L4+Fletcher,+Caleb

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

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : ** Mr. Fletcher **__Lesson #: 4__** **__Facet: Empathy__**
 * __ Grade Level __**** : High School ** **__ Numbers of Days: 3 __**
 * __ Topic: CSI Ax2 __**


 * __ PART I: __**
 * __ Objectives __**
 * Student will understand that a quadratic will produce a parabola **
 * Student will know about linear functions, parabolas, vertex, roots, standard form, vertex form, roots, and complex roots. **
 * Student will be able to compare and contrast different functions from parabolas. **
 * Product: Podcast **

Common Core State Standards Content Area: Algebra Domain: Reasoning with Equations and Inequalities Standard: Solve Equations and inequalities in one variable Added with Content Area: Functions Domain: Interpreting Functions Standard: Analyze functions using different representations
 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**
 * Rationale: ** In this lesson the students will be analyzing their own interpretation of the graphs shown so they can better understand the complexities of parabolas and the quadratics that go along with them.


 * __ Assessments __**

During the instruction there will be post-it notes handed out. On these post it notes whenever I cover a new subject or talk about new material I want the students to write their own ideas on the subject (a brief sentence) about their thoughts and or questions they have. This is called flagging. When a student is feeling confused instead of quickly calling out their question this gives them a chance to be patience and to see if I will be explaining the answer further along in my lesson. After the students have worked on their products( i.e the podcasts), they will be given a checklist as well as a rubric to fill out. The checklist is what it sounds like a way for the students to have the necessary materials needed to pass the project. While the rubric will give the student an idea of how to make a better project.
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **
 * Section II – timely feedback for products (self, peer, teacher) **

The final product that the students will be making is a podcast. Now, this podcast will explain to me that they know the differences between parabolas and other functions depending on a few qualities. This podcast is treated like a Doctor's Diagnosis it explains a system of steps being taken to know what the graph is and then it the from there we should know what to do with it.
 * __ Summative (Assessment of Learning): __**

Medical Podcast- Students will diagnosis an equation in order to make it better. This will require great knowledge on behalf of the student, it will require teamwork from his or her team as well. This function is suffering from a random aliment that attacks parabolas viciously. Hurry, to find out if these equations that have been given to you need more attention or less attention then before.
 * __ Integration __**
 * Technology: **


 * Biology ** - Students must be familiar with diseases and how to spot them.
 * English- ** Students will learn how to become a certain type of character and understand how he or she thinks

The students will be using Venn diagrams during the lesson. This organizer will show us the similarities between a parabola and the various other geometric graphs that have been constructed over the many years. There will be three minute reviews done after each point made, so the students can remain on task and so the information taught can be reinforced. During the product there will be groups made. These groups will be focused the class choosing it's own peers. Groups will be separated into groups of 3's and 4's. The roles for the product are going to be focused around a medical team. You'll have the doctor, who is the person making the diagnosis, the chief of medicine seeing if his diagnosis is viable, and finally there will be a nurse to check the doctor's own work and see if he is doing a far job.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**
 * __ MI Strategies __**


 * Visual- ** Through graphs, and diagrams I will show the students just how exactly a quadratic differs from another equation.
 * Verbal- ** Tell them the reasons behind the differences between a parabola and a linear equation.
 * Logical ** - Show the reasoning behind every facet of a parabola which will explain to them why a parabola is different then a line.
 * Kinesthetic- ** Bring back the human function so they will be able to physically see the main difference behind the line and the parabola.
 * Interpersonal ** - Have the students talk amongst themselves during the end of the class to allow them time to reflect with their peers about what has been taught
 * Intrapersonal- ** Giving students a few question that they only have to think about such as "Why does a parabola curve?" and "What else acts like a parabola?"
 * Naturalist- ** Bring back elements from the story given at the beginning of class and show them the nature aspect of what was being told.
 * Musical- ** Find music that tends to fluctuate in sound, and then fine music that tends to stay a one pitch to show them the differences.


