L3+Fletcher,+Caleb

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

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : Mr. Fletcher ** **__Lesson #: 3__ __Facet:__** **__Explanation__**
 * __ Grade Level __**** : High School ** **__Numbers of Days: 3__**
 * __ Topic:Parabolas __**


 * __ PART I: __**


 * __ Objectives __**
 * Student will understand that a quadratic will produce a parabola. **
 * Student will know about parabolas, vertexes, and roots. **
 * Student will be able to prove how a parabola is formed by a quadratic. **


 * Product: Comic Life **


 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**

Added with
 * Content Area ** : Algebra
 * Domain: ** Reasoning with Equations and Inequalities
 * Standard: ** Solve Equations and inequalities in one variable
 * // Content Area: //**// Functions //
 * // Domain: //** //Interpreting Functions//
 * // Standard: //** //Analyze functions using different representations//

parabolas.
 * Rationale: ** //This lesson will teach the common core standards by giving the students background knowledge about the wonders of//


 * __ Assessments __**

At the beginning of the lesson students will be answering what is known as an exit ticket. I give them this ticket so they can write down a few thoughts on what is puzzling them about this lesson so when I am finished talking about what is going on with parabolas they can proceed to ask me questions.
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **

The student's comic lives, and other assignments during this lesson will be given feedback by their own selves with a personal evaluation on how they thought they did as well as a group survey. Along with this survey as a teacher I will be going around to teach group and checking up on them to see how they are doing.
 * Section II – timely feedback for products (self, peer, teacher) **

Comic Life- Students will use comic life to tell us how a parabola is created and why it looks the way it does. I tended to think of a parabola as a superhero. It’s an amazing geometric device that is more complex then people think at times. Thus, I want you guys to construct an origin story for the grand parabola. Tell me how with the help of a quadratic it is formed.
 * __ Summative (Assessment of Learning): __**


 * __ Integration __**
 * Technology: ** A comic life, which is a comic book creator, will give students a chance to have a little creativity while constructing a story.

English: The elements of a story Art: The contrast of certain colors.

Students are going to have an inverted triangle organizer to recognize the expanding process of a parabolas formation. Once these organizers have been filled out we will proceed to use think-pair-share so students can vocalize there own ideas on how the method has been used.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

Each of these groups will be separated by favorite primary color. It will depend on the class size and the varying opinions but once they have separated as a teacher I will make sure that the groups are even. Now, these groups will be mainly for the lesson. When the time comes for the project I'll allow them to choose their own groups so they can work on it with their fellow peers outside of class. There will be three people in a group and the roles for these members will consist of a writer, an illustrator and an editor. Someone who comes with the a story, someone who puts the story together, and someone to comply the comic together making sure it looks good and then presenting it.
 * Section II – Groups and Roles for Product **
 * __ Differentiated Instruction __**


 * __ MI Strategies __**
 * Verbal- ** I will explain how a parabola is formed, as well as give some analogies to the outside world, such as saying that when you put a drop of water on a rock it tends to spread out in different directions much like plugging in a single point into a quadratic.
 * Visual- ** I will show graphs and equations to let them see how parabolas are being formed.
 * Kinesthetic- ** Reminding them of what a parabola looks like through hand-motions.
 * Logical- ** Allowing the students to figure out the step by step process of how a quadratic is formed from me going through each quadratic in that very same fashion.
 * Musical- ** Demonstrate musical parabolas when discuss what happens when parabolas are formed like certain drums, and how certain pitches tend to make an arc like shape.
 * Naturalist ** - Along with the musical parabolas show some natural parabolas such as valleys, spider webs, the whole sha-bang.
 * Intrapersonal ** - Students will be given time in class to reflect about this work
 * Interpersonal ** - Students will be given time in class to interact with their peers to discuss their own thoughts on parabolas


 * __ 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: ** If students are absent their groups that they have been assigned to will be responsible for the notes and if there is any further questions they have about the lesson


 * __ Extensions __**

The students will be creating a comic life.
 * Type II technology: **

If students are learning quickly about parabolas then the rest of the students then I will show them various examples of parabolas of various different functions
 * Gifted Students: **

