L3+Reynolds,+Allison

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

** LESSON PLAN FORMAT ** ** __ Teacher’s Name __ **** : ** Allison Reynolds **__Lesson #:__** 3 **__Facet:__** Self-knowledge
 * __ Grade Level __ **** : ** High school **__Numbers of Days:__** 3
 * __ Topic: __ ** Exploring where exponential equations can be used in the real world.


 * __ PART I: __ **


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


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


 * Student will be able to do ** recognize the situations where exponential equations would be applied


 * Product: ** Photo Portfolio


 * __ 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: ** This lesson meets to standard because it is working with structures in the real world that are shaped and designed with exponential equations in mind.


 * __ Assessments __ **

Students will be given an ISP graphic organizer to put information about structures, shapes, pages, books, and other information needed for the assignment. Throughout this lesson, on any work that students find confusing, I will ask them to put sticky notes on the section with a question or an explanation why it is unclear. That way, when I walk around or if they pass in work, I can see exactly where they think they need help.
 * __ Formative (Assessment for Learning) __ **
 * Section I – checking for understanding during instruction **

Students will self assess with the rubric that I gave them while working on the projects. They will be responsible for explaining why they did well on some aspects and why they may have not done so well on others. Students will also have an interview with me after the project so I can give them feedback and they can make the appropriate edits.
 * Section II – timely feedback for products (self, peer, teacher) **

Students will take photos of objects shaped like functions and use programs to find the equation for the shape. Students will be encouraged to look beyond the classroom to find the shapes of the graphs in the real world in art, structure, people, or other areas.The students will work in pairs, groups, or individually in order to capture the still photos of these shapes. Then, the students will find the equations of these shapes and estimate the values of certain points in the shape through the Geogebra program. Students will see how these equations can be used not only for science but inspiration for other things in the real world.
 * __ Summative (Assessment of Learning): __ **


 * __ Integration __ **
 * Technology: ** The technology that students will be working with is Geogebra. This program is a geometric and algebraic program that can read pictures and give a best guess for the line they represent. The students can work with the program to adjust the line and see and automatic response to the picture. This will help them learn what needs to change in an equation to do a certain response.

Science: This project helps deal with the projection of some items. It can also work with showing students how to use this graphing program in order to use it for other shapes and ideas later on. Art: Students will be using artistic skills in capturing and finding beautiful pieces of art and structure that are shaped like exponential equations. They will need to be able to see the shapes in other things as well. Photography: Students will be taking photos of shapes that resemble the exponential equation. They will need to get a good quality picture in order for the program to recognize and work with the lines. History: While students are looking for shapes and designs, students can learn about the history of the structures they are seeing. For instance, in a student is in the park and take a photo of a memorial statue, he/she can look at the statue and the plaque and learn more.
 * Content Areas: **

Students will be working with an ISP (Information, Source, Page) graphic organizer in order to work with the books and resources they will be using. This will be a way for them to structure their ideas when working with the information. The students will not be grouped in small groups, but as an entire class. The students will be working together in order to create a list of ideas of shapes or places they would see the equation. Students will write down an idea, then careful toss it to the next person. The list will go around and around until no one else has ideas. That way, the entire group is working together while still thinking individually.
 * __ Groupings __ **
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

Students can have the opportunity to work in small groups of 2-3. The students will each be responsible to taking their own photos and such, but they can work together for finding the photos and putting the project together. Students will have a requirement of a number of shapes per team member, thus not one student is doing all the work. They are able to work together but are responsible for getting the same amount of work done.
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __ **


 * __ MI Strategies __ **


 * Logical/Mathematical: ** Students will have to estimate the equation in order to get a starting shape and then logically move through the parts of the equation in order to find the equation that matches the picture.
 * Visual/Spatial: ** Students will be taking photos of structures, sculpture, and other pieces of art that could produce beautiful pieces. Students will be analuzing wha they see in order to create the equations in the program.
 * Musical/Rhythmic: ** Students can use musical instrument shapes as their pictures, or take photos of someone singing and look at the shape of the mouth for different sounds.
 * Intrapersonal: ** Students will be passing the piece of paper to each other, forcing them to interact and warn the other person when the ball is coming. The group will work together in order to create a full list.
 * Interpersonal: ** Students have the opportunity to take photos of things that mean a lot to that particular student to show things that are close to that student.
 * Naturalist: ** Students will have the opportunity to take photos of things in nature such as tree shapes, animal print patterns, river bends, and other things to bring to the portfolio and find exponential shapes in.