 * __ Modifications/Accommodations __**
 * // From IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan) //** //I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.//
 * Plan for accommodating absent students: ** Students are going to be part of a group, and in this group they are all reliable to each other. If one person is absent then the notes from the lesson that they have missed will be filled in by his or her peers. If they do have any questions I will be more then willing to help plus I will offer them other alternative methods to get caught up like from a youtube video or from a slideshow I have found.


 * __ Extensions __**
 * Type II technology: Podcast a digital diagnosis. **
 * Gifted Students: If students are grasping the idea of quadratics, and parabolas in a quicker manner then most I will prose new and exciting parabolas that look a bit off. They will still have to figure out more complex parabolas and give me a more in-depth diagnosis into every part of that parabola. **

// Handouts // // Checklist // // LCD Projector // // Tape Recorder // // A clip of a Scrubs // // Rubrics // // Laptop //
 * __ Materials, Resources and Technology __**

http://labnol.blogspot.com/2006/09/audio-podcasts-tips-video-tricks.html - This website offers advice to make a good podcast http://mathworld.wolfram.com/Parabola.html - Shows a better explanation of a parabola and it's different parts of the body. http://www.feedforall.com/effective-podcast-tips.htm -Gives more tips on how to make a podcast http://www.npr.org/templates/story/story.php?storyId=8892053 -Insight into how a doctor's mind works http://www.futurity.org/health-medicine/why-medicine-hearts-math/ -The love between medicine and math http://webmath.com/parabolas.html - Further explanations of parabolas.
 * __ Source for Lesson Plan and Research __**


 * __ PART II: __**


 * __ Teaching and Learning Sequence __** **(Describe the teaching and learning process using all of the information from part I of the lesson plan)** //Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages)//

The classroom will be set up in a perimeter fashion for this lesson.

Day 1:
 * Tell the grand story of the two legendary tribes (15 minutes)
 * Talk about what the story was about and what it means in the math world (15 minutes)
 * Review the parts of a parabola (10 minutes)
 * With graphic organizers in hand tell the differences between a linear function and a parabola (20 minutes)
 * Introduce the students to vertex form and how they can create a parabola easily with that form as well as determine an equation using that form. (20 minutes)

Day 2:
 * Review the ideas about parabolas (15 minutes)
 * Go into a bit more depth into finding the equation of a parabola (20 minutes)
 * Discuss what a podcast is (10 minutes)
 * Split the class up into various groups (5 minutes)
 * Tell them what their project is going to be an assign them their roles (10 minutes)
 * Allow them to work for the rest of the class on their product (20 minutes)

Day 3:
 * Give a brief review of what has been covered thus far (10 minutes)
 * The rest of the time will be spent of answering questions and working on their products (70 minutes)

"There were two legendary tribes" is how the lesson will start on this fateful day. The students will be seated in their seats which are back in a perimeter fashion so I'll have room to roam and to tell my story. This story will continue to describe two famous native american tribes that will become symbols for parabolas and linear functions. As I tell the grand epic known as the battle between the raising valleys and the setting plains, I'll be incorporating various mathematical terms. At the end of my fable I'll ask the students what they think of these heroes that I've described. We'll talk about the story a little bit and the I'll bring the story and it's various elements back to the main point which is comparing parabolas to other functions. To these students this might seem like a tedious task but comparing and contrasting different functions on a graph is much like comparing and contrasting to different forms of literature. It will teach the students how to pick out certain details in a fashion that they haven't used yet. They will understand that by just raising a number to the second power it tends to cause vast changes. So, after we talk about the math behind the story I'll be introducing them to the idea of analytical comparing and contrasting. This analytical nature will have them thinking more like a doctor. Trying to deduce what is going on in this function and hopefully be able to deduce what sort of function is creating such a graph.
 * What, Where, Why, Hook, Tailors: Naturalist, Visual, Verbal, interpersonal **

