L1+Freeman,+Zackary

F**UNIVERSITY OF MAINE AT FARMINGTON COLLEGE OF EDUCATION, HEALTH AND REHABILITATION LESSON PLAN FORMAT**


 * __Teacher’s Name: __** Mr. Freeman **__Date of Lesson:__** Lesson 1 (Application)
 * __Grade Level:__** 11 **__Topic:__** Basic Trigonometry

Student will understand that angles can be converted from degrees to radians and radians to degrees. Student will know radians, degrees, radian = degrees*pi/180, degree= radians*180/pi. Student will be able to realize that radians and degrees are interchangeable.
 * __Objectives __**

 Maine Learning Results: Mathematics- C Geometry Geometric Figures Grades 9- Diploma 3. Students understand and use basic ideas of trigonometry a. Identify and find the values of trigonometric ratios and for angles in right triangles. the parameters of radians instead of what they were taught of degrees.
 * __Maine Learning Results Alignment __**
 * Rationale:** To be able to solve for sin, cos and tan students must be able to complete their work inside

The formative assessment for this section will be conducted through a checklist, making sure that they have completed each section of the organizer, and edited it before passing it in. Students will join in groups to search the internet for different ways to solve radians and degrees. Students will compare these results to the original chart that they have filled out. Students will change their graphic organizer to better fit what they believe to be the easiest way to solve this question. Students will than discuss what they have learned to make sure that what they have updated to their organizers makes mathematical sense.
 * __Assessment __**
 * Formative (Assessment for Learning) **

Wiki: You as the student must make sure you wiki page and the class wiki page is up to date on all of the information that is asked of you, a list will be kept online of what you must have on your wiki space page. All assignments must be complete; one missing assignment means a zero on this section. All students must be able to show their understanding of degrees and radians in the real world.
 * Summative (Assessment of Learning)**

will also be using the internet to explore and research the topic of radians vs. degrees.
 * __Integration __**
 * Technology: ** Students will use a Wiki space to collaborate their information in a class setting. Students
 * English:** Students will be reading trigonometry on the internet and collaborating it on a wiki space this will allow students to use proper English mechanics, while also having to read the material on the internet.

<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be given a number, each number that matches will be within one group. Each group is looking for information online; each of their roles is to find at least one different website from the rest of their group. All students must report out the site that they have found and students will be asked to tag the rest of their group’s sites. These groups will than collaborate their information onto their graphic organizers.
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Groupings __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">

appropriate for themselves.
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Differentiated Instruction __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">
 * <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Strategies **<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">
 * Verbal:** Students will listen to the original filling out of the graphic organizer; they will also be able to speak their mind during the group sections.
 * Visual:** Students will be able to see the graphic organizer laid out in front of them.
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to learn the subject.
 * Interpersonal:** Students will be given the opportunity to talk in small groups collaborating on the material given to them.
 * Intrapersonal:** Students will be given the opportunity to change their graphic organizers to what they believe will be the best for themselves.
 * Logical:** Students will be given the opportunity0 to set up their graphic organizer that seems the most


 * Modifications/Accommodations**
 * //I will review student's IEP, 504, and EELIDEP and make appropriate modifications and accommodations.//**

student must also come see the teacher for a review of what all of the notes mean. Students are expected t see other students to gather websites for their graphic organizers.
 * Absent Students:** Notes from each class will be posted online, these notes may be printed out but the


 * Extensions:** Students will use a Wiki space to collaborate their information in a class setting. This will extend their knowledge since connecting the real world to the math that is being done is not necessary but will extend their learning by tenfold.

