L6+Reynolds,+Allison

** COLLEGE OF EDUCATION, HEALTH AND REHABILITATION **
 * ** UNIVERSITY OF MAINE AT FARMINGTON **

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : ** Allison Reynolds **__Lesson #:__** 6 **__Facet:__** Perspective
 * __ Grade Level __**** : ** High school **__Numbers of Days:__** 2
 * __ Topic: __** Exponential equations in the real world


 * __ PART I: __**


 * __ Objectives __**
 * Student will understand that ** exponential equations can be used in the real world.


 * Student will know ** exponential equations, rates, percent rates, exponential formulas, parts of rates, rates in and out of the classroom.


 * Student will be able to ** analyze functions in the real world that are based on exponential function


 * Product: ** Wordle.


 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**

Common Core State Standards Content Area: Functions Grade level: High School Domain: Linear, Quadratic, and Exponential Models Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. Standard: 1: Distinguish between situations that can be modeled with linear functions and with exponential functions.


 * Rationale: ** Students will be able to see through this lesson where situations of exponential equations would occur in the real world. Students will be able to see the distinction of the earlier lessons on linear lines and the cross over between them.


 * __ Assessments __**


 * __ Pre-Assessment: (Lesson 1 only) __**

Students will be given a word cluster graphic organizer when researching areas that use exponential equations in the real world. Students will also be working in groups to rotate around the room to see if situations would work for different equations. This way, they can see some ideas, use their brains, and check in with me in the discussion afterwards. When the group comes together, they will use the 4 corners method to see if they thought it was a good, bad, or not applicable situation for each station.
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **

Students will be given a rubric checklist that will show what they need to have in the Wordle. This will allow the teacher and the student to give their own grade then have a discussion about the overall project. Students will be working together throughout the lesson that will allow them to brainstorm and discover different situations together. The teacher will give feedback later one after the project has been handed in. The students will make corrections and revisions and then resubmit the Worlde for another round of grading.
 * Section II – timely feedback for products (self, peer, teacher) **


 * __ Summative (Assessment of ____ Learning): __** The students will be handing in a Wordle, which is a creative word cloud that represents something. This word cloud will represent how the students see these equations in the real world. This will show that students can not only do the mathematics, but apply it to situations outside of the classroom.


 * __ Integration __**
 * Technology: ** Students will create a collage of situations where equations can be used. There are careers, real life situations, stories, and plenty other examples of times where these equations will be used. Students will create their own list and create their own Wordle which will graphically display the words. After the assignment is completed, the class together will create a Wordle that best displays all the ideas together in one cloud.


 * Content Areas: **

Life planning classes: Classes that look at the future of students can use parts of this lesson in order to integrate mathematics together. Since the students will be looking at outside careers and opportunities, they may see careers that they are interested in using these equations.

The graphic organizer is a word cluster organizer. The project will be creating a word cloud, so this graphic organizer will help students see which words go with which equation. They will get two, one for linear and one for exponential. They may see some overlap and that is ok. During the lesson, students will be at stations to see if situations would apply to different equations. Students will then check in with the teacher using the 4 corners method. This method is when each corner is assigned an opinion, such as "This is a good example" or "This is not a good example". When the example is called, the students go to that area and represent what they thought as a team. This will lead to discussion and further learning on the teacher's part.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

Students will be working in teams for the stations around the room. The teams will be assigned randomly. The team will move from station to station, working together and developing their own opinions on each situation. Students can use these situations for starting places for the product itself.
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**


 * __ MI Strategies __**
 * Verbal-Linguistic: ** Students will be acting out scenes that show good examples and bad examples infront of the class. In the scenes, students must be able to describe their character and through that show why the example is good or bad.
 * Logical/Mathematical: ** Students, when working in the scene, will use
 * Bodily/Kinesthetic: ** Students will be acting the scenes out in front of the class, allowing the bodily/kinesthetic learners the chance to be part of the scene and learn from being part of the production.
 * Intrapersonal: ** Students will have to be willing to work with others in the scene and create the good and bad examples together.
 * Interpersonal: ** Students who are interpersonal have the opportunity to watch the rest of the group perform while he or she writes down the interesting, plus, or minus ideas on their own.
 * Naturalist: ** The scene that the students could do, instead of a bank, could be scientists traveling to find the plant that grow exponentially and see if the other students in the class find that as a good example, bad example, or interesting example.


