L5+Emery,+Jordan

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


 * __Teacher’s Name__****:** Ms. Emery ** __Date of Lesson__:** Lesson 5 (Self-Knowledge)
 * __Grade Level__****: **10 ** __Topic__:** Functions

Students will understand that functions have various real-world applications. Students will know the definitions of degree and logarithm and will know the techniques substitution, factoring, and the quadratic function. Students will be able to compare methods of solving functions and apply their knowledge to real world experiences.
 * __Objectives__**

Maine Learning Results: Mathematics - D. Algebra Functions and Relations Grades 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques. a. Recognize the graphs and sketch graphs of the basic functions
 * __Maine Learning Results Alignment__**

There are many formative assessments of learning in this lesson. Many of them are self-assessments, however, this is the best type of assessment for students to gauge their understanding of the material. The first type of formative assessment that is designed in this lesson is when students are in their Team-Pair-Solo structure. They will students will begin working on the graphic organizers to compile information about each of the topics according to which they chose to do first. Then, they will break into pairs to determine which function they believe is appropriate to model the real-life situation. Finally, the student will work on his or her own to complete the solving of the problem. This allows me to see where everyone is at in terms of understanding functions and solving for x and it provides students with a self-assessment. Another way that they are formatively assessed is by me going back and changing one of the variables that was proposed to them in the beginning of class. They will have to go back and explain their same reasoning with a different variable to compare and contrast the differences in the situation. Students will also be formatively assessed by brainstorming to explore the each of the situations further, looking for more evidence on the matter. Students will use this time to electronically submit their answers via Google Docs and a bar graph will be formed. Any "other" answers will be addressed and clarified. Students will work with their teams to compare answers and correct any mistakes they had. After the group discussion, students will be able to hold mini-conferences with other students and teachers at the end of class and in a wiki discussion. They will be able to make any alterations they feel necessary before moving on to modeling their final task. The final way that students are formatively assess is by forming a "closing circle" to discuss the happenings of the day. Students will be asked to address (1) their answers and (2) what they felt the big idea is. I will note the biggest understandings and complaints and provide feedback (both in a group and individually) for major concerns.
 * Rationale:** Students will work with the solving for "x" techniques learned in last lesson along with their graph recognition skills to better understand the characteristics of graphs and the way that they translate into our everyday lives.
 * __Assessment__**
 * Formative (Assessment for Learning)**

Students will create a short film (no more than five minutes) that addresses one of the ways to solve a function. In groups of 3, students will find a real-life example that incorporates their assigned function. In the movie, they need to address (1) their problem, (2) what function models their problem, (3) what method they use to solve the problem, and (4) how to solve the problem. Students will be asked evaluate other's performances (as well as their own) for the use of functions and methods to solve the function in their movie. Students will be assessed using a checklist.
 * Summative (Assessment of Learning)**

__Technology:__ Students will be asked to do a majority of the lesson on a Webquest. Students will also be asked to create an iMovie to demonstrate their learning on the applications of functions and why solving equations and being able to recognize functions is useful.
 * __Integration__**

__Social Studies:__ Students will consider various issues throughout the world and apply mathematical functions and equations to try and solve the problems that occur. They will have to think about what problems they need to address or what factors may affect the outcome of the functions and equations that we are applying.

__English:__ Students will work to write out a script that is a "how to" on how to go about determining and solving a problem.

In this lesson, students are asked to be put in teams, pairs, and then end up working individually. To organize teams, I will ask students to move to a corner of the room. Only a particular number of people (number of students in the class divided by four) can be in a corner. Then, I will ask them to number themselves off, starting with the number 1. Then I will ask all the ones to meet together, all the twos to meet together, and so forth. When they are in groups, each student is going to be assigned a role. One student is going to be a recorder (and keeps a record of the group's thoughts and progress). Another student is going to be "assessor" and devise a list of all the possible functions that could go along with the situation. A third person will become the "expert", the one who reasons which functions are more probable than others to be used. The last person becomes the spokesperson for the group any time that another group or the teacher comes around, this person is to answer questions on the task. When they are asked to get in pairs, they are going to be asked to find person from another group that has obtained a different role than you. After students have found a pair, one student will become the calculation expert and the other will become recorder. Students will have to work together to reason which function is the best one to use in the situation they have been posed with. Then, once they have determined the function that is to be used, they will work alone and complete the calculations.
 * __Groupings__**

