L5+Fletcher,+Caleb

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

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : Mr. Fletcher ** **__Lesson #:__ 5 __Facet:__ Interpretation**
 * __ Grade Level __**** : High School __Numbers of Days: 4__ **
 * __ Topic: CSI AX2 __**


 * __ PART I: __**

Student will understand that using quadratics can solve real world problems Student will know about the meaning of the vertex, roots, and the importance behind standard and vertex form Student will be able to evaluate a real world problem.
 * __ Objectives __**

Product: Multimedia project- Prezi

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: ** The students will be analyzing real world parabolas so that they may solve for their roots thus solving equations with one variable.

During the lesson the students will be using an idea wheel to get their first thoughts about famous natural arches and parabolas down on paper. Also this will spark their imagination so they can use their problem solving to acquire the equation to those parabolas. Also the students will be filling in their thoughts on certain topics. They will be thinking about the lesson material and writing down any information they find confusing so I can help them further their knowledge.
 * __ Assessments __**
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction- **

In order to see how the students are learning, there will be a rubric attached to the final project. This rubric will have clear guidelines that will give the students a reliable source to show how they can further their improvement. Along with this the students will take a self-poll, They will be answering questions that pertain to how they did, this will be done in poll form so I get to see how the class thinks whilst the individuals get a chance to voice their opinions.
 * Section II – timely feedback for products (self, peer, teacher) **

Students are going to create a multimedia presentation that will encompass a Google Earth video along with various pictures. This project is going to be based around finding the equations of famous parabolas and giving them a slight backstory. This backstory will add more depth to the project and allow the students to indulge in the material. From there the students will show their presentation to the class explaining how they found the equations of the parabolas
 * __ Summative (Assessment of Learning): __**


 * __ Integration __**
 * Technology: ** We will be using the Prezi technology to perform a multimedia presentation. This technology promotes the use of multiple intelligences along with a incorporating a variety of medians along with it. For instance the students can add not only music but videos and images as well. It's a good way for the students to indulge in their creativity and show their ingenuity with parabolas.


 * History: ** Exploring the wonders behind some of the famous landmarks
 * Geography: ** Learning where these parabolas are located.

We are going to be using an idea wheel and a fill in the thought exercise during the lesson. This graphic organizer is more or less a creative way to get the kids brainstorming about famous parabolas during our lesson. In one space the students will think of a place and then in the next place they will look for famous architectural feats and then they will list famous natural parabolas. Along with this the students are going to fill in their remaining thoughts about natural parabolas in our world today. This will allow the students to reflect on what they have learned thus far.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

Groups are going to be separated by famous artist. Why famous artists? Well, because they are the ones that constructed some of these famous arches. This will get the students a bit more interested in the history behind these famous parabolas. It's just a different way to think about how some of the famous pieces of architecture. The products require a group of four to complete. Students are going to have to get into the mindset of fictional world creators. In their groups there is going to be one Manager, the group’s coordinator and task manager. This means that when the students are trying to think of the next step to do the Manager gives them an idea on what they can do next. A surveyor will be next an individual who is in charge of deciding what architectural parabolas and natural parabolas the group uses during their project. They are also in charge of searching for information about these parabolas as well. The other member of the group is going to be the architect who takes the information that he has gathered with everybody else, and is in charge of constructing the Prezi. Finally, the last position in this group is going to be the historian. Who takes all of the information researched and complies it into a nice summary, with the help of his or her group. This historian will make sure that the information is kept up to date and is viable.
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**


 * __ MI Strategies __**
 * Visual- ** Show them real-life scenarios and once again show the step-by-step process out on the board. Also in the hook the students will be searching for the parabolas that are going to be surrounding them.
 * Verbal- ** Have a catch word “Muffin” during my hook so that when the students hear muffin they will instant look or think of a parabola. Along with this the students will see me do some physical step-by-step math with the help of various parabolas that I have found.
 * Intrapersonal- ** A student will have the opportunity to think of parabolas while brainstorming by themselves about the many parabolas in our world.

**Interpersonal-** While working on their projects the students will have be in groups thus allowing for them to have a conversation or whatever is necessary to fill that social requirement they have for learning.
 * Kinesthetic- ** They can construct their own parabola to play with.
 * Musical- ** They’ll find that musical instruments have a variety of parabolas in the them, along with that I’ll talk briefly about Tool and their song parabola and how it pertains to that mathematical nature.
 * Naturalist- ** A variety of parabolas are going to be shown during the hook and also during the project so the students who want to know more about these parabolas outside the classroom can find them.
 * Logical- ** This whole lesson is about looking at a natural parabola and then logically figuring out their equations through the lessons we have learned so far.