 * __ Modifications/Accommodations __**
 * // From IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan) //**// I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. //


 * Plan for accommodating absent students: ** Students who are absent from my class will be expected to notify me as soon as they know they will be missing class. It is highly encouraged that students check with classmates on what they missed before coming to see me. Students should see me as soon as they are back in school to see what they missed. Some notes and links will be on the wikispace, but students will miss the activity and the chance to work with others. Students can go through each situation with the teacher, or find a group of other students who may have missed the class or willing to do it again. All work will be expected to be made up within the time the teacher and the student decide is best appropriate for the situation. Students with any questions can email me at any time for clarification and help.


 * __ Extensions __**


 * Type II technology: ** The Wordle that the students will create will show the differences between which careers and situations use these equations most often than not. They will be able to see which situations use them the most and which ones do not. They will be able to share these through the internet as well as with each other.


 * Gifted Students: ** Students who are in need or looking for a challenge in this lesson have some options. Students can be a sound board for other students who are struggling. They can help guide other students to thinking critically of situations where exponential equations would be used. They can not give any situations though. Another option is that the students critically analyze why there would be overlap between exponential and linear equations when they are so different. Students can report to the class why there could be overlap and where we might see it. This will help students who may not make the connection have another chance to see while "gifted" students can dive deeper into the information.

// whiteboard // // markers // // content notes // // questions for stations // // homework assignments // // tutorial // //rubric// //graphic organizer// //computer access for each student// //Wordle//
 * __ Materials, Resources and Technology __**


 * __ Source for Lesson Plan and Research __**

www.wordle.net Wordle!

http://centre4.core-ed.net/viewfile.php/users/10/1965015605/Wordle_QST.pdf Wordle tutorial

[] Rules of Logs and natural logs.

[] notes on exponential equations involving logarithms.

[] More help solving exponential equations

[] great site for students to have access to for practicing all kinds of math.

[] real world applications for exponential equations.

[] Solving for exponential equations

[] Help for solving exponential equations and practice problems

http://highered.mcgraw-hill.com/sites/dl/free/0072867388/374777/ch05.pdf Notes for more exponential equations and practice problems.


 * __ PART II: __**


 * __ Teaching and Learning Sequence __**** (Describe the teaching and learning process using all of the information from part I of the lesson plan) **// Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages) //

Agenda: Day 1(80 minutes): Homework: Continue building lists of situations. Practice problems if needed with students.
 * Students will walk in to class and sit in one of the 5 groups. (2 minutes)
 * Review any questions about exponential equations (10 minutes)
 * Graphic organizer will be given out and explained (2 minutes)
 * The groups and the rotation cycle will be explained (2 minutes)
 * Students will work throughout the stations (25 minutes)
 * Class will discuss the good, bad, and interesting examples from the stations with 4 corners (15 minutes)
 * Research and work to create lists of situations in which equations used (20 minutes)
 * Any last minute questions or concerns (4 minutes)

Day 2 (80 minutes): Homework: Complete the rubric to hand in next class. Students will have the opportunity to work on Wordle again after passing in the rubric.
 * Introduce Wordle to the class (10 minutes)
 * Hand out rubric (2 minutes)
 * Discuss the criteria and needs of project (4 minutes)
 * Explain how to break word list down into categories (4 minutes)
 * Have students work on breaking down list into categories (15 minutes)
 * Have students create a Wordle account (5 minutes)
 * Have students create a test Wordle about themselves (10 minutes)
 * Have students complete their Wordle during class (20 minutes)
 * Create large Wordle based from small wordles (7 minutes)
 * Ask if there are any questions over anything (3 minutes)

Classroom arrangement: Desks will be in groups for the first part of the lesson. The second part of the lesson, the tables will be in a circle for the remainder of the lesson.

