L2+Fletcher,+Caleb

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

**LESSON PLAN FORMAT**


 * __ Teacher’s Name __**** : ** Mr. Fletcher **__Lesson #:__ 2 __Facet: Perspective__**
 * __ Grade Level __**** : ** High School **__Numbers of Days:__ 3**
 * __ Topic: CSI AX^2 __**


 * __ PART I: __**


 * __ Objectives __**
 * // Student will understand that quadratics can be solved in multiple ways. //**


 * // Student will know tips about factoring, completing the square, the square root method, and the quadratic formula. //**


 * // Student will be able to do solve quadratics //**


 * // Product: Video Game //**

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

// 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 //


 * // Rationale: //** // The Common Core Standards will be meet by the students learning the variety of strategies to solve a quadratic, along with various tips that will make these strategies easier to solve. //


 * __ Assessments __**


 * __ Formative (Assessment for Learning) __**


 * Section I – checking for understanding during instruction **

While I am teaching the lesson students will be giving me thumbs up or thumbs down. Thumbs up will show me that they understand the lesson, and thumbs down will tell me that there is probably an area I need to cover more.


 * Section II – timely feedback for products (self, peer, teacher) **

Using a checklist the students will see how far they have come when they are constructing this product. When the video games, which are the product, are presented fellow classmates will be given time to have feedback with the creators of the video games. Finally as a teacher I will grade these video games based upon a rubric.

Using a program called //StencylWorks// the students will be constructing a flash video game that will test the other student's skill and mathematical expertise. By creatively introducing problems that use quadratics the students will understand how to tier different quadratic problems to make the game progressively more and more challenging.
 * __ Summative (Assessment of Learning): __**


 * Art: ** When constructing their Video game students will have to recognize what colors best go with the area around them, and what colors best represent what they are trying to show the player.
 * Science: ** Most of these games the students will be generating will require knowledge of physics and gravity to perfect them.

By using the graphic organizer "Problem/Solution" students will be able to write down a quadratic and then list the probable ways to best solve it. They will also be working in a large team, breaking down into pairs, and then going at some of these problems solo. This method will allow a large network of thoughts about quadratic to occur and thus the students can focus their own personal tips and strategies to solve a quadratic.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

When these individuals are working in a larger group, which mostly will consist of 4 people, there roles will entail to be a recorder, a contributor, and an analysts. These roles mean that someone will write down the groups thoughts, another one will give ideas of problems and possible solutions, and the analysts will take all their thoughts and synthesize them.
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**


 * __ MI Strategies __**
 * Verbal ** - Explain to the students how to choose the best procedure, and relate it to an analogy


 * Visual ** - Draw out each quadratic equation and show the process on how to choose and how to solve them.


 * Interpersonal ** - Group the students up into teams so they can work out the answer together


 * Intrapersonal ** - Once the group work is done I'll have the students work by themselves and think about which procedure works the best.


 * Kinesthetic ** - Figure out someway that students can physically hold onto a quadratic so they can move it around to figure out the best result. Having an actual tangible equation.


 * Musical ** - In the background have some music going while they are working in their groups


 * Naturalist ** - Talks about how quadratics relate to the world outside.


 * Logical ** - Allow them to dive deeper into the quadratic to understand the logical behind it.


 * __ 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. //

Students will be working together in a group setting for the lesson. This group of students will be a safety net for each other thus if one student is absent the others will make sure that they are caught up. Along with this if a student is in dire need of more assistance they can come see the teacher to discuss a plan that will best for them. There will be a wiki set up with all the notes that have been taken thus far, so a student will have the ability to check out what they have missed online.
 * Plan for accommodating absent students: **


 * __ Extensions __**

Using a program called //StencylWorks// the students will be constructing a flash video game that will test the other student's skill and mathematical expertise. By creatively introducing problems that use quadratics the students will understand how to tier different quadratic problems to make the game progressively more and more challenging.
 * Type II technology: **

StencylWorks has quite a database of unique features. Students can create a simple game, but for those more gifted students I would have the tap into the potential of stencylworks so they can use quadratics more as a mechanic during the game then as a random portion of it.
 * Gifted Students: **

// Handouts //
 * __ Materials, Resources and Technology __**

// LCD Project //

// Laptops //

// Stencylworks //

// Knowledge of Stencylworks //

// Dongle //

// Paper //

// Graph Paper //

// Problem Solution Graphic Organizer //

// [|http://www.youtube.com/user/EpicStencylTutorialz#p/u] //
 * __ Source for Lesson Plan and Research __**

