L3+Freeman,+Zackary

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


 * Teacher’s Name: ** Mr. Freeman **Date of Lesson:** Lesson 3 (Interpretation)
 * Grade Level:** 11 **Topic:** Basic Trigonometry

measurements.
 * __Objectives __**
 * Student will understand that ** you are able to use the unit circle to find ratios.
 * Student will know** Unit Circle, radians, hypotenuse, adjacent, opposite, A^2+B^2=C^2, Unit Circle
 * Student will be able to do** to make meaning of all the different parts of the unit circle.

 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. Students need to realize that inside the unit circle is all kinds of triangles, and that these triangles are unitized from larger triangles, therefore this is the reason that trigonometry works.
 * __Maine Learning Results Alignment __**
 * Rationale:**

Each student must bring the completed unit circle to me and I will ask them one question, once the student gets the question right they will be given a check in the grade book. This will show that they have an understanding of the subject matter along with that they are able to verbalize what they are thinking.
 * __Assessment __**
 * Formative (Assessment for Learning) **

You as the student should be able to manipulate the program (Geologabra) to do what you wish to do. Students must be able to manipulate this program to do what they wish to do with it. In the end the students must write a paragraph that relates the angle to the sides. They must show that they are related in some way they do not need to show that they are related fully yet, just that there is a relationship.
 * Summative (Assessment of Learning)**

Technology: You as the student should be able to manipulate the program (Geologabra) to do what you wish to do. Students must be able to manipulate this program. English: Students will have to come up with a report that can be used to help ask questions of the others in the group. This will be used so that students may quiz each other on the information.
 * __Integration __**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be arranged in groups of four so that when they are reporting with each other they will be able to report in pairs with 2 pairs reporting together easily. This will also make it so that students may collaborate with each other on questions they may have. This will lead them to ask more pertinent questions while still having everyone's questions answered.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Groupings __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">

the groups. the subject.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Differentiated Instruction __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Strategies **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
 * Verbal:** Students will be able to listen to the lesson from the teacher; they will be able to talk amongst
 * Visual:** Students will be able to see the unit circle and each of the separate parts inside of the unit circle.
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to learn
 * Interpersonal:** Students will be given the opportunity to talk in small groups collaborating on the material given to them.
 * Interpersonal:** Students will be given the opportunity to work by themselves figuring out the different parts of the unit circle.
 * Logical:** Students will be given the opportunity to set up their graphic organizer that seems the most appropriate for themselves, they will also be given the opportunity to answer question making them think about the subject at hand.


 * 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 must still be able to complete the questionnaire of them about the different parts of a triangle.
 * Absent Students:** Notes from each class will be posted online, these notes may be printed out but the

Students will be able to use the program called Geologabra. This program will allow them to see the differences between the different sections of triangles and how they are related to the length. This program will show them that there is a relationship between an angle and the sides of the triangles.
 * Extensions**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Materials, Resources and Technology __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Laptops with Internet
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Markers
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Board
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Questions for Frisbee
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Frisbee
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Geologabra
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Pencils
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Pens
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Questions for after reporting
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Protractor

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Organizers for the Frisbee and for the Class, also the triangle that will be used for a graphic organizer: <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> These are the sources for the content notes for the lesson that is being given <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Source for Lesson Plan and Research __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Blank Unit Circle Graphic]
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [|http://mathforum.org/~sarah/hamilton/ham.namesides.html]
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []

<span style="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 write down the order of the operations that we do. The environment 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 should know; that there is a relationship between the angle of a right triangle and sides.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Maine Standards for Initial Teacher Certification and Rationale __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">
 * //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 will be able to talk with each other in a report style that will give them a chance to listen to their peers about the subject as well as giving them the chance to teach the subject. This is proven to provide the students with a better chance to learn the subject at hand. The students will also be applying the knowledge they learned to the computer by using the program Geologabra. In this they will see finally that there really is a connection between all triangles and the unit circle that we have been talking about the entire time. Students will go through the program playing around with the gadgets in it using the triangle tool. The students will learn by hands on access to it that it is possible to make it so that they are able to learn more than if they are just sitting behind the desk listening to a lecture.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** the groups. the subject. You as the student should be able to manipulate the program (Geologabra) to do what you wish to do. Students must be able to manipulate this program to do what they wish to do with it. In the end the students must write a paragraph that relates the angle to the sides. They must show that they are related in some way they do not need to show that they are related fully yet, just that there is a relationship.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Verbal:** Students will be able to listen to the lesson from the teacher, they will be able to talk amongst
 * Visual:** Students will be able to see the unit circle and each of the separate parts inside of the unit circle.
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to learn
 * Interpersonal:** Students will be given the opportunity to talk in small groups collaborating on the material given to them.
 * Interpersonal:** Students will be given the opportunity to work by themselves figuring out the different parts of the unit circle.
 * Logical:** Students will be given the opportunity to set up their graphic organizer that seems the most appropriate for themselves, they will also be given the opportunity to answer question making them think about the subject at hand.
 * Technology:**

Rationale:** Each student must bring the completed unit circle to me and I will ask them one question, once the student gets the question right they will be given a check in the grade book. This will show that they have an understanding of the subject matter along with that they are able to verbalize what they are thinking.
 * //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)**

