S+Doran,+Christopher

**Office:** 224 **Office Phone:** 207-778-xxxx **Office Hours:** Tuesday & Thursday 2-4 ** E-mail: ** christopher.doran@maine.edu
 * Teacher:** Mr. Doran

=Summary of Unit=

In this unit, students will learn about different types of functions and their relations. The topics that will be explored include multiple types of equations and graphs such as linear and quadratics. They will be able to recognize these different types of graphs and eventually be able to illustrate these graphs on their own. Students will also learn different concepts to help in identifying graphs such as rate of change, asymptotes, increasing and decreasing over intervals, just to list some examples. They will be able to consider these concepts and then demonstrate them in identifying graphs. Students will then delve into real world applications that use the functions and graphs that they have learned over the course of the unit. They will be able to analyze and create real world applications based on their previous knowledge of functions. This unit will feature creative projects that use softwares such as iMovie, Glogster, Geogebra, Blogs, and the National Library of Virtual Manipulatives (NLVM) that will allow the students to show their understanding of the topics in this unit.

=Establish Goals=

Maine Learning Results: Mathematics - D. Algebra Functions and Relations (4) Grades: 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.

= = =Students will understand that=

• there are multiple types of graphs, functions, and the techniques used to identify them. • all sorts of functions are used in real world problems every day. • concepts such as rate of change, increasing/decreasing over intervals, and intercepts are used to identify graphs.

= = =Essential Questions=

• How to recognize the different types of functions based on the graphs shown and vice-versa? • How will real world situations use these functions in their applications? • Why do different algebraic techniques affect the function and its graph?

= = =Students will know=

• Formulas: Quadratic formula, slope formula, distance formula, midpoint formula • Definitions: Function, limit, rate of change, x-intercept, y-intercept, asymptote, matrix, vector, position, velocity, acceleration • Terminology: Variable, distributive property, associative property,commutative property

= = =Students will be able to=

• demonstrate the concepts involved in identifying graphs. • illustrate the multiple types of graphs. • create a real world situation involving algebraic functions. • analyze real world applications of algebraic functions. • consider the different concepts that help identify graphs. • recognize the multiple types of graphs.

**Performance Task Overview**

Renowned Hollywood movie production company, Paramount Pictures, has just announced their next idea for a movie that features math used in the real world. As actors, your job is to create a short film that uses algebra in a real world setting in two developed ways. After your submission, the production crew will review all auditions. Whichever team creates the best film will become the stars of their new movie being shot in the San Francisco area. Because they will be reviewing a lot of films, they ask that your submission be between 3-5 minutes. Going over that allotted time will hurt your chances to land the job. Get creative and think of a way that math is helpful in problem solving; for the executives will want to make sure that whoever is starring in their film has a solid knowledge of functions and their uses. Go break a leg!

=Expectations=
 * Absent/Late Policy:** If you are absent from class, please e-mail me with your plans for making up the work. Math requires a lot of note taking and missing one class could have a negative impact if proper actions are not taken. Each student will have at least one other person that they could contact to discuss what was covered in class and what notes were given out before the next class meeting period.


 * Assignment Expectation:** Assignments are to be completed fully and will be collected at the beginning of class. If there is a question on the homework that you, as students, have, then I will be more than happy to answer these. Homework may be completed either individually or with a peer unless otherwise noted.


 * Classroom Expectations:** The classroom is a place for learning. I expect each of my students to come in to class prepared to learn and to have fun. At the end of the class period, I expect each student to have walked out with something new that they learned. Also, respect for peers is something I expect from everyone. Each student has an equal opportunity to learn and thus shouldn't be subject to ridicule for not understanding something. It's alright to ask questions about something that is unclear. No question is a stupid question.


 * Plagiarism Policy:** Students will be working on many different projects over the course of the year. It is expected then, that all work done by the student be of their own work. This includes homework. Students will have the option to work together on homework assignments, however, copying another students work is violating the schools plagiarizing policy and thus I will have to follow that rule accordingly.

=Benchmarks (425 Total Points)=

• **Geogebra**: In teams of 2, students will create a position/velocity/acceleration function using Geogebra software. During the presentation, you will need to explain to the class which function is the position function, which is the velocity, and which is the acceleration. In addition, you will also need to explain what each part of the formula represents. Grading will be done by using a checklist. **//(30 points)//**

• **NLVM**: In teams of two, students will give a presentation on a given function using the National Library of Virtual Manipulatives' graphing tool (navigation and explanation will be done in class). In this presentation, you will each need to explain the process of identifying the type of function you have. Make sure to use key terms including: rate of change, increasing, decreasing, asymptote, and limit. Grading will be done using a checklist. //**(30 points)**//

• **Geogebra**: In a team of 3, students will find a correct set of functions that will create a shape with a given area using GeoGebra. You will be given one function (each group will have a different function and area) and be asked to find the other two functions that will give you the correct area. A separate sheet of paper should be handed in so that I can check the process and work involved in arriving to the solution. Grading will be done by using a checklist. //**(25 points)**//

• **Glogster**: Students will correctly identify pictures of graphs by matching them to their functions. Work should be completed on a separate sheet of paper before the results are made using Glogster. When presenting, be sure to explain the strategy you used in matching your graphs to the functions. **//(////25 points)//**

• **Blog**: Students will create a blogger account at the beginning of the unit. At the end of the week students will post focusing on what they learned that week. For each blog, answer the questions: "What did you learn this week?", "How can this be used in the real world?", and "What (if anything) do you still not understand?" This is a great way for the students to reflect on what they learned this week in classes as well as know the areas where they need to improve their skills. **//(60 points)//**

• **Quizzes**: Students will take short quizzes at the beginning of class to check for their understanding of certain topics. Notification will be given ahead of time so that there are no surprises. Only the best 5 quizzes will be counted towards the final grade. The material on the quizzes will never cover what was taught in the class date prior to the quiz. **//(50 points)//**

• **Tests**: There will be a final test at the end of the unit to assess student learning of the material taught over the course of the entire unit. This test will encompass areas such as, but not limited to, how to recognize graphs, how to graph functions, and real life applications of functions. **//(80 points)//**

• **iMovie**: This is the big project assigned to you during this unit that will bring everything together towards the end of this unit. Renowned Hollywood movie production company, Paramount Pictures, has just announced their next idea for a movie that features math used in the real world. As actors, your job is to create a short film that uses algebra in a real world setting in two developed ways. After your submission, the production crew will review all auditions. Whichever team creates the best film will become the stars of their new movie being shot in the San Francisco area. Because they will be reviewing a lot of films, they ask that your submission be between 3-5 minutes. Going over that allotted time will hurt your chances to land the job. Get creative and think of a way that math is helpful in problem solving; for the executives will want to make sure that whoever is starring in their film has a solid knowledge of functions and their uses. Go break a leg! The iMovie and Presentation will be graded using two separate rubrics, and the two will be averaged together for a final grade on the project. **//(125 points)//** =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)