· __Verbal__**:** Students will receive all information, instruction, and descriptions in this manner. Students will also have to use verbal skills to successfully communicate ideas with peers. · __Logical/Mathematical__**:** Students will use their Logical/Mathematical Intelligence to process information and develop and solve the problems that are involved in this lesson. · __Visual:__ Students will be provided with visual prompts of each of the different types of functions so that they are able to better determine which one of the functions models the situations at hand. · __Bodily/Kinesthetic__**:** Students will have to gather their own data (taking measurements, collecting data by doing an activity) for at least one of the activities). ·  __Intrapersonal__**:** Students are asked to solve the equations of the tasks by themselves. ·  __Interpersonal:__ Students are asked to work in teams and pairs for a majority of the lesson to gather and interpret information about how data models a real-life function and how to solve that function.
 * __Differentiated Instruction__**
 * Strategies**


 * Modifications/Accommodations**

I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.

Absent students will be expected to come prepared for class by looking at the wiki and doing what they can on the class agenda. They will be expected to have at least tried the WebQuest and come with a list of problems or questions that they had when completing this task. If they come back before the lesson is over, I will have them pair with their absent buddy and consult with this person about what was done in class. I will also provide this student with the same in class activity of "what would you do if you had this function" and help this students start the problem. I will outline the steps involved in developing an answer and then have the student complete on his or her own. This student can copy the graphic organizer and notes and get up to speed with the lesson before the iMovie needs to be made. A student that has been absent the entire lesson will have to meet during a study hall or after school and we'll hold a discussion about what was done in class. I will give this student only one situation to work through and ask this student to see his or her absent buddy before creating the iMovie.

The product for this lesson is an iMovie. In this lesson, students will be working with solving for equations and learn how to apply the mathematical aspect of solving to a real-life situation. In order to make the lesson come to life and produce an authentic product, the students will have to create their own iMovie explaining a situation and explaining how to solve a function and what purpose this serves in real life. This is a Type II technology because students are asked to take skills that they already know and produce a tool to help others understand how to solve real-life situations and why this is important. The iMovie forces students to go beyond explanation and really demonstrate their understanding of solving functions in real-world applications. They have to integrate a clear and logical order of thoughts and create images, video clips, music, and other resources that enriches their iMovie. This product could not have been produced using other resources, making it a fantastic and enriching Type II product.
 * Extensions**

__Materials:__ · //Laptops// · //Wiki Space (for [|WebQuest link] )// · //Paper// · //Pencils// · //  [|"Cycle" Graphic Organizer]  // · //WebQuest Instruction **Handout [|webquestinstruction.doc] **// · //Dominos// · //Probing Software// · //Video Cameras// · //Microphones// · //iMovie Task **Handout [|imovieabstract.doc] **// · //iMovie Checklist (Scoring) **Handout [|imoviechecklist.doc] **// · //Calculators// · //Projector/SmartBoard//
 * __Materials, Resources and Technology__**

__Resources//://__ ·  [|WebQuest] ·  [|What does it mean to substitute] ·  [|Substitution with two equations] ·  [|The Substitution Method] ·  [|Factoring] ·  [|Discussing Factoring] ·  [|Factoring Calculator] ·  [|Quadratic Formula:] ·  [|Solving with the Quadratic Formula] ·  [|Quadratic Equation Calculator] ·  [|Solving exponential equations] ·  [|Using logs] ·  [|Solving exponential equations] ·  [|Quadratic Function Applications] ·  [|Linear Function Applications] ·  [|Cubic Function Applications] ·  [|Square root Applications] ·  [|Cube Root Function Applications] ·  [|Sine and Cosine Function Applications] ·  [|Tangent Function Application] ·  [|iMovie '09 Tutorial] ·  [|Windows Movie Maker Tutorial]

__Technology:__ · Calculators · Probing Software (for hook) ·  [|WebQuest] · Laptops · Microphones · iMovie/ Windows Movie Maker Software ·  [|iMovie '09 Tutorial] ·  [|Windows Movie Maker Tutorial] · Video Cameras · Projector/SmartBoard

