L6+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 6 (Self Knowledge)
 * Grade Level:** 11 **Topic:** Basic Trigonometry

theta, adjacent, hypotenuse, opposite, triangle, graphs. 
 * __Objectives __**
 * Student will understand that ** 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,
 * Student will be able to do** to compare and contrast sin, cos, and tan.

 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 know that sin, cos and tan are related, but they need to realize that their is another relation, instead of solving for sin, cos and tan, you may use it the opposite way to solve for the ratio, to do this they must use arcsin, arccos, and arctan.
 * __Maine Learning Results Alignment __**
 * Rationale:**

Students will be asked one question and using their cheat sheet they must answer it correctly, until than they do not receive a check. This will show that the students have successfully discovered how to use the steps that were taught to them. It will also prove very valuable when the students decide it is time to take the test. Students will also be given a chance to re engrave into their mind the ideas that were learned from the first few sections and show that there is a huge correlation between that information learned and the information being learned now.
 * __Assessment __**
 * Formative **

Students will be asked to use Garage band and analyze songs to see what graphs they create. By doing so students will fill out a worksheet in which they will be asked to correlate the beat of the song to one of the three graphs that were learned about. By doing this students will show that they can recognize when in life these graphs appear and that they are actually more common than originally perceived. Students than must write up a paper on why there is a correlation between the sides of a triangle and the rhythm of a song, the true answer is that it just fell into place like that.
 * Summative**

Technology: Students will be given the opportunity to use Garageband to be able to solve for a correlation in the song to the graphs that look like sin, cos and tan, all music is is the combination of sin, cos and tan in the context of movements. Music: Students will be asked to listen to songs that I choose to find out where their are sin, cos and tan sets inside of them, doing so students will be able to show that even in the most simple part of life there is sin, cos and tan.
 * __<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 broken into groups of two, which will be divided by students randomly walking into the classroom, with the teacher placing them in random groups. By doing so students should end up with a partner they have yet to work with. Students in these groups will at the end of class come up with a cheat sheet in which they may use on their final test. This cheat sheet will also be a cumulative assessment of all of the information that is retrieved in the unit. Doing so will allow the student opportunity to work well together, as well as giving the students a chance to figure out what information was, or is important.
 * __<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. the subject. of the graphs. students will have to think about what is and is not important for the cheat sheet.
 * __<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 view the graphs and see what they do when pulled, and tugged upon.
 * Interpersonal:** Students will be given the opportunity to talk with partners gathering information about
 * Intrapersonal:** Students will be given the opportunity to work by themselves figuring out the different parts
 * Musical:** Students must listen to a song in which they will than see how the subject relates to music.
 * Logical:** Students will be given the opportunity to set up their cheat sheet in the most efficient manner,


 * 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. Students will need me to approve their cheat sheet before they are allowed to begin work on the final project.
 * Absent Students:** Notes from each class will be posted online, these notes may be printed out but the

Students will analyze a song using Garage band and compare the ups and downs in the beat to the sin, cos and tan functions. Students will be asked to choose 4 out of 10 songs that have a constant beat. They must show that there is a sin, cos or tan function that lasts more than 5 seconds. After this is done students must discuss whether or not there is a reason there is a sin, cos or tan function in a song, aka rhythm.
 * 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;">Garageband
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Calculator
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">SMART Board
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Songs
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Pens
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Pencils
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Graphs
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Note cards
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Worksheet for Garage band

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Sin, Cos, Tan information that will be used in 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;">

ArcSin, ArcCos, ArcTan information that will be used in content notes: [] [] []

Garage Band tutorials to help students figure out what is being asked of them [] []

Graph students will use for the graphic organizer: []

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Rationale:** Students will be given a look into the sin, cos and tan functions in a different light, instead of looking at them together, the students will look at them individually, this alone is variety. They will look at them three different ways though, through graphs, through garage band and lastly a cheat sheet. Students will be given the option to continue on the songs and do as many as they wish. At the beginning of class I will give the students a list of the things that we will be doing over the course of the lesson. They will be told exactly what is expect of them when they finish the day in the classroom. Students will be creating a cheat sheet, and using garage band to discover real life circumstance in which they appear. Lastly, the classroom will be arranged in a way that optimizes the students learning along with letting the student be themselves with out the pressure of the others to learn more quickly than they can.
 * __<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 Garage band 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 and actually they will learn that it can now be applied to music. 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. By doing the cheat sheet students will be able to reinforce the ideas that were learned in the first few sections. 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, the cheat sheet will show that these abstract ideas are not very abstract if looking at the big picture.
 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//

Rationale:** amongst the partners. the subject. of the graphs. students will have to think about what is and is not important for the cheat sheet.
 * //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 view the graphs and see what they do when pulled, and tugged upon.
 * Interpersonal:** Students will be given the opportunity to talk with partners gathering information about
 * Intrapersonal:** Students will be given the opportunity to work by themselves figuring out the different parts
 * Musical:** Students must listen to a song in which they will than see how the subject relates to music.
 * Logical:** Students will be given the opportunity to set up their cheat sheet in the most efficient manner,