// Handouts, graphic organizer, laptop, smart-board, Angry Birds, a lcd-projector, and a checklist. //
 * __ Materials, Resources and Technology __**

http://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php- an interactive grapher that will allow students to get hands on the idea of what a parabola is. http://www.intmath.com/plane-analytic-geometry/4-parabola.php- gives more examples of why parabolas are important. http://www.rovio.com/en/our-work/games/view/1/angry-birds- Information about angry birds. http://chrome.angrybirds.com/- The actually game of angry birds http://www.knowyourmobile.com/mobile-games/mobilegamesnews/745542/angry_birds_popularity_blamed_on_arc_trajectories.html- An article talking about the scientific evidence behind people's favorite game that has them throwing birds at pigs. http://online.wsj.com/article/SB10001424052748703779704576074222543274268.html - An article going into more detail about the wonders of the parabola. http://www.youtube.com/watch?v=b_83FgdOlM0 - Video tutorial of Comic Life.
 * __ 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 semi-circle. They desks will arch so that I have the chance to have a bit of a stage before me.

Agenda: Day 1:
 * A brief review of quadratics and the material we've learned so far. This shall be presented in a game like form, either through jeopardy or any other board game that requires guessing. (15 minutes)
 * Introduce Angry Bird with an explanation of what it is (3 minutes)
 * Play a few rounds of Angry Birds and talk about the parabolas that are made every time a bird is shot from the sling shot. (17 minutes)
 * Talk about the articles that tell us that humans love parabolas and it's just a part of who we are (20 minutes)
 * Introduce the group what a parabola looks like and how we get one from our quadratic. (20 minutes)
 * Review this lesson briefly at the end and ask if the students have any questions (5 minutes)

Day 2:
 * Re-introduce parabolas and talk about their anatomy. (15 minutes)
 * Talk about real-world parabolas (15 minutes)
 * Relate parabolas to superheroes and then the product, which is a comic life shall be introduce along with that. (30 minutes)
 * Give the students a re-cap of all they have learned with parabolas (10 minutes)
 * Spilt the class up into pairs and then into teams and then have them share their own thoughts with the entire class (10 minutes)

Day 3:
 * Reflect upon all we have learned with parabolas and then from split the class into various groups that are chosen by themselves (20 minutes)
 * The rest of the class is spent upon working on their comic lives with me walking around giving them assistance. (60 minutes)

My students will be creating an origin story, a beautiful epic that is designed to help them understand the wonders of the parabola. This lesson and the grand journey into the greatness known as the parabolas have to start off with a single step. This step is centered on the popularity most of the world has with Angry Birds. Angry Birds is a video game that requires someone to use a slingshot to throw various kinds of birds at pigs and their houses. Needless to say that it's a premise that seems a bit to ridiculous and rather fun at the same time. The class will play a few round with me and from there I will introduce them to the articles that talk about Angry Birds and their popularity. From these articles I will talk about the real-life parabolas and how such wonderful arcs fascinate us as humans. The main point behind all of these parabolas is to get the students interested in another geometric figure that hasn't been widely used.
 * Where, Why, What, Hook Tailors: Kinesthetic, Visual, Logical, Verbal, Existential, Naturalist **

As the class sits down after the angry birds presentation I will present a few examples of problems that we have gone over so far. I'll start with the square root method, then factoring, followed by quadratic formula, and then finally completing the square. From here we will talk about why we solve a quadratic. What is the purpose behind the equation? I'll explain that it is to find the roots of a parabola and to determine a proper formula. Once we have mentioned that I will show the students a line on a graph. This line is a linear function, and then I'll proceed to ask them what they think will happen when we plug in numbers for a quadratic. Hopefully, they guess parabolas; after all we have been talking for the past ten minutes about them. Anyhow, we'll take a look at plotting points on a graph. We will see how a parabola is formed. By constructing a table of points we will be able to see the bend in the graph that will show the symmetry on that axis. As soon as we talk about plotting points I'll pull on various quadratic functions and have the students analyze them. Are they curving upwards or downwards? If so what does that mean? These questions are vital. From there we will take a look at the rest of the anatomy of a parabola and dive into each little piece. While the students are learning they will be taking notes on an inverted triangle to see keep track of the layers behind most of the parabola. Now the inverted triangle has various spaces going down thus we can fill in the level of depth behind each piece of the parabola is needed. Sometimes we'll discuss the meaning behind such parts, other times we will talk about the math behind it. Everything, however, is related. So after the students have been taught this lesson they will get together in order to communicate what they think is going on. From there we they will go to the big group and talk about what they've learned and observed. Following up this whole conversation they will spend a few minutes by themselves to repertoire.
 * Equip, Explore, Refine, Rethink, Tailors: Intrapersonal, Interpersonal, Logical, Verbal, Visual. **