Students will understand that exponential equations can be used in the real world. // Distinguish between situations that can be modeled with linear functions and with exponential functions. //Students have worked with all the equations, but they have not focused on the idea of exponential equations as a whole. They have seen what an equation looks like when raised to a new power, but how exactly these equations differ from the others. By seeing how these equations differ in the real world by the applications and careers, students will see what these equations are used for and how. It is not just in the classroom that exponential equations are useful. The hook for this lesson will be to have students decide when would be a good time to use these equations, based on the problem. This will get them thinking of the different scenarios on when to use them. The student will truly have to juxtapose the types of equations and really understand what each equation is used for. They will mark whether or not it is a good idea, bad one, or an unsure/interesting one. The groups of students will discuss them, but the student will have to make their own decision based on their own knowledge. The class will then discuss them as a whole.
 * Where, Why, What, Hook, Tailors: Verbal, Logical, Bodily, Interpersonal, Intrapersonal.**

Students will know (please see content notes). Students will be given a cluster graphic organizer in order to document what words, situations, or careers work with exponential equations. This will be used in order to categorize and see how many times a certain idea or topic comes up with exponential equations. These exponential words can be formulas, situations, careers, ideas, anything that relates. This will be used later with the Wordle that they will produce. Students will have the opportunity to begin class with any questions over the overall idea of exponential equations and what they learned from earlier lessons. They will have the opportunity to practice through the hook situations. The first 4 stations will have equations and situations which the student will have to decide whether or not the work. The students will be able to relearn or master the information through these stations, with some guidance from peers and myself. The last station is where students will construct a graph of an exponential equation with their hands. This will help produce a real life picture that the group will have to work on together. The class will then discuss the answers and ideas as a whole. This will allow the students to see which classmates are thinking like they are, while others may have different ideas. The teacher will be able to see the ideas through an activity called the 4 corners. With each situation, the students will go to a corner or location of the room based on their ideas. The corners represent a range, as in a 1-4 scale, of the ideas in the room. Each student will have the chance to defend their opinion and the students can switch corners at anytime. This will show the teacher who is thinking what and why for each situation.
 * Equip, Explore, Rethink, Tailors: Verbal, Interpersonal, Kinesthetic, Naturalist.**

Students will be able to analyze functions in the real world that are based on exponential functions. Students will be using Wordle in order to demonstrate if they can analyze these situations. The Wordle is a word cloud that shows the main ideas in larger font than the smaller supportive ideas. After the hook is complete and the students have done the 4 corners exercise, the teacher will move on to the work sessions. At this time, students will start creating lists of words, situations, professions, ideas, or anything that relates to exponential equations. I will be taking attendance and monitoring students activity at this time. I will be able to help generate and edit some ideas if need be. Students will end class on that day by finishing up the lists for the Wordle that will be done in class the next day. When students arrive in the next class, the list should be completed. The class will open with introducing [|Wordle] to the class. The rubric for the project will be handed out and discussed. Students will hear what is expected of them before running wild with Wordle. Students will then break the words they have created into categories, saying if it is a formula, a career, or anything. They will break each idea down into words that can repeat with other ideas. They will put every word in as many times as it is found in the word cluster. Students will then be working with Wordle with the [|tutorial]. The tutorial will first walk them through creating a username and password for the account. The first task is for the students to play with Wordle in class. They can create it about themselves, their pet, whatever is school appropriate. At this time, I will take attendance for the day. After that, I will help students work with Wordle, or help them with their categories on their paper. This can also be a time for students to work together to solve problems or share ideas for the word clusters. Students will be working in a circle in order to be able to help one another, but still work independently. Finally, the students will pass in their Wordle during class. Students will share their Wordle with me as well as the text they sent in. This will be done through email or pen drive. While the students pass in their work, I will be creating a larger Wordle that shows all the ideas into one giant Wordle. The students will then be able to see the class's ideas and opinions in one place. If students are done passing in their Wordle, they can quietly discuss what they passed in and why. I will be compiling all the information together. The class will end with students asking any last minute questions or concerns. **Explore, Experience, Rethink, Revise, Refine, Tailors: Verbal, Logical, Interpersonal, Naturalist**  Students will self assess their work by completing the rubric for themselves after handing in the project. Students will show how well they think they did and why so the teacher can see where the student is comfortable. Students, throughout the lesson, have the opportunity to change their opinions about when and where to use exponential equations. During the group work, students can bounce ideas and form ideas through their peers and work. Then, during the 4 corners portion, students will be able to represent their opinions and then change their minds if they want to. This will let students fully reflect and revise their work. When they hand in their Wordles, I will also be looking at the rubrics when filling them out. I will be giving feedback through the rubric and can talk to students if need be. I can also see students work right away with the text and Wordle the students will send me. I will be able to see, right away, what the class's big ideas were. I will also be able to see what specific students will say and work with them should they need it. The homework for the class is to get the project done and fill out the rubric. This will help them see their own work and make improvements. The idea of the Wordle is that students can critically think of when to use and what is related to exponential equations. This will help build that mastery for exponential equations and more information to come in future lessons. **Evaluate, Tailors: Logical, Intrapersonal, Interpersonal, Naturalist**