·  [|WebQuest]  : Students will use this WebQuest to learn how functions are used to model real-life situations. From this, they will take away not only how to model a situation, but also how to solve for "x" to determine what is going on at a particular point in time. ·  [|What does it mean to substitute]  : A guide or resource for students to use in order to remind themselves about what substitution is and how to use it. ·  [|Substitution with two equations]  : Another resource for students to use to help remind themselves how to solve equations. ·  [|Factoring]  : A resource for students to refer back to in order to remind themselves how to factor. ·  [|Discussing Factoring]  : Another approach at explaining factoring and how to do it. ·  [|Factoring Calculator]  : This website provides students that choose to work with the quadratic functions a means of checking their answer (if it is factorable). ·  [|Quadratic Formula:]  This website provides students with a reminder on what the quadratic formula is as well as how to use it. ·  [|Solving with the Quadratic Formula]  : This website is another resource that students can use to see how the Quadratic Equation is used to solve Quadratic functions that are not factorable. ·  [|Quadratic Equation Calculator]  : This website is a good resource for students that choose to work with a quadratic function and would like to check their work. ·  [|Solving exponential equations]  : This website reminds students how to use logs to solve exponential equations. ·  [|Using logs]  : This resources allows students to revisit the idea of what logs are and how to use them. ·  [|Solving exponential equations]  : This website demonstrates how logs are used to solve exponential equations. ·  [|Quadratic Function Applications]  : This website is used as research to give students an index of real-life examples to work from. It will also serve as a resource for students when working during this lesson. ·  [|Linear Function Applications]  : This website was used for research to provide students with an index of ideas for what the linear function is used to model. It will also serve as a resource for students. ·  [|Cubic Function Applications]  : This website was used for research (and can be available for students) to think of ways that the cubic function is used in real life to give students some ideas or situations to work from. ·  [|Square root Applications]  : This website is a research site for me as well as a resource for my students for ideas and examples of how the square root function is used in real-life. ·  [|Cube Root Function Applications]  : This website is a research site so that I could provide students with an index of examples of how the cubic function is used. It will also be a resource for students. ·  [|Sine and Cosine Function Applications]  : This website was used for research on the applications of the sine and cosine function. It will also serve as a resource for students. ·  [|Tangent Function Application]  : This website was used to research how the tangent function could be used in real life. It will be available for students to use as a resource as well. ·  [|iMovie '09 Tutorial]  : This is a resource for students to use in order to remind themselves and look up how to perform different tasks using iMovie. ·  [|Windows Movie Maker Tutorial]  This website is a resource for those students using Windows to learn and perform different functions in Movie Maker.
 * __Source for Lesson Plan and Research__**


 * __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.//**
 * //Rationale://** Providing students with an optimal amount of resources and choices is essential in any classroom. In this lesson, all students are asked to complete the WebQuest, but there are many directions that the student can go with the WebQuest. Students are given a chance to explore their idea throughout the WebQuest. After, they have a choice of situations to choose and work from. This provides students with an adaptive environment and personal choice on how they want to learn this lesson.

This lesson is also designed to be organized and provide sequential learning and structure for students. Students worked simply with the concept of solving equations using various methods in last lesson, and in this lesson, they are now asked to apply their knowledge. The WebQuest, handouts, and instruction help provide for an organized and structured atmosphere for students to work in while still giving enough freedom. There are clear expectations listed in all of the handouts as well as the WebQuest, so students are clear on their objective for the lesson.

This lesson is designed with the intent to get students thinking about what they have learned. During the WebQuest, they are going to be asked to consider what method they would use to key in at a specific point during the situation. Then, I will ask them to use the index and think of how to model this situation. Then I am going to ask them how they would solve this problem. I will then manipulate the equation and ask them how their equation has changed. They will have to focus on details to get a good idea on how the data set changed. They will be asked to deeply explore the function that they have chosen and gain ownership over their explanation in the iMovie product.

This may be one of the most challenging lessons that students have had to complete, but they are given many chances to meet and discuss their understandings, creating a comfortable environment and encouraging atmosphere. They will be asked to participate in Think-Pair-Share time as well as in the closing circle, which provide students with a comfortable atmosphere to address problems that they are still having. Both these methods obligate others to be supportive and sensitive to their peers.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**
 * //Rationale://** This lesson is designed around the facet "self-knowledge" In this lesson, students will be provided with the resources that remind them of what they have learned from last lesson. Then, they are asked to apply their knowledge in a new way and reconsider what methods they would use in order to solve these equations. This will get them thinking and will reveal information about self-knowledge. Each student will see something that another students does not. They will become aware of how their perspective changes the assignment for them, what limits their understanding and what they still need to work on. From this, they will also consider what may have made this lesson better. This lesson helps student explore what they know and become more familiar with their learning styles.

