S3+Emery,+Jordan

=Stage 3 - Plan Learning Experiences and Instruction=

// **Note:** // (How are you using technology as a teacher? How are your students using technology?) [|Verbal-Linguistic] [|Logical/Mathematical] [|Visual/Spatial] [|Bodily/Kinesthetic] [|Musical/Rhythmic] [|Intrapersonal] [|Interpersonal] [|Naturalist]
 * 1. (W)** **Where** (Students understand that....), **Why** (Real Life), **What** (MLR)
 * 2. (H)** **Hook** (Engage)
 * 3. (E)** **Equip** (Content - Students will know...), **Explore** ([|Graphic Organizer]), **Experience** ([|Cooperative Learning]), and Resources (Include Web resources)
 * 4. (R)** **Rethink, Revise, Rehearse,** and **Refine** (Feedback, [|Checking for Understanding])
 * 5. (E)** **Evaluate** (Formative Assessment)
 * 6. (T) Tailor** (give an example of each Multiple Inteligences)
 * 7. (O)** **Organize** (Students will be able to ...), Product (Technology) [|Recipes4Success Lesson Library]. Here you will find exciting, standards-based lessons for Tech4Learning products. Each lesson includes step-by-step directions for both teachers and students, as well as links to high-quality examples, templates, and support resources.

=Lesson 1= Functions can be found in doctors charts, exercise equipment, measuring the pitch of music, and to demonstrate the path of an object. Where else are functions found in real-life? **(Why)** 2. Students will listen to a variety of different music clips (created in garage band or found in popular songs) that symbolize the shape of various functions. Students will have to react to/explain what they feel each clip is representing. **(Hook)** 3. Students will know the definitions of "domain", "range", "ordered pair", "function" and the vertical line test. **(Equip)** Students will use the "ticktacktoe" chart to write record each function and what details they feel are important. **(Explore)** Students will use a 3-minute review with a peer to compare charts and add/change any information on their graphic organizers. **(Experience)** 4. Using new knowledge, students will go back to the "hook" and match the music clip description with the graph of the function. **(Rethink)** After each clip is played, students will hold their hands up and a consensus will be taken on which function the clip represents. Students will then turn to a partner to clear up any misunderstandings or confusion. **(Revise)** Students will be able to return to their graphic organizer to add/change details once the activity is complete. Teacher will provide students will feedback on organizers so that they will be able to produce a good e-folio. **(Refine)** 5. After students complete their lesson on recognizing graphs, they will complete a checklist of their understandings. There will be a space for additional comments where they can write if they have any other questions. **(Evaluate)** 6. **Verbal**: I will be directing students on how to recognize graphs, what the graphs look like, and how to complete tasks all in a verbal manner. 7. Students will be able to recognize the graph and sketch graphs of basic functions. **(Application) 3 Days** Product: E-folio (using Inspiration) || =Lesson 2=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 1. Students will understand that functions can be expressed in several ways. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logical:** Students are in a Logical/Mathematical setting in which students need to use mathematics skills to compute answers and process information.
 * Visual:** Graphs of each of the functions are going to be on the screen (produced with GeoGebra) so that students will have a visual demonstration of what each looks like.
 * Musical:** Students will listen to music clips that represent the shape of functions.
 * Intrapersonal:** Students work individually to fill out graphic organizer and process the information.
 * Interpersonal:** Students will work in cooperative learning to clear up misconceptions with understanding functions as well as when they revise their thinking about functions. **(Tailor)**