 * __ 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 on any of the days of this lesson will be expected to obtain any notes given that day. They can either find a classmate or myself for the notes. The general notes will be posted on the class wiki. Students will have to make up the day of working with the books in class. Students will be given one extra class day to complete the assignment. This can be changed due to the circumstances of the situation. Students will have to notify when they are missing class and why they are missing class so I can decide the best course of action. Students will be able to work with me before and after school to catch up on any work.


 * __ Extensions __ **

The technology that students will be working with is Geogebra. This program is a geometric and algebraic program that can read pictures and give a best guess for the line they represent. The students can work with the program to adjust the line and see and automatic response to the picture. This will help them learn what needs to change in an equation to do a certain response.
 * Type II technology: **


 * Gifted Students: ** Students who are looking for or need a challenge in this lesson can do research on the meaning and reasons behind the structures they are taking photos of. What was the artist inspired by? What sort of building shape did the person want to create? Did the person actually consider these equations when looking at designing this piece of art? These questions can be researched and answered through the presentation in order to have a stronger connection to the art and the mathematics.

white board markers content notes notes taken during class wiki up and running rubric for project sticky notes books for the hook cameras computers Geogebra tutorial for Geogebra Graphic organizer presentation options for gifted students homework assignment rules for logarithms
 * Materials, Resources and Technology **

__ **Source for Lesson Plan and Research ** __

[] Solving for exponential equations

[] Help for solving exponential equations and practice problems

[] Practice problems with solutions that I will give out for homework as a reminder

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

[] real world applications for exponential equations.

[] Shows examples of real world applications as well as the formulas. Walks through the process of solving with the equations.

[] video explanation of solving these equations.

[] notes on exponential equations involving logarithms.

[] More help solving exponential equations

[] Practice solving all sorts of equations

[] notes with practice problems on the bottom

[] Only practice problems with logarithms, regular, and word problems.

http://www.rapidtables.com/math/algebra/logarithm/Logarithm_Rules.htm Rules of Logs and natural logs.

[] Graphic organizer for lesson

[] Tutorial on GeoGebra

__ **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: Practice problems over exponential equations.
 * Go over any questions from previous class. Start talking about exponential equations (5 minutes)
 * Start talking about the shape of exponential equations (10 minutes)
 * Show the book and talk about architecture. (5 minutes)
 * Pass the books around (12 minutes)
 * Present content notes to class. (25 minutes)
 * Pass out graphic organizers. Explain the graphic organizer (5 minutes)
 * Have students brainstorm ideas of places to see these shapes (15 minutes)
 * Last minute questions about the class or unit (3 minutes)

Day 2 (80 minutes): Homework: Take photos for the portfolio and do more research for the portfolio. Extra problems should the students want or need.
 * Ask students if they have any questions over the homework (7 minutes)
 * Review the graphic organizer with students. (5 minutes)
 * Pass out the rubric for the product. (1 minute)
 * Go over the rubric (4 minutes)
 * Group students into groups of 2-3 randomly (5 minutes)
 * Allow students to start researching architecture and taking photos (35 minutes)
 * Last minute questions about the class or unit (3 minutes)

Day 3 (80 minutes): Homework: Finish the project to pass in for next class.
 * Start class by passing out tutorial (1 minute)
 * Discuss project and Geogebra with students (4 minutes)
 * Have students play around with Geogebra with St. Louis Arch (10 minutes)
 * Have students resume research and taking photos (20 minutes)
 * Start working on project again with photos and software (30 minutes)
 * Go over last night homework if needed (10 minutes)
 * Time for last minute questions over assignment or unit (5 minutes)

Classroom setup: The desks will be ste up in groups of 4. The students can work together this way while having their own place to work.


