L6+Emery,+Jordan

COLLEGE OF EDUCATION, HEALTH AND REHABILITATION LESSON PLAN FORMAT** Students will understand that functions have various real-world applications. Students will know the definitions of domain, range, function, vertical-line test, and polynomial. Students will be able to consider the role functions play in real-world problem solving. 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 Student will be exposed to formative assessment for learning several times throughout the course of this lesson. First, students will be asked to use the Numbered Heads together learning technique to collaborate about functions in real-life. This will serve as a self-assessment of sorts to see if students understand that roles that functions take in the real-world. This also serves as a formative assessments because students will need to do some work to think about and consider how to solve these functions and why it is important to solve these functions. Then, students will be formatively assessed by self-assessing their skills with finding functions. Students will put their heads down and students will put a thumbs up to acknowledge if they have been successful in finding an example of a certain function. Students will do this for each function. Then, students will use a checklist to evaluate how they feel they have meet each of the standards or expectations covered in this lesson. They will also have to address how they though their Numbered Heads Together time went and then discuss what was useful and what was not useful. ** __ Technology: __ Students will be asked to use technology throughout the course of the lesson. Students will be asked to consider and work with images that are projected on the SMARTboard and they are going to be asked to submit their answers on the SMARTboard. Students will be expected to look up images to "fit" their functions, so they will be able to use their laptops and the GeoGebra program to make this happen. Finally, students will be asked create a digital scrapbook, which requires heavy computer usage.  __ Photography/Art __ : Students will be asked to produce a scrapbook that is full of images that model functions. Students will have the option to take their own pictures and then manipulate/highlight the function that they are representing using paint, GeoGebra, or Photoshop. All students will have to create a scrapbook, which requires some creative thinking and demonstration of understanding.  __ Social Studies: __ Students will be asked to look at several different sets of data that pertain to various national and international demographics. They will be asked to consider why it seems to be this way using their knowledge on the world. · __ Verbal __ : Students will communicate with peers, share ideas, and get instructions verbally. ·  __ Logical/Mathematical __ : Now that students have gained a good sense of functions and their capabilities, students are asked to apply all of their mathematical knowledge to demonstrate their understandings of modeling functions in real-life. Students are asked to go beyond finding shapes, and think of situations where functions do actually need to be solved. ·  __ Visual: __ Students are asked to find pictures to represent each situation. ·  __ Naturalist __ : Students will be required to include personal photographs that model a pattern in nature as one of the photos for the product on the digital scrapbook. ·  __ Bodily/Kinesthetic: __ Students will be asked to take their own pictures to model functions/situations that involve functions. ·  __ Interpersonal __ : Students are asked to work in a group during the Numbered Heads Exercise. ·  __ Intrapersonal __ : Students work alone to complete the graphic organizer and to complete the self-assessment of learning. I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. Absent students in this lesson will be asked to come in when they return and collect any handouts that we have done. They will be expected to have visited the class wiki and attempted to complete what they can from it and copied notes from their absent buddy. Then, I will ask them to come in during a study hall so that I can run through the examples that we have done in class using the Numbered Head Together technique. Once the student has mastered these concepts, I will assign him or her the digital scrapbook assignment.  For this lesson, students will be asked to create a digital scrapbook. This is an example of a Type II Technology because students will need to do some major adjustments to the pictures (make equations and identify functions) before they post them to the digital scrapbook. Also, the digital scrapbook will be full of resources that students have created to demonstrate their understandings on the lesson. Others have the opportunity to comment on the Digital Scrapbook and explore. Students will have to extend their knowledge and find themes that fit their page and find ways to digitally represent their understanding of functions in real life in a scrapbook. Students will be producing a lot during this project, which makes it a Type II technology.  __Materials: __ · SMART board · Projector · Calculators · Laptops (with GeoGebra) · Paper · Pencil · Strips Solving for "x" to group students [|stripsforgroups.doc] · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Idea Wheel Graphic Organizer]  <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Mini White Boards · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Dry Eraser Markers · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Checklist of understandings and questions handout [|checklistofunderstandings.doc] · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Student art from art classes · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Digital Cameras · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Digital Scrapbook Abstract Handout [|digtialscrapbookabstract.doc] · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Digital Scrapbook Rubric [|scrapbookrubric.xls] · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">PowerPoint for Numbered Heads Together Exercise [|NumberedHeadsTogether.ppt] · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Cardboard