// [] //

// [] // /

// community.stencyl.com/index.php?topic=1233.0 //

// Each of these links provides the students with resources to construct their very own video game. The first one is to a set of video tutorials that will best help them out. The second link introduces them to a game that will take them through each of the steps to construct their own video game, the next game is to show more steps to creating your own game, and the last link is to a discussion about how to create your own stencylwork games so students can get their own feedback if needed. //

// [] -Provides students a variety of tips for factoring //

// [] -Gives students tips on the quadratic equation //

// [] - Offers students different tips to completing the square. //


 * __ PART II: __**

For this lesson the desks will be arranged in centers, which will give students a better time talking with peers.
 * __ 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) //

Agenda:

Day 1:
 * Watch Portal Video and explain how it deals with quadratics (15 minutes)
 * Go over Web-quests, and review what has been taught so far (15 minutes)
 * Introduce tips and other strategies to make solving quadratics easier (20 minutes)
 * Separate them into groups and have them figure out which strategies would work best for each quadratic given (20 minutes)
 * Question, and help time. (10 minutes)

Day 2:


 * Introduce StencylWorks, as well as introduce their project. (10 minutes)
 * Give a tutorial of StencylWorks as the students work on their own project, after they have been given a partner to work with. (40 minutes)
 * Have them play with the system for a little bit by making a very short game (30 minutes)

Day 3:


 * Talk about the students' tool-belts they have created and provide a few practice problems of various degrees of difficulty. (20 minutes)
 * The rest of the class will be devoted to their projects, so they can have enough time to make everything work. (60 minutes)

Day 4:


 * Students will present their video games (40 minutes)
 * Students will play everybody else's video games. (40 minutes)

We have constructed a tool-belt of different strategies for solving quadratics. We know that we can tackle problems that deal with the square root method, completing the square, factoring, and the quadratic formula. This means that we have a set of tools and we know how to use them. So, know we need to figure out when we are approached by a random quadratic which tool best work. **(Students will know how to solve quadratics in multiple ways)** When the students take their seats I will be discussing with them a love of mine, which just so happens to be video games. From shooters, to puzzle games I love them all. But there has always been one series of games that have stuck out the most of a kid like me. These games came from a series known as //Portal//. Now, these games involve creating portals to solve your puzzles and these puzzles tend to be very intricate and complex. That is way there are multiple ways to go about solving a puzzle. Much like //Portal// there are many different ways to solve a quadratic. We remembered our first lesson. Now, the purpose behind the //Portal// video that I have shown is to teach the students that there may be many solutions to a problem but there usually tends to be a better way to solve it. That's what this lesson is all about, finding the best way to solve a quadratic? Thus our students will be focusing on the tools that they have and looking over example problems. We know that we can solve a quadratic in multiple ways; now it's time for us to figure out which way can best solve the quadratic. This technique of choosing the best solution is what life is all about. It's developing a simple tool belt and then using the right tool that will best fit that situation. For instance, a student is in the hallway and at the moment he can see a rather angry man coming towards him. In his experience in life he has a select number of tools, he has to determine which one will get him out of this sticky situation.


 * Where, How, Why, Hook Tailors: ** Verbal, Visual, Logical

Once we've talked about how this ability to solve a quadratic in multiple ways we can use this knowledge to what we have learned thus far. The first step to do is to bring up our web-quests that we have made. Once we have them up I will present a variety of problems. These problems will require one of the four tools that we have that need to be used. Once they are up on the board will we talk about how we can notice which strategy to use? These problems will focus on observation, and the ability to differentiate between all of our strategies. For example the classroom conversation might sound like this "Alright, we have this problem x2=9 which strategy will best solve this problem." "How about factoring?" "No, factoring would require more variables shown!" "How about completing the square?" "Won't that be too much work?" "I know, let's use the square root method!" "Now, that sounds like a plan!" This is what I hope to accomplish in my lesson. The students will look at a problem and try to deduce what the best strategy to use. Now, in order to do this the students must have a complete knowledge of all four tools, which are factoring, the quadratic formula, completing the square, and the square root method. Now once we start this conversation and after solving a few example problems the students will be separated into teams. Once in teams, the graphic organizer "Problem/solution" will give the students a better way to organize their own thought patterns. Once they have a graphic organizer the students will be given a few examples to work on. These groups will give them the chance to talk, and to explore what they believe is to be the best strategy. Now, from there the students will be broken up once more into pairs to tackle some more complex problems. Finally, so they can feel like a detective themselves the students will go off into their own solo work trying to deduce the best way to solve a quadratic. Now these students when they are solving their own problems can use whatever method they wish to remember which strategy to use. Thus they can sing a song, do some sort of body movement or relate it to something.