·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Laptops with Internet ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Frisbee ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Criss Cross Graphic Organizer ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Pencils ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Assessment Checklist ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Wiki's   ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">  <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Calculators ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Smart board ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Completed Graphic Organizer ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Red Pens/ Blue Pens/ Black Pens ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Handout discussing how to use Wiki space <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Materials, Resources and Technology __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">

<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Information that was used to create my content notes came from these websites: <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [|http://id.mind.net/~zona/mmts/trigonometryRealms/degMinSec/degMinSec.htm] [] [] [] [|http://en.wikipedia.org/wiki/Degree_(angle] ) []
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Source for Lesson Plan and Research __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">

These are different websites that may be used to compel the students to do more work: <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [] <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [] []

<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">This the organizer that the students will be using to put in their notes. <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Blank Unit Circle Graphic]

<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> Rationale:** In this lesson I will make sure that all of the students know what is being expected of them at all times by providing them with an agenda. I will make sure students have copies of all of the necessary worksheets before we begin to work upon them. Students will be given the option to right down the order of the operations that we do. The enviorment in the class will be serious yet very lax in nature. Students will be allowed to think for themselves by using the internet to find more sources on how to complete this lesson. Students will be asked to ask questions of the period of lesson to make sure that they are grasping all of the knowledge. Students will be given a set of plans in which they will customize to their favorite style in which they are able to learn. Students are being asked to learn the material three different ways, once by my presentation, once by their research online and lastly through their groups and their group findings online. In the end I will wrap the unit up by again explaining exactly what the students are doing when they convert radians and degrees back and forth.
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Maine Standards for Initial Teacher Certification and Rationale __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">
 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//

Rationale:** Students are being asked to explain what they know about the subject to their peers, it is said that if someone is able to teach a subject they are more capable of doing it than most anyone else. They are being asked to research why we care about switching back and forth between radians and degrees, and why students need to know this. Students are being asked to find how radians and degrees relate to everyday life by creating a wiki space that shows the connection between the real world and what the student is learning. By researching this subject students will learn when it is justified to be using radians and when it is justified to be using degrees. This will allow students to use what they have learned in the real world to solve every day problems. Students will learn that a radian is just the distance around the outside of a circle that the radius creates. Students need to realize that this is not just another quick lesson in math this lesson will cause them to be able to succeed in all future classes of math. Lastly, students will know that this is just the basis of a much broader section of math and ahead of them is a lot of work but with a lot of work leads to great accomplishments.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** appropriate for themselves.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Verbal:** Students will listen to the original filling out of the graphic organizer; they will also be able to speak their mind during the group sections.
 * Visual:** Students will be able to see the graphic organizer laid out in front of them.
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to learn the subject.
 * Interpersonal:** Students will be given the opportunity to talk in small groups collaborating on the material given to them.
 * Intrapersonal:** Students will be given the opportunity to change their graphic organizers to what they believe will be the best for themselves.
 * Logical:** Students will be given the opportunity to set up their graphic organizer that seems the most

Students will use a Wiki space to collaborate their information in a class setting. This will extend their knowledge since connecting the real world to the math that is being done is not necessary but will extend their learning by tenfold.

Rationale:** The formative assessment for this section will be conducted through a checklist, making sure that they have completed each section of the organizer, and edited it before passing it in. Students will join in groups to search the internet for different ways to solve radians and degrees. Students will compare these results to the original chart that they have filled out. Students will change their graphic organizer to better fit what they believe to be the easiest way to solve this question. Students will than discuss what they have learned to make sure that what they have updated to their organizers makes mathematical sense.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//
 * Formative (Assessment for Learning)**

Wiki: You as the student must make sure you wiki page and the class wiki page is up to date on all of the information that is asked of you, a list will be kept online of what you must have on your wiki space page. All assignments must be complete; one missing assignment means a zero on this section. All students must be able to show their understanding of degrees and radians in the real world.
 * Summative (Assessment of Learning)**

<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">The desks in the classroom will be set up in groups of four to five so that when students are asked to be in groups to explore the internet for more information they will be able to quickly able to get into these groups.
 * __<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Teaching and Learning Sequence __**<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">

Introduction to the lesson and the unit. (10 Minutes) Frisbee Activity (10 Minutes) Presentation of the original notes (10 Minutes) Groups (20 Minutes) Class Collaboration (20 Minutes) Wiki space Introduction (20 Minutes)
 * Day 1:**

Review the graphic organizer (10 Minutes) Wiki space Presentations (50 Minutes) Self Evaluation (10 Minutes) Discuss minutes and seconds according to degrees (10 minutes)
 * Day 2:**