cutouts of functions · <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Yard Stick (for "Vertical Line") <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> __<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Resources: __<span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Domain]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Range]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Ordered Pair]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Function]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Vertical Line Test]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Logarithms and Exponential Equations]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Quadratic Function in Real Life]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Linear Functions in Real Life]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Using Cost, Profit, and Revenue and Linear Equations]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cubic Functions in Real Life]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Square Root Function in Real Life]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cube Root Function in Real Life]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine and Cosine Function Applications]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine Function Model]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine and Cosine Used to Model Real-Life Applications]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Tangent Function Application]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Applications of Exponential Functions]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Creative Commons Search Engine]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Smilebox Tutorial]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Pixys Image Search]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Applications of Quadratic Functions-1.doc] · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cubic Function Applications]  <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> __<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Technology: __<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">SMART board · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Projector · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Calculator · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Laptops (with GeoGebra) · <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Digital Cameras · <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Domain]  : This site explains what the domain is, how it is used, and it's role and importance in the use of functions. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Range]  : This link explains what the range is, the purpose it serves, and it's role and importance in conjunction with functions. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Ordered Pair]  : This link explains how an ordered pair relates to a function and how to determine whether a set of ordered pairs is a function or not. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Function:]  This link gives a definition of what a function is, what aspected need to be included for it to be a function, and modeled some situational examples of functions. ·  <span style="color: #0000fb; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Vertical Line Test]  : This link gives a brief summary of what the vertical line test is and how to use it to determine whether or not something is a function. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Logarithms and Exponential Equations]  : This website is used to create examples and exercises for students while they are in their Numbered Heads Together group. This may also serve as a resource for students when they begin to think about what photos they would like to use to model each function. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Quadratic Function in Real Life]  : A research website to provide students with examples and problems to work through during the Numbered Heads Together cooperative learning technique.This may also serve as a resource for students when they begin to think about what photos they would like to use to model each function. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Linear Functions in Real Life]  : This website is used as a resource to develop questions for students to answer during the numbered heads together. This may also serve as a resource for students when they begin to think about what photos they would like to use to model each function. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Using Cost, Profit, and Revenue and Linear Equations]  : This is another resource used to provide students with questions during their Numbered Heads Together Activity ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cubic Functions in Real Life]  : This is a resource that poses many examples of how the cubic function could be used. This is a good resource for students to get an idea on what they may include in their scrapbook, and works well for the Numbered Heads Together Technique ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Square Root Function in Real Life]  : This source provides me with the resources necessary to include the square root function into the Numbered Heads Together exercise. Students will also have this website available to them when creating their scrap books. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cube Root Function in Real Life]  : This is another source that acts as research and a rich resource for proving students with problems to solve during the Numbered Heads Together Technique. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine and Cosine Function Applications]  : This website is both a resource for me and my students. I will use this for examples during the Numbered Heads Together Technique as well as provide my students with this resource for when they create their scrapbooks. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine Function Model]  : This is used as a resource for me to provide my students with an example during the numbered heads together technique. