Scott's+Lesson+Plans

** Unit: ** Exponential and Logarithmic Functions ** Subject /Grade level **// : // Algebra II/Grades 10-12
 * Lesson 3 Title: ** How do you solve that?

** Brief Description ** The use of digital storytelling in the classroom can have many benefits for students. These benefits include building an understanding of the content and media, strengthening their visual literacy, allowing them to display their creativity, creating a product that can easily be shared, and building skills in research, problem solving, and communication (Laureate Education, Inc., 2009). While the use of this technology in the math classroom may not seem to be a natural fit like it is in other content areas, it can be a powerful learning tool. Many math concepts are abstract, so the use of digital storytelling to make these ideas concrete can help students to better understand them (Laureate Education, Inc., 2009). In this lesson, I will have students create digital stories to help them remember the steps in solving exponential and logarithmic (log) functions, which are very abstract concepts. There are various ways to solve these problems, and students often struggle to remember when they are supposed to add a log to both sides, drop the logs, equate exponents, or switch forms, so my hope is they will have a better understanding of this after they create their digital stories.

** Goals ** ** Content Standards **
 * Wisconsin Common Core State Standards for Mathematics
 * F-BF.5. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
 * F-IF.8.b. Use the properties of exponents to interpret expressions for exponential functions.
 * F-LE.4. For exponential models, express as a logarithm the solution to //ab//ct = //d// where //a//, //c//, and //d// are numbers and the base //b// is 2, 10, or //e//; evaluate the logarithm using technology.


 * International Society for Technology in Education National Educational Technology Standards for Students
 * Communication and collaboration
 * Conduct research and use information
 * Use technology effectively and productively
 * Demonstrate creativity and innovation

** Instructional Objective ** Students will understand the steps in solving exponential and logarithmic equations. They will also build skills in collaboration, communication, research, creativity, and use of technology as they create a digital story to display what they have learned about the topic.

** Action ** ** Before class Preparation **
 * Reserve computer lab and digital cameras
 * Find online examples of digital storytelling for other math topics
 * Construct rubric for evaluating the digital stories

** During Class ** Research has shown that using technology in nonroutine ways can positively affect student achievement in math by deepening their understanding of the topics (Cennamo, Ross, & Ertmer, 2010). One example of a nonroutine use for technology in math is having students use digital storytelling to display the steps in solving an equation. In this lesson, students will work in groups to create a digital story explaining which method to use and the steps for solving the different types of exponential and logarithmic equations. During the previous two class periods student will have learned the methods for solving these equations during whole class instruction.

** Activities ** (2 class periods)
 * Students will be told that they are going to create a digital story that explained what they learned about solving exponential and logarithmic equations. They will need to create a story that explains how to solve exponential equations or logarithmic equations, but not both.
 * Several short digital stories will be shown to the class on the SMART Board that display different math concepts. This should help to get them excited about the project and give them an idea of what is expected.
 * The students will be allowed to form their own groups of 3-4 students. Since some work might be done outside of school, this allows for them to choose classmates that they can easily meet with.
 * During the first class period the students will stay in my classroom and brainstorm ideas for their digital story. They will be encouraged to form an idea, make a list of needed materials, and develop a game plan to complete the project before they leave class.
 * The next two class periods will be used to learn new materials. During these days, students should be completing any work that needs to be done outside of class, such as gathering materials and recording video.
 * A second class period will then be given for this project. Students will be in the computer lab, and they can use this day for any part of the project, such as editing their digital story or shooting video if they were not able to work together outside of class.
 * The final version of their project will be due one week from the date it was assigned. They will be evaluated using a rubric and we will watch all of them during class.

** Monitor ** ** Ongoing Assessments ** During the two class periods devoted to this project, I will monitor the groups to make sure that they are making adequate progress, help them with any technology issues that arise, and answer any question they might have about the math content being displayed. My goal is to take on a facilitator role and let the students figure most of it out on their own.

