S+Haase,Kaitlyn+Nicole

** Teacher: Ms. Haase ** ** Office: Ed. Center 006 ** ** Office Phone: (207) 867-5309 ** ** Office Hours: 1:30-2:30 M-F ** ** E-mail: kaitlyn.haase@maine.edu  **

** Summary of Unit ** Welcome to Algebra: Functions and Relations! Functions are everywhere! Amusement parks, sporting events, in music... all over! Since functions are so prevalent in our world, it is important for students to understand, manipulate, and illustrate these algebraic curvatures. Students will first learn of basic functions and their graphs; this will give them a basis of the behavior of the functions. After becoming familiar with the shapes, students will learn multiple techniques for solving functions; such as using the quadratic formula. With this new knowledge, students will be able to combine graphing and solving functions to solve real world problems.

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

** Students will understand that ** • functions can be solved using various methods. • functions can be interpreted using graphs, tables, and algebraic techniques. • learning basic functions translates to the ability of solving problems.

** Essential Questions ** • Why are different methods used to solve functions? • How can functions be interpreted by using graphs, tables, and algebraic techniques? • How do we use basic functions to solve problems?

** Students will know ** • Formulas: Quadratic • Definitions: function, variables, domain, range, graphs, tables, and relations • Critical Details: function notation, labeling graphs, vertical line test

** Students will be able to ** • describe various methods to solve functions • illustrate graphs of the basic functions • solve problems using basic functions • compare various methods to appropriately solve functions • consider solving real-world problems by using basic functions • recognize the graphs of the basic functions

** Performance Task Overview ** Your team of architects has been nominated to compete in Extreme Makeover: Home Edition's "Math Makes a Difference" challenge! Each team in the challenge will be assigned a basic function. The task is to present an explanation of the assigned function and at least two examples of how that function is used in the real world. Your team will also design a house using Google SketchUp by compiling shapes created by the graphs of the basic functions (a/x, x^n where n= 1-3, square root of x, ax^2+bx+c, absolute value of x, and kx+b). Your goal is to express your knowledge of functions and creativity to convince the producers at ABC that your team is the best! The grand prize of the challenge is $50,000 and the use of your team's blueprints on a future episode of Extreme Makeover: Home Edition.

** Expectations ** Students are expected to come to class prepared. This includes having homework and other assignments completed when they are due. Late work will not be accepted, unless permitted by me in advance. If a student is absent (and it is excused) he or she will need to communicate with me to make up missing work. Unexcused absences will result in no credit for missed work.

Students are also expected to show up to class on-time. Habitual tardiness will result in disciplinary consequences, such as detentions.

On homework, tests, and quizzes, students are expected to show all of their mathematical work. This will allow me to follow their thought processes and give more meaningful feedback. If no work is shown, students will not receive credit for that assignment.

When students are assigned written work, they are expected to express their own original thoughts and ideas. If any resources are used, students must cite them accordingly. There is zero tolerance for plagiarism in this class. Any plagiarized work will result in a 0, and further consequences may be enforced.

** Benchmarks (450 total pts) ** ** • Blog: ** Students will keep an ongoing blog to explain of different techniques they have been using to solve functions functions. Students can include questions and concerns on their blog, and I will give them immediate feedback. **(35 pts)**

** • Digital Scrapbook: ** Students will listen to music and develop ideas of curvatures based on their interpretation of the tones, pitches, volume.. etc. In pairs, students will use GeoGebra to make digital copies of their functions. They will need to include a table of values, domain, range, and label the graph correctly. The students will then compile their graphs and tables to create a digital scrapbook. *All functions must pass the vertical line test. **(50 pts)**

<span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** • iMovie: ** Students will work in teams to create a lesson in iMovie to teach a lesson to their classmates about solving quadratic functions by using GeoGebra and compile them into a digital scrapbook • iMovie: Create an informative iMovie to teach a lesson about functions • Comic Life: Use a certain method (quadratic formula, factoring). The iMove will be assessed using a rubric with the components: content, collaboration with peers, originality, script/storyboard, enthusiasm, and credits. **(70 pts)**

<span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** • Comic Life ** : There are so many techniques used to solve functions. Students will work in pairs. Each pair will be assigned a function and they will create a digital story using Comic Life to solve the function. For example, a given function could be x2 + 5x + 6 = 0, and the students would create a story line about finding the appropriate method to factoring (x2 + 5x + 6 = (x+2)(x+3)) and then solve a particular function by setting (x+2)(x+3)=0. The solution to x^2 + 5x + 6 = 0 is x= -3, -2. The Comic Life will be assessed using a rubric with the components: content, collaboration with peers, originality, script/storyboard, enthusiasm, and credits. **(65 pts)**

<span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** • Podcast: ** Students will use real-time webcams (such as the ones found on http://www.earthcam.com/ ) to find examples of functions in the real world. The examples could consist of applications of the functions or shapes that resemble the graphs of the functions (a/x, x^n where n=1-3, absolute value of x, square root of x, ax^2+bx+c, kx+b). Students will individually record their findings in Garageband or Audacity to create a podcast that they can share with the class. **(50 pts)**

<span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** • Glogster: ** Students will create a Glogster that will be a digital poster of reference for the sketches of the basic functions (a/x, x^n where n=1-3, absolute value of x, square root of x, ax^2+bx+c, kx+b). Glogsters will be assessed based on a checklist of necessary components that all graphs must have: labels (x-axis and y-axis), appropriate independent and dependent variables. **(60 pts)**

<span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** • Google SketchUp: ** Students will take on the role of architects to participate in a house design challenge. Students will work in teams, and will be assigned a function (a/x, x^n where n=1-3, absolute value of x, square root of x, ax^2+bx+c, or kx+b). They must explain the equation and graph of the function, in addition to providing at least two real world applications of that function. The house design will be created by incorporating shapes created by the functions’ (a/x, x^n where n=1-3, absolute value of x, square root of x, ax^2+bx+c, and kx+b) graphs. The team will create a 2D plan on paper, and then use Google SketchUp to create a house design, incorporating shapes of graphs of basic functions. make it into a 3D model. Their presentation will be assessed using a rubric with the components: content, collaboration with peers, preparedness, time limit, enthusiasm/speaks clearly, and stays on topic. The product created in Google SketchUp will also be assessed with a rubric, but the components are: content, attractiveness, originality, time/effort, workload, and plan. **(120 pts)**

<span style="line-height: 27.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** Grading Scale ** <span style="line-height: 19.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">** 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)