. What is the distance around a circle with a radius of 1?
3. Why do we have radian measure?
4. In your opinion, what is the preferred way to measure an angle and why?
5. What is an angle that is not part of a triangle?
6. If you were on the London Eye and traveled one and a half revolutions, what angle will you have created?
page 1 of 4 Teaching Phase: How will the teacher present the concept or skill to students?
Day 1 Timeline
1. Bell Ringer 1 - Day 1
See Guided Practice CPALMS Bell Ringer Day 1
2. Review answers to Bell Ringer 1 - Day 1
3. Hand out Teacher/Student Lesson notes to each student. Teacher will broadcast these notes using a computer or a board on which to draw. Alternatively, teacher
may use a document camera or Mobi board. Students are expected to write down examples as the teacher explains them.
Teacher Student Lesson Notes
4. Show Video clips of the London Eye and the ice skater
London Eye http://www.youtube.com/watch?v=-iobx2tKvCA&safety_mode=true&persist_safety_mode=1&safe=active
Ice Skater: http://www.youtube.com/watch?v=MQK1lOkA2rE&safety_mode=true&persist_safety_mode=1&safe=active
5. Pose Guided questions and refer back to the video clips shown
6. Lesson:
(a) Discuss the definitions of angle of rotation, initial side, terminal side and an angle in standard position on the x-y coordinate plane (draw this out on the
board to demonstrate)
(b) Discuss the measure of an angle (amount of rotation from the initial side to terminal side where 1 degree = 1/360 of a rotation)
(c) Discuss positive and negative angles in terms of the rotation around the circle (positive = counterclockwise and negative = clockwise) - show this as part of
the graph drawn in 5a)
(d) Refer back to the ice skater - pose question as to how many times can we go around the circle?
(e) Introduce radian measure by posing Guiding Question #3 & 4 and why we use it
(f) Discuss how radian measure is correlated to arc length (review how to find arc length)
(g) Discuss the definitions of complementary, supplementary and coterminal angles and give examples each on the graph
(h) Give conversion formulas to rewrite radians to degrees and degrees to radians and give examples of each
7. Break students into pairs and have them work on Guided Practice Activity 1 - Day 1 while circulating around the room answering questions students may have
8. Review the answers to Activity 1-Day 1
9. Close the lesson with asking Closure questions
Day 2 Timeline
1. Bell Ringer 2 - Day 2
2. Review answers to Bell Ringer 2
3. Review vocabulary from Day 1: radian, standard position, complementary/supplementary angles, arc length
4. Break students into pairs and have them work on Guided Practice Activity 2 - Day 2 while circulating around the room answering questions students may have
5. Review the answers to Activity 2-Day 2
6. Discuss the debate regarding the use of degrees vs radians when measuring angles, pose questions regarding the students' answers to the Activity 2.
Teaching Note: Radian measure is convenient and preferred because it is real-valued. When trig functions are defined for radian measure, the real number line
can be used as the domain. This is most helpful when students learn to graph sine and cosine functions on the coordinate plane.
7. If the Independent Practice Worksheet was not given for homework after Day 1 the teacher has the option for students to work independently during class at this
point or to work on it at home for Day 2 lesson's homework.
8. Close the lesson with asking Closure questions
Guided Practice: What activities or exercises will the students complete with teacher guidance?
page 2 of 4 The following documents are the Bell ringer activities (with answer key) for the lesson. The teacher could broadcast the bell ringer on a document camera, via
computer, or print out for the students to use paper/pencil.
CPALMS Bell Ringers 1&2.pdf
Answers to Bell Ringers.pdf
If the teacher has the TI Navigator system, the bell ringers could be entered as questions with open responses into a TI document and then sent to the students.
Students could then answer the questions and send them back to the teacher for the Navigator system to grade and provide instant feedback to students.
The following document contains both Activity 1 and Activity 2. The document can be broadcast from the computer or printed for each student to have a copy.
Activity Day 1&2.pdf
Activity 1- Day 1: Use on Day 1 after the vocabulary has been reviewed. Students may work independently or in pairs.
Activity 2 - Day 2: Use on Day 2. Students may work independently or in pairs to complete.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The Angles and Angle Measure worksheet is intended to be used as either an in-class activity if time permits or out-of-class activity for more practice. The teacher has
the option of assigning some or all of the worksheet to the students.
Angles and Angle Measure.pdf
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
As a wrap-up to each day's lesson, the teacher should ask a closure question. Students may answer on a sticky note and place on the board as they exit the class or
they may answer as a group:
Day 1 Closure questions:
How do you convert radians into degrees?
Degrees into radians?
Day 2 Closure questions:
Suppose a ferris wheel has a diameter of 50 ft and takes 30 seconds to complete one rotation.
If you ride the ferris wheel for 2 min 45 sec, through what angle do you rotate?
If your seat is at the outer edge, how many feet have you travelled?
Summative Assessment
The teacher can use the summative questions as exit questions or part of a unit assessment.
Summative Day 1.docx
Formative Assessment
1. Teacher will use a bell ringer (document located in Guided Practice as Bell Ringer 1- Day 1) to have students answer questions regarding complementary and
supplementary angles by drawing a figure with multiple angles intersecting at one point and asking students to determine which angles are complementary and
which are supplementary. This activity will gauge the level of understanding of the terminology.
2. Teacher will ask the students for the definition of a central angle and the process by which to find the arc length of a circle using the degree measure of the central
angle given.
3. Teacher will assess students' understanding on Day 2 of the lesson by giving the students an activity that has the students finding one positive and one negative
angle that is coterminal to the given angle and by rewriting each given angle in degrees into radians and each given radian into degrees.
Feedback to Students
Teacher will give students feedback for the bell ringer while reviewing the answers in class either orally or via the TI Navigator system (if applicable).
Teacher will give feedback to students on the formative assessment questions as they proceed through the lesson and with verbal and nonverbal cues.
Teacher will give feedback to students on the summative assessment after it is graded.
Teacher will give feedback to students for each activity as the teacher circulates throughout the room and checks answers with each pair.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: All activities can be undertaken in pairs if necessary to accommodate students with difficulties.
Notes and directions will be written and projected using a document camera or the projector as reinforcement for all students, and especially for students with auditory
impairments.
All instructions will be given in writing to students with needed accommodations.
Extensions: Use the link to show how the rotating ferris wheel can be graphed using shifts of trigonometry graphs.
http://www.youtube.com/watch?v=RFkLdiDcJKc&safety_mode=true&persist_safety_mode=1&safe=active
Suggested Technology: Graphing Calculators, Computer for Presenter, Internet Connection, LCD Projector, Speakers/Headphones, Adobe Flash Player, Microsoft
page 3 of 4 Office, Computer Media Player
Special Materials Needed:
Mobile Interactive Whiteboard (such as a Mobi board)
TI Navigator Software and Calculator hardware (if possible)
Further Recommendations: The intended use of this lesson is to be taught over the course of two days.
Day 1 consists of the a bell ringer (see timeline in Lesson Content), activity (guided practice) and lesson notes used as direct instruction by the teacher.
Day 2 consists of a bell ringer (see timeline in Lesson Content for Day 2), activity (group activity) and review of the lesson as a whole.
Additional Information/Instructions
By Author/Submitter
Lesson may align with the following standard of math practice:
MAFS.K12.MP.6.1 - Attend to precision. (Reason - Students attend to precision of terminology relating to angular measurement.)
SOURCE AND ACCESS INFORMATION
Contributed by: Jayne Baxter
Name of Author/Source: Jayne Baxter
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.F-TF.1.1:
Description
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; Convert
between degrees and radians.
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