· __Verbal__**:** Students will receive all information, instruction, and descriptions in this manner. Students will also have to use verbal skills to successfully communicate ideas with peers. · __Logical/Mathematical__**:** Students will use their Logical/Mathematical Intelligence to process information and develop and solve the problems that are involved in this lesson. · __Visual:__ Students will be provided with visual prompts of each of the different types of functions so that they are able to better determine which one of the functions models the situations at hand. · __Bodily/Kinesthetic__**:** Students will have to gather their own data (taking measurements, collecting data by doing an activity) for at least one of the activities). ·  __Intrapersonal__**:** Students are asked to solve the equations of the tasks by themselves. ·  __Interpersonal:__ Students are asked to work in teams and pairs for a majority of the lesson to gather and interpret information about how data models a real-life function and how to solve that function.
 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**
 * //Rationale://**

The product for this lesson is an iMovie. In this lesson, students will be working with solving for equations and learn how to apply the mathematical aspect of solving to a real-life situation. In order to make the lesson come to life and produce an authentic product, the students will have to create their own iMovie explaining a situation and explaining how to solve a function and what purpose this serves in real life. This is a Type II technology because students are asked to take skills that they already know and produce a tool to help others understand how to solve real-life situations and why this is important. The iMovie forces students to go beyond explanation and really demonstrate their understanding of solving functions in real-world applications. They have to integrate a clear and logical order of thoughts and create images, video clips, music, and other resources that enriches their iMovie. This product could not have been produced using other resources, making it a fantastic and enriching Type II product.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**
 * //Rationale://** There are many formative assessments of learning in this lesson. Many of them are self-assessments, however, this is the best type of assessment for students to gauge their understanding of the material. The first type of formative assessment that is designed in this lesson is when students are in their Team-Pair-Solo structure. Another way that they are formatively assessed is by me going back and changing one of the variables that was proposed to them in the beginning of class. They will have to go back and explain their same reasoning with a different variable to compare and contrast the differences in the situation. Students will also be formatively assessed by brainstorming to explore the each of the situations further, looking for more evidence on the matter. Students will use this time to electronically submit their answers via Google Docs and a bar graph will be formed. Any "other" answers will be addressed and clarified. Students will work with their teams to compare answers and correct any mistakes they had. After the group discussion, students will be able to hold mini-conferences with other students and teachers at the end of class and in a wiki discussion. They will be able to make any alterations they feel necessary before moving on to modeling their final task. The final way that students are formatively assess is by forming a "closing circle" to discuss the happenings of the day. Students will be asked to address (1) their answers and (2) what they felt the big idea is.

Students will create a short film (no more than five minutes) that addresses one of the ways to solve a function. In groups of 3, students will find a real-life example that incorporates their assigned function. In the movie, they need to address (1) their problem, (2) what function models their problem, (3) what method they use to solve the problem, and (4) how to solve the problem. Students will be asked evaluate other's performances (as well as their own) for the use of functions and methods to solve the function in their movie. Students will be assessed using a checklist.


 * __Teaching and Learning Sequence__****:**

For this lesson, the classroom will be arranged in clusters with the focus of the classroom to be orientated to face the SmartBoard or the projected image from the computer. This will allow students to easily work for their Think-Pair-Share time as well as hold small discussions while working on the WebQuest.

__Day 1:__ · Students will come in, unpack laptops, and log onto wiki page (3 min) · Students will watch the "hook" (dominos fall over) and we will interpret the data (5 min) · Students will receive the [|Cycle" Graphic Organizer] as well as the WebQuest Instruction Handout (2 min) ·  Students will be reminded of the terms polynomial and degree and the methods substitution, factoring, the quadratic formula, and logs (10 minutes) ·  Students will work on the WebQuest (40 min) ·  Students will use the Think-Pair-Share time to complete their graphic organizers (10 min) ·  I will hand out the iMovie task handout as well as the iMovie checklist so students are prepared for next class (5 min) ·  Students will be directed to an index and asked to pick a function application (and do research on it) for next class (5 min)

__Day 2:__ · Students will come in, unpack their laptops, and log onto wiki pages (3 min) · Students will be asked to display the resource that they found their application and students will go around and share what application they have chose (and I'll approve it) (7 min) · Students will have a work session where they have their peers, computers, and me available to work through their problem and solve for x. (30 min) · We will form a closing circle. I will tell all students to manipulate their equations by reflecting them over the x-axis. I will now ask them to reconsider what their data is telling them. (10 min) · Students will get a tutorial on how to use [|iMovie '09] as well as the video camera and microphones. (15 min) · Students will have an opportunity to begin their iMovie based off of the application they have worked through in class. (10 min) · Students will be asked to complete this assignment and have it done a week from when it has been assigned. (5 min)