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Sine and Cosine Used to Model Real-Life Applications]  : This is another resource for both my students and I. I will use this website to create examples and pose problems for my students to solve during the Numbered Heads Together activity. Students will have access to this site to gather ideas for images and explanations for their scrapbook. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Tangent Function Application]  :I will use this as an example of how the tangent function is used during the Numbered Heads Together technique. This will not be a research tool for students because they will be asked not to attempt finding a real-life example to model this situation, for it is too challenging. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Applications of Exponential Functions]  : This website provides several rich examples that I intend to use in the Numbered Heads Together Powerpoint that I am arranging for students. They will have this as a resource when they go to make their scrapbook. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Creative Commons Search Engine]  : I will provide this search engine to students if they plan on posting their scrapbook to the world wide web. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Smilebox Tutorial]  : This is a resource that I will use to teach my students how to use SmileBox. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Pixys Image Search]  : This site is another search engine that searches solely for videos and images off of the web. ·  <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Applications of Quadratic Functions-1.doc] : this document is another resource that I plan to pull examples from to include in my powerpoint. ·  <span style="color: #520f92; font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> [|Cubic Function Applications]  : This is another resource that provides examples for how the cubic function is used. I will use it for the Numbered Heads Together PowerPoint as well as provide it as a resource for my students. Though there is much freedom and independent work (with little instruction), the lesson is organized through the power point and the numbered heads together technique. There are going to be visual directions posted on the SMART board that helps remind students of the problem that they are on. Before we being, I will outline the procedures and rules involving in the Numbered Heads Together game. Students will be introduced to the digital portfolio before this project, so they will understand why this assignment is purposeful and the expectations that go along with it. This lesson accommodates learners whose focus is on detail and deep exploration because they not only have to solve the problems or come up with an answer that I have posed on the PowerPoint, but they will have to ensure that everyone in the group has the ability to understand the group's thought process. They will have to focus on details and analyze concepts to understand what some of the scenarios are modeling. This is going to be very appealing to some learners, for they are going to have to gain ownership over what they believe is true and be able to back up their thoughts with specific examples.
 * UNIVERSITY OF MAINE AT FARMINGTON
 * __ Teacher’s Name __**** : ** Ms. Emery ** __Date of Lesson__:** Lesson 6 (Empathy)
 * __ Grade Level __**** : ** 10 ** __Topic__:** Functions
 * __ Objectives __**
 * __ Maine Learning Results Alignment __**
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Rationale: ** In this lesson, students will interpret graphs and tables of functions that correlate with real-life examples of functions and find meaning in what the function is telling us.
 * __ Assessment __**
 * Formative (Assessment for Learning)
 * Summative (Assessment of Learning)
 * 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 for their summative assessment. 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 and their importance in real life. The scrapbook will be graded using a checklist that lists everything that should and will be considered in the scrapbook.**** **
 * __ Integration __**
 * __ ____Groupings____
 * In this lesson, students will participate in the Numbered Heads Together cooperative learning technique. To group students in this lesson, I will hand out a small strip of paper that has a function that needs solving. The x-value that the student is solved for will have an answer ranging from 1-5. Students will have to work individually to solve these functions and then get into their groups depending on the equation that they have solved "x" for. Then, within the group, students will be given another function to solve x for. Whoever finishes this first will be designated as number one for their group, the person who finishes second will be number two, and so on. Once they are given their numbers, all students have the same role: a participant in the game that we are going to play. One student should obtain the role of time keeper. Another student should become a group leader that ensures that everyone understands what is going on during the time of discussion. A third person should record the answer and make sure that everyone understands the math. These roles will switch for every round. Some students will not have a role during the lesson.** __**
 * __ Differentiated Instruction __**
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Strategies **<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * Modifications/Accommodations **
 * Extensions **
 * __ Materials, Resources and Technology __**
 * __ 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: //** This lesson is very accommodating to all students. First, students are exposed to personal freedom and extensions to activities through the Numbered Heads Together technique. I will provide my students will their laptops as a resource as well as their previous products that they have created for me and they will be given time to explore the answer to the question. They are exposed to spontaneity when I call a number after an elapsed amount of time and ask randomly for a group to reveal their answers and be ready to explain.