 * __ 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. //

On the very first day for students I will be talking about my **“Do or Do Not there is No Try”** policy. This policy of mine is revolves around the students creating a plan for tackling assignments they have missed. There are many options for them to do, but in the end they will have to tell me how they are going to accomplish this task. For instance, if a student is light they might ask a friend to get the notes or they could use the online resource database that I have been constructed since the start of this lesson. Either way, they will have to come see, or I will have to ask them what their plan I is to figure how to complete assignments. The students either come up with the plan or they don’t they can’t put half of the effort into them because they weren’t there.
 * Plan for accommodating absent students: **


 * __ Extensions __**


 * Type II technology: ** We are going to be using a Prezi, which the students will create a multimedia presentation on the parabola shapes that need to be included in this new world.


 * Gifted Students: ** If a student is getting the lesson so far I would proceed to ask them to dig deeper into the history of the parabola. For instance, with the St.Louis example a student may want to talk more about the western expansion that was going on during that time. Also if a student is excelling with the whole design of the Prezi, ask them to use more of the complex features like themes or organizations charts. If a student has gotten the math, then I’ll be asking them to find harder parabolas to equate.

// Laptop, Internet Access, Lcd Projector, Various pictures of famous parabolas, handouts, TI-84 project, TI-84(or Graphing calculators) //
 * __ Materials, Resources and Technology __**


 * __ Source for Lesson Plan and Research __**

http://www.aplusalgebra.com/parabolas.htm - Ideas for the various famous parabolas. http://architecture.about.com/od/arches/Arches_Great_Arches_Engineering_and_Construction_of_Arches.htm - other ideas for parabolas http://en.wikipedia.org/wiki/Valley#Famous_valleys - the final selection of parabolas http://mscir.tripod.com/parabola/ - Creates an image of a parabola http://prezi.com/ - The site where we will be making our product. http://pixlr.com/ - An online photo editor [] - Parabola by Tool [] - A good resource site


 * __ 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 desks are going to be set up in equal groups formations (4 desks per group) that resemble mini arches.

Day 1:
 * Review parabolas and how to derive an equation from one (10 minutes)
 * Take the class on a journey through the halls of Parabola ( 3 minutes)
 * Talk about the importance of the video and the wonders of natural parabolas (7 minutes)
 * Bring up the St. Louis Arch and solve for it’s own equation (20 minutes)
 * Brainstorm other famous arches, at this time the students will be broken into groups (15 minutes)
 * Solve for an arch found (15 minutes)
 * Tell them to find the equation to one of the arches brainstormed or another one they can think of, and if they need help figuring out the equation I’ll be walking around (10 minutes)

Day 2:
 * Review the St. Louis arch example (5 minutes)
 * Talk about the equations of their arches, have a few students come up to the broad to show what they did to find their own equation (25 minutes)
 * Explain their project, which has them using a Prezi to show us where in the world their arch is, along with that they will provide a digital picture of their arches with their own parabola photo-shopped. (15 minutes)
 * Go into more depth about the online Photoshop and then talk about their product more about their final project which is a multimedia presentation using the website Prezi (25 minutes)
 * The rest of the class will be given to the students to explore Prezi and the wonders behind it. ( 10 minutes) They’ll be asked to construct their layout for their Prezi for homework

Day 3:
 * Using their layouts they will construct their Products (80 minutes)
 * During the time when they are constructing their products I will be calling them up one by one and having a brief interview with the students about what they have done so far and what they would like to see in their presentation (80 minutes)

Day 4:
 * The first few minutes of class are devoted to the students who might need to polish their Preezyies (20 minutes)
 * The rest of the class is devoted to their presentations (60 minutes)

On that first day the students will sit down, and we will review what we have done so far in a dramatization of an doctor’s office where we have to diagnosis the patient. After all, the previous product was to create a podcast of someone in a career that uses deductive reasons. Thus, when the class starts I’ll do that brief dramatization with the students getting their minds back into the state of quadratics. After this brief review I’ll take them on a journey, which shows a plethora of parabolas man-made and in nature. This journey will take place in the hallways and around the school. We’ll be moving quickly and during this journey I’ll be telling an unrelated story about muffins. Why? Because every time I mention the word muffins I am going to throw my hands up in the air like a parabola which will let the students know if they are close to a parabola. After we have finished this journey I’ll talk about what they have seen and ask how many parabolas were spotted. Some might say random images, and some might say parabolas. In the end I’ll explain to them the multitude of parabolas in our lives and how we can actually figure out their equations. Meanwhile, whilst I’m talking to the kids Tool’s song Parabola will be playing in the background.
 * Tailors: Visual, Logical, Verbal, Musical, Naturalist **