Once my story has been told I will then pass out the graphic organizers. These organizers are going to be a vital role in the notes the students will be taking as well as understanding the analytical reasonings behind a parabola. The lesson will start with plotting a linear function on a graph and having the students tell you all the know about it. There should be a few things that are prone to stick out to them, mainly the slope. But this will be covered more in the content notes. Once we have taken a look at a function we will then put a quadratic function and then a cubic on the board and have the students describe the differences. From there I'll introduce the various arm moments that one needs to learn to remember what certain graphs look like. If it's a straight line make your arms into a straight line, if it is a parabola then make a parabola with your arms. It'll be like a giant u. Now, after we have down that I'll start dissecting all that we have learned from the previous lesson and applying it to the this parabola at the moment. From here I'll ask the students to show me where each of the terms are from what we have talked about in the last lesson. This will give students the chance to move and to have a hands on approach to the operation. As soon as we finish with this we will do a quick three minute review and try to figure out what questions they have. During this lesson the students will be writing down post-it notes that are full of questions about what we have covered thus far. After pick apart each of these functions that are up on the board I'll start going into detail about what their functions look like in algebraic form. I'll introduce standard form, and vertex form. I'll discuss how we can form a parabola much easier once we know how to handle the forms that have come up. Once we have compared the algebraic forms of parabolas we will get a chance to deduce an equation from of a parabola. From deducing an equation we will have another quick three minute review before moving onto a few selected handouts that I have given them. Whilst working on their handouts they can ask questions as well as work on the project that I'll be describing in the next section.
 * Equip, Explore, Rethink, Revise, Tailors: Logical, Kinesthetic, Visual, Verbal, Interpersonal, Intrapersonal **

Maybe it's that I watched to many episodes of Scrubs or maybe it's that I've fallen into an obsession with the art of the medical field. But after watching my favorite T.V show, and that was diagnosis a diseases seems a lot of like deducing an equation out of a formula. This is the product that I want to see my students creating. When a doctor is diagnosing his or her patient then tend to have a tape recorder that is with them that tells them what they have noticed and what is going on. From this recording the doctor will be able to deduce the disease or in the student's case deduce the equation of that graph. Thus, with your "medical team" you'll be given a task to figure out what is wrong with the parabola. In order to do so you need to go through each part of the parabola that has been taught so far and pick them apart analyzing each little aspect of them to figure out what the "ailment" is. Thus the student needs to deduce and solve the "diseases" that has baffled them.
 * Equip, Explore, Revise, Refine, Tailors: Logical, Visual, Verbal, Interpersonal, Musical **

Now students will be graded on this medical diagnosis by checklists and rubrics. These will give students structured for them to follow. After all when a doctor is diagnosing a patient they have to be able to use all their knowledge and see all of the diseases signs in order to cure what is ailing their patient. Luckily, there isn't anybody's life on the line when we are dealing with parabolas. There is, however, a way to figure out what started this parabola and what has formed it. It's is incredible what one person can figure out from just looking at a graph. That is what the students will be figuring out, in order to show me that knowledge that they have.
 * Evaluate, Tailors: Intrapersonal, Interpersonal, Visual, Verbal **