You and your parents have a relationship. So don't you and your friends, you signifiant other, etc. Functions demonstrate relationships, and like your personal relationships, each are different. **(Why)** 9. Students will walk in to see an video of an interpretive dancer playing. I will let them watch the video, but not answer any questions. In a 3 minute planning time, students will need to work in groups of 5 to find body movements that represent each of the functions and choreograph them in a way in which they flow together. 10. Students will know the definitions of polynomial and degree. **(Equip)** Students will use "thought web" to record each function and record (a) the equation, (b) the graph, (c) odd behaviors. **(Explore)** Using the "Think-Pair-Share" approach, students will reflect on what they have learned about the different types of functions and then find a peer to express their thoughts with. **(Experience)** 11. I will now manipulate the functions (adding a negative, moving the units up) and have the students think about how the shape of the functions are affected. Students will now hold an in-class debate about why functions appear as the do. **(Rethink)** Students will receive an "exit ticket" where they are to answer two questions before leaving class. One question requires a factual answer about the shape or algebraic equation of a function, and the second answer ties together more than one of the concepts in class. The answers will be collaborated by the teacher and prompted at the beginning of next class. **(Revise)** Students will get a chance to make notes and change any of the information on their graphic organizer, ask questions and work with peers on topics they are still struggling with for ten minutes before producing the wiki page product. 12. Students will answer questions about how they feel about the information presented in class. They will be asked to specifically respond to how the "Think-Pair-Share" time went, and what they gained from that experience. **(Evaluate)** 13. **Verbal:** Students will be exposed to verbal explanations, descriptions, and processes throughout the duration of this lesson. 14. Students will be able to express a variety of functions through graphs and algebraic equations. **(Explanation) 2 Days** Product: Wiki || =Lesson 3=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 8. Students will understand that functions can be expressed in a variety of ways. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logical:** Students will be asked to evaluate graphs, the effects of numbers, and how graphs and algebraic equations work together to produce a function.
 * Visual:** Students will be exposed to several pictures of the graphs. Also, I hope to provide some sort of visual prompt so students are able to link the equations with the graphs.
 * Intrapersonal:** Students will work individually to fill out "exit tickets", "think" during "think-pair-share", and fill out graphic organizer.
 * Interpersonal:** Students have to work in pairs during "think-pair-share" to eliminate any misunderstandings.
 * Bodily/kinesthetic: Students will use body movements to represent the shape of functions.  (Tailor)**

What happens when you look in a mirror? How about when you flip yourself upside down? What does the world look like? Functions go through the same changes that we experience everyday, just on an x-y plane. **(Why)** 16. Students will be asked to log on to their computers and play a quick "find the 5 differences in the two pictures games". I will then ask how they think it relate to functions. Then I will pull up a picture of two functions (one has been manipulated), and asked what's changed. From that, I will introduce my lesson on graph transformations. **(Hook)** 17. Students will know the techniques horizontal stretch, vertical stretch, reflection over x-axis, reflection over y axis. **(Equip)** Students will fill out the "K" "W" of the KWHL graphic organizer after being presented with a digital presentation of graph transformations. **(Explore)** Using "Round Robing Brainstorming", students will work together to add to their "W" column and create a list for the "H" column. **(Experience)** 18. Students will be asked to think about how the ordered pair are affected by graph transformations. Students will also be asked to think about what a graph would look like if it were reflected across the y=x line. **(Rethink)** Students will be asked to list the "big ideas" that were covered in the class. Also, there is a separate column for students to include any misconceptions they are still having so I will know if I have to revisit that topic before moving on. **(Revise)** Students will work become part of a small group to quickly engineer a model to explain a reoccurring misconception and explain it to the class. The teacher will probe the students in the right direction, but not give them the answer. **(Refine)** 19. Students will be asked to revisit their graphic organizer. Students will highlight the answers that they feel were answered and explain how their questions were answered. Students should also include what extra material they learned that they did not expect to learn. **(Evaluate)** 20. **Verbal:** Students will be in a classroom setting where explanations, descriptions, and instructions are verbal. Students need to listen to teachers and peers for key information. 21. Students will be able to translate functions of graphs according to equation manipulations. **(Interpretation) 3 Days** Product: Garage Band Production || =Lesson 4=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 15. Students will understand that there are many techniques used to solve functions and change the appearance of functions. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logical/Mathematical:** Students are asked to use their knowledge of functions and apply their knowledge of their shapes and how a number or negative sign will affect the appearance of the graph.
 * Visual:** Students will be exposed to "before" and "after" pictures of graphs so that students can visualize the affects transformations have on graphs.
 * Musical:** Students are asked to create a Garage Band product that entails the information learned in the lesson. They are also to include their own interprertation of musical symbolization of the newly transformed functions.
 * Intrapersonal:** Students are asked to work individually to complete the tasks of filling out the two first columns of the graphic organizer as well as revisiting the organizer to assess their personal learning growth.
 * Interpersonal:** Students are asked to work in groups to complete the graphic organizer as well as to refine some topics that are unclear. **(Tailor)**

