Bryan+Bird

=Bryan Bird=

**Problem-Based Learning Lesson **

Grade Level: 10th grade

Subject: Mathematics

Description of Lesson: A local man wins a large amount of money in the lottery and asks for advice on how to invest his winnings wisely. Students explore the concept of investing and learn investment terms. They contact local financial institutions to understand how the financial industry works, and find the best place for the man to invest his money. They will explore the different accounts and the formulas used to create their accounts and identify the mathematical characteristics of each of them.

Learning Outcomes:
 * Students will explore exponential properties of different investment accounts
 * Students will identify the characteristics of the exponential equations
 * Students will make predictions on the amount of interest earned based on the exponential growth models found from each account.

Skills:
 * Graph exponential functions
 * Solve simple exponential equations
 * Use the compound interest formula

Content Standards from the Georgia Performance Standards:
 * Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.
 * Graph functions as transformations of f(x) = ax.
 * Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Lesson: To begin the lesson, students in groups of three will choose at least three different investment accounts from at least two different banks to research in order to choose which account to use. Students should choose at least one account from one local bank, and one from an online bank.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Once they have chosen their accounts to research, students should contact representatives from each of the financial institutions that house those accounts to discuss the mathematics behind each account, specifically the formulas used to calculate interest. They would also ask the representatives for advice on investing in their accounts with reasons for doing so.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Once the groups have completed this research, they will then explain the exponential characteristics of the formulas for each of the accounts. They will include graphs of the formulas for each account in these explanations. They will then make predictions about what each account will yield after a certain amount of time. They will also make calculations based on a potential change in the interest rate on the account. In addition, they will make predictions about how long it will take an account to yield a certain amount of money.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">As a conclusion, students will suggest a plan of action to the local man for the best accounts to invest his money in. This could include one account, or a combination of all the accounts. Students should include a brief written rationale for their choices.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Use of Technology:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Students will need access to computers with internet access.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">They will also need access to calculators with graphing capabilities.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Customization for Diverse Learners: To accommodate for diverse learners, students can present their findings using a written format, or use visuals such as charts and graphs, or use recordings from their discussions with the bank representatives along with an oral component.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Method of Assessment: Students will be assessed in three areas. First, they will be assessed on the correctness of their explanation on the exponential characteristics of the investment accounts. Secondly, they will be assessed on the correctness of their calculations and predictions of the different accounts’ earnings. Lastly, they will be assessed on their choice of assessment and reasoning behind it.

Bryan,

I really wish I had a lesson like this in high school. I would have been more confident in how to invest my money and the options that are available.

If you have any macs available, the iWork's numbers program has several spreadsheets already designed to compare loans, budget, net worth, and savings. One of these templates might be a useful tool to implement in this particular lesson. If you want students to create graphs and charts from scratch, this might be another way to differentiate for students that have a more difficult time with abstract concepts.

Keri

=Online Collaboration/Social Networking Lesson=

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Grade Level: 10th grade

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Subject: Mathematics

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Description of Lesson: The characteristics of exponential functions are usually the most difficult standard for students to learn in this unit. I will have students work collaboratively using a wiki to learn and study these characteristics. I will assign each group of students a particular characteristic to take ownership of and be responsible for teaching it to the rest of the class. Groups will create a lesson on their characteristic and share it with the class on the wiki. They must include an assignment for students to complete as part of the lesson. Students will use their knowledge of these characteristics and discover how they relate to the formulas and investment accounts they found in their previous activity to better inform their decision about which account to choose.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Learning Outcomes:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Students will identify the characteristics of the exponential equations
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Students will rationalize how the characteristics relate to a real world context

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal; margin-bottom: 0pt;">Skills: <span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal; margin-bottom: 0pt;">Content Standards from the Georgia Performance Standards:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Graph exponential functions
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Identify characteristics of exponential functions given a graph or equation
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal;">Graph functions as transformations of f(x) = ax.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal; margin-bottom: 0pt;">Lesson: Students will stay in the same groups they were in for the last activity. I will assign each group one characteristic listed from the content standards above. Students will have to create a lesson to teach this standard to the rest of the class. It must include an assignment for students to complete at the end of the lesson to make sure they have learned their characteristic. I will model a lesson for what I expect from students as a lesson including an essential question, activating strategy, teaching strategy, summarizing strategy, and a short assessment assignment. Students will upload their lesson to a class wiki for others to view, comment, and add to. When each group has done this, students will be required to the assignments to each lesson, and turn those in to me. <span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: normal; margin-bottom: 0pt;">Creative Thinking Component: The creative thinking aspect of this lesson will be that each group will have to discuss and present how their characteristic relates in context to the investment problem from the last activity. They will need to include in the wiki what considerations this characteristic should bring forth when deciding on an investment account.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: 115%;">Customization for Diverse Learners: The wiki is a way of customizing for diverse learners because they can present their lesson in whatever format they choose. This could be traditional lecture/notes, video, podcast, etc.Method of Assessment: Students will be assessed in three areas. First, they will be assessed on their lesson, and whether it includes the five components listed above: essential question, activating strategy, teaching strategy, summarizing strategy, and assessment. They will also be assessed on their rationale for how their characteristic relates in context to the investment account problem from the previous lesson. Lastly, they will be assessed individually on their completion of each of the mini assessments for each lesson.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px; line-height: 115%;">Management in the classroom: I will have to have time for students to work on this activity in the computer lab, so I will need to book the lab for at least two class periods. I will have to guide students through the process of planning lessons by helping them find resources both print and electronic. I will also have to direct each group how to set up their lesson on the wiki.