After we have completed this video we’ll start diving into the lesson. The students will be separated into groups, and my idea wheel graphic organize will be handed out. This will give them the chance to brainstorm different famous arches, as well as have a place to keep their measurements down. After the students have received their own graphic organizers, I will proceed to show them my own famous arch that I have found. This will give the students an example of what they should be doing in order to derive the equation of a natural parabola. I’ll have to make sure I mention that these are going to be perfect parabolas that we are creating, after all most parabolas in a nature may have a general shape by they are not straight edged. I’ll go through each one of steps to how we go about solving the equation for one of these real-life parabolas. While I am going through my example I will be using my arms, and having the students join me to show the different parts of the parabola. From there I will split off the students into various groups so they can brainstorm. These groups will be based upon their favorite historical time period. (I hope that this will spark some ideas in their heads of some famous arches from that time period as well). From there I’ll ask each group to brainstorm a list of 5 famous arches so they can have an idea of what some famous arches might be as well as present more ideas for their fellow classmates. After this brainstorm session I’ll pick one of the arches and ask a group to find me it’s dimensions, another group to tell me a little more about the parabola, another group will be talking about where it’s located, and the last group will check my work as I figure out the equation of a parabola. Once that last example is done we will move on and I’ll bring out the idea spinner will give the students a chance to think about some of the rough patches they are having with the lesson based upon pure fate. We will go through a few rounds of this answering any question the students are having.
 * Tailors: Visual, Logical, Verbal, Kinesthetic, Naturalist, Interpersonal **

The product that we are constructing is known as a Prezi, which is a much more powerful version of a power point. Along with this Prezi the students will be asked to use Google Earth to create a map of all their famous parabolas. The total number of parabolas that will be talk about will be three. There will be a brief introduction to the parabola, and the students will answer a few question. Where is it? What is it? What’s cool about it? How about a little back-story? After these questions the student will show us their equation they have found by using the dimensions of the natural landscape. From here the student will construct a multimedia presentation of all the information. This project will have a brief layout that I’ll go over to make sure that everything is going according to plan. The student will work by themselves constructing this presentation of the three parabolas they have found and their equations.
 * Tailors: Intrapersonal, Visual, Logical, Naturalist **

The students will end up presenting this material in front of the entire class. A rubric will be handed out to them prior to this presentation that will be graded by the teacher. This will be the Teacher’s rubric. Now, during the presentation the students will also be handed a peer rubric that will be used to give feedback as well as general idea of what the other students thought of their projects. Finally, the students will participate in an online poll that will ask them questions about their evaluation on themselves.
 * Tailors: Visual, Musical (depending on the project), Logical, Interpersonal **

Content Notes:

St. Louis, the capital city of Michigan is where we are going for this lesson of ours. In St. Louis there is a architectural feat that stands out from most landmarks, it’s the giant metal arch that looks over the great Edison Bridge. This St. Louis Arch is also known as Jefferson Memorial Expansion Bridge, in honor of the Louisiana perchance. Anyhow, here is what we know about the grand arch. First off, the arch has a height of 630 feet, and the remarkable thing about the this specific architectural achievement is that it’s also 630 feet between it’s legs. Meaning the St. Louis arch lies within square, which is 630x630. Anyhow, we know that a parabola is a symmetrical geometric figure by our previous lessons pertaining to the anatomy of a parabola. So we know that a line of symmetry must line between both legs, thus cutting the parabola in half. This will make our vertex of the St. Louis arch (315, 630) (half of 630 will give us the in-between, and the tip of the arch as will) Now that we know our vertex we can plug this number into our vertex form.

Equation:

a(x-h)2+k=y

So, a(x-315)2+630=y

Now we have to figure out a point to use in order to find the standard equation to the St. Louis arch. If we were to plot the arch on a coordinate plan we can put one of the legs at the origin. Thus, let us use the point (0,0) as one of our points. So from here let us construct our vertex form equation again.

a(-315)2+ 630= 0

99225a+ 630 =0 99225a= -630

a =-2/315

(-2/315)(x2-630x+99225)+630=0

(-2/315)x2+4x-630=0

So this is our final equation.

Now, students are going to be using other various famous landmarks or natural occurrences to use for their own parabolas. So what in order to help the students out try to think of the natural landmark as on a coordinate grid with one of it’s legs crossing the origin point. Much like I did with the St. Louis example. From there just follow the steps of solving an equation with a parabola. The students should be getting the other points by asking for their dimensions on various search engines or through encyclopedias whatever floats their boat.

