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Best Practices of Technology Integration Title: How Much Does That Car Cost??? Subject: Mathematics Intended Grade Level(s): 8th – 12th Grades Description: This project will have students of driving age find out how much it costs to buy a used car and finance it through a bank. Students in Algebra or Advanced Algebra can find the amount of a car using periodically compounded interest or continuously compounded interest formulas. The students will find a suitable car in a given price range, find an appropriate loan for the car, and create a convincing report that states why the particular loan is chosen. First, the students will find the car they wish to purchase in a local newspaper. Students will next search the Internet to find current auto loan interest information for four different states and also an Internet loan corporation. The students will create a spreadsheet and charts to organize, calculate, display, and compare information in a professional manner. Finally, the students will create a convincing report detailing their reasoning for choosing the loan, and why it is the most appropriate and affordable. Narrative: Finding interesting lessons for high school mathematics students can be difficult. In the lesson I chose to explain, students will use a real- world example to integrate technology and mathematics as well as make decisions on issues dealing with money. This is an excellent lesson to do with students who are of driving age so they understand that there is more to owning a car than being able to drive. This topic can be of interest to the students when they are able to make their own decisions on what car they want to buy and how much to spend. The students have an opportunity to discuss the many budgeting decisions involved when deciding what type of car to purchase. Some of these decisions are: finding out a reasonable interest rate for the car, deciding which bank to do business with, calculating the final cost of the car over the course of the loan, and determining an appropriate monthly payment. The students also can discuss why different states are chosen for analysis, and what factors to look for when making decisions on a loan. Students are able to investigate using interest formulas through the use of technology. They are to use technology to calculate and organize information in a manner that would help the students compare and contrast information to make decisions. Through the use of technology ,such as spreadsheets, charts, and the Internet, students can collect up-to-date and accurate information as well as present that information in interesting and creative ways. How Much Does That Car Cost??? 1 In the end, the students must make their own decision about the loan and detail their reasoning for choosing their particular loan. The students must organize and compose a half-page paper where the arguments are clear and concise. Curriculum Benchmarks: MI.MAT.I.1.HS.3 Study and employ mathematical models of patterns to make inferences, predictions and decisions. MI.MAT.III.1.HS.2 Organize data using tables, charts, graphs, spreadsheets and databases. MI.MAT.V.1.HS.4 Efficiently and accurately apply operations with real numbers, complex numbers, algebraic expressions, matrices, and vectors in solving problems. MI.MAT.V.2.HS.5 Explore problems that reflect the contemporary uses of mathematics in significant contexts and use the power of technology and algebraic and analytical reasoning to experience the ways mathematics is used in society. Detailed Timeline: The lesson should take the students 150- minutes to complete the lesson; either two 90- minute block periods or three 50- minute class periods. • Teaching the short lesson on interest rates with student discussion (30-35 min) • Looking up a car to purchase in the newspaper and cutting out or scanning into a word processing document (10-15 min) • Looking up the interest rate information on the Internet (15-20 min) • Creating the spreadsheet with formulas (25 min) • Creating the charts (35 min) • Analyzing information and deciding which loan to pick (10 min) • Writing up and printing out the project (20 min). Materials/Hardware/Software: Ø Recent newspaper with the automobile advertisement section. Ø Computer lab with Internet access. Ø Spreadsheet software (the example is in Excel® 2000). Ø Word processing software (such as Word® 2000) Ø Scanner (optional). Teacher Preparation: The teacher should either use the attached example to follow or create his or her own example. The teacher should know the formulas needed to create the spreadsheet, know how to format spreadsheets, and know how to create the charts needed for the project. The teacher should search and bookmark sites for the interest rate information. If a scanner is available, the teacher should be familiar with using the scanner and importing the picture into a word processing How Much Does That Car Cost??? 2 document. If the teacher is familiar with spreadsheets, charts, and the Internet, then teacher preparation time will be minimal. However, if the teacher is not familiar with these items, more time may be required to prepare for the lesson. The teacher should be sure that he/she can create the spreadsheet and charts before taking students to the computer lab. The teacher can click on the cells to view the formulas for the spreadsheet. To review how the charts were created, the teacher can click on the chart, then click on the chart wizard and retrace the steps required for creating the chart. Prerequisite Student Skills: Students should be familiar with formatting spreadsheets, calculating formulas, and creating and formatting basic charts. If students are not