In this lesson, students will understand that functions have various real-world applications. It is important for students to understand this content because many of life's situations can be modeled using different functions. Having the ability to solve these functions have provided us with specific and essential data that helps us solve problems. For example, how fast will something slide down a ramp or a hill? What is a medicine's half-life? Without the ability to solve functions, we would not know the answers to these questions without much (potentially harmful) trial and error. This lesson meets the MLR standard that **//students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.//** To hook my students, I will have dominos set up with probing equipment. I will let the dominos topple over and have the probing equipment model the data. Then I will ask students what function is modeling the data based on the results. I will ask them how the dominos falling individually may create a different function in a class discussion. This will serve as a pre-assessment for my students to see what they understood or gathered from last lesson as well as a way to engage my students for what is going on in this lesson.
 * Where, Why, What, Hook, Tailors: Visual/Spatial, Logical/Mathematical, Intrapersonal, Interpersonal, Verbal**

Students will be equipped with the terms in the previous lesson. Therefore, I will briefly remind them of the definitions of [|degree] and [|logarithm] and will know the techniques [|substitution], [|factoring] , [|the quadratic formula]. They will be able to have their Method of Solving Equations (from last lesson) out and I will provide them with some links as a refresher if they need it throughout the lesson. After I present the hook, I will give students a handout and ask them to go to the [|WebQuest]. During this section, students are fairly independent in completing the assignment. They will be asked to complete a " [|Cycle" Graphic Organizer] which will help them refine their understandings on how to recognize and solve a function when it is related to real life. I will instruct during this time by answering any questions that they have. After, I I will have an index of links posted on the wiki and I will give students freedom in choosing whatever function they want in order to solve. If students want to, they can collect their own data to examine and model. I will help students solve their equations by refining their skills and answering specific questions about their problem. I will make sure that all students are learning because they are responsible for choosing and solving their own specific problem. I will check for understanding by using individual conferences with students to make sure they know where they are going with their individual projects. I will also monitor their progress through the Think-Pair-Share time as well as during the closing circle. (See content notes) (See content notes)
 * Equip, Explore, Rethink, Revise, Refine, Tailors: Logical/Mathematical, Interpersonal, Intrapersonal, Verbal/Linguistic, Bodily/Kinesthetic, Visual**

Students will explore the idea of functions being used to model real-life examples by working through the [|WebQuest] and considering the functions that can model the situation being discussed. After they work through the entire WebQuest, they will be asked to explore their understandings by generalizing the steps that were taken to determine which function models the situation, how to solve, and what the information is telling us using a " [|Cycle" Graphic Organizer]. This will get them thinking about the order in which they need to consider the situation. Then, students will experience the lesson by choosing their own example and going through the same process to solve for x and determine why it is important to have this skill. By the end of this lesson, students will be able to compare methods of solving functions and apply their knowledge to real world experiences. For this lesson, students will be asked to do a Think-Pair Share. To organize teams, I will ask students to move to a corner of the room. Only a particular number of people can be in a corner. Then, I will ask them to number themselves off, starting with the number 1. Then I will ask all the ones to meet together, all the twos to meet together, and so forth. When they are in groups, each student is going to be assigned a role. One student is going to be a recorder (and keeps a record of the group's thoughts and progress). Another student is going to be "assessor" and devise a list of all the possible functions that could go along with the situation. A third person will become the "expert", the one who reasons which functions are more probable than others to be used. The last person becomes the spokesperson for the group any time that another group or the teacher comes around, this person is to answer questions on the task. When they are asked to get in pairs, they are going to be asked to find person from another group that has obtained a different role than you. After students have found a pair, one student will become the calculation expert and the other will become recorder. Students will have to work together to reason which function is the best one to use. Then, once they have determined the function that is to be used, they will work alone and complete the calculations. They will show evidence of learning throughout the lesson. In the hook, they will demonstrate what they know about solving functions. Then, they will demonstrate their learning through the Think-Pair-Share, during the individual conferences, and during the closing circle. Students will have the opportunity to rethink their work when I ask them to consider how reflecting the function they have chosen over the x-axis has changed their answers. They will revise their work in the mini conferences that they are holding with me. They will refine their understanding in the closing circle and by creating their product comfortably.
 * Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical/Mathematical, Visual**

In this lesson, students are constantly self-assessing their work. During the Think-Pair-Share time, they are self-assessing their learning by seeing if what they understood from the WebQuest correlates with what others understood. They will also self-assess in the closing circle when the discussion of understanding and problem solving surfaces. Another means of self-assessment can be what they get out of having the conference with me over their understandings and progress with their specific function. I will provide timely feedback by holding these conferences with students to monitor progress. I will also be able to answer questions and clear up misunderstandings (and hurdles) when students have work time as well as in the closing circle. Most of the feedback will be verbal until the final product. For the final product, I will provide feedback by a checklist. The homework assignment continues to keep the students thinking about solving functions. I am in hopes that sense I have provided them with an index of applications for functions, they will take the time to explore different functions. They may question how to solve some of these problems for "x", which is how I will keep them thinking. In the next lesson, students need to again understand how functions are modeled using real-life applications, so this is a good and moderately easy way to introduce students to how functions are used in real-life.
 * Evaluate, Refine, Tailors:** **Interpersonal, Intrapersonal, Logical/Mathematical, Verbal, Visual**