When you have a plumbing problem, you don't look up an electrician and when your pet is sick, you don't call an exterminator. In this lesson, students will learn how to solve their problems by "looking up" the right solution. **(Why)** 23. Moosehead Lake has seen some major developmental changes over the past 100 years. As the face of the lake changes, erosion, tree populations, and pollution are all becoming big concerns to locals. By bringing up local data and showing how it can be modeled in functions, I can demonstrate to students that by knowing what methods to use to solve functions will help up save the habitat. **(Hook)** 24. Students will know the definitions of degree and logarithm and will know the techniques substitution, factoring, the quadratic formula, and factoring. **(Equip)** Students will use the internet (and research each of the methods on pre-researched websites) to fill our the "scale" graphic organizer, organizing the techniques from "the most commonly used" to the "least commonly used". **(Explore)** Students will use a jigsaw and become an expert on one of the techniques used to solve functions. They will discuss and solidify their understanding in their "expert" group and then report back and teach their findings to their group members. **(Experience)** 25. Students will be given a complex function (that looks like two functions combined) and they will be asked to determine which method would be the best way to solve this function. Students will be able to use bookmarked online resources to aid in their thinking. **(Rethink)** After students "rethink" about solving functions, the class will work as a whole (using a SMARTboard and a digital TI-84 to demonstrate the different ways of solving the functions. **(Revise)** After I get a chance to scan all of the blog entries and acknowledge all misunderstandings, students will return to their jigsaw groups and give a quick overview of when to use all of the techniques to their peers. With the help of peers and myself, we will be able to clear up any lingering misconceptions. **(Refine)** 26. Students will write a "three minute essay" explaining the big ideas that were expressed in the lesson (for one minute), what they learned (for one minute), and what they still feel like they need to work on/do not understand (for one minute). They are to post this as the beginning of their blog entry. **(Evaluate)** 27. **Verbal:** Students will be given all instructions, examples, and demonstrations verbally. Students will mostly be addressed in this manner in this lesson. 28. Students will be able to solve functions using a variety of methods. **(Perspective) 3 Days** Product: Blog entry that explains/provides links on how/when to use various methods || =Lesson 5=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 22. Students will understand that there are many techniques used in order to solve functions and change the appearance of functions. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logical/Mathematical:** Students will have to use their Logical/Mathematical skills to solve first determine which method should be used to solve the problem and second how to solve the problem.
 * Visual:** Students will required to give one another a visual demonstration on how to solve the problem (the process) and also be able to draw a situation that demonstrates how to solve the problem (with using as few mathematical symbols as possible).
 * Intrapersonal:** Students will write their three minute essay and fill out their graphic organizer individually.
 * Interpersonal:** Students will work in a jigsaw to learn the different methods that are available to solve functions.
 * Naturalist:** Students are asked to apply their knowledge about logarithmic functions and exponential functions to nature and how they would be able to pinpoint particular dates of good/bad growth in nature. **(Tailor)**