The lesson is also designed to address those students who do not feel confident gaining ownership over their feelings. The Numbered Heads Together technique is designed to create supportive grouping that ensures that all students will come out of this lesson understanding the material. The challenge and grouping forces colleagues to be respectful and provide a safe climate for thinking. The group will be able to refine their ideas by discussing their thought process with the teacher. The encouraging atmosphere comes with having each student feel comfortable enough to present their findings to the class. · __ Verbal __ : Students will communicate with peers, share ideas, and get instructions verbally. ·  __ Logical/Mathematical __ : Now that students have gained a good sense of functions and their capabilities, students are asked to apply all of their mathematical knowledge to demonstrate their understandings of modeling functions in real-life. Students are asked to go beyond finding shapes, and think of situations where functions do actually need to be solved. ·  __ Visual: __ Students are asked to find pictures to represent each situation. ·  __ Naturalist __ : Students will be required to include personal photographs that model a pattern in nature as one of the photos for the product on the digital scrapbook. ·  __ Bodily/Kinesthetic: __ Students will be asked to take their own pictures to model functions/situations that involve functions. ·  __ Interpersonal __ : Students are asked to work in a group during the Numbered Heads Exercise. ·  __ Intrapersonal __ : Students work alone to complete the graphic organizer and to complete the self-assessment of learning For this lesson, students will be asked to create a digital scrapbook. This is an example of a Type II Technology because students will need to do some major adjustments to the pictures (make equations and identify functions) before they post them to the digital scrapbook. Also, the digital scrapbook will be full of resources that students have created to demonstrate their understandings on the lesson. Others have the opportunity to comment on the Digital Scrapbook and explore. Students will have to extend their knowledge and find themes that fit their page and find ways to digitally represent their understanding of functions in real life in a scrapbook. Students will be producing a lot during this project, which makes it a Type II technology.
 * // Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. //**
 * // Rationale: //** This lesson's primary focus was around the facet of "empathy". It may seem odd to apply this concept to Mathematics, but students will need to work together to understand and feel confident about the answers they come up with during the Numbered Heads Together game. They need to understand that not everyone has the same perspective and that just because it may seem a particular way to one person, it is not this way for all students. Students will also have to consider what my intentions are for them in this assignment and what I am trying to get them to take from this lesson.
 * // Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. //**
 * // Rationale: //**
 * // Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. //**
 * // Rationale: //** Students will be asked to complete a variety of formal and informal assessment strategies to evaluate the development of the learner. For informal assessment, students will be exposed to formative assessment for learning several times throughout the course of this lesson. First, students will be asked to use the Numbered Heads together learning technique to collaborate about functions in real-life. This will serve as a self-assessment of sorts to see if students understand that roles that functions take in the real-world. This also serves as a formative assessments because students will need to do some work to think about and consider how to solve these functions and why it is important to solve these functions. Then, students will be formatively assessed by self-assessing their skills with finding functions. Students will put their heads down and students will put a thumbs up to acknowledge if they have been successful in finding an example of a certain function. Students will do this for each function. Then, students will use a checklist to evaluate how they feel they have meet each of the standards or expectations covered in this lesson. They will also have to address how they though their Numbered Heads Together time went and discuss what was useful and what was not useful.