Students will understand that angles can be converted from degrees to radians and radians to degrees. The reason for radians to degrees is to use sin, cos, tan which have real world applications. **//Students understand and use basic ideas of trigonometry.//** Students will throw the Frisbee around the class, and I will quiz them, the top of the Frisbee will be the "key" to the quiz. This key will include degrees and radians, so students will convert back and forth between the two different types. As the teacher I will be giving the students the question in which I wish for them to answer. Students will be given a short amount of time to respond to this question and once they have they will be allowed to sit down. This will show students the material that they are about to learn is actually very easy but people think that it is abstract therefore think it is impossible to do unless they are very good at math.
 * Day 1:**
 * Where, What, Why, Hook Tailor:** Verbal, Logical, Interpersonal, Kinesthetic **(30 Minutes)**

Students will know radians, degrees, radian = degrees*pi/180, degree= radians*180/pi. A cross chart will be used to introduce the content for this lesson. Students will compare these results to the original chart that they have filled out. As the teacher I will be teaching the lesson to the student so that they have the basis of the knowledge. As the teacher at this time I will be walking around the class making sure the students are on task and looking at sites where they will be able to find good information about degrees vs. radians. As the teacher I will make sure that students are paying attention to their peers in their groups since this will be the time where they will be able to learn the most. Students will be thinking inside and outside of themselves for examples of degrees and radians in the real world. An extra exercise that may be used here is a spontaneous, students will receive points for how creative they answer, and students are to come up with answers to the questions: What real world possibilities are there to use degrees and radians?
 * Equip, Explore, Rethink, Tailor:** Interpersonal, Intrapersonal, Verbal, Logical, Visual **(40 Minutes)**

Students will be able to realize that radians and degrees are interchangeable. (Application) Students will be asked to create a wiki page that will bring real life example of degrees and have them change them to radians. Students will join in groups to search the internet for different ways to solve radians and degrees. Students will change their graphic organizer to better fit what they believe to be the easiest way to solve this question. Students will than discuss what they have learned to make sure that what they have updated to their organizers make mathematical sense. Students will compare these results to the original chart that they have filled out. I will tell them how to set up and use a wiki space. As the teacher I will remind them that they are have just come up with a large amount of information already when they did the spontaneous, all they are doing on the wiki's is organizing their thoughts. This is the time that they will also be asked to take time and read through a handout on how to set up a Wiki account and how to use wiki's.
 * Explore, Experience, Rethink, Revise, Refine, Tailors:** Interpersonal, Intrapersonal, Verbal, Logical, Visual **(70 [10 first day, 60 second day] Minutes)**

The formative assessment for this section will be conducted through a checklist, making sure that they have completed each section of the organizer, and edited it before passing it in. Students will first go through the checklist and then pass their checklist in. As a teacher I will go through each person's wiki's making sure that they have completed everything on the checklist. Each student will be able to see and evaluate for themselves the wiki space of the other people. By doing this, students will be able to critically critique their own work compared to that of their peers. Students will also learn at this time that there is a thing called minutes and degrees relating the position that you are in the world to a precise minutes and seconds from the prime meridian. Students will change some positions from minutes and seconds to degrees and then to radians, this will show that they have mastered the subject.
 * Day 2:**
 * Evaluate, Tailors:** Interpersonal, Intrapersonal, Verbal, Logical, Visual **(20 Minutes)**

Day 1:** First off I will tell the students what trigonometry is. I will tell them that it is the method that we use to find angles of objects that are not easily able to have the angle taken of them. I will tell them that to learn this material they will need to learn the part of a right triangle; they also must learn how to convert back and forth between radians and degrees. I will tell them what exactly a radian is by demonstrating on the board that a radian is exactly the length of the radius around the curve. I will also state that the reason that we know that a pi is 3.14.... is because that is how many radii it would take to go halfway around a circle. That will lead us into the Frisbee activity.
 * __Content Notes__

On top of the Frisbee will the amount of information that they will be accountable for over the course of the day’s lesson. This will include a picture of the unit circle partition into different parts. There will be two sets of parts, one set will be degrees which will show 30, 60....360, and another that will show the radians that are of multiples of 1/4 pi's. After this is set up I will have the students pass the Frisbee around the classroom while I ask them which they believe the answer is in the other format.