Once everything is said and done and the students have calculated thus far for the equation of a parabola they need to learn how to graph it. Get a TI-84 or any sort of graphing calculator; the majority of the students have a higher possibility of getting one of these TI-84’s then anything else. Now, click on the y= button type in the formula for the parabola you have calculated for, if need be trying using a ^ for a power sign. Anyhow, once they formula is in click on the graph but and the graph will pop up. If there is any help needing zoom, tell them to hit either zoomfit or zoom square to get everything back to normal.

// Rubrics, Graphic Organizers //
 * __ 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: //** In this lesson of ours the students will have a rubric that will list the designated items needed. Also, the information that I am requiring is very step-by-step, information and math. Along with the math portion we will see a very straightforward procedure that is right up the ally of most clipboard learners.


 * // Microscope: //** This lesson is focused around taking a natural parabola and analyzing it. Students will get the chance to dive deeper into the mathematics behind what we have learned for so long. This lesson will take the real world and put it into the classroom thus having students analyzing the bigger world that is around them with the math they are learning at the moment.


 * // Puppy: //** During the brainstorming session of this lesson the students will be having a conversation with me and the rest of the class. This will spark their interest, and then the group work on the product they will have more chances to converse with one an other and create an environment for them to thrive.


 * // Beach Ball: //** The creativity in their products will allow them to choose what parabolas they can choose. There is going to be some structure but they can set up their Prezi anyway they want to. This will give students the ability to explore but in their own sections.


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


 * // Content Knowledge: //** The knowledge in this section really catches the students. It combines both common core standards into a nice little package. Students are not only solving equations with one variable but they are analyzing graphs, and to put the icing on the cake the students are going to be analyzing real life parabolas. This will let them see something beyond just graphed parabolas.

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: //**


 * // Facet: //** Interpretation is the facet being used in the lesson. Students are going to be interpreting the world around them into a something that is applicable in the classroom. It’s taking all the math that we have learned and actually using it to see through a new lens, a lens that shows how math is an integral part of our world.


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


 * // MI Strategies: //**
 * Visual- ** Show them real-life scenarios and once again show the step-by-step process out on the board. Also in the hook the students will be searching for the parabolas that are going to be surrounding them.
 * Verbal- ** Have a catch word “Muffin” during my hook so that when the students hear muffin they will instant look or think of a parabola. Along with this the students will see me do some physical step-by-step math with the help of various parabolas that I have found.
 * Intrapersonal- ** A student will have the opportunity to think of parabolas while brainstorming by themselves about the many parabolas in our world.

**Interpersonal-** While working on their projects the students will have be in groups thus allowing for them to have a conversation or whatever is necessary to fill that social requirement they have for learning.
 * Kinesthetic- ** They can construct their own parabola to play with.
 * Musical- ** They’ll find that musical instruments have a variety of parabolas in the them, along with that I’ll talk briefly about Tool and their song parabola and how it pertains to that mathematical nature.
 * Naturalist- ** A variety of parabolas are going to be shown during the hook and also during the project so the students who want to know more about these parabolas outside the classroom can find them.


 * Logical- ** This whole lesson is about looking at a natural parabola and then logically figuring out their equations through the lessons we have learned so far.


 * // Type II Technology: //** We are going to be using a Prezi, which the students will create a multimedia presentation on the parabola shapes that need to be included in this new world. Now with this Prezi, the students are going to be creating a presentation of multiple parabolas. It gets them using a technology to create product that will sum up their learning. It takes the information they are going to be looking up and combines it into a well done slide-by-slide presentation.


 * // Rationale: //** Each of the MI are going to be used during this lesson. My hook as well as the product itself mainly accomplished this. In the hook I’ve done various parts to tailor whatever information my students have to their own learning style. This will get the students engaged and willing to participate. For instance, one of my students could learn best through music and because of that I’ve incorporated musical instruments into my opening hook.


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


 * // Formative: //** The big part of the formative assessment for these students is feedback. I’ll be talking with their groups and having small meetings where we talk about our rubrics. Their graphic organizers and thinking activities are another great way to meet to see what they have done to make my own feed backing complete.

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 * // Summative: //** The students are going to be asked to research earth on the subject of parabolas. Why? So they can bring back the information to World Builders incorporated who are in charge of creating vast new worlds using different geometric shapes and Earth has been known for some famous ones. With your team you’ll be building a presentation to show to your bosses on how the information could be used to benefit other planets by reporting on this one.
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