For a formal assessment, 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 for their summative assessment. 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 and their importance in real life. The scrapbook will be graded using a checklist that lists everything that should and will be considered in the scrapbook. The classroom will be arranged in centers for this lesson. In this lesson, students will be spending a majority of time working in their Numbered Heads Together groups. The centers will be labeled with numbers 1-5 so that students will know where they are going to be placed in the room. The centers will be arranged around the SMART board so that it is not blocked and students and all students will have a good view of the front of the room. The lesson agenda is as follows: <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> __ Day 1: __ ·  Students will come in and take their seats (2 min) ·  Students will observe the art work and identify functions within the artwork (5 min) ·  Students will use the cardboard cutouts from lesson 3 to remind themselves of the vertical line test (2 min) ·  Students will be asked to find the domain and range of example functions (2 min) ·  We will review the terms function and polynomial (2 min) ·  <span style="font-family: "Times New Roman"; font-size: 10.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> Students will receive the [|Idea Wheel Graphic Organizer] and asked to complete it (5 min) ·  Students will receive a strip of paper with an equation on it. They will solve for x and get into groups (5 min) ·  Students will receive their Digital Scrapbook Assignment and be asked to start thinking about it (5 min) ·  Students will do the Numbered Heads Together Activity (50 minutes) ·  Students will be asked to complete a blog entry on the progress the team has made for homework. (2 min) <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> __ Day 2: __ ·  Students will return to their Numbered Heads Together groups (3 min) ·  Students will continue the Numbered Heads Together Activity (20 min) ·  Students will fill out a Checklist of Understandings Handout and review it (10 min) ·  Students will hold a discussion and self-evaluate by rating their understandings with their thumbs(10 min) ·  Students will have an opportunity to change their understandings from any of the examples in the Numbered Heads Together Group (10 min) ·  Students will have a short tutorial on how to use Smilebox (7 min) ·  Students can begin their scrapbooks (20 minutes) <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> In this lesson, students will understand that functions have various real-world applications. Though it may not seem important, but having the ability to recognize functions in real-life can be very helpful in predicting outcomes. I will give the following "teaser" (if you will) to get students thinking about the importance of functions in real life: "Think of the shape of a water bottle or the path a baseball follows after it is hit by a baseball player. Functions do more than keep track of order pairs and relationships: they create lines. Without these functions in our daily lives, we would be essentially shapeless!". With this in mind, students will meet the Maine Learning Result Standard that // students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques //. In this lesson, the focus is on interpreting the graphs and what they mean in real life. I will hook my students by having students observe abstract pieces and have them identify functions that show up within paintings. This will serve as a pre-assessment to help me see how many students can recognize without having labels or words for them to work from as well as gets students thinking about functions in different ways. <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; line-height: 19px;"><span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> This lesson, students have already been equipped with all of the terms that they need to know in previous lessons. The terms are: [|domain], [|range] , [|function] , [|vertical-line test] , and [|polynomial] .In order to ensure that my students have an understanding with these terms, I will do an activity with the cardboard cutouts in lesson three to remind them of what the vertical line test means. Then, I will ask students to get up and act out domain and range. They will then be asked to find the domain and range of a few sets of numbers quickly for practice. For polynomial and function, they will be asked to quickly converse with a partner and report out in a class discussion on what these terms mean. I will deliver most of my instruction through posing a question for my students to explore and helping them work through the answer. After they have confirmed their understandings, I will present the digital scrapbook project so that students will have a clear view on where the lesson is going and what the intentions for the assignment is. After, I will have them work through the PowerPoint and work in groups to present their findings by calling out random numbers to come work out the activity. I will not say a word when they are presenting and I will let them determine whether or not their thought process is correct. When they do the thumb activity, I will get a feel on who is confident with this lesson or not. i will hand out an answer sheet to their questions and students will have a chance to go back and revise any of their thoughts now knowing the answers to the problems. They will be asked to consider what details they missed or how they misinterpreted the lesson. I will check for understanding in several ways. First, students will have to identify functions in the art pieces that I have in the room and that serves as a pre-assessment. Then, students will be asked to report their findings for every problem, so I know if they