Sorry! This resource requires special permission and only certain users have access to it at this time.
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?
 Student should understand what a radian is, and why it is useful.
 Student will be able to fill in radian measures given a blank unit circle.
 Students will have some reallife examples of radian measure.

Prior Knowledge: What prior knowledge should students have for this lesson?
How to construct a circle using a compass
 Definition of radius
 Knowledge of standard angle locations on unit circle (e.g., 30, 60, 120, ...)
 How to do unit conversions
 How do use ratios and proportions to solve for unknowns
 Definition of domain and range

Guiding Questions: What are the guiding questions for this lesson?
 Are there any other ways to measure angles besides degrees?
 What is a radian?
 What are some examples of radians in real life?

Teaching Phase: How will the teacher present the concept or skill to students?
Teacher should already have circle drawn on board to help guide students visually. After passing out materials, teacher leads students in the following activity: Construct a circle on paper with a radius of 2 to 3 inches.
 Draw a radius from center to the right. Label the radius r = 1, to indicate that the circle is a "unit circle."
 Lay pipe cleaner on top of the radius and mark off length of radius. Cut the pipe cleaner off so that its length is the same as the radius.
 Now, place one end of the pipe cleaner at the intersection of radius and circle and lay it counterclockwise along the circumference. Mark where the other end ends.
 Tell students that this arc of length 1 subtends an angle of one radian, as seen from the center (vertex) of the circle.
 Ask students to observe how big this angle looks (Most will say about 60 degrees.)
 Now ask students to count many times the pipe cleaner wraps around the entire circumference (Answer: About 6.3 +/ 0.1).
 Congratulations! Students have discovered that the circumference of a unit circle is approximately 6.3 units.
 Remind students that the circumference of a circle is . Substituting r = 1 for the unit circle, it's easy to see why they got this result.
 Teacher explains that there are exactly radians in 360 degrees.
 Setting up a proportional relationship, teacher shows how to find the exact value of a radian:
, where X = number of degrees in a radian.
Solving for X, the result is
This is very close to the value of 60 degrees that students previously observed using the pipe cleaner.
Now, teacher can ask some additional questions, such as:
 How many radians in 90 degrees?
 How many radians in 180 degrees?
 How many radians in 360 degrees?
 How many degrees in radians?
 How many degrees in radians?
 How many degrees in radians?

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will label both degree and radian angles on a blank unit circle. Students will complete this under guidance of the teacher. This will be done after teacher has checked students work on unit circle given during lesson, and read through the students thought processes, and students have had an opportunity to correct any miss conceptions.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will be given the following assignment:
Independent Practice
For purposes of this lesson, Problems 114 are most relevant to the skill level of students after they have been taught this lesson.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teacher will take up Independent Practice, check for correctness, give feedback on thought process, and return for students to review and revise.
Teacher will explain that radian measure will be used extensively in their subsequent studies of trigonometric functions and in modeling periodic phenomena (waves and oscillations).

Summative Assessment
Teacher will assess prior knowledge (degrees) and current (radian) using a Blank Unit Circle. Students should miss no more than three to show mastery.

Formative Assessment
While students are working on activity/assignment, teacher should be walking around to different groups observing, correcting as needed, answering questions, and asking questions that assess students' understanding of lesson. Some questions include:
 What does the length of the pipe cleaner represent?
 What degree angle does a radian appear to equal?
 Why are you using those scissors to cut up your notebook?
This gives us the opportunity to correct, individually or as a group, on the spot so students can stay on track.

Feedback to Students
Students will receive instant feedback during activity/assignment, enabling them to correct and proceed with their learning without misconceptions.
ASSESSMENT
 Feedback to Students:
Students will receive instant feedback during activity/assignment, enabling them to correct and proceed with their learning without misconceptions.
 Summative Assessment:
Teacher will assess prior knowledge (degrees) and current (radian) using a Blank Unit Circle. Students should miss no more than three to show mastery.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
ELL / ESOL 
Provide vocabulary words a day or two prior to introducing the lesson to the class. Use written and pictorial forms to teach: Maps, graphs, charts, pictures, and audiovisual aids. Extend assignments. Give handson experience. Use small group instruction, and/or break the class into teams.
ESE / 504 Use handouts to emphasize major points. Write key points of the lesson on the board. Pose questions with short answers  clues given. Do not grade handwriting. Use calculator, computer, reference materials, or manipulatives (3D models). Provide clear, visually uncluttered handouts / worksheets. Encourage peer assistance.
OTHER Clear, detailed, printed directions could be provided for students who have difficulty maintaining focus.
 Large diagrams of each step can be provided.
 Teacher needs to read all instructions and repeat several times.
 Students with accommodations may need more review on ratios or fractions
 More time to work on assignment or use peer teaching.
Extensions:
As an extension to this introductory lesson, teacher can explain that the number of radians subtended by an arc of length s in a circle of radius r is.For example:If s = 1 cm and r = 2 cm, then .
Special Materials Needed:
compass, scissors, pipe cleaners
Additional Information/Instructions
By Author/Submitter
Lesson may align with the following standards of math practice:
 MAFS.K12.MP.2.1  Reason abstractly and quantitatively. (Reason  students must explain verbally and in writing what they have learned.)
 MAFS.K12.MP.6.1  Attend to precision. (Reason  Students must be precise in the positioning of numbers in diagrams and in their computations.)
SOURCE AND ACCESS INFORMATION
Contributed by:
caroline Campbell
Name of Author/Source: caroline Campbell
District/Organization of Contributor(s): Jackson
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.