Begin the lesson by performing the domino falling over hook. This demonstrates a linear function, but each domino toppling over explains a quadratic function.
 * Content Notes**

 A falling object is an object that you drop from some height. The assumption is that the object is simply dropped and not accelerated up or down. There are simple equations that allow you to calculate the velocity and distance traveled, as well as the time taken to achieve a given velocity or distance.


 * Note**: You normally do not need to memorize these equations, but you should know where to find them in order to solve equations.

Questions you may have include: This lesson will answer those questions. There is a [|mini-quiz] near the end of the lesson.
 * What are the velocity equations?
 * What are the distance equations?
 * What are the time equations?

Velocity equations
The equations for the velocity of a falling object are:


 * v = gt**


 * v = √(2gx)**

Distance equations
The equations for the distance that the object falls are:


 * x = gt2/2**


 * x = v2/2g**

Time equations
The equations for the elapsed time of a falling object are:


 * t = v/g**


 * t = √(2x/g)**

This will give students an idea on what they are going to be doing in the lesson and give them hints to all of the aspect that they need to consider. Explain how the domino situation can be explains in terms of velocity, distance, and time. Then, ask them to examine the probing software and determine they are measuring in.

Now, I will direct them to go to the [|WebQuest]. I will have them read the introduction, the task and complete the process according the instructions on the WebQuest. They can omit the instructions to refer to unit 2 in the text book as well as the "Guidance" section. They will need to create the graphs in Lesson 5-1 and Lesson 6-6 and do the complete process for the steps under Lesson 7-4.

 Now, students will be asked to use an index of links that I have provided with them on a wiki page to choose a function that they would like to work with. This is the index that I have provided them with: > **[|Quadratic Function Applications]
 * [|Linear Function Applications]
 * [|Cubic Function Applications]
 * [|Square root Applications]
 * [|Cube Root Function Applications]
 * [|Sine and Cosine Function Applications]
 * [|Tangent Function Application]

**From [|Substitution with two equations] :**
x + y = 3 and 2x + 3y = 8 (Answers: x =1, y= 2) Solving simultaneous equations means finding the values of "x" and "y" that make them true. The following steps will demonstrate how to solve simultaneous equations by the substitution method.

x + y = 3 x= 3 - y 2x = 3y = 8 2 (3 - y) + 3y = 8 (3) 6 + y = 8, y = 2
 * We will use the example equation to demonstrate the procedure...
 * (1) Isolate one of the variables ('x') one side of the equations
 * Isolating 'x':
 * (2) Substitute for the isolated variable in the other equation:
 * Substituting 3-y for 'x':
 * Now, this equation has one variable, so we can solve:
 * Substitute y in and solve for x.

**From [|Factoring] :**
**// x // 2 ** **+ 5** **// x //** **+ 6** I need to find factors of 6 that add up to 5. Since 6 can be written as the product of 2 and 3, and since 2 + 3 = 5 , then I'll use 2 and 3. I know from [|multiplying polynomials] that this quadratic is formed from multiplying two factors of the form " (//x// + //m//)(//x// + //n//) ", for some numbers // m // and // n //. So I'll draw my parentheses, with an " // x // " in the front of each: (//x// )(//x// ) Then I'll write in the two numbers that I found above: (//x// + 2)(//x// + 3  This is the answer: //x//2 + 5//x// + 6 = **(//x// + 2)(//x// + 3)**       This is how all of the "easy" quadratics will work: you will find factors of the constant term that add up to the middle term, and use these factors to fill in your parentheses.

Note that you can always check your work by multiplying back to get the original answer.

