L5+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 5 (Explanation)
 * Grade Level:** 11 **Topic:** Basic Trigonometry

hypotenuse, opposite, triangle, graphs. 
 * __Objectives __**
 * Student will understand that ** sin, cos and tan are related to triangles.
 * Student will know** sin, cos, tan, all of the equations for these, SAHCOHTOA, unit circle, radians, pi, theta, adjacent,
 * Student will be able to do** d erive and find the value of trigonometric ratios in a right triangle. 

 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. During this section students will be discussing the basic trig functions of sin, cos and tan. This is what can derived from the ratios of the sides of right triangles.
 * __Maine Learning Results Alignment __**
 * Rationale:**

Students will be evaluated on a checklist making sure they have completed all of the necessary adjustments to their lists. By doing this students will make sure that they have realized what occurs in the world that relates to sin, cos and tan. They will also be asked to make sure that their graphic organizer is filled out correctly. By doing so we know that the student is capable of the stuff that is written down and will be to use in some real life situations.
 * __Assessment __**
 * Formative (Assessment for Learning) **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">

Students will be asked to use Mathematica to solve for sin, cos and tan. By using this program students will be able to solve for sin, cos and tan. By doing this students will be able to realize that there is a correlation between sin, cos and tan that is not just hypotenuse, adjacent and opposite. They will realize that the relation is that sin and cos are inverse of each others. They will also be able to realize that tan is just sin divided by cos. By using this program the student will learn for themselves through the use technology rather than myself lecturing to them.
 * Summative (Assessment of Learning)**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Technology: Students will be asked to use mathematica to solve for sin, cos and tan. Using this program students will be able to solve for the correlation between sin, cos and tan. English: Students will be asked to use good note taking ability when trying to fill out their notes on the sin, cos and tan graphs and relation to the unit circle and triangles.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Integration __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be asked to sit in small groups that will be broken up by random selection, as people enter the classroom they will go to a different group than the person before them. In these group students will be asked to come up with real life situations in which they will be able to use to combine into a list for an online source. The students will be given time to discuss all possible ways that sin, cos and tan may be used in the real world. They will be asked to come up with some types of jobs that would need to know how to use sin, cos and tan.
 * __<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Groupings __**<span style="font-family: "Times New Roman","serif"; font-size: 18pt;">

figure out how to use sin, cos and tan. use and which ones not to use. world, including music. people, via the internet.
 * __<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 have to read many different blogs learning things from each.
 * Visual:** Students will be able to see the equations for sin, cos and tan as they find them online.
 * Interpersonal:** Students will be given the oppurtunity to talk with people all around the world trying to
 * Interpersonal:** Students will be given the oppurtunity to work by themselves figuring out which blogs to
 * Naturaralist:** Students must find things that are found in nature that cause sin, cos and tan to occur.
 * Musical:** Students will be given the option to look up how sin, cos and tan are connected to the real
 * Logical:** Students will be asked to find out the meaning of sin, cos and tan through the use of other


 * 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 to 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

Students will be using the program called Mathematica to solve different equations using sin, cos and tan. Students will be filling out a worksheet in which they will be solving whether or not there is a inverse correlation between sin and cos, they will also be trying to figure out whether or not tan is comprised of sin, and cos combined to create a formula that tan may also equal rather than just opposite over adjacent.
 * 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;">SMART Board
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Mathematica
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Google Earth
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Calculators
 * <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;">Worksheets
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Handout on Mathematica
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Graphic Organizer of Graphs

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Sin, Cos, and Tan Information that will be used for the content notes: [] [] [] [] []
 * __<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;">

Graphs that will be used for the students to take notes []

Mathematica tutorial just in case students get stuck doing the worksheet []

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Rationale:** Students will be given many different resources in order to finish this section, for example they will be given the opportunity to see it in the real world; they will also be able to see it through the logical sense of comparing all of the different tan, sin, and cos formats. Students are given the option to work on all of the work by themselves or in groups it is up too the student to choose. At the beginning of class I will give the students a outline of what will be discussed during the class and what will need to be completed. During the worksheets, the worksheets will be step by step so that the clipboards are able to follow along easily. During the mathematica part of the lesson students will be asked to create a hypothesis on what the relation between sin, cos and tan are. Lastly the classroom is a place of learning students will be allowed to ask any question at any time, making them feel very comfortable.
 * __<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 working in small groups to come up with the real life situations, they also may help each other on the Mathematica program, by doing so they will learn more than if I just lectured to them. Students will need to know these relations to solve for most things that deal with engineering, or other mathematical fields. Students need to know that it is possible to solve for angles and ratios via right triangles, given only two pieces of information than it should be simple any other part of the triangle. Everything in math is assumed and based on facts that are also assumed, it may be completely wrong but in the end it is the only thing that has proven the test of time. Students are going to need to realize that it is possible to put this math to most parts of life people just do not see it that way. Lastly, students are only able to think so abstractly before it is impossible, students can not be expected to fully understand this the first time taught, it needs to be reinforced over and over.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** figure out how to use sin, cos and tan. use and which ones not to use. world, including music. people, via the internet.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//
 * Verbal:** Students will have to read many different blogs learning things from each.
 * Visual:** Students will be able to see the equations for sin, cos and tan as they find them online.
 * Interpersonal:** Students will be given the oppurtunity to talk with people all around the world trying to
 * Interpersonal:** Students will be given the oppurtunity to work by themselves figuring out which blogs to
 * Naturaralist:** Students must find things that are found in nature that cause sin, cos and tan to occur.
 * Musical:** Students will be given the option to look up how sin, cos and tan are connected to the real
 * Logical:** Students will be asked to find out the meaning of sin, cos and tan through the use of other