We have three functions on our graph. y=x^2, y=x and y=x^3. How do we know which function goes to which graph? That my friends is the easy part. Whenever we have a u shaped graph we can determine that it's y= x^2 because we know how a parabola is formed. When we look at the y=x function there should be a sense of linearity to it. Thus when a function has a power of one in it the graph is going to be liner. Lastly, cubic functions create an s shape on our graph. This is just the first part of learning how to differentiate graphs, at least the physically aspect of them. We’ve taken a look at what a parabola looks like, and how a quadratic equation forms a parabola. We are now going to look at the forms we can see a quadratic in. When we write an equation we notice that we tend to place our variables and constants in this order x2+x+5=y. This specific placement is called standard form. If we remember our quadratic formula we can change this equation to a constant form that can be used for any equation, which is ax2+bx+c=y. This form should look rather familiar, due to the quadratic formula (as stated above) and our vertex equation (b/2a). Now, let us take a look at the parabola above, there are a few things we can determine right off that bat. First off, is that our roots are non-existent due to the why the graph is curved, our vertex is at the point (3,6), and since our equation is smiling we know that we are going to have a positive curve. When we talk about the placement of an equation there is another form that we can use that is similar to the standard form. It’s known as the vertex form. The vertex from, which was mentioned in the previous lesson, looks like this a(x-h)2+k=y. As we can see instead of having an a,b, and c we just have an a, h, k. We call this the vertex form because the h, and k variables make up the vertex. These variables actually make the ordered pair of the vertex, which means that our ordered pair looks like this (h,k). With our parabola above I have stated that the vertex is at the point at (3,6), which means that our 3=h and our 6=k. Now, let’s take these points that we have and plug them back into the our vertex form to try to figure out the equation of this parabola. After all this is what our lesson is all about. We want to be able to deduce an equation of a line by just looking at our parabola. So when we plug in that ordered pair on formula changes to a(x-3)2+6= y. We are one step closer to solving this equation, but our next step is where we have to get gritty with our math. There is a variable that is all along in this equation that wants some parabola love. This variable is our a-term. If we can figure out what that a-term is we can figure out our equation. Now, how do we go about figuring that out? What we have to do is choose a point on our parabola and plug in it’s point for our x term and y term. For instance in this parabola we have a point (-2,10), we are able to find this by just looking at our parabola and the graph. Now, once we have this we have to do a bit of algebra. First we plug in these points so our equation changes to a(-2-3)2+6= 10. Let’s go ahead and simplify things out, meaning square numbers and add them together. Thus we have a(-5)2+6=10 or 25a+6=10 which means that 25a=4 or a= 4/25. So now that we have our a term let’s plug it back in and see what our vertex form looks like, 4/25(x-3)2+6=y. That is our final equation. Now there is one last step that we must do, and that is convert the vertex formula to standard form. How do we do this? Well, simplify your equation, square that (x-3) so we get (x2-6x+9) then multiply that by 4/25 so we get (4/25)x2- (24/25)x + (36/25)+ 6 now add your constants together so we get (150/25)+ (36/25)= (186/25) so our equation in the end will end up looking like this (4/25)x2- (24/25)x +(186/25). I do not know about you but being able to come up with a nasty equation like that from simple points is relatively cool. So here are the steps laid out in a clear and friendly order.
 * __ Content Notes __**

Steps to finding the formula of a line: 1.) Find your vertex 2.) Substitute the vertex into the vertex form of a quadratic (plug in for h and k)  3.) Find another point on your graph  4.) Substitute that point for your remaining variables (plug in for x and y)  5.) Simplify your equation  6.) Solve for a  7.) Plug in a into your original vertex form equation  8.) Convert vertex form into standard form 9.) REJOICE!
 * Simplify your equation
 * Combine like terms

Let’s work on two more examples so we have a graph that looks like this…(picture of graph) So let’s go back to our step-by-step guide and look at what is next for us. Find our vertex (2,4)

Plug it in for h and k a(x-2)2+4=y

Find another point (0,6)

Plug that in for x and y a(0-2)2+4=6

Simplify a(0-2)2+4=6 a(-2)2+4=6 4a+4=6 4a=2 a=(1/2)

Plug in a (1/2)(x-2)2+4=y

Simplify (1/2)(x2 -4x+4) +4 (1/2)x2 -2x+2 +4 (1/2)x2 -2x+6 =y is our equation

Example 2:

Vertex: (-3,-2)

Plug in for h and k a(x+3)2-2=y

Find a point (1, 5)

Plug in for x and y a(1+3)2-2=5

Simplify a(1+3)2-2=5 a(4)2-2=5 16a-2=5 16a=7 a= (7/16)

Plug a back in (7/16)(x+3)2-2=y

Convert to standard form (7/16)(x2+6x+9)-2=y (7/16)x2+(42/16)x+(63/16)-2=y (7/16)x2+(42/16)x+(63/16)-(32/16)=y (7/16)x2+(42/16)x+(31/16)=y is our final equation

// Worksheet, Checklist, Graphic Organizer, Rubric //
 * __ Handouts __**


 * __ Maine Standards for Initial Teacher Certification and Rationale __**


 * // 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. //**
 * //__ Learning Styles __//**


 * // Clipboard: //** The nature of the product itself and the layout of the lesson is a very step-by-step process that clipboard learners will thrive in. Since there is such as structured plan to this lesson so far the environment needed to have all the information is going to be meet just fine.