Students will analyze a song using Garage band and compare the ups and downs in the beat to the sin, cos and tan functions. Students will be asked to choose 4 out of 10 songs that have a constant beat. They must show that there is a sin, cos or tan function that lasts more than 5 seconds. After this is done students must discuss whether or not there is a reason there is a sin, cos or tan function in a song, aka rhythm.
 * Technology:**

Rationale:** Students will be asked one question and using their cheat sheet they must answer it correctly, until than they do not receive a check. This will show that the students have successfully discovered how to use the steps that were taught to them. It will also prove very valuable when the students decide it is time to take the test. Students will also be given a chance to re engrave into their mind the ideas that were learned from the first few sections and show that there is a huge correlation between that information learned and the information being learned now.
 * //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 Garage band and analyze songs to see what graphs they create. By doing so students will fill out a worksheet in which they will be asked to correlate the beat of the song to one of the three graphs that were learned about. By doing this students will show that they can recognize when in life these graphs appear and that they are actually more common than originally perceived. Students than must write up a paper on why there is a correlation between the sides of a triangle and the rhythm of a song, the true answer is that it just fell into place like that.
 * Summative**

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Students will be broken down into groups of two through a random process. Students will be asked to discuss the topic among themselves along with making sure that the two students work together while completing the cheat sheet for the entire unit.
 * __<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 lesson (5 Minutes) Song Analysis (10 Minutes) Lesson (15 Minutes) Compare Wiki to Info (10 Minutes) Cheat Sheet (40 Minutes)

Day 2: Garage Band Activity (80 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 in almost any faucet of the world. Students will listen to a song and than analyze the behinds of it whether it forms sin, cos, or a tan graph. At this time the teacher will show the student that the graph lines up perfectly on the song that is being analyzed. The teacher will then tell the students that this is not a coincidence and that on all song with a beat that they can do it to and will in fact do it to later in the lesson.
 * Where, What, Why, Hook Tailor:** Verbal, Logical, Interpersonal, Kinesthetic, Visual, Musical **(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 be given a paper with three graphs upon it, they will fill out these graphs with explanation from the teacher. Students will compare what they have learned to the class wiki in the last class, to see why it works as so. At this time the teacher will give the lesson on how sin, cos and tan go much deeper than just the surface. This lesson will cover the inverse of all of the trig functions, arcsin, arccos, and arctan.
 * Equip, Explore, Rethink, Tailor:** Verbal, Logical, Interpersonal, Kinesthetic, Visual, Musical **(20 Minutes)**

Students will be given a paper with three graphs upon it, they will fill out these graphs with explanation from the teacher. Students will than be shown how it relates to the up and down beats of a song with rhythm. Students will compare what they have learned to the class wiki in the last class, to see why it works as so. Students will re-evaluate the wiki and make sure all of the information on the wiki is correct. Students must than create a cheat sheet with a partner that may be used on the next test. At this time the teacher will be walking around the classroom making sure that they are creating the cheat sheet with the correct information on them. The teacher will put points on the board that the students will most likely not want to forget to put on their cheat sheet.
 * Explore, Experience, Rethink, Revise, Refine, Tailors:** Verbal, Logical, Interpersonal, Kinesthetic, Visual, Musical **(20 Minutes)**

Students will be asked one question and using their cheat sheet they must answer it correctly, until than they do not receive a check. This will show that the students have successfully discovered how to use the steps that were taught to them. It will also prove very valuable when the students decide it is time to take the test. Students will also be given a chance to re engrave into their mind the ideas that were learned from the first few sections and show that there is a huge correlation between that information learned and the information being learned now. As the teacher I will be making sure that the student knows the material before moving onto the project.
 * Evaluate, Tailors:** Verbal, Logical, Interpersonal, Kinesthetic, Visual, Musical **(20 Minutes)**

To begin the lesson the teacher will play a song in which the students will be asked to decide whether the interval that is being discussed is a sin, cos or tan graph. Then the teacher will show them by shifting left or right it can change it into a cos or sin graph depending on what you began with.
 * Content Notes**

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

Arcsin: To solve for ratio instead of the angle someone must place in calculator 2nd, than sin, than the angle, that will give the ratio. Inverse sin will give you the ratio that must be plugged into the sin function to give you that angle.

Arccos: To solve for ratio instead of the angle someone must place in calculator 2nd, than cos, than the angle, that will give the ratio. Inverse cos will give you the ratio that must be plugged into the cos function to give you that angle.

Arctan: To solve for ratio instead of the angle someone must place in calculator 2nd, than tan, than the angle, that will give the ratio. Inverse tan will give you the ratio that must be plugged into the tan function to give you that angle.

Lastly, students will choose four songs out ten given to analyze the pieces of the songs to show that they can show in real life situations the sin and cos functions.

<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> This graph will be used for students to be able to draw the arcsin, arccos and acrtan graphs on. It will provide a basis on why they are related to the original. Students will be able to put their own thoughts down on this paper. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> As with all trig classes it is important to write down the formulas. I feel it is irrational for me to ask my students to come up with the formula's off the top of their heads therefore I am asking them to take down the formulas on this cheat sheet. <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Students will be asked to fill out this worksheet which they will need to copy the graph of four songs onto, they will need to tell at what time it occurs and what type of graph it is, and why.
 * Handouts**
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> [|Graph]
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Note Card
 * <span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Garage Band