 * Student will understand that ** e xponential equations can be used in the real world. // Distinguish between situations that can be modeled with linear functions and with exponential functions. // Students have seen that equations are in the real world, but sometimes not where you necessarily where you would expect it. This assignment it meant for students to find exponential equations in art and in structure. First I will introduce some of the ideas of exponential equations and how they look on a graph. Then I will show one architecture book and explain that there is a way to see these shapes outside of the classroom. Then we will start with the hook. The hook is to pass around the books on architecture or art that uses the shape of these equations. Students can discuss and see where the shape of the graph can be found outside of mathematics. While the students look at the books, I will take attendance. Students can keep a book at a desk or see other books. The idea of this hook is to get students thinking about what they may see.
 * Where, Why, What, Hook, Tailors:** Naturalist, Visual, Intrapersonal

Students will know (please see content notes). The students will be given an ISP graphic organizer to organize their thoughts. This graphic organizer shows where student get their information for the project and is a resource for them to use. First I will present the information to the class about the situations in which exponential equations are used. I will present the example of the frogs in the tree. A tree frog population doubles every three weeks. Suppose that currently, there are 10 tree frogs in your back yard. How many tree frogs will there be in 6 months, assuming that there are four weeks each month? We can start with a table, just to get an idea of what we are looking at. We know that we have started with 10 frogs. That will come into the equation at some point. We know that the number doubles every 3 weeks. So, it is like we are multiplying by 2 everything 3 weeks. Ah, this is what we see as being multiplied by itself over and over again. so, this is going to be raised to an exponent. Now, we know that it get's multiplied every 3 weeks, we want it by every week. That way, we can find it for any number of weeks, say, 24 weeks. So, we can divide the unknown number of weeks, n, by 3. Therefore, we have the equation 10*2 (n/3). We can plug in whatever number we want in order to find how many weeks. We know that it is 24 weeks, so 24/3 is 8. Therefore, we have 10*2 8 which is 2560. That is a lot of frogs! That will be the last example for the work unless students need more examples to work with. During this, students can write sticky notes and post them to the corner of the desk for me to pick up. I can come over and see exactly what they need help with. At this oiint the students will start working with the project.
 * Equip, Explore, Rethink, Tailors:** Visual, Logical, Interpersonal


 * Student will be able to do ** recognize the situations where exponential equations would be applied. Students will be using a photo portfolio to show that they understand exponential shapes and equations. They will show a portfolio that is filled with pictures of exponential shapes that are in the real world. They will also use Geogebra to show the shape and the line of the equation in the shape. They will be given a rubric in order to see how they are doing with the project. This will also give students a chance to assess themselves. Before they start the project, students will brainstorm ideas by passing a piece of paper around with ideas. During the first few minutes of this, I will be taking attendance. While a student is waiting for the paper, they can work on their homework that will be due the next day. After I take attendance, I will be walking around checking the paper for ideas. I will be working with students while they pass the paper around. Once the time is up or the list is exhausted, the class will take the last minute questions. The next day, students will walk in with questions on the homework. They will use sticky notes to mark where they had questions on the work. Students will then go over the rubrics and the graphic organizers for the project. Students will break into teams of 2-3 by random number selection and will get to work. Students can start doing research online or in the library for architecture books. Students will have access to the library as well as the books I brought to class earlier. They will be fillin gout the graphic organizers during this time to help organize where they got their information Students can also start walking around the school to take photos of the school or shapes around the area. These photos can be things that are close to the student, help the student learn, or even new pieces of art. The students will have to take school appropriate photos. Students can then save the photos from the camera onto the computer. They can also use a computer camera to have the picture. They are also welcome to use their phones as long as they use them appropriately. At this time I will be walking around monitoring what is going on. I will quickly take attendance then walk around again to check in with students. I can be referencing them to websites or books. I can also help students see things in the area around them. Students will end class with last minute questions. The next day will be working with the software and working on the portfolio. I will start class by passing out the [|tutorial]for Geogebra. I will discuss the project and Geogebra in turn with the portfolio. Students will be given the task of marking the St. Louis Arch for creating a line. Then, the students will adjust the line as needed to fit. At this time I will be taking attendance and walking around helping students. Students will commence working on their projects and using Geogebra to help. As students continue to work, I will be in and out of the classroom seeing where my students are and how they are doing. I will have announced by email to the teachers and administrators that my students will be walking around quietly to take photos. This way, the school knows that there are going to be students working while the students know they are being supervised. Students will then save and stop their process as we talk about exponential equations. Students at this time will have the chance to ask questions about the homework assignment from the night before. Students will have extra time to work on any problems they may have and check in with me using the sticky notes method again. Finally the class will end with final questions for the unit or lesson. During this lesson, students will be working with others while responsible for their own work.
 * Explore, Experience, Rethink, Revise, Refine, Tailors:** Visual, Interpersonal, Intrapersonal, Naturalist, Musical, Logical.