are understanding the content or not. Next, I will monitor the understandings by doing the thumb rating activity to check how they feel they have progressed in their learning during this lesson. Finally, students will be given a formal checklist so that I have a written response about the progress of the lesson. They will be formally assessed on their understandings through the digital scrapbook. Students will be asked to include some images from nature, so that they know that we do not need to fabricate every example of the functions (See content notes) <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> In this lesson, students will be given the opportunity to explore their knowledge by using the [|Idea Wheel Graphic Organizer] to think about how functions are modeled in real life. They will then experience the way that functions are modeled in real life by doing the PowerPoint Activity in the Numbered Heads Together groups. Students will have to apply what they have learned in previous lessons to recognize the shape of the graph and understand what is is that they need to represent. They will be given an array of situations so that the thought process does not become routine and they will need to formulate their responses. By the end of this lesson, students will be able to consider the role functions play in real-world problem solving. For this lesson, students spend a large majority of time in their Numbered Heads Together groups. To group students in this lesson, I will hand out a small strip of paper that has a function that needs solving. The x-value that the student is solved for will have an answer ranging from 1-5. Students will have to work individually to solve these functions and then get into their groups depending on the equation that they have solved "x" for. Then, within the group, students will be given another function to solve x for. Whoever finishes this first will be designated as number one for their group, the person who finishes second will be number two, and so on. Once they are given their numbers, all students have the same role: a participant in the game that we are going to play. One student should obtain the role of time keeper. Another student should become a group leader that ensures that everyone understands what is going on during the time of discussion. A third person should record the answer and make sure that everyone understands the math. These roles will switch for every round. Some students will not have a role during the round. In this lesson, students will have optimal chances to rethink, revise and refine their product. Students will revise their understanding about functions using the information that they have filled in on the idea wheel and considering if there is a better way to model the data using another function. Students will revise their thinking after they have completed the Numbered Heads Together task and have received their answers. Finally, students will refine their understanding by changing the examples that they have misinterpreted. <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> Students will self-assess throughout the course of the lesson. Their first self-assessment is when they walk through the door and they are given the task of recognizing functions. The next self-assessment comes when students are asked to complete a checklist of understandings that determine whether the student feels confident with his or her ability to recognize functions and modeling real-life data. Students will also self-assess using the "thumbs" rating system so I can see where all my students feel they are in their learning progress. I will provide timely feedback to students by answering questions and commenting on the blog entries that they post. I will address any reoccurring problems as a class so that students are not being mislead in this process. The homework for this lesson is to write an informal blog entry on the progress that was made in the classroom. This is a great homework assignment that connects to the lesson because students are forced to reflect on the day's events. This lesson connects to future assessments because it prepares them to do the // Donald in Mathemagic Land // movie. In the movie, they are asked to find examples to represent their function, and this gives them some practice before working with it in the final assessment.
 * __ Teaching and Learning Sequence __**** : **
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Where, What, Why, Hook, Tailors: Visual, Interpersonal, Intrapersonal, Mathematical/Logical, Bodily/Kinesthetic. **<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Equip, Explore, Rethink, Revise, Refine, Tailors: **<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;"> **Interpersonal, Mathematical/Logical, Verbal/Linguistic, Visual/Spatial, Naturalist, Intrapersonal.**
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">Explore, Experience, Rethink, Revise, Refine, Tailors: Interpersonal, Intrapersonal, Logical/Mathematical, Verbal. **<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt;">
 * <span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">Evaluate, Refine, Tailors: Intrapersonal, Logical/Mathematical, Visual, Verbal. **<span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Arial; mso-bidi-font-size: 13.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">


 * Content Notes**

For the hook, there will be many answers to what may be found in the art examples. All students have a different perspective and they will see various things, so I will acknowledge their understandings based off what the image is and how they are looking at it. There is no right or wrong answer here, I just want to see how creative and observant my students are before beginning the lesson.

Then, I will need to equip (or at least remind my students) of the terms that they will need to know.