Your text or teacher may refer to factoring "by grouping", which is covered in the lesson on [|simple factoring]. In the "easy" case of factoring, using "grouping" just gives you some extra work. For instance, in the above problem, in addition to finding the factors of 6 that add to 5, you would have had to do these additional steps: //x//2 + 5//x// + 6 = //x// 2 + 3//x// + 2//x// + 6 = (//x// 2 + 3//x//) + (2//x// + 6) = //x//(//x// + 3) + 2(//x// + 3) = (//x// + 3)(//x// + 2)

=**From [|Definition of a logarithm]**= Since the logarithms on either side of the equation have the same base (" 2 ", in this case), then the only way these two logs can be equal is for their arguments to be equal. In other words, the log expressions being equal says that the arguments must be equal, so I have: //x// = 14 And that's the solution: **//x// = 14**
 * ** Solve //log//2(//x//) = //log//2(14) . **

//log//2(8) = //x// 2 //x// = 8 But 8 = 23, so: 2 //x// = 23 **//x// = 3
 * Solve //log//2( 8  ) = //x//.
 * I can solve this by converting the logarithmic statement into its equivalent exponential form, using The Relationship:

**From [|Solving with the Quadratic Formula]**
The Quadratic Formula:** For //ax//2 + //bx// + //c// = 0, the value of //x// is given by  ** Looking at the coefficients, I see that //a// = 1, //b// = –4 , and //c// = –8. I'll plug them into the Formula, and simplify. > > **__Some Hints or Tips to provide to the Quadratic Function Application students:__** >  **Some hints and tips to provide the Linear Function Application Students: > Some hints and tips to provide to the Cubic Function Application Students:
 * ** Use t he Quadratic Formula to solve //x//2 – 4//x// – 8 = 0.  **
 * 1) Consider if your function is free-falling or if it has been launched.
 * 2) Gravity is g = 9.8 m/s2 in the metric or SI system of measurement or g = **32 ft/s2 in the English system of measurement - **
 * 3) Gravity affects your equation if it is a falling object
 * 4) ** The quadratic equation that is modeled has the standard form: // s // ( // t // ) = – // gt // 2 + // v // 0 // t // + // h // 0
 * 1) Find out the relationship between the x and y values
 * 2) Is your function's slope increasing or decreasing
 * 3) x + y= constant is the standard form of an equation
 * 4) y= mx+b is the slope-intercept form
 * 5) **Know what your question is asking and what units of measure they are using. How does this work into your answer?**
 * 1) Use a text book or other online resources to get a measurements and rate for each of the situation
 * 2) What is the equation for the volume of a cube?
 * 3) What is the volume of a sphere?
 * 4) What sort of methods would you use to solve this function?

Some hints and tips to provide to the Square Root Function Students:
 * 1) How do you find the lengths or sides of a triangle?
 * 2) What is the pythagorean therom? How is this useful to you.
 * 3) NOTE: This example is only good for students that know trig identities and right triangle trig.

__**Some hints and tips to provide to the Cube Root Function Students:**__ There's certainly one use for it -- determining the edge of a cube having a given volume. Aside from that, what else might there be? Here's one -- the height of a geostationary satellite, which stays over the same equatorial spot on the earth's surface as it orbits the planet in the direction of the earth's rotation. How high is the orbit? Too low, and the satellite must have a higher angular speed to apparently "travel eastbound"; too high, and it slips behind to apparently "travel westbound". (Away from the equator, and the component of gravity not needed for centripetal acceleration pulls the satellite toward the equator.) Assume a perfectly-spherical Earth that stays at a fixed point, with a satellite in a circular orbit at altitude "h", in whose plane the Equator lies.

code R (radius of Earth)         6.37 x 106 meter w (angular speed of Earth)  7.2921 x 10-5 rad/s M (mass of earth)           5.97 x 1024 kilogram G ([|Gravitational Constant])  6.67259 x 10-11 m3*kg-1*s-2 code h (height of satellite) m (mass of satellite) -- irrelevant to the answer The attractive force "FG" between the two objects: G * M * m FG = -  (R + h)2

__**Some tips and hints for Sine and Cosine Applications students:**__
 * 1) What are the trig identities associated with the Sine and Cosine Function? Are these useful to you?
 * 2) What does it mean to be periodic?
 * 3) How to do you interpret the results when they are in radians?
 * 4) Provide them with [|this] resource if they do not understand radians and degrees


 * __Some hints and tips for the Tangent Function Applications students:__**
 * NOTE: must know trig formulas and techniques**
 * 1) what is the relationship that tangent has in the pythagorean theorm?
 * 2) How does your data relate to triangles?
 * 3) What does it mean to be tangent?
 * 4) Which period are you in?

After students have completed this, they will be asked to reflect their function over the x-axis and consider how much the function has changed. I will note to students that the application really no longer makes sense in most cases. They will have to provide an explanation as to why. The explanation will be different for each student.

For the closing circle questions, I will ask students the following questions: 1) What was the biggest challenge in your activity? 2) How did you solve your function? 3) Did flipping it over the x-axis make sense for you?