 * Equip, Explore, Rethink, Revise, Tailors: ** Verbal, Visual, Interpersonal, Intrapersonal, and if they choose Kinesthetic, Musical, and Naturalist.

Since we have talked about video games in the beginning of the lesson it only seems natural to make the product of everything that we are learning a videogame. Using a wonderful free program known as Stencylworks, the students will construct their own flash games. I will be separating them into groups of four so one of them can come up with the examples of problems, another can one can work on how to create the game, another can figure out what they want the game to be about, and the last individual will present their game to the entire class. Now, each student will be given the chance to be as creative as possible in this manner. From here I will be providing the students with assistance as they try to figure out the programs and problems. The way they will go about it is that they will have to tier their problems. Since this is a video game they have to make a variety of difficulties. Thus students will learn what is a complicated quadratic and what is a simple quadratic.


 * Equip, Explore, Rethink, Revise, Tailors: ** Logical, Interpersonal, Artistic(Visual)

Now when everything is said and done the students will be given a checklist as well as a survey. These surveys will ask how the team worked with each other and how the work was split up. Whereas the checklist that is provided for them will ask if they've done the work that is needed. The last portion of feedback will be a rubric that I have passed out. This rubric will make sure that students remember that math that is needed in this project. These projects are going to be used as a way to help the students study for an exam as well as practice the different ways to develop some mathematical detective skills that will be needed much later on.


 * Evaluate, Tailors: ** Interpersonal, Intrapersonal, Logical, and Visual.

Students will learn a more in-depth knowledge over the strategies that we have learned about so far. First we start off with the square root method. Now, if we see an x2 all by it's lonesome with only a coefficient to bother it, and then there is a good guess that we will have to use the square root method. Why? The main reason why we know that this is the best method is that it's the fastest way. If we are completing the square we are adding in numerous steps that don't need to be there, and the same goes for the quadratic formula. If we were to factor it the problem would be that we would get to x's in a row, which does us, now good. Thus, when we see a single squared variable a first thought in our head should be to use the square root method.
 * __ Content Notes __**

Now, after we see which problems can be best used by the square root method, let's take a gander at factoring. The best way to know when to factor is to look at the problem, and develop an observation skill. If the numbers seem like they correlate with each other, then your best bet would be to use factoring. For instance if we were to see a problem that resembled x2+4x+3, and a problem that looked like x2+4x+5 We take a look at the first and think about each of the factors. Always look towards the constant term first when you are factoring. If you are able to find two factors of this constant that add up to the coefficient of the x then you have found your solution. So, when we are looking at this problem we notice that 3's factors are 3, 1, where as 5 has the factors 1, 4. Which one of these factors has the ability to add up to four? As we can see 3+1=4. This is very important step to remember. So, when you are looking at a variety of quadratics always looks at the constant term. When you see a quadratic that is not equal to zero, and when you are dealing with factoring make sure that this equation is equal to zero. Factoring doesn't work unless the equation is equal to zero. This is because we want to be able to set each x equal to zero because we are trying to solve for the roots of the parabola. Once you have done this and taken a gander at the constant term in the end try to figure out if there is a simple way these numbers fit together.

Factoring, and square root method are now under our belts. Let us take a look at the best way to use the quadratic formula. Now, the cool aspect of the quadratic formula is that when all the other formats fail, the quadratic formula tends to win out in the end. The reason why we tend not to use the quadratic equation all the time is that it's a very long-winded formula and takes more time then if we were to factor it. So, it is true that the quadratic formula can solve just about any quadratic but these quadratic that it can solve tend to look something like this 6x2+5x- 20. Taking a look at this equation we know that it would take us longer to factor this quadratic, and we are not even too sure if it factors. Also, there is another x in here so the square root method doesn't appear like it would work. Along the same lines since we can't really figure out how to factor out anything from this equation completing the square also looks like it's another miss. To wrap it all up, when all else fails use the quadratic formula.

The last strategy that we are going to talk about is for completing the square. Now remember that completing the square has us using the knowledge of foiling to its greatest ability. Which is when we see an equation that looks like this (x+1)2, we have to square the constant to figure out our c term, and then double that constant and add an x to get our b term. This means that (x+1)2 is equal to x2+2x+1. Now that we understand this nifty trick we can use it to complete the square. Now the good way to spot completing the square is when we see an equation like this 4x2+8x+12=4. There is a want to subtract the four and then combine it with the twelve but that will make our process longer. So instead we are going to divide by 4 so our equation looks like x2+2x+6=1, then from here we'll remember that in order to complete the square we have to subtract -2 from both sides. Thus we will have a quadratic that can be simplified to down to one term squared. To sum it up, use the completing the square when you can easily see a squared factor in the equation and it is equal to a constant that if changed would mess up the entire function.