Students will self assess their work through the rubric that was given out during the class. Students will use the rubric to see where their portfolio would fall within the grading scale. I will see how they graded themselves while I grade their rubric. Then, the students and I will have a discussion about what the grading was for each and how they can make improvements. I will talk to students about their process and their portfolios as teams. I will be available to talk to and work with if needed, and will give feedback through the rubric and a second round of grading. The students will conference with me after to compare the two rubrics as well. Each member of the team will fill out their own rubric and report on who did what. Since they are working together, they will conference and get feedback from each other. The homework assigned is practice for students to understand the idea of exponential equations and the methods to use for these equations. The assignment will lead to a larger idea unit at the end over all the equations. There are other assignments before the final one that will deal with exponential equations. The assignments are to help practice and master the information.
 * Evaluate, Tailors:** Logical, Interpersonal

__ **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.

These rates are used for many instances. Exponential rates are used when something is gaining very quickly or loosing something very quickly. For instance:

A tree frog population doubles every three weeks. Suppose that currently, there are 10 tree frogs in your back yard. How many tree frogs will there be in 6 months, assuming that there are four weeks each month?

We can start with a table, just to get an idea of what we are looking at. We know that we have started with 10 frogs. That will come into the equation at some point. We know that the number doubles every 3 weeks. So, it is like we are multiplying by 2 everything 3 weeks. Ah, this is what we see as being multiplied by itself over and over again. so, this is going to be raised to an exponent. Now, we know that it get's multiplied every 3 weeks, we want it by every week. That way, we can find it for any number of weeks, say, 24 weeks. So, we can divide the unknown number of weeks, n, by 3. Therefore, we have the equation 10*2 (n/3). We can plug in whatever number we want in order to find how many weeks. We know that it is 24 weeks, so 24/3 is 8. Therefore, we have 10*2 8 which is 2560. That is a lot of frogs!

That is how we use these equations in real life. Exponential equations can help us with money, population, and other things that grow really quickly over time.

__ **Handouts ** __ rubric sticky notes tutorial for Geogebra paper for passing around ideas homework assignment Graphic Organizer Logarithm notes


 * __ 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 need more structure in my class will feel comfortable and confident to learn. The design of this lesson is to understand which equations go with what. In order to evaluate that, students will need to know the step by step instructions on how to work with these equations. The designing of the product as well as the rubric will ensure that clipboard students can succeed in this class comfortably.


 * // Microscope: // ** Students who are microscopes will truly thrive in this lesson because it is all about the "why". This lesson was designed to have students actually see where these equations can be seen in the real world. Although these equations are used primarily in mathematics and in solving problems, the shapes and the ideas behind the graphs can be seen in the real world. These students will have the chance to explore on their own or in groups to find where they can see the equations. They will also have the chance to dive in and see if the artist or architect had thought of these equations when designing the pieces of art seen.


 * // Puppy: // ** Students who are puppies will be able to work well with their surroundings in this lesson. Students will be able to work in groups in order to find things that show these shapes in the real world. Students will also be working and talking with professionals passionate about their work, should they choose to do the gifted section on the task. Students will also have the opportunity to work with me and their friends throughout the project.


 * // Beach Ball: // ** Beach balls in this lesson will highly enjoy finishing the product that is assigned. The students will have free reign over finding pieces of art and structures in the real world that reflect these pictures. The students will also be working on passing ideas around the classroom in a new and inventive way. These students can also work in groups that think a like or want to find similar pictures. Beach balls students do not have to just work with cameras, but with cell phones or their own personal cameras.


 * // Rationale: // ** Students have a variety of learning styles and all of them need to be addressed. This lesson was created with the learning styles in mind. Having structure, real life connections, a variety of methods, and a comfortable environment will allow the students in this class to learn. The teacher and the students will learn from each other as well as themselves through this lesson.