** Accommodations and Extensions **
 * If there are groups of student who are unable to find time to work together outside of school, I will request them to come in and work during the Extended Learning Time at the end of our school day. Any individual students who I notice are struggling with the content or technology will also be requested to come in for help.
 * As an extension, groups may choose to create a digital story that explains how to solve both exponential and logarithmic equations, rather than just one of these as was required in the original directions.

** Evaluate and Extend ** The digital story that each group created will be evaluated using a rubric. Both the teacher and students from the group will use the rubric to grade the project, and a score will be calculated using input from both. This evaluation will judge how well the students explained the content that was learned, how well they worked together, and the quality of the video that was created.

** References ** Cennamo, K., Ross, J., & Ertmer, P. (2010). //Technology integration for meaningful classroom use: A standards-based approach.// Belmont, CA: Wadsworth, Cengage Learning.

International Society for Technology in Education National Educational Technology Standards for Students retrieved July 31, 2011 from []

Laureate Education, Inc. (Executive Producer). (2009). Program twelve. Spotlight on Technology: Digital Storytelling, Part 1 [Webcast]. //Integrating technology across the content areas.// Baltimore, MD: Author.

Wisconsin Common Core State Standards for Mathematics retrieved July 31, 2011 from []

** Lesson 2 Title: **// e // is a Number? ** Unit: ** Exponential and Logarithmic Functions ** Subject /Grade level **// : // Algebra II/Grades 10-12

** Brief Description ** Requiring students to use online collaboration tools can have many benefits for them educationally. They allow students to interact with other students or experts from around the world, provide an authentic audience for their work, can help the students receive ongoing feedback, and provide a means for differentiating instruction (Laureate Education, Inc., 2009).In order to take advantage of these tools, I have developed the following lesson in which students will collaborate to create a wiki that explores one of the most important numbers in mathematics, the natural base //e// (or simply //e//). Students often struggle to understand exactly what //e// is and why it is important in math. This lesson will help to give them a better understand of this topic.

** Goals ** ** Content Standards **
 * Wisconsin Common Core State Standards for Mathematics
 * F-LE.1.c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 * F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
 * F-IF.8.b. Use the properties of exponents to interpret expressions for exponential functions.
 * F-LE.4. For exponential models, express as a logarithm the solution to //ab//ct = //d// where //a//, //c//, and //d// are numbers and the base //b// is 2, 10, or //e//; evaluate the logarithm using technology


 * International Society for Technology in Education National Educational Technology Standards for Students
 * Communication and collaboration
 * Conduct research and use information
 * Use technology effectively and productively

** Instructional Objective **

Students will understand what the natural base e is, where it occurs in the real-world, and how it is used in mathematical computations. They will also gain experience collaborating online with other students through the use of a wiki.

** Action ** ** Before class Preparation **


 * Reserve computer lab
 * Bookmark wiki sites for student use
 * Construct rubric for evaluating the wikis

** During Class **

Research has shown that if students collaborate in small groups to complete learning tasks they tend to learn more, retain it for a longer period of time, and are more satisfied with their learning experience (Hargis & Wilcox, 2008). Using online tools to support collaboration has the added benefit of allowing students to complete their work either synchronously or asynchronously (Hargis & Wilcox, 2008). In this lesson, students will experience these benefits of online collaboration as they work in small groups to research a topic and create a wiki to share their findings.

** Activities ** (2 class periods)


 * Each class will be divided into seven groups (3-4 students each). During the first class period of this lesson, the students will be told that there is another important value besides π and //i// that every good mathematician should know. But rather than telling students what //e// is, they will be required to research it on their own and report their findings in a wiki.
 * Students will spend the class period working in their groups to set up a wiki and start researching //e//. Their wiki must address (at a minimum) the following questions:


 * What is the full name for //e// and what is its numerical value?
 * Who discovered it and how?
 * Where does //e// occur in the real world? List a minimum of ten examples of where it is used.
 * In what other subjects besides math might you see //e//?
 * What will //e// be used for in math class?