Once we have learned the wonders of this super-powered geometric shape we'll begin to construct our own superhero origin story for the parabola. These students will be asked to write a comic book to inspire the youth of today for Detective Comics. If there comic is selected their version of the parabola will be brought to life for the world to see. The students will be given the choice to be creative and create a variety of powers and villains. After all I will have to give them the outline of what a superhero origin story entails. This means that they will create a love interest, a superpower, a setting, and a villain that all relates back to the parabola in the end. After all this crime fighting mathematical wonder has to be given proper tribute.
 * Explore, Experience, Revise, Refine, Tailors: Verbal, Interpersonal, Visual, Logical **

Every comic needs some very specific guidelines to completion. That is why my students will be using a checklist to determine if their comic life is completed. Now, this comic life is going to start these students onto the path of exploring parabolas. The next few lessons after this are going to entail many other aspects about the geometric figure. That is why this is a good place to start them on their journey by allowing them to create their own version of the origin of a parabola. It's a simple concept that will fortify their own learning.
 * Evaluate, Tailors: Visual, Naturalist, Verbal, Logical **


 * __ Content Notes __**

What is a parabola? If we were to give it a shape it would kind of look like an arc. Actually, if we are to plug in a simple quadratic ( y=x2) we see that it looks like Figure 1 // Figure 1 //

Now, how does a what we use to graph, lines, to into a parabola? It all starts off with the points we plug in. When we are plugging in points we realize that when we start there seems to be a symmetry behind them. For instance when we look at y=x2 we notice when we plug in positive numbers one side of the graph appears to be going up rather fast. That is because when we substitute a three in for x we are squaring that number and thus making it a 9. Which is a huge leap from the x value before that which happens to be 2. So, our first observation is to notice that there our numbers are now moving in an exponentially fashion. This just means that they are going up at a pace much faster then our normal lines. After we have plugged in a view positive numbers let's plug in some negatives. When we do this we start to notice that our graph now has symmetry to it. When x=-3, our y value is always going to be 9, and so on and so forth. The negative and positive points seem to stem off from the point (0,0). This stem off creates a curve. Now, the reason behind this curve is that if we were to take all the little numbers in between our integers we would notice that the points create that sort of curve. That is why we can't just make a v shaped graph on our coordinate plan.



Since we now know how our parabola is formed. Let us look at the what makes up the parabola. First off we have the point of symmetry. This point is where the graph splits off into two separate yet equal arcs. This point is also called the vertex. The vertex is a very important part of our graph. It tells when our parabola splits. We can figure out how to solve for the vertex by using the standard form of our quadratics. This form looks like this ax2+bx+c=0. This should remind us of the quadratic formula that we used so long ago. This will now become a vital part of how we shape our parabola. While look at our standard form we can take our b and our a terms to figure out our vertex by this formula. -b/2a. Like I have stated before finding the vertex is crucial in graphing an equation. Now, the next part of a parabola that I need to cover is the roots. We have been working with the roots for the past two lesson nows. That's right every time you are solving a quadratic for the x term you are finding the roots of a function. Why? It all deals with setting your y value equal to zero and then solving for the x to find that term. Thus, why our root terms will always lie on the x-axis. What does this mean on our graph? It means that we can now find out where our arcs touch on the x-axis. Remember since we are using quadratics we will always have two roots to find. // Checklist, Worksheet, Guides //
 * __ 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 graphic organizer is going to support the clipboard's learning style. Along with that a checklist is going to be provided for the project so people who need to have that structured style of teaching will get the chance to have it. During the lesson itself I'll be breaking down parabolas in a very step by step process. This logical and slow process will give enough backing to a clipboard style learning so they can see everything in front of them.


 * // Microscope: //** This lesson is all about analyzing the wonder of parabolas. Hopefully students who tend to enjoy diving further into their studies will be more then happy during this lesson. But, as a teacher I'll be giving the students the opportunity to analyze what a parabola is by the project that we will be doing. In order to concoct a story about a superhero one has to know who the superhero is.