You as the student should be able to manipulate the program (geolgabra) to do what you wish to do. Students must be able to manipulate this program to do what they wish to do with it. In the end the students must write a paragraph that relates the angle to the sides. They must show that they are related in some way they do not need to show that they are related fully yet, just that there is a relationship.
 * Summative (Assessment of Learning)**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be arranged in groups of four so that when they are reporting with each other they will be able to report in pairs with 2 pairs reporting together easily. This will also make it so that students may collaborate with each other on questions they may have. This will lead them to ask more pertinent questions while still having everyone's questions answered.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Teaching and Learning Sequence __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">

Day 1: Overview of Days Lesson: (5 Minutes) Frisbee Activity 2: (10 Minutes) Presentation of Lesson: (15 Minutes) Reporting with each other: (10 Minutes) Questions students on knowledge: (10 Minutes) Geologabra: (25 Minutes) Review: (5 Minutes)

Students will understand that you are able to use the unit circle to find ratios. **//Students understand and use basic ideas of trigonometry.//** The reason for the unit circle is so that it will give a basis for the Pythagorean Theorem in accordance to sin, cos and tan, so that they may be able to be used in the real world. Frisbee Part 2: Students will again through the Frisbee around the classroom so that students can answer questions as a pre-assessment, on the circle will be the unit circle. As the teacher I will make sure that the students are acting appropriately with the Frisbee. I will make sure that they are answering the questions correctly. This will show students that there is at least some type of relationship between a triangle and the unit circle. Students will notice at this point that the goal of the class is to teach them that there is at least some type of relationship between the sides of a triangle and the angle.
 * Where, What, Why, Hook Tailor:** Interpersonal, Kinesthetic, Intrapersonal, Verbal, Logical, Visual (20 Minutes)

Students will know Unit Circle, radians, hypotenuse, adjacent, opposite, A^2+B^2=C^2, Unit Circle measurements. Students will be given a blank form of the unit circle to fill in over the course of the lesson. Students will be then taught the lesson on all the different parts of the unit circles. Students need to know that the unit circle is the basis of all the trigonometric functions, all twelve of them, that is why it is vital that students learn this perfectly. Students will be asked to fill in the information of the unit circle that relates to the triangle and why it is important that we study the triangle along with the unit circle as pretty much one in the same.
 * Equip, Explore, Rethink, Tailor:** Interpersonal, Intrapersonal, Verbal, Logical, Visual (20 Minutes)

Students will be given a blank form of the unit circle to fill in over the course of the lesson. Students will join up in groups of four, two searching for the ratios, two searching for the meaning of the unit circle. Students will be then taught the lesson on all the different parts of the unit circles. Students will than discuss all the difficulties that they are having with the unit circle one another, answering the questions themselves. Students will then change places with the previous two people in their group and must explain that aspect of the unit circle to the other set of people. The teacher at this time will be watching over the students making sure that they are researching and then presenting. Students will make sure that they are researching the topic to have the information they need. After this point the teacher will than tell the students to present in which they will.
 * Explore, Experience, Rethink, Revise, Refine, Tailors:** Interpersonal, Intrapersonal, Verbal, Logical, Visual (20 Minutes)

Each student must bring the completed unit circle to me and I will ask them one question, once the student gets the question right they will be given a check in the grade book. Students will be prepared greatest if they are asked a completely random question. This shows that they don't know just the surface but have a deep understanding of the knowledge needed to move onto the cos, sin and tan functions in the next section. Students will know that there is a relationship and that it is vital that we know what parts of the triangle these relationships come from.
 * Evaluate, Tailors:** Interpersonal, Intrapersonal, Verbal, Logical, **Visual (20 Minutes)**

Frisbee Activity #2: For this activity using the Frisbee the students will be given a unit circle with 12 triangles inside, they will be asked one of the 12 ratios and to give the other part of the ratio. Through this activity the student is expected to learn that the units for a right triangle are the same no matter the size, the thing that matters is that the ratio is the same.
 * Content Notes**

Right Triangle- A triangle in which one of the three angles is exactly 90 degrees.

Ratio- The proportion of one side of the triangle to another, it may either be the ratio of any of the three sides.

In this short lesson students need to learn that the size of the triangle does not matter, what really matters is that all of the ratios are the same. So in this lesson students will be asked to compare triangle using a protractor. By using a protractor the students will realize the angle of triangle with the same ratio has the same angle.

The whole class will then proceed to then report to each other findings that they find on the internet about this subject that all ratios are the same. Students need to know that in the real world all things do not fall into the unit circle, rather though they fall into ratios that can be minimized into the unit circle.

Students will then be given the chance to ask question about the ratios and why in fact they exist, this will give the students a chance to understand the material that is given to them.

Lastly the students will be asked to use the program Geologabra to solve for a set of different angles using different side lengths. The second part will be finding three more numbers that give the same ratio. At the end of each section the student will be asked to print out their shapes from Geologabra.

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Students will receive this so that they are able to jut down new notes that they receive before they continue on to learn about cos, sin and tan. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Students will use this graphic organizer so that they are able to talk about the relationship between the edge of the triangle and the fact that there is a set ratio for each time it is used. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> This worksheet will give explicit instruction on how to use the different parts of Geologabra, while also incorporating the use of their mind to be able to find the ratios.
 * Handouts**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Blank Unit Circle Graphic]
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> []
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Geologabra