 * The students will be told during class that they will be completing the wiki with the help of another group in one of my other Algebra II classes. They will learn who the group is and start to determine how the groups will collaborate to finish the project. The groups will have three days to complete the wiki.
 * During the next two class periods, students will be learning about exponential growth and decay functions and how to graph them. Since the natural next step after these lessons is to learn about //e// and how it is used in exponential functions, when the students come to class the next day we will introduce //e// by briefly displaying each group’s wiki on the SMART board. The class will create a concept map to summarize the responses to each of the questions that the groups had to answer.

** Monitor ** ** Ongoing Assessments ** As students are conducting their research and setting up their wikis, I will circulate in the room to make sure the groups are headed in the right direction and to answer any questions they might have. One particular area of confusion will be the full name for //e//, since there are several different names for it. I also anticipate some struggles setting up and working on the wiki. All students have worked on them before but it may have been awhile, so I will give help as needed. My goal is not to give them the answers, but instead guide them to finding the answers themselves.

** Accommodations and Extensions **
 * Students who are struggling with the concept of //e// or with the creation of a wiki will be requested to come in for extra help during the Extended Learning Time at the end of our school day.
 * As an extension, groups will be asked to add to their wikis any other interesting information that they come across in their research. Extra credit will be given for this work.

** Evaluate and Extend ** The final wiki that each group created will be evaluated using a rubric. Both the teacher and students from the group will use the rubric to grade the wiki, and a score will be calculated using input from both. The evaluation will address how well the learning objectives were met, how well the group worked together collaboratively, and the quality of the wiki that was created. This lesson was just an introduction to e, so as an extension the lessons in the following class periods will investigate how it is used in calculations and this knowledge will be used to solve problems.

** References **

Hargis, J., & Wilcox, S. M. (2008). Ubiquitous, free, and efficient online collaboration tools for teaching and learning. //Turkish Online Journal of Distance Education//, 9(4), 9–17.

International Society for Technology in Education National Educational Technology Standards for Students retrieved July 31, 2011 from []

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: 115%; margin-left: 0.25in; text-indent: -0.25in;">Laureate Education, Inc. (Executive Producer). (2009). Program ten. Spotlight on Technology: Social Networking and Online Collaboration, Part 1 [Webcast]. //Integrating technology across the content areas.// Baltimore, MD: Author.

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin: 0in 0in 0pt 0.25in; text-indent: -0.25in;">Wisconsin Common Core State Standards for Mathematics retrieved July 31, 2011 from []

** Lesson 1 Title: ** Watch it Grow! ** Unit: ** Exponential and Logarithmic Functions ** Subject /Grade level **// : // Algebra II/Grades 10-12

** Brief Description ** Problem-based learning activities have many benefits for students, including building students’ self-directed learning and collaboration skills, learning the content at a deeper level, being able to apply learning to new situations, and exploring content in an authentic and meaningful way (Laureate Education, Inc., 2009). With these benefits in mind, I intend to use a problem-based learning approach to help my students learn about compound interest. Below I explain my GAME plan for this lesson in which students will explore how credit card debts and savings account investments can grow exponentially over time.

** Content Standards **
 * Goals **
 * Wisconsin Common Core State Standards for Mathematics
 * F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 * F-LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
 * International Society for Technology in Education National Educational Technology Standards for Students
 * Communication and collaboration
 * Research and information fluency
 * Critical thinking, problem-solving, & decision-making
 * <span style="color: black; font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin-bottom: 0pt;">Technology operations and concepts

** Instructional Objective ** Students will understand that things that grow exponentially start by growing slowly and then increase rapidly. They will also gain an understanding of the dangers of credit card debt and benefits of investing money long term because of compound interest.