 * // Puppy: //** Students who enjoy the conversation and people in general will be given time to have those discussions needed to learn. Since the project, and our lessons will focus around separation into groups the puppy style learning will be at home with the conversations that are going on. During the lesson these students will have a chance to voice their own opinions and have their peers support and or alter their own beliefs about quadratics.


 * // Beach Ball: //** In a math classroom it is awfully tricky to have those small sparks of creativity that will have get the Beach Ball engaged. Luckily, the product that these students will be making will give them the chance to have those moments of creativity. Along with that during the lesson there will be options ofr them to interact with the graphs.


 * // Rationale: //** The comic life that we are going to be creating will give the students the chance to dive into the parabolas. During the lesson along with each graphic organizer and cooperative learning technique the students will grow and become more comfortable with their own learning styles. There will also be a chance for them to express themselves in conversation and to ask me any important questions and the end of each lesson.


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


 * // Content Knowledge: //** Analyzing and being able to reflect upon a function when graphed is my lesson in nutshell. In order to fully understand a parabola, students must understand how a parabola is formed. It is almost like trying to bake a cake, you have to know a little about the ingredients before you can actually back it. Thus students will be able to understand the origin of a parabola as well as specific forms for functions so they can accurately understand what is going on.

Added with
 * Content Area ** : Algebra
 * Domain: ** Reasoning with Equations and Inequalities
 * Standard: ** Solve Equations and inequalities in one variable
 * // Content Area: //**// Functions //
 * // Domain: //** //Interpreting Functions//
 * // Standard: //** //Analyze functions using different representations//


 * // Facet: //** Explaining how a parabola came to be is an important part of quadratics. We are taking a step to connecting quadratics to a coordinate plan. When we explain what is going on we have to explain everything about it and this lesson through the product of the superhero comic can easily explain all the aspects of a parabola.


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


 * __ MI Strategies __**
 * Verbal- ** I will explain how a parabola is formed, as well as give some analogies to the outside world, such as saying that when you put a drop of water on a rock it tends to spread out in different directions much like plugging in a single point into a quadratic.
 * Visual- ** I will show graphs and equations to let them see how parabolas are being formed.
 * Kinesthetic- ** Reminding them of what a parabola looks like through hand-motions.
 * Logical- ** Allowing the students to figure out the step by step process of how a quadratic is formed from me going through each quadratic in that very same fashion.
 * Musical- ** Demonstrate musical parabolas when discuss what happens when parabolas are formed like certain drums, and how certain pitches tend to make an arc like shape.
 * Naturalist ** - Along with the musical parabolas show some natural parabolas such as valleys, spider webs, the whole sha-bang.
 * Intrapersonal ** - Students will be given time in class to reflect about this work
 * Interpersonal ** - Students will be given time in class to interact with their peers to discuss their own thoughts on parabolas


 * // Type II Technology: //** Constructing a comic life enables the students to think creatively about what is going on in the world. It will give them the chance to see that they can take an ordinary bland subject such as quadratics and turn it into a story. Using this type II technology is perfect for allowing that level of creativity.


 * // Rationale: //** The type II technology along with the tailors is heavily focused around the lesson and the product. If students feel the need to branch out into their own worlds to complete a task, that is fine by me. I want to give students the chance to learn about parabolas the best way they know how. That is I believe that I have offered enough chances for students who are of different minds to succeed in their own way.


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


 * // Formative: //** The exit ticket will give me an idea of how well the students did as they walked out. This will show that their level of understanding complies to the standard. Along with this checking for understanding tool, I will be using a checklist which will offer key insights into what I want to have happen in this project. It will be a more straightforward rubric that will allow the students to self- evaluate their work. By the amount of days spent with these students I will determine what they believe is going to happen.

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 * // Summative: //** Detective Comics is looking to expand their comic book database to a new line of ideas that they haven’t yet turned to, which are educational comics. For this new branch of the Detective Comics Corporation they are sending out a call to all aspiring comic book writers and enthusiast. Your team consists of a writer, a editor, and an illustrator. Together your task is to make an educational comic about the greatest mathematical hero of all time, the parabola. You need to make sure that it is fun and engaging to students while conveying the information needed to support their growing minds.
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