 * __ Content Notes __**

Students will know exponential equations, percent rates, exponential rates formulas, difference in rates, rates in and out of the classroom.

An exponential rate is when something is being raised to a power of another something. For instance, we have seen x^2 in other equations. We could also see x 4, or X 5 + 3x 3 -6x 2 =1. This is an exponential equation. Something is being raised to the power of something else. There are a variety of ways to solve exponential equations.

First, let's start off with something easy. For instance:

x 4 =16. This is saying some number we don't know yet it multiplied by itself for four times or it is being raised to the fourth power. We know that if we multiply 2 by itself four times we get 16. So, 2 4 =16. This is just trying to find out what number belongs in the X spot.

Now, for something a little harder. This is when we don't know the power. Let's say we see the problem 6 x =6 7. What is x? One of the rules of logarithms is that when the bases are the same, the exponents are the same if the two terms are set equal to each other. Since 6 does = 6, then x does equal 7. Same if it was 10 x = 10 3. The bases are the same, thus the exponents are the same. Therefore, x=3.

This method can be used to solve more advanced problems of this nature. For instance, 7 x-3 = 7 7. Since the bases are the same, we know that x-3=7. Solving for x, we get that x=10. The same idea is being used in order to solve these exponents. Now, what if the bases are not the same? Let's say that we have 4 x =2 8. What do we do? We know that we have to have the bases the same, so let's make them the same. We can change 4 into 2 2. Now we have 2 2^x = 2 8. The rules of exponents and powers say that a power raised to a power you multiply the exponents. Thus the new statement says 2 2x =2 8. Now we solve as we have before. Thus, 2x=8, and x=4.

Exponents and the rules of powers can be very easy to learn and remember. It is when the equations are not so simple that we step into a new area of math. This is called logarithms. A logarithm has a formula that looks like //log// b (m)= n where b n =m. B is called the base. There are an infinite number of bases for logs because there are an infinite number of numbers! We work in the base 10 number system, so when you see log (3) it is really log 10 (3). We assume the 10 is there. If it is any other base we put the number. This method is used when we can't simply use the exponent rules to solve the equation. For instance, 2 x =30. 30 is not a multiple of 2, so it really doesn't work. Thus, x=log 2 (30). This does have a value. You can either look it up on a table or you can use a calculator to find the numerical value of this statement. Logarithms are the opposite of exponents. They are inverses of each other. Much like squares and square roots. We don't always need the square root to know the square root of a number. For instance, we know that 4 square rooted is 2. But that is the method we use to solve it. Same idea happens with exponents and logarithms. This is what we use to solve examples in real life that use these rates.