Then, I will introduce them to iMovie '09. These are the steps I will show them as a class:

Before you can edit your footage you must import it into the computer. To start importing footage, do the following: Click on the Camera Mode **icon to make sure iMovie 09 is in **Camera Mode **(//Fig //3//) Set the switch on the left to //**//Automatic **if you want iMovie to log the clips for you. To do it **Manually**, hit the **Capture **button to start importing and stop to end that particular clip (**//**Fig 4//). Use the VCR controls on the camera to move the tape to where you would like to import it. When you hit //**//Capture**, it will ask you to add the clips to an existing event, or to create a new event ( **//**Fig 5).

//__To add clips to your movie, do the following:__ Click on any of the clips within the //**//Event Browser. **A yellow box will appear on the thumbnail; adjust the edges of the box so that all of the footage you want to add to your project is within the yellow box. After you have done this, your mouse pointer will appear as a hand. Grab the thumbnail within the yellow box and drag it to the **Project Browser **to add it to your movie (**//**Fig 9//). The clip adjustment bar (//Fig 10//) alters how many frames of each clip appear as a thumbnail. Adjusting this can make selecting larger or smaller portions of clips easier.

Sometimes you may need to switch the position of some clips in your movie after you have added them to your Project Browser. To reposition clips, just click and drag them to a new position, which is apparent when you see a bold green line appearing when you try and reposition your clip. You also have the option to split clips into pieces. Click on the clip you would like to split and use the yellow box to select the portions of the clip that you would like to separate, then click //**//“Split Clip” **in the edit menu. Getting rid of unwanted clips can also make your workspace less crowded. This will make it easier to organize your movie. To remove clips from your iMovie 09 project, do the following: Select a clip you wish to get rid of and press **DELETE.

CLIP ADJUSTMENTS Once you have placed a clip into your project. You have a variety of options for **adjusting the clip. These options include:** **TRIM** **,**

**CROP, ADJUST AUDIO, **ADJUST VIDEO, and VOICEOVER.

To TRIM a clip: click the clock icon that appears when you hover your mouse over a clip in your project//.

//Just like when inserting a clip, just drag the sides of the yellow box to manipulate what portion of the video is included in your project (//Fig 12//). Press the play button to preview your clip; press done when finished. To CROP a clip: click on the cropping icon in the thumbnail of any clip, or clip on the cropping icon in the Options Tab (//Fig 13//) and then clicking on the clip you’d like to crop.

You can then resize the green box (//Fig 14//) that appears on the clip to control how much of the footage will be visible.

To ADJUST AUDIO in a clip: click on the speaker icon in the thumbnail of the clip (//Fig 11//), or click the speaker icon on the Options Tab (//Fig 13//). Now you can adjust the audio of the clip, add an audio fade-in or fade-out, or apply ducking— which makes other sounds, such as music, “duck” below the volume of your clip. To ADJUST VIDEO in a clip: click on the sun icon located in the top left corner **of the thumbnail of any clip; or** **click on the circle icon** **located on the far right of **the Options Tab. or This will allow you adjust the following: Exposure – shadows and highlights Brightness – overall light levels Contrast – difference between white a black Saturation – color intensity White Point – changes color range by resetting the color white

To add VOICEOVER to any clip: click the microphone icon on far left of the Options Tab (//Fig 13)//. You have the options to select which microphone you would like to use, control the level at which your voice records, apply noisereducing vocal enhancement, and play your projects audio while you record. When you are ready to record click on the clip you would like to record a voiceover for. After a three second countdown just begin talking as your video plays. ADDING MEDIA iMovie 09 gives you the option of adding sound files or images to your project. To add a sound file click the music note icon in the Edit Browser (//Fig 15//).

Then simply browse for the sound file that you would like too add and drag it into your project. To add an image file, click the camera icon in the Edit Browser, browse for the film, and then drag it into your project. ADDING TITLES To add titles to a clip, click the “T” icon on the Edit Browser (//Fig 15//). Once you have selected the type of title you would like to add, just drag the title on top of the clip you would like to add it to. Then click within the thumbnail of the clip to alter the titles to suit your video. **You can adjust the font of the titles by** **clicking the Show Fonts button** **at the top of the preview window.** **To add transitions to your project click the transition icon on right of the** **Edit **Browser. Then drag the type of transition you would like to the place in the timeline that you choose.


 * Then, I will let students work and the lesson is over!**//



Handouts ||  ||
 * [|"Cycle" Graphic Organizer]
 * **WebQuest Instruction** Handout [[file:webquestinstruction.doc]]
 * **iMovie Task** Handout [[file:imovieabstract.doc]]
 * **iMovie Checklist (Scoring)** Handout [[file:imoviechecklist.doc]]