// Rubrics, Handouts, Checklist, and surveys. Along with an opportunity to print out their web-quests. //
 * __ 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: //** Providing a checklist, and a step-by-step process on how to solve quadratics has given the clipboard's organized, and rather structured learning style room to blossom. Since I have laid the lessons out and the process on how to construct a video game in a rather straightforward manner that will also help those students that enjoy placing ideas in an organized manner.


 * // Microscope: //** This lesson about quadratics is all about going deeper into how they work. This deeper exploration will excite those students that have a rather microscope-like learning style. With our graphic organizer we will not just be writing down the steps like we did in the previous lesson, instead we are going to be looking at the multiple ways to solve a quadratic. Thus, a microscope has a chance to analyze a problem and pick them a part piece by piece to figure out the best solution to the equation.


 * // Puppy: //** After each lesson students will be put into teams. Thus they will have the chance to talk and communicate with their peers about the information provided for them. Since, a puppy learner needs to have that chance to talk and have that conversation about the material then this lesson will provide the students time for groups and partners.


 * // Beach Ball: //** Beach balls need the chance to have a spark of creativity. If I don't provide them choices then they tend to feel limited in their own learning. Thus during our final assessment they can run wild and create the video game that they want to make. They get too decided how to best present the material and then from there they get to just run wild.


 * // Rationale: //** In each part of this lesson we see the learning styles being used. From keeping a structured checklist to allowing them the freedom to create a game that is unique in it’s own way. During this lesson the tips and tricks we have learned will go along with each learning style. Not only does it give the students the option of figuring out quadratics, it allows them to solve them their own way.


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

If we take a gander back at my notes we see that the common core standards are covering the subject matter. Part of solving multistep of equations in one variable is having the ability to recognize the various tips and tricks of quadratics. Thus, it covers that common core standard about solving equations and inequalities in one variable.

Common Core State Standards
 * // MLR or CCSS: //**

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


 * Rationale: ** The Common Core Standards will be meet by the students learning the variety of strategies to solve a quadratic, along with various tips that will make these strategies easier to solve.


 * // Facet: //** The facet that I am covering is perspective. The perspective that a student needs to take is unbiased view of a quadratic. This means that while a student is trying to solve an equation they need to take a look at the problem from all angles changing their perspective as they go. That is the purpose behind all of these tips and tricks being taught to them. So they can have the ability to change their perspective on a certain equations to develop the best plan possible.


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


 * __ MI Strategies __**


 * Verbal ** - Explain to the students how to choose the best procedure, and relate it to an analogy


 * Visual ** - Draw out each quadratic equation and show the process on how to choose and how to solve them.


 * Interpersonal ** - Group the students up into teams so they can work out the answer together


 * Intrapersonal ** - Once the group work is done I'll have the students work by themselves and think about which procedure works the best.


 * Kinesthetic ** - Figure out someway that students can physically hold onto a quadratic so they can move it around to figure out the best result. A tangible equation.


 * Musical ** - In the background have some music going while they are working in their groups


 * Naturalist ** - Talks about how quadratics relate to the world outside.


 * Logical ** - Allow them to dive deeper into the quadratic to understand the logical behind it.


 * // Type II Technology: //**

Using a program called //StencylWorks// the students will be constructing a flash video game that will test the other student's skill and mathematical expertise. By creatively introducing problems that use quadratics the students will understand how to tier different quadratic problems to make the game progressively more and more challenging.

Now the reason why I have used a game as well as breaking up the lesson into those tailors, is because a game gives a student the drive to use the various tips. These clues that have been based unto us need to broken down for each student. When a student find his or her tool belt and their own way then they are more likely to enjoy quadratics. When someone plays a game they develop their own strategy, which is exactly the reason behind the product and the tailors.
 * // Rationale: //**


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

After each lesson there will be a chance for the students to tell me about their own issues with the lesson as well as do a simple handout that I have given them. This handout consists of quadratics and a chance for the student to use their own strategies to tackle each problem that comes their way.
 * // Formative: //**

Now when these students are working diligently on their products I’ll be telling them that Blizzard Games are looking for their next big hit. They want to start tackling educational games and they know that young minds are the best place to get it. So you and your group of designers are asked to make a small sample of how math can be incorporated into the game.
 * // Summative: //**

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