S+Emery,+Jordan

Office: Room 14, Green Section Office Phone: 207- 399-8807 Office Hours:** 12-2 (MWF) 8-9:30 (Tu/Th) ** E-mail: jordan.emery1@maine.edu **
 * Teacher: Ms. Jordan Emery

=Summary of Unit= Bridges, skateparks, roller coasters, music, and population growth: functions are everywhere! Because functions are such a large part of our everyday life, students must be able to gain an understanding of these algebraic curvatures. To begin, students will explore a variety of functions and observe the behavior that each displays and acquire key skills before applying their knowledge. After becoming familiar with the shapes of the functions, students will solve various functions using an array of mathematical techniques that are demonstrated in the real-world. After becoming function gurus, students will apply their newfound knowledge of functions to real-world situations in a creative and imaginative way. Everything that students have acquired about functions is essential for it WILL be brought to life by the end of the unit through a creative project that demonstrates their full mastery of functions.

=Establish Goals= 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 = = =Students will understand that= • functions can be expressed in several ways. • functions have various real-world applications. **• there are many techniques used in order to solve functions and change the appearance of functions.

Essential Questions** • How are functions expressed in different ways? • How can functions apply to the real world? • Why are a variety of techniques used to solve functions and change the appearance of functions? = = =Students will know= • Definitions of: domain, range, ordered pair, function, polynomial, degree, logarithm, and absolute value function. • Formulas: the quadratic formula. • Techniques: substitution, factoring, the quadratic formula,factoring, properties of logarithms, the vertical line test, horizontal stretch, vertical stretch, reflection over x-axis, reflection over y-axis. = = =Students will be able to= • express a variety of functions through graphs and algebraic equations. • translate functions of graphs according to equation manipulations. • solve functions using a variety of methods. • compare methods of solving functions to determine which is appropriate for the problem being solved. • consider the role functions play in real-world problem solving. • a. recognize the graph and sketch graphs of basic functions.

**Performance Task Overview**  Congratulations! You have just been invited to join the Disney Dream Team! After happily accepting the offer, the executive producers of Disney approach the Dream Team with a challenging task. They want the Dream Team to develop a new chapter on fucntions to include in the remake of the 1959 version of Donald in Mathmagic Land. You and a group of four fellow Dreamers has been assigned a particular function to address. For each function, the producers would like you to address the function's equation, the function's graph, at least two real-world examples of the function, and how your function can be used with other functions to create a shape that you and your fellow Dream Team members agree on. The more you work with your group of four and your fellow members, the better the remake is going to be! Work hard and make your section shine, because there a rumor around the office that the group that produces the best clip is in line for a promotion. Good luck and let the show begin!

=Expectations= Education is a vital key in today's world. In a world of constant change, development, and growth, having an education works to your advantage. As a student, you are expected to learn, but learning does not stop once you leave the classroom. Learning happen all around you. As a teacher, it is my job not only to give you an education, but to provide you will skills on how to learn to material in a meaningful way. All I ask of you is take the time to learn the material.

Attendance and participation is critical in this class. The only way to truly understand and learn that material is to work with it and think through the process with peers. It is hard to simulate what happens in class in a make-up assignment, so please, attend class regularly and participate in the class activities. __**If for some reason you are unable to attend, contact me**__ by e-mail: jordan.emery1@maine.edu. We will make arrangements to make up the work.

All assignments and projects are expected to turned in on the due date (unless other arrangements have been discussed). Assignments should be written legibly on white-lined paper with your name, the date, the class period, and the assignment written in the top right-hand corner or typed (formatting will be discussed when appropriate). Graded assignments can be redone for full credit. Students must make corrections and attach their revised assignment to their original assignment. Homework (such as bookwork and worksheets) is practice and will not be graded, but will be collected and returned promptly with feedback.

Academic Integrity is important and needs to be honored. Plagiarism will not be tolerated in the classroom. Please refrain from copying and pasting directly from the internet, or using the exact phrase from a book. If you do so, cite your sources. If it is obvious that you have plagiarized, repercussions will be in order. I will be checking for plagiarism throughout the semester, so if you use a website, make sure to give credit to the sources that you use! Improper citing of sources will be excused but will asked to be corrected.

The classroom is a place of learning. Respect for the teacher and for one another is important. Students should refrain from making jokes about one another or laughing when someone does not understand something. If you have a question, ask! If you have a question, somebody else in the room probably has the same question too. Your peers are your greatest learning tools, use them! It is amazing what you can learn. If you have a learning disability or other concerns, please let me know and I will help find a way to accommodate you.

=Benchmarks= Below is a list of assignments that you will asked to complete throughout our unit on functions. Each benchmark has been assigned a point value. Your grade will be determined from a percentage of points earned out of 7**00 points**.