Students will be using the program called Mathematica to solve different equations using sin, cos and tan. Students will be filling out a worksheet in which they will be solving whether or not there is a inverse correlation between sin and cos, they will also be trying to figure out whether or not tan is comprised of sin, and cos combined to create a formula that tan may also equal rather than just opposite over adjacent.
 * Technology**:

Rationale:** Students will be evaluated on a checklist making sure they have completed all of the necessary adjustments to their lists. By doing this students will make sure that they have realized what occurs in the world that relates to sin, cos and tan. They will also be asked to make sure that their graphic organizer is filled out correctly. By doing so we know that the student is capable of the stuff that is written down and will be to use in some real life situations.
 * //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)**

Students will be asked to use mathematica to solve for sin, cos and tan. By using this program students will be able to solve for sin, cos and tan. By doing this students will be able to realize that there is a correlation between sin, cos and tan that is not just hypotenuse, adjacent and opposite. They will realize that the relation is that sin and cos are inverse of each others. They will also be able to realize that tan is just sin divided by cos. By using this program the student will learn for themselves through the use technology rather than myself lecturing to them.
 * Summative (Assessment of Learning)**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be randomly split into groups of three to four people in which in these groups they will come up with real life situations in which they may use what they have learned to solve for sin, cos, tan of these objects. It may range from jobs that can be used all the way to different structures that use it.
 * __<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 lesson (5 Minutes) Google Earth (10 Minutes) Lesson on graphs (10 Minutes) Wiki page additions (10 Minutes) Evaluation of Wiki Page and Class List (10 Minutes) Mathematica Project (35 Minutes)

Students will understand that sin, cos and tan are related to triangles. **//Students understand and use basic basic ideas// //of trigonometry.//** The students will be able to see that the angle found by the sin, cos, and tan operations may be used inalmost any faucet of the world. Google Earth: Students will see the use in everyday life that will create there wanting to learn more about the subject. During this time the teacher will be at the SMART board showing the students the program Google Earth, they will also be using the math learned the ratios line up correct all the time to compare it to the unit circle to find the angle between cities.
 * Where, What, Why, Hook Tailor:** Verbal, Logical, Interpersonal, Kinesthetic, Musical, Intrapersonal, Visual **(20 Minutes)**

Students will know sin, cos, tan, all of the equations for these, SAHCOHTOA, unit circle, radians, <span style="color: black; font-family: "Times New Roman","serif";">pi, theta, adjacent, hypotenuse, opposite, triangle, graphs. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will look up blogger on the topic of trigonometric funtions and ratios. The teacher will than create a class wiki in which students must add at least two blog posts they have found, citation is required, all students must read this. During this time the teacher will be showing the students what sin, cos and tan functions look like. The teacher will also show them that it works like this because when you plug in the ratios is the answers that are received.
 * Equip, Explore, Rethink, Tailor:** Verbal, Logical, Interpersonal, Musical, Intrapersonal, Visual **(20 Minutes)**

Students will look up blogger on the topic of trigonometric functions and ratios. Students must reply to at least three different blogger and state what they have learned from their blog. The teacher will than create a class wiki in which students must add at least two blog posts they have found, vitiation is required, all students must read this. Students will than create a web of the most important things, and give examples of real world things that can be found in nature of at least half of their findings. Students must than create a class list of the most important information on their lists. At this time the teacher will be walking around the classroom to make sure that students are on topic and is making sure that they are on target.
 * Explore, Experience, Rethink, Revise, Refine, Tailors:** Verbal, Logical, Interpersonal, Intrapersonal, Visual **(20 Minutes)**

Students will be evaluated on a checklist making sure they have completed all of the necessary adjustments to their lists. By doing this students will make sure that they have realized what occurs in the world that relates to sin, cos and tan. They will also be asked to make sure that their graphic organizer is filled out correctly. By doing so we know that the student is capable of the stuff that is written down and will be to use in some real life situations. As the teacher I will make sure that the list is complete so that the student may be able to go on to using the program Mathematica to show that there is a relationship between sin, cos and tan that is not ratios.
 * Evaluate, Tailors:** Verbal, Logical, Interpersonal, Intrapersonal, Visual **(20 Minutes)**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Content Notes **<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">

The students will begin this lesson by experiencing the sin, cos and tan functions in action showing the angles of two different cities from one point using the program Google earth. To do so set up a triangle on the earth between cities, and than plug the ratios into the arc function of any of the ratios.

Sin: The graph of sin begins at zero and continues up to 1 at pi / 2, fro, here it continues down to 0 at pi and at 2 pi / 3 is at -1, at this point it continues up to 0 again at 2 pi. This continues onward and backward through all of the real numbers.

Cos: The graph of sin begins at 1 and continues down to 0 at pi / 2, fro, here it continues down to -1 at pi and at 2 pi / 3 is at 0, at this point it continues up to 1 again at 2 pi. This continues onward and backward through all of the real numbers.

Tan: The graph approaches negative infinity at - pi and approach infinity at pi. This interval continues on forever.

Sin = Opp / Hyp Cos = Adj / Hyp Tan = Opp / Adj

Students will look into different blogger's in which they will look to see whether or not the blog discusses the real life situations in which they may be used.

Lastly, while using Mathematica the students will be trying to derive the formula that tan also equals sin/cos. To do so the students will be doing a set of problems in which in the end they will be asked to notice whether or not there is a correlation between any of their answers.

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Students will be asked to put the sin, cos and tan graphs on these graph papers, doing so students will see the correlation between right triangle ratios vs. the height of the graph. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Students will be asked to fill out this worksheet in order to show that there is more than just a relationship between the sin, cos, tan and how they are related to each other. Such as the inverse of sin is cos, and vice versa.
 * Handouts**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Graph for Graphic Organizer]
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Mathematica Worksheet