Use: Degrees: 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, 360 Radians: pi/ 6,4,3,2 2pi/ 6, 4, 3, 2

Radians: Radian is the arc length of a circle. It exactly means the distance of exactly one radius length around the circumference of a circle. Example: pi= 180 degrees, this is true since the distance around the unit circles circumference is exactly pi when you go about the circle once.

Degrees: The angle that is formed between two lines that intersect. Examples: 90 degrees is created since when two line intersect at a perpendicularly the angle that they create is a right angle.

Converting: To convert back and forth between the two are two equations. To convert from degrees to radians: radian=degree * pi /180 Examples: 60 degrees *pi / 180 = 1/3pi 40 degrees *pi / 180 = 2/9pi

to convert from degrees to radians" degree= radians 180/ pi (1/5) pi *180/pi= 36 degrees (1/6) pi *180/pi= 20 degrees

Why use radians vs. degrees? To solve sin, cos and tan it is impossible to solve using degrees; therefore students must know how to convert back and forth between the two. When setting up sin and cos, the sides of triangle that is formed will be done in length, not in angles.

What is the difference between radians and degrees? One is measuring the angles while the other is measuring the actual distance of the outside of the unit circle.

What is the unit circle? The unit circle is the circle created by the radius of 1 unit. Radians work with all other circles since a radian is converted quickly back into the unit circle style by creating ratios with the sides of triangles. The distance pi is created exactly once around the outside of the unit circle halfway around.

What happens if the radians go past 2pi? The degrees are transferred as either greater than 360 degrees which means you are going around the circle more than once or it may be changed into a degree or radian form that is between 0 and 360 or 0 and 2pi. To do these students must add or subtract 360 or 2pi until they fall within the range. Students need to know that angles and radians repeat once they go around twice.

What if a radian is negative? A negative radian is the same as a radian in the positive direction that is a 2pi multiple of it. For example -pi/2 is the same as 3pi/2 since 2pi added to -pi/2 is 3pi/2.

Students will than join in groups to discuss and look up sites that pertain to radians and degrees.

Wiki Space Introduction Students will be asked to create a wiki space for the class; students will follow this [|guide] to do so. After which I will have students use their laptops to create a wiki space. Students are asked to show me they know how to read the history, post new things, and comment on other people’s wiki's. Students will then be given the assignment to look up as many things in the real world that are degree or radian based. Students will comment on at least three other wiki's and show that they have compiled a large amount of resources that include wiki's.

Students will come to class and report what they have learned through the wiki space each student will be given 2-3 minutes, at the end of each student we will add their list to the class wiki list. Students will then be asked to create a self evaluation sheet for themselves using some of the degree radian objects the rest of the class has found and convert them into radians. After this students will fill out a self evaluation making sure that they have completed everything that was asked of them during the wiki project and then they will pass this in.
 * Day 2:**

At the end of this class I will leave about 10 minutes in which I will discuss the earth and the angles and radians that are formed by it. I will [|show] them that it is as simple more multiplying by 1/60 and than multiplying 1/3600. Since 1/60 is the amount of degrees between each degree and 1/60 is the distance between each second.


 * __Handouts__**

·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Blank Unit Circle] <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will use this incomplete unit circle to fill in during the presentation; they will fill in with details afterwards to make sure that they understand what the difference between a radian and a degree is.

·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Wiki page tutorial] <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will use this as a supplement to the movie that they watched in class so that they know how to use the wiki space effective enough to be able to create a page in which they are willing to show the class. ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Degree/Radians Worksheet <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will complete this worksheet quickly after they have learned the difference between radians and degrees this will show that they have a grasp on what the information that they are supposed to know down to heart. ·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Degrees/Minutes/Seconds Worksheet <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will complete this short worksheet after I have finished discussing how to transform these into normal degrees.

·<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Completed unit circle] <span style="color: black; font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be able to use this as a supplement to their original for a future guide to the information in front of them. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">