 * // Microscope: //** While we gaze over the lesson on parabolas we noticed what we are doing, and that is using what we know and analyzing it to find an equation to a geometric shape. Microscope learners are going to enjoy picking apart the aspects of parabolas to figure out what their original equations are in the end.


 * // Puppy: //** Conversation, and people are needed for a puppy style learner to fully grasp the lesson. That is why there will be a group diagnosis to help them understand how the other students think. Along with that I will be providing assistance to those who need help.


 * // Beach Ball: //** The product will offer those who enjoy creative freedom a chance to choose between their occupations of deductive professionalism. Meaning that the students will get to decide which career they will choose and then get into character from that. This shows that student can think up a different career that focuses around deductive reasoning as well as come up with a creative way of thinking.


 * // Rationale: //**


 * // Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. //**


 * // Content Knowledge: //** This lesson dives into science and into English. There are times when I think that I have the soul of an English teacher inside the body of a math teacher. But that has nothing to do with this section, back to business as usual. The world is full of individuals who use deductive reasoning. This lesson is getting students to learn about that reasoning and to slowly start developing it. It’s a handy tool that goes further then in just some career.

Common Core State Standards Content Area: Algebra Domain: Reasoning with Equations and Inequalities Standard: Solve Equations and inequalities in one variable Added with Content Area: Functions Domain: Interpreting Functions Standard: Analyze functions using different representations
 * // MLR or CCSS: //**

Having students being able to take an equation and convert it back into standard form will give them the chance not only to solve an equation with one variable it will also help them analyze a graph. Due to the nature of this lesson the student will be using both standards interchangeably to complete the tasks given.


 * // Facet: //** The students are going to look at themselves as well as various other graphs and differenatiate them by using viable reasoning. Now, deductive reasoning has to be treated with caution, after all if it is set loose we might have a problem on our hands with stereotyping. But, if it’s tackled correctly students can relate to various problems and from their use their own deductive skill to find the best solutions by themselves.


 * // Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. //**


 * // MI Strategies: //**
 * Visual- ** Through graphs, and diagrams I will show the students just how exactly a quadratic differs from another equation.
 * Verbal- ** Tell them the reasons behind the differences between a parabola and a linear equation.
 * Logical ** - Show the reasoning behind every facet of a parabola which will explain to them why a parabola is different then a line.
 * Kinesthetic- ** Bring back the human function so they will be able to physically see the main difference behind the line and the parabola.
 * Interpersonal ** - Have the students talk amongst themselves during the end of the class to allow them time to reflect with their peers about what has been taught
 * Intrapersonal- ** Giving students a few question that they only have to think about such as "Why does a parabola curve?" and "What else acts like a parabola?"
 * Naturalist- ** Bring back elements from the story given at the beginning of class and show them the nature aspect of what was being told.
 * Musical- ** Find music that tends to fluctuate in sound, and then fine music that tends to stay a one pitch to show them the differences.


 * // Type II Technology: //** A podcast is going to be used so that students can generate more of the thoughts behind a character. If a student was to make a movie they would get more of a superficial view of a character but seeing as how thoughts are voices added to pictures we’ll be getting a clearer idea of how the students are figuring out how to use that reasoning.


 * // Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. //**


 * // Formative: //** During the lesson in order to check for understanding there will be three minute reviews. Now, these reviews will have me giving a brief synopsis of what we just covered and then asking questions. During the lesson this will give students the opportune moment to ask questions. Along with these reviews a small worksheet will be handed out that shall guide the students along so when they get to work on their product they will be all set to go.


 * // Summative: //** The product that they will be creating has the students entering the role of a professional that uses deductive reasoning. They are going to be working on a specific case for their profession that has them figuring out the craziness behind a parabola. The students will be giving aspiring teens a look into their own professional lives hoping that they too might join in the students chosen career.

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