L4+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 4 (Perspective)
 * 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 solve for a ratio using 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 will learn that the ratio in the unit circle that is set up applies to all triangles, they will notice that for every angle there is a set ratio that can be used to find all of the sides and angle of the triangle.
 * __Maine Learning Results Alignment __**
 * Rationale:**

Each student will be asked to create 5 questions about the section in which they will research the answer with their partner to make sure they understand what is actually happening. By doing this students may see what sections they, they need help on. This will allow students to get the answers to their problems that not all students in to class may have. In the end it is a positive activity for the students in the sense that they learn what they need to learn.
 * __Assessment __**
 * Formative **

Students will be asked to use the program Mathematica to solve for the ratios of triangle using the programs manipulative properties. By using this program students will be able to see the steps a calculator takes to solve a problem. By doing this it allows students the ability to be able to come up with answers while also being allowed to see what is happening. Students need to realize that whatever they do on the calculator may be related to math easily in the sense that it is possible to see what is occurring.
 * Summative**

Technology: Students will be asked to use the program Mathematica to solve for the ratios of triangle using the programs manipulative properties. By using this program students will gain an understanding on the processes that an actual calculator takes to solve. English: Students will be asked to come up with 5 questions about this section. They will have to use the internet to find the answers to these questions in each group of two people. This means that in the end the students will have to write up a report.
 * __Integration __**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be aligned into 3 two desk rows, each row will be touching one other desk so that the people at these two desks may work together quietly on the report when they are asked to do the report. Students will be aligned in rows so that they are able to look forward during class at the presentation on the smart board using the Mathematica program. This will allow students to pay attention while also having an extra resource available during class.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Groupings __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">

amongst the partners. inside of the unit circle. learn the subject. about the subject. parts of the triangle, they also must think inside themselves for the questions. appropriate for themselves, they will also be given the opportunity to answer question making them think about the subject at hand, they will also benefit from being able to think of different questions that pertain to what they are thinking.
 * __<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
 * Visual:** Students will be able to see the triangle and each of the separate parts inside of the triangle
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to
 * Interpersonal:** Students will be given the opportunity to talk with partners gathering information
 * Intrapersonal:** Students will be given the opportunity to work by themselves figuring out the different
 * Logical:** Students will be given the opportunity 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 must still be able to come up with a questions to ask the teacher in which the teacher will provide them the correct answer to the question that is posed by the student.
 * Absent Students:** Notes from each class will be posted online, these notes may be printed out but the

Students will be asked to use the program Mathematica to solve for the ratios of triangle using the programs manipulative properties. This will allow students to be able to use the program while also being able to grow further in their respected ways. This will allow students to see what exactly is happening when they are using a calculator to solve an equation.
 * Extensions**

<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: 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;">SMART board

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Organizers for the Frisbee and for the Class <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Mathematica reference for when students need help with the program <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Information on Right Triangles and their angles vs. side ratios that will be used in the content notes <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;"> []
 * <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. 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. Students will have a chance to talk with their partners while also being given the chance to succeed for themselves.
 * __<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 are being asked to provide knowledge to each other on the subject at hand. They are being asked to research the topic while also being asked to provide questions on what they research. This will teach them that research is never finished and that there is always unanswered questions. Students will be able to ask questions that pertain to their knowledge and have a partner there to reform what they have already learned. Students will be asked to use the program Mathematica which will help the students learn the basis of the different ways a computer is able to solve a large equation quickly. Students are given the time to refine their graphic organizer as they see fit this will allow them to pick up important information as they go rather than me just telling them all of the important and key facts directly.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** amongst the partners. inside of the unit circle. learn the subject. about the subject. parts of the triangle, they also must think inside themselves for the questions. appropriate for themselves, they will also be given the opportunity to answer question making them think about the subject at hand, they will also benefit from being able to think of different questions that pertain to what they are thinking. Students will be asked to use the program Mathematica to solve for the ratios of triangle using the programs manipulative properties. By using this program students will be able to see the steps a calculator takes to solve a problem. By doing this it allows students the ability to be able to come up with answers while also being allowed to see what is happening. Students need to realize that whatever they do on the calculator may be related to math easily in the sense that it is possible to see what is occurring.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Strategies**
 * Verbal:** Students will be able to listen to the lesson from the teacher, they will be able to talk
 * Visual:** Students will be able to see the triangle and each of the separate parts inside of the triangle
 * Kinesthetic:** Students will be given time to move around with the Frisbee, along with the ability to
 * Interpersonal:** Students will be given the opportunity to talk with partners gathering information
 * Intrapersonal:** Students will be given the opportunity to work by themselves figuring out the different
 * Logical:** Students will be given the opportunity to set up their graphic organizer that seems the most
 * Technology:**

Rationale:** Each student will be asked to create 5 questions about the section in which they will research the answer with their partner to make sure they understand what is actually happening. By doing this students may see what sections they, they need help on. This will allow students to get the answers to their problems that not all students in to class may have. In the end it is a positive activity for the students in the sense that they learn what they need to learn.
 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//
 * Formative**