There are other types of exponential equations that can be used. For instance, compound interest. Compound interest is a way for interest to build in a bank account. The formula for compound interest is A= P(1+ r/m) n. P is the beginning value, the principle value. r is the annual rate that is compounded over m number of times a year. This is important that it is in years. Finally, n is the number of times at the end it has been compounded. So, for instance:

If you deposit $5,000 in an account paying 9% compounded daily,* how much will you have in the account in 5 years? Compute the answer to the nearest cent.

Our P is 5,000, our r is .09, m is 365 and n is 5(385) or 1825. This is because this is is compounded every day. The rate though is a set rate for the year. So, what would it be? It would look like:

A=5000(1+ .09/365) 1825. The answer would be 7,841.13. That isn't bad!

There is another type of interest equation that uses exponential equations. This is called Continuous Compound interest. The equation is: A=Pe rt. The only difference is the t, which is how much time has passed in years. The e is a number, not a variable. This irrational number that never ends, so we gave it the name e. It comes from the natural log. When rewriting the equation, part of the proof calls that as a certain number approaches infinity, the answer reaches e. That is why it is in the equation. That is not really part of this lesson and won't really be discussed here.

An example would be: If $100 is invested at an annual rate of 8% compounded continuously, what amount, to the nearest cent, will be in the account after 2 years? The equation would look like 100e .08*2 .08*2 is .16. Therefore, the answer is 117.35. That is how much money would be earned over 2 years

// Tutorial // // word cluster graphic organizer // // rubric //
 * __ Handouts __**


 * __ Maine Common Core Teaching Standards for Initial Teacher Certification and Rationale __**


 * // Standard 1 – Learner Development. The teacher understands how learners grow and develop, recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.//**


 * //__ Learning Styles __//**


 * // Clipboard: //** Students who are clipboards will find structure in this lesson. Students will have a structured station setup for learning the situations where each equation would be used in. This way, students will have the structure and be able to learn the information. The product will also need to have a rubric filled which will let students know what they need to have completed before passing in the product.


 * // Microscope: //** Students who are microscopes will be able to dive in to the why of these equations. Why are the seen in the real world? Why do they apply to different situations? Why would one be better than the other? Who uses them? These are all questions that students will answer in this lesson in order to work with the information on a higher thinking level.


 * // Puppy: //** Puppies will be supported and comfortable throughout the lesson. Students will be working collaboratively with their teams in order to work around the information and discover the meanings together. Students will be able to bounce ideas off of each other and form their opinions together. Then, the class will create a master Wordle and see the work all together into one Wordle.


 * // Beach Ball: //** The Beach Balls in this class will be working with a variety of tools and methods to learn the information. Students will be working in teams to work with the information and then share their own ideas in the 4 corners lesson. Then the students will work alone on the Wordle but see the collaborative work with the class as a whole. Beach Balls will have enough variety to feel free to express themselves but enough structure to keep them on task.


 * // Rationale: //** Each learning style is addressed and introduced into the lesson so each type of student can access the information. The information is not just presented in the class, but uncovered and shared with the group together. The students are working with other learning styles in order to learn and adapt to other learning styles while strengthening and learning with their own.


 * // Standard 6 - // //Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their on growth, to monitor learner progress, and to guide the teacher's and learner's decision making.//**


 * // Formative: //** The graphic organizer, the station work, and the 4 corners check in are all formative assessments for this lesson. The students will fill the graphic organizer in order organize their thoughts throughout the lesson. The group will learn new ideas from the station work and check in with their results with the 4 corners activity during class. By checking in with their opinions and ideas, I can see where the class is at as a whole while seeing the individual voices speak their minds.


 * // Summative: //** The summative assessment for this lesson is the Wordle that the students will produce at the end of the lesson. This will show that they have thought critically and deeply about the information. Exponential equations are more than just things used in a math class, they are equations that represent real life situations. This will show me that the students are able to not only know the idea of exponential equations, but where they are applied beyond the classroom.