__[|Domain and Range:]__ <span style="display: block; font-family: Times; font-size: medium; line-height: normal; text-align: left;"> <span style="font-family: arial,helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">Let's <span style="font-family: Arial,Helvetica,sans-serif;"> to the subject of domains and ranges. When functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, being just sets of points. These won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. For instance: > {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} <span style="font-family: Arial,Helvetica,sans-serif;">The above list of points, being a relationship between certain //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">'s and certain //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">'s, is a relation. The domain is all the //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-values, and the range is all the //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">-values. To give the domain and the range, I just list the values without duplication: domain: {2, 3, 4, 6} range: {–3, –1, 3, 6} (It is customary to list these values in numerical order, but it is //<span style="font-family: Arial,Helvetica,sans-serif;">not //<span style="font-family: Arial,Helvetica,sans-serif;"> required. Sets are called "unordered lists", so you can list the numbers in any order you feel like. Just don't duplicate: technically, repititions are okay in sets, but most instructors would count off for this.) While the given set does represent a relation (because //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">'s and //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">'s are being related to each other), they gave me two points with the same //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-value: (2, –3) and (2, 3). Since //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> = 2 <span style="font-family: Arial,Helvetica,sans-serif;"> gives me two possible destinations, then this relation is not a function. Note that all I had to do to check whether the relation was a function was to look for duplicate //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-values. If you find a duplicate //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-value, then the different //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">-values mean that you do //<span style="font-family: Arial,Helvetica,sans-serif;">not //<span style="font-family: Arial,Helvetica,sans-serif;"> have a function. > {(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}  <span style="font-family: Arial,Helvetica,sans-serif;">I'll just list the //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-values for the domain and the //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">-values for the range: domain: {–3, –2, –1, 0, 1, 2} range: {5} Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved <span style="font-family: Arial,Helvetica,sans-serif;">This is another example of a "boring" function, just like the [|example] <span style="font-family: Arial,Helvetica,sans-serif;"> on the previous page: every last //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-value goes to the exact same //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;">-value. But each //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">-value is different, so, while boring, this relation is indeed a function. In point of fact, these points lie on the horizontal line //<span style="font-family: Arial,Helvetica,sans-serif;">y //<span style="font-family: Arial,Helvetica,sans-serif;"> = 5 <span style="font-family: Arial,Helvetica,sans-serif;">. <span style="font-family: Arial,Helvetica,sans-serif;">There is one other case for finding the domain and range of functions. They will give you a function and ask you to find the domain (and maybe the range, too). I have only ever seen (or can even think of) two things at this stage in your mathematical career that you'll have to check in order to determine the domain of the function they'll give you, and those two things are denominators and square roots. <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">The domain is all the values that //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> is allowed to take on. The only problem I have with this function is that I need to be careful not to divide by zero. So the only values that //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> can //<span style="font-family: Arial,Helvetica,sans-serif;">not //<span style="font-family: Arial,Helvetica,sans-serif;"> take on are those which would cause division by zero. So I'll set the denominator equal to zero and solve; my domain will be everything //<span style="font-family: Arial,Helvetica,sans-serif;">else. // //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;">2 <span style="font-family: Arial,Helvetica,sans-serif;"> – //<span style="font-family: Arial,Helvetica,sans-serif;">x // <span style="font-family: Arial,Helvetica,sans-serif;"> – 2 = 0 > (//<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> – <span style="font-family: Arial,Helvetica,sans-serif;">2)( //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> + 1) = 0 <span style="font-family: Arial,Helvetica,sans-serif;"> > //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> =2 or //<span style="font-family: Arial,Helvetica,sans-serif;">x //<span style="font-family: Arial,Helvetica,sans-serif;"> = –<span style="font-family: Arial,Helvetica,sans-serif;">1 <span style="font-family: Arial,Helvetica,sans-serif;">Then the domain is "all //<span style="font-family: Arial,Helvetica,sans-serif;">x // <span style="font-family: Arial,Helvetica,sans-serif;"> not equal to –1 or 2". <span style="font-family: arial,helvetica,sans-serif;">
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">State the domain and range of the following relation. Is the relation a function?
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">State the domain and range of the following relation. Is the relation a function?