How fast will something slide down a ramp or a hill? What is a medicine's half-life? Without the ability to solve functions, we would not know the answers to these questions without much (potentially harmful) trial and error. **(Why)** 30. There will be a domino structure set up. Probing software will be attached so that the start and stop time will be graphed onto a computer. Students will watch as a maze of dominos topple over. I will then ask them how does the dominos falling over (as well as the data we collected in the computer with the probing software) be used to solve functions. **(Hook)** 31. Students will know the definitions of degree and logarithm and will know the techniques substitution, factoring, the quadratic formula, and factoring. **(Equip)** Students will the Webquest provided to them, as well as additional (predetermined websites) to choose from one of three situations to (1) model a function after, (2) pick a point in time in which they foresee a problem, (3) solve the equation for that time. They will record each step in the "cycle" graphic organizer to outline their ideas. They will ultimately complete all three situations. **(Explore)** In a Team-Pair-Solo structure, students will begin working on the graphic organizers to compile information about each of the topics according to which they chose to do first. Then, they will break into pairs to determine which function they believe is appropriate to model the real-life situation. Finally, the student will work on his or her own to complete the solving of the problem.**(Experience)** 32. After completing each of the three tasks, I will go back and change the one aspect in each of the of the situations. I will have students brainstorm ideas (and compile them as a class) as to how the answers would change. (Rethink) Students will use the brainstorm to explore the each of the situations further, looking for more evidence on the matter. Students will use this time to electronically submit their answers via Google Docs and a bar graph will be formed. Any "other" answers will be addressed and clarified. Students will work with their teams to compare answers and correct any mistakes they had. **(Revise)** After the group discussion, students will be able to hold mini-conferences with other students and teachers at the end of class and in a wiki discussion. They will be able to make any alterations they feel necessary before moving on to modeling their final task. **(Refine)** 33. Students will form a "closing circle" to discuss the happenings of the day. Students will be asked to address (1) their answers and (2) what they felt the big idea is. I will note the biggest understandings and complaints and provide feedback (both in a group and individually) for major concerns. **(Evaluate)** 34. **Verbal:** Students will receive all information, instruction, and descriptions in this manner. Students will also have to use verbal skills to successfully communicate ideas with peers. 35. Students will be able to compare methods of solving functions and apply their knowledge to real world experiences. **(Self-Knowledge) 2 Days** Product: iMovie || =Lesson 6=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 29. Students will understand that functions have various real-world applications. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logical/Mathematical:** Students will use their Logical/Mathematical Intelligence to process information and develop and solve the problems that are involved in this lesson.
 * Visual:** Students will be provided with visual prompts of each of the different types of functions so that they are able to better determine which one of the functions models the situations at hand.
 * Bodily/Kinesthetic:** Students will have to gather their own data (taking measurements, collecting data by doing an activity) for at least one of the activities).
 * Intrapersonal:** Students are asked to solve the equations of the tasks by themselves.
 * Interpersonal:** Students are asked to work in teams and pairs for a majority of the lesson to gather and interpret information about how data models a real-life function and how to solve that function. **(Tailor)**

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! **(Why)** 37. There will be an art exhibit (provided by the school art class) set up when the students walk in. There will also be a virtual tour of famous art exhibits displayed on the board as well as business graphs that model functions. I am going to ask students to carefully consider both before asking any questions. Then I will ask how they think it relates to today's lesson. **(Hook)** 38. Students will know the definitions of domain, range, function, vertical-line test, and polynomial. **(Equip)** Students will use the idea wheel graphic organizer to pick four different areas of everyday life that they are interested in. After students label each of the four areas of the diagram, they will think about how functions appear in those parts of their life. They will have to find one function in common for all four of the sections. Then, students will be exposed to an online image archive where they will need to find examples of their brainstormed ideas.**(Explore)** Using the Numbered Heads Together learning technique, students are to collaborate about functions in real-life. I will show a visual or describe a situation and the student whose number is called is to give the answer that their group has established as correct. Students will need to do some actual computations in this exercise.**(Experience)** 39. I will now go back and make students reevaluate their own examples. What other functions do you think could be seen in this example that you may not have considered before? Also, how would you go about designing these functions. **(Rethink)** 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, I will call randomly on students to ask for what they feel like their best example is, but have their peers guess which function it represents. **(Revise)** Students will change any of the examples that they have until that have one original example that models each of the functions. They will need to use the web to find a visual to match each of their examples (off a pre-researched image search engine) and present their ideas in pairs. **(Refine)** 40. Students will use a checklist to evaluate how well they feel they have met each of the standards that were covered in this lesson. They will have room to answer questions about their group's presentation (what they thought was clear, what wasn't, etc) and any questions that they have. **(Evaluate)** 41. **Verbal:** Students will communicate with peers, share ideas, and get instructions verbally. 42. Students will be able to consider the role functions play in real-world problem solving. **(Empathy) 2 Days** Product: Digital Scrapbook ||
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 36. Students will understand that functions have various real-world applications. **(Where)**
 * //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//**.**(What)**
 * Logically/Mathematically:** 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. **(Tailor)**

2004 ASCD and Grant Wiggins and Jay McTighe