 * // Rationale: //** This lesson is meant to work with the way students learn and see how much they have learned as well. If students are working through new and inventive ways to see growth, the students are more willing to work with the information and master it. This is avoiding the one way thinking of exams and tests that can block certain learners. This lesson was designed to address all learners and show the teacher what the students can do.


 * // Standard 7 // - //Planning Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum, cross -disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.//**


 * // Content Knowledge: //** Please see content notes.

Common Core State Standards Content Area: Functions Grade level: High School Domain: Linear, Quadratic, and Exponential Models Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. Standard: 1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
 * // MLR or CCSS: //**


 * // Facet: //** Perspective: This lesson is meant to have student consider examples that may or may not be obvious examples of exponential equations. Students will have to critically think whether or not to use these equations. Some situations may have multiple ways of solving, so students will see what others say while building their own opinions.

//**Rationale:**// Exponential equations are seen throughout the world and our daily lives. By showing students that these equations are in the real world, they can have a better connection to the information and the content. By having the critically think of each situation and dissecting whether or not the equation would be used, they are thinking on a new level that will allow them to truly learn the information; not memorize.


 * // Standard 8 - // //Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.//**


 * // MI Strategies: //**


 * Verbal-Linguistic: ** Students will be acting out scenes that show good examples and bad examples infront of the class. In the scenes, students must be able to describe their character and through that show why the example is good or bad.


 * Logical/Mathematical: ** Students, when working in the scene, will use


 * Bodily/Kinesthetic: ** Students will be acting the scenes out in front of the class, allowing the bodily/kinesthetic learners the chance to be part of the scene and learn from being part of the production.


 * Intrapersonal: ** Students will have to be willing to work with others in the scene and create the good and bad examples together.


 * Interpersonal: ** Students who are interpersonal have the opportunity to watch the rest of the group perform while he or she writes down the interesting, plus, or minus ideas on their own.


 * Naturalist: ** The scene that the students could do, instead of a bank, could be scientists traveling to find the plant that grow exponentially and see if the other students in the class find that as a good example, bad example, or interesting example.

The Wordle that the students will create will show the differences between which careers and situations use these equations most often than not. They will be able to see which situations use them the most and which ones do not. They will be able to share these through the internet as well as with each other.
 * // Type II Technology: //**


 * // Rationale: //** This lesson was meant to meet the needs of a new varied group of learners. Each student has different strengths and areas for growth and this lesson works to improve those. By using the multiple intelligences, students can learn how they learn as well as learn the content. The content can be provided in a variety of ways. These students are also in a world of technology. Integrating technology into the lesson allows them to see and use technology that will help them learn.

__//**NETS STANDARDS FOR TEACHERS**//__
 * 1. Facilitates and Inspire Student Learning and Creativity. Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments.**

a. //__**Promote, support, and model creative and innovative thinking and inventiveness**__//

b. Engage students in exploring real-world issues and solving authentic problems using digital tools and resources

c. //__**Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes**__//

d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in face-to-face and virtual environments

//**Rationale:**// Students will work with Wordle in order to see the big picture of exponential equations. This will show that they have truly thought about the experience of exponential equations and how they work in the real world. The Wordle program will also allow the teacher and the students to see what are the bigger key words versus the smaller ideas in exponential equations.

a. //__**Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity**__//
 * 2. Design and Develop Digital Age Learning Experiences and Assessments. Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop knowledge, skills, and attitudes identified in the NETS-S.**

b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants in setting their own educational goals, managing their own learning, and assessing their own progress

c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources

d. //__**Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching**__//

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 * //Rationale://** This technology will allow students to work with a variety of ways to learn. The content of learning the bigger picture and the technology will allow the teacher to see what the students consider more important than other ideas. This will help the teacher plan and accommodate for students who may struggle or students who are exceeding. Also, the students are using this technology to see their opinions come to life. ||  ||   ||
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