Students will be asked to take part in a pre-assessment that covers a wide range of material about functions. The pre-assessment is meant to serve as an informative tool to help the teacher understand where each of his or her students are at with the material, so that he or she knows how to design the lesson to best fit the learners. By just taking the pre-assessment, students will earn 15 points, for it is a vital part in the learning process.
 * __Pre-Assessment__** (25 Points)

Students will be asked to create an electronic portfolio using Noteshare that demonstrates their understandings on functions. In this e-folio students will be asked to explain and provide examples the terms: domain, range, ordered pair, function, and the vertical line test. Then, students will be asked to explain the shape of the following function and create a graph in Geogebra after completing some computations: f(x)=x, f(x)=x², f(x)=x³, f(x)=x^(1/3), f(x)^(1/2), f(x)=ln(x), f(x)=sin(x), f(x)=cos(x), f(x)=tan(x).
 * __E-folio on Functions:__** (75 Points)

In class, students will be asked to defend what they believe a shape of a particular function should look like and why. They need to gather evidence and their brainstorming process should be posted in the "preparation for debate" on the wiki. After the debate is complete, students will be asked to return to the wiki and now defend the opposing side. Students will need to retrace their thoughts and think about looking at the function in a different way. At the end of defending this side of the argument, students will need to determine what they ultimately believe the function should look like, regardless to which side they argued for in the end.
 * __Wiki Response:__** (50 Points)

__**Garage Band Production:**__ ( 75 Points) Students will be asked to create a five minute podcast the explains each of the graph transformations. In their podcast, they will need to create an informational segment that covers 1) a horizontal stretch, 2) a vertical stretch, 3) a reflection over the x-axis, and 4) a reflection over the y-axis. In this segment, students should address how different functions react differently to these transformations as well as how the domain and range change. Music that is being played while speaking should reflect the affects of the graphical transformation.

**__Formal Blog Entries:__** (50 Points) Students will enter a blog entry in which they explain each of the methods that are used to solve functions. In the blog entry, students should include: (1) which function(s) does this method solve, (2) the process (in your own words), (3) an original example of the method being used. If there is more than one way to solve the function, the student should state that there are two different ways to solve this function, but only describe one process. In this assignment, each method needs explained AT LEAST once. Only one example of a process is necessary for each example.

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.
 * __iMovie:__** (100 Points)

Students will be asked to produce a digital scrapbook (using Smilebox, or some other digital scrapbooking site) that models situations where functions arise in real life. Students will be asked to use web photos, documents, as well as their own original photos to create their scrapbook. For each photo uploaded, students will need to create a link, or post to a wiki why they have decided to include this picture in their scrapbook/how it relates to functions.
 * __Digital Scrapbook:__** (75 Points)

Over the course of the unit, students will be asked to respond to blog questions. These questions may range from asking the student to summate factual information to having the student brainstorm some new ideas about functions. This is a good source for students to go and post questions they have about the unit or record their thoughts about the day's lessons as well. These blog entries are not graded on correctness, they are graded on completeness. If all entries are posted when they are supposed to be, the student receives all of the points.
 * __Informal Blogs:__** (25 Points)

Throughout the unit, you will be asked to take part in a variety of cooperative learning techniques, including 3-Minute Reviews, Think-Pair-Share, Round-Robin Brainstorming, Jigsaws, Team-Pair-Solo, and Numbered Heads Together. These techniques are used to help the student improve his or her understanding on the "big ideas" that are promoted in these units. If the student actively participates in these activities, he or she will accumulate 25 points.
 * __Cooperative Learning:__** (25 Points)

After students have completed their unit on functions, they will be asked to work in small groups as well as a class to complete the following prompt:
 * __Performance Task (Unit Project):__** (200 Points)

Congratulations! You have just been invited to join the Disney Dream Team! After happily accepting the offer, the executive producers of Disney approach the Dream Team with a challenging task. They want the Dream Team to develop a new chapter on fucntions to include in the remake of the 1959 version of Donald in Mathmagic Land. You and a group of four fellow Dreamers has been assigned a particular function to address. For each function, the producers would like you to address the function's equation, the function's graph, at least two real-world examples of the function, and how your function can be used with other functions to create a shape that you and your fellow Dream Team members agree on. The more you work with your group of four and your fellow members, the better the remake is going to be! Work hard and make your section shine, because there a rumor around the office that the group that produces the best clip is in line for a promotion. Good luck and let the show begin!

The task will be grading using two rubrics, one for the actual movie and one for the oral presentation of the video. I will organize all the student's videos to create the finalized "functions" chapter and show it to the class". Each student will have to get up and explain their own part of the movie, each part of the movie will make up a finalized class product.

=Grading Scale=
 * A** (93 -100), **A-** (90 - 92), **B+** (87 - 89), **B** (83 - 86), **B-** (80 - 82), **C+**(77 - 79), **C** (73-76),
 * C-** (70 - 72), **D+**(67 - 69), **D** (63 - 66), **D-** (60 - 62), **F** (0 - 59).