 * // 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: // ** For the formative assessment portion of this lesson, students will be working with a graphic organizer to plan their portfolios and information. This can help me see what they have connected to the material. Also, students will be using sticky notes to label their questions. That way, if students are nervous to ask or even are unsure about a certain section, I can easily see it and address it.


 * // Summative: // ** When the lesson is complete, students should have completed the final product for this class. The product is a photo portfolio that shows how students see the shapes of the equations in the real world.


 * // Rationale: // ** The assessment pieces of this lesson will allow the teacher to see exactly where the students are. Students will not be tested in the traditional ways of whether or not they can memorize the information. This will allow students to show, creatively, that they know and understand the material. Students will have to have an idea of how to use and work with the equations shown in order to have a successful final product. The check ins and the formative assessments along the way will allow the teacher to see if they will succeed. The lesson was design so that the students can progress naturally and the teacher can work with them along the way.


 * // 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


 * // MLR or CCSS: // **

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.


 * // Facet: // ** Self-Knowledge- This lesson was designed to have students focus on discovering for themselves where in the real world can these equations be seen. Sometimes, it is not just in mathematics or in solving rates. Sometimes these equations can be seen in art and structure. By having the students go out and discover this information on their own, they can have a new appreciation for the equations as well as the new art and pieces they find along the way.


 * // 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: // **
 * Logical/Mathematical: ** Students will have to estimate the equation in order to get a starting shape and then logically move through the parts of the equation in order to find the equation that matches the picture.
 * Visual/Spatial: ** Students will be taking photos of structures, sculpture, and other pieces of art that could produce beautiful pieces. Students will be analuzing wha they see in order to create the equations in the program.
 * Musical/Rhythmic: ** Students can use musical instrument shapes as their pictures, or take photos of someone singing and look at the shape of the mouth for different sounds.
 * Intrapersonal: ** Students will be passing the piece of paper to each other, forcing them to interact and warn the other person when the ball is coming. The group will work together in order to create a full list.
 * Interpersonal: ** Students have the opportunity to take photos of things that mean a lot to that particular student to show things that are close to that student.
 * Naturalist: ** Students will have the opportunity to take photos of things in nature such as tree shapes, animal print patterns, river bends, and other things to bring to the portfolio and find exponential shapes in.

The technology that students will be working with is Geogebra. This program is a geometric and algebraic program that can read pictures and give a best guess for the line they represent. The students can work with the program to adjust the line and see and automatic response to the picture. This will help them learn what needs to change in an equation to do a certain response.
 * // Type II Technology: // **


 * // Rationale: // ** This lesson was intended to have students access a new way of learning the information. By reaching out to the intelligences in the classroom, students can not only build on their weaker ones, but have comfort and find understanding in their strong ones. Students can learn the information with their stronger intelligences and truly connect the information. The technology is also bringing the student outside of the classroom in order to explore the world around them.

__ //**NETS STANDARDS FOR TEACHERS**// __ a. Promote, support, and model creative and innovative thinking and inventiveness
 * 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. **

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

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


 * //Rationale:// ** For the first standard, students will have to use their own planning and tools in order to learn. This entire lesson is designed to have their choices and opinions first. Students will be using great pieces of technology, like Geogebra, in order to learn. Yet the information they gather is all their own. The second standard is met by the students working on their own. The students are completely making this product their own, which allows them to better connect to the information. The assessments along the way, as presented above, show that the students are being assessed through creative ways that tap into their learning styles. The students can represent how they know the information through how they learned it.

||  ||   || About · Blog · [|Pricing] · Privacy · Terms · [|**Support**] · [|**Upgrade**] Contributions to http://edu221spring11class.wikispaces.com are licensed under a [|Creative Commons Attribution Share-Alike 3.0 License].
 * [[image:http://www.wikispaces.com/_/9x256kq1/i/bBL.gif width="8" height="8"]] |||| [[image:http://www.wikispaces.com/_/4k0z606x/i/c.gif width="1" height="1"]] || [[image:http://www.wikispaces.com/_/60jk45v8/i/bBR.gif width="8" height="8"]] ||

Portions not contributed by visitors are Copyright 2011 Tangient LLC.