Students will be asked to use the program Mathematica to solve for the ratios of triangle using the programs manipulative properties. By using this program students will be able to see the steps a calculator takes to solve a problem. By doing this it allows students the ability to be able to come up with answers while also being allowed to see what is happening. Students need to realize that whatever they do on the calculator may be related to math easily in the sense that it is possible to see what is occurring.
 * Summative**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be sitting in three rows of double desks so that they are able to communicate with their partners while also being able to pay attention to the lesson at hand. This will allow them to follow along on the SMART board what is occurring on the program Mathematica.
 * __<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 the Days Lesson (5 Minutes) Frisbee Activity 3 (10 Minutes) Lesson on Ratios of Triangle always going to be a ratio of a larger triangle (10 Minutes) Research (10 Minutes) Questions (10 Minutes) Mathematica (35 Minutes)

Day 1: Students will understand that you are able to use the unit circle to find ratios. Students will understand that it is possible to just use the ratios in the unit triangle to find the angle of the triangle. **//Students understand and use basic ideas of trigonometry//**. Students will need to know that these ratios are the reason that it is possible to solve for the angle. The students will be able to see how every day triangles will fall into these ratios, which are used for sin, cos and tan. The students will for the last time throw around the Frisbee they will begin to learn about the relationships between the angle and the sides of a triangle. The teacher at this point will be using the key to the Frisbee to ask the students different questions on the different sections of the Frisbee. The teacher will also give an overview to the student on why it is important that we need to know there is a ratio.
 * Where, What, Why, Hook Tailor: Verbal, Logical, Interpersonal, Kinesthetic (15 Minutes)**

Students will know Unit Circle, radians, hypotenuse, adjacent, opposite, A^2+B^2=C^2, Unit Circle measurements. Students need to know each part of the triangle and the fact that there is a thing called the Pythagorean Theorem. Students also must know that a triangle easily fits within side the unit circle and that is why we actually use the unit circle because the C never changes while the A and B do which change the angle. Students will have to fill in a organizer dealing with a right triangle and every part of it paying special attention to the angles. By doing this organizer students will see as the A get bigger, the B gets smaller and therefore there is a change in the angle.
 * Equip, Explore, Rethink, Tailor: Interpersonal, Intrapersonal, Verbal, Logical, Visual (10 Minutes)**

Students will have to fill in a organizer dealing with a right triangle and every part of it paying special attention to the angles. Students will be asked to come up with a hypothesis about the correlation, if any between the sides and angles. Students will then be asked to explore the internet with a partner about ratios in unit circles dealing with triangles, at this point they will find out about adjacent, hypotenuse and opposite. Students will add all of the different ratios to the triangle organizer, making sure that they have all of them. Students will redo the triangle organizer but set up in a way that they are able to understand easily to themselves. At this time the teacher will be walking around the classroom making sure that the students are on task as they research the different parts of the triangle and the relations called sin, cos and tan. The teacher will also be giving a quick preview to the students on why ratios never change.
 * Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical, Verbal, Visual (20 Minutes)**

Each student will be asked to create 5 questions about the section in which they will research the answer with their partner to make sure they understand what is actually happening. This will give students the ability to figure out what they need to on the subject and skip what they already know. As the teacher I will answer these questions to the best of my ability while providing the students with an array of questions for them to ask themselves. The more I get the students to think abstractly the better the chance of me being able to provide the students with the best knowledge of the subject. Students will not be pressured into learning things that they have already learned; they will learn brand new things.
 * Evaluate, Tailors: Intrapersonal, Interpersonal, Logical, Visual, Verbal (35 Minutes)**

Students will begin the lesson by having a quick overview of the subject, this will include a quick introduction on the sin, cos and tan functions. Students will know that these are set ratios that increase and decrease as the sides of a triangle increase and decrease. The point of this class will be to find what sides increase, and what sides decrease according to the angle. This will be the basis of the next lesson.
 * Content Notes**

Students will than complete their third and final Frisbee activity in which they will learn that there is a relationship of side A, side B and the angle of the triangle. The questions that will be asked are if, A is increase and B is decreased will the angle increase, or decrease and changing the starting point so that the students have a challenge.

A^2+B^2=C^2 is the Pythagorean Theorem in which is used to find the hypotenuse of a triangle. If we held the hypotenuse still and changed A and B what happens to the angle.

Does this happen on triangle of the same ratios but larger sides, show the students that increasing the sides of a triangle does not mean the angle of the triangle actually changes, all it means is you have a bigger triangle. This will be able to be used as a fact so that we do not need to reduce all triangles to the unit circle to be able to solve for the answer of sin, cos and tan.

After showing these facts algebraically and geometrically the students will then research the subject online coming up with questions for the teacher about the subject, these may range from anything to anything therefore the teacher needs to be prepared with all of their content knowledge to be able to solve these correctly.

The teacher will then ask the students to open up the program Mathematica and put in the equation sin(pi/2) and ask them what the answer is. The students will state the answer which is 1, they will proceed to do this for angles between 0 and pi/2 for sin, cos and tan until they are able to come up with a hypothesis on what each function has for a ratio to be able to solve for radians. Students will be told that during the next lesson they will find out whether or not their hypothesis is correct.

<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;"> <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;"> Students will use this as a guide for the beginning of the Mathematica section; this will give students a set of parameters to use while beginning their study on sin, cos and tan.
 * 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;"> []