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Determine the domain and range of the given function:

This characteristic of non-functions was noticed by I-don't-know-who, and was codified in "The Vertical Line Test": Given the graph of a relation, if you can draw a vertical line that crosses the graph in more than one place, then the relation is not a function. Here are a couple examples:
 * __[|Vertical Line Test:]__

[|Function] ** There are different ways of looking at functions. We will consider a few. But first, we need to discuss some terminology. A "relation" is just a relationship between sets of information. Think of all the people in one of your classes, and think of their heights. The pairing of names and heights is a relation. In relations and functions, the pairs of names and heights are "ordered", which means one comes first and the other comes second. To put it another way, we could set up this pairing so that either you give me a name, and then I give you that person's height, or else you give me a height, and I give you the names of all the people who are that tall. The set of all the starting points is called "the domain" and the set of all the ending points is called "the range." The domain is what you start with; the range is what you end up with. The domain is the // x // 's; the range is the // y // 's. (I'll explain more on the subject of determining domains and ranges [|later] .) A function is a "well-behaved" relation. Just as with members of your own family, some members of the family of pairing relationships are better behaved than other. (Warning: This means that, while all functions are relations, since they pair information, //not// all relations are functions. Functions are a sub-classification of relations.) When we say that a function is "a well-behaved relation", we mean that, given a starting point, we know exactly where to go; given an //x//, we get only and exactly one //y//. Let's return to our relation of your classmates and their heights, and let's suppose that the domain is the set of everybody's heights. Let's suppose that there's a pizza-delivery guy waiting in the hallway. And all the delivery guy knows is that the pizza is for the student in your classroom who is five-foot-five. Now let the guy in. Who does he go to? What if nobody is five-foot-five? What if there are //six// people in the room that are five-five? Do they all have to pay? What if you are five-foot-five? And what if you're out of cash? And allergic to anchovies? Are you still on the hook? Ack! What a mess! ||

[|Polynomial] A mathematical function that is the sum of a number of terms)

Now that I have provided my students with the proper knowledge, I will begin the Numbered Heads Together Activity using the PowerPoint here:

This document provides the answers for the Powerpoint:

[|Smile Box Instructions] <span style="font-family: arial,verdana,tahoma,helvetica,sans-serif; font-size: 9px; line-height: normal;"> <span style="font-family: Arial,Helvetica,sans-serif;">hree Step Process I had a little play with Smilebox service today and it was surprisingly easy. There are three basic steps to the process: <span style="font-family: Arial,Helvetica,sans-serif;">Creating A <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">Scrap <span style="font-family: Arial,Helvetica,sans-serif;">book With Smilebox In just a few minutes, I created this four page digital <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">scrap <span style="font-family: Arial,Helvetica,sans-serif;">book from scratch with my own photos: Smilebox <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">Scrap <span style="font-family: Arial,Helvetica,sans-serif;">book Example (use the right arrow to move between the pages) <span style="font-family: Arial,Helvetica,sans-serif;">How Much Does It Cost? The basic Smilebox service is free but your design is shown with a short ad. If you viewed my Smilebox <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">scrap <span style="font-family: Arial,Helvetica,sans-serif;">book, you'll see some Google Ads down the right hand side of the screen, which in reality isn't all that intrusive. The premium version of the service costs a one time fee of US$1.99 (per design). The benefits of the premium service include being able to play the full screen version without ads and perhaps more importantly, the ability to print the design (you and your recipients). Making Memories and <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">Scrap <span style="font-family: Arial,Helvetica,sans-serif;"> Girls Something else you might find interesting about the Smilebox service is that they are using hundreds of designs from content partners such as Making Memories, Madison Park Greetings (a leading designer and manufacturer of gift and stationery products), <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; text-decoration: none;">Scrap <span style="font-family: Arial,Helvetica,sans-serif;">girls.com and other independent Flash designers. Making Memories have even further involvement with the Smilebox organization (going by their About Page at least!) Something for us mere mortals to keep an eye on.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Select a design
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">Personalise the design (add photos, words, music, select colours and embellishments etc.)
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Share via email or print

Handouts
 * Strips Solving for "x" to group students [[file:stripsforgroups.doc]]
 * [|Idea Wheel Graphic Organizer]
 * Checklist of Understandings and Questions Handout[[file:checklistofunderstandings.doc]]
 * Digital Scrapbook Abstract Handout [[file:digtialscrapbookabstract.doc]]
 * Digital Scrapbook Rubric [[file:scrapbookrubric.xls]]
 * PowerPoint for Numbered Heads Together Exercise[[file:NumberedHeadsTogether.ppt]]