** Before class Preparation **
 * Action **
 * Reserve computer lab
 * Make copies of activity sheets
 * Bookmark sites that will be used for activities
 * Construct rubric for product evaluation

** During Class ** One of the key components of a good problem-based learning project is that it is meaningful to students (Laureate Education, Inc., 2009). Since students at the high school level are starting to earn and spend money, it is meaningful for them to learn skills that relate to this topic. The following activities are meant to introduce students to compound interest and how it can be both a good and bad thing.

** Activities ** (3-4 class periods)
 * To introduce the lessons, I will pose the question “How can interest on money be both good and bad?” In small groups, students will come up with examples and a class discussion will follow. This should lead into a discussion about interest on credit cards, savings accounts, and other investments.
 * Students will work in groups of 3 or 4 for each activity. In the computer lab, students will use a spreadsheet program to explore how quickly money grows when it increases by a percentage over time. They will be asked to determine how $1000 grows over time at different interest rates, and compare the results using the table and using the graphing feature on the program. A class discussion will follow about the power of compound interest and how it can increase the value of an account quickly over time.
 * Each group will be provided copies of the Savings Account Activity Sheet and Credit Card Activity Sheet found at []. They will use the Compound Interest Simulator found at [] to explore compounded interest in different scenarios.
 * Each group will then be given the choice to complete one of the following two tasks:
 * 1) They must research the price of a major purchase they hope to make once they graduate. Since they do not have enough money to make the purchase, they will intend to borrow money for the entire amount of the purchase and pay it back within five years. They need to determine the total amount the item would cost them and how much their payments would be if they made the purchase using a credit card or if they took out a loan from a bank.
 * 2) They just found out they inherited $10,000 from a rich relative, but there is a catch. They must invest all of the money and they cannot withdraw any of it for ten years. They must research different ways to invest the money which will guarantee them a return on their investment, and determine which way will make them the most money.
 * Students will create a final product of their choosing to display their findings. The final product must make use of some type of technology and the students will present their findings to the class.

** Ongoing Assessments ** As students are working on the activities, I will monitor their progress and ask questions to make sure they understand the basic ideas of compound interest. I will provide assistance when needed, but I hope the groups will be able to complete the work with little or no help. This is important because the role of a teacher in a collaborative classroom should be facilitative rather than directive (Ertmer & Simons, 2006). The activity sheets will be collected and graded for each group. Feedback will be given on these sheets to help clear up any misconceptions.
 * Monitor **

** Accommodations and Extensions **
 * Students who are struggling with the concepts or technology will be requested to come in for extra help during the Extended Learning Time at the end of our school day.
 * As an extension, groups that are excelling will be encouraged to try both tasks presented in order to receive extra credit.

The final products that each group produces and their presentations will be evaluated using a rubric. Each member of the group will grade their final product using this rubric, and that will account for a portion of their final grade on the work. Other assignments will be given to extend these concepts to other exponential growth and decay problems, and for extra practice. These assignments will be given a completion grade. At the end of the unit these skill will be evaluated in an exam.
 * Evaluate and Extend **

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin: 0in 0in 0pt 0.25in; text-indent: -0.25in;">Ertmer, P., & Simons, K. (2006). Jumping the PBL implementation hurdle: Supporting the efforts of K–12 teachers. //The Interdisciplinary Journal of Problem-Based Learning, 1//(1), 40–54.
 * References **

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin: 0in 0in 0pt 0.25in; text-indent: -0.25in;">International Society for Technology in Education National Educational Technology Standards for Students retrieved July 31, 2011 from []

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin: 0in 0in 0pt 0.25in; text-indent: -0.25in;">Laureate Education, Inc. (Executive Producer). (2009). Program eight. Spotlight on Technology: Problem-Based Learning, Part 1 [Webcast]. //Integrating technology across the content areas.// Baltimore, MD: Author.

<span style="font-family: 'Times New Roman'; font-size: 16px; line-height: normal; margin: 0in 0in 0pt 0.25in; text-indent: -0.25in;">Wisconsin Common Core State Standards for Mathematics retrieved July 31, 2011 from []