familiar, then class time (approximately 30 minutes) should be spent teaching about creating formulas in spreadsheets, formatting cells, and creating charts. Activities/Procedures: LESSON: The teacher will teach a short lesson on interest formulas. This should fit directly into an Algebra or Advanced Algebra curriculum. Algebra students will learn about the periodically compounded interest formula: A=P(1+r/n) nt ; where P is the principal amount of the loan for the car, r is the interest rate, n is the number of times the loan is compounded in a year, and t is the number of years of the loan. Advanced Algebra students will learn to use the formula for calculating interest continuously: A=Pert ; where P is the principal amount of the loan for the car, the number e is used here, r is the interest rate for the loan, and t is the number of years of the loan. DISCUSSION: It is important for the teacher and students to discuss the factors that loans have such as the number of years, the interest rate, the overall payment required for a loan, etc. The students should brainstorm in small groups of three or four the many aspects to collecting the information, organizing and calculating the data, displaying the information, and finally making an informed decision. The teacher should then ask each group to share one item that they discussed in their small groups. When all ideas have been shared, the students are to work individually on the following project, however they can ask other students or the teacher for help. LOOKING UP CAR AND INTEREST RATES: The students are going to look up their own car to purchase and loan interest rate information for a car they would like to purchase. The students will be asked to look through a local newspaper to find a used car that they would like to buy. The teacher needs to set maximum and minimum limits on the amount a student can spend for the car. After the students find a car they would like, they can cut out of the paper the article that describes the car (the students could also scan in the newspaper clipping if you have the capability). Then they are to go on the Internet and find current interest rates on the computer. Two helpful web sites are: www.rate.net and www.banx.com. The students are to find the current rate for five banks, one in Michigan, Florida, California, New York, and an Internet corporation. The reason behind this is to check out how the State of Michigan compares with other states around the country. How Much Does That Car Cost??? 3 CREATING SPREADSHEET: The students are then to go to a spreadsheet and input the information and calculate the cost of the car using the different state’s interest rates for both a three-year loan and a four- year loan. The spreadsheet should be formatted so that the rows will have the titles of the five banks, the columns will have the titles of: original cost of car, total amount of car for three year loan, amount of interest on car for three year loan, monthly payment on car for three year loan, total amount of car for four year loan, amount of interest on car for four year loan, and monthly payment on car for a four year loan. (See spreadsheet example.) Under the original cost of car column, each cell should contain the cost of the car the student chose in the newspaper. In the total amount of car for three year loan column, the interest formulas learned in class and stated above should be used. Example for Algebra: = (original cost of car)*(1 + interest rate/365)^(365*3) for loan compounded daily. In the amount of interest on car for three year loan column, use the formula: = total amount of car – original cost of car. In the monthly payment on car column, use the formula: = total amount of car / 36, since there are 36 months in three years. The formulas for the four year loan are similar; just make adjustments in each of the formulas for the different years. CREATING CHARTS: The students are then to make bar, line, and a bar/line combination graphs that compare these five things (see example): 1. A comparison between the different states’ interest rates. 2. A comparison between the total amount paid for the car for a three year loan versus a four year loan for all states. 3. A comparison between the interest paid for the car for a three year loan versus a four year loan for all states. 4. A comparison between the monthly payment on a three year loan versus a four year loan for the Michigan bank and the Internet loan corporation 5. A comparison between the original cost of the car and the final cost after the interest is calculated for each type of loan. The students are to make the graphs creative by choosing color schemes that enhance the look of the graph, and by formatting the chart so it looks professional. WRITE UP: Then the students must analyze the information from the spreadsheet and graph to decide which state’s loan they are going to go with and the number of years for the loan. The students must type using word processing software a half-page (minimum) paper on the factors that influenced their decision for that particular loan, and the details that made the loan worth choosing. The students will hand in the spreadsheet with formulas, the charts, the newspaper clipping, and the written document to the teacher. (If students scanned in the newspaper, they can input the picture into their word processing document.) How Much Does That Car Cost??? 4 Assessment/Evaluation: The students will be assessed with the following rubric: Students will receive a score from 0 to 5 in each of the following categories: v Spreadsheet: • Formulas 0 1 2 3 4 5 • Formatting 0 1 2 3 4 5 v Chart: • Information 0 1 2 3 4 5 • Formatting 0 1 2 3 4 5 v Paper: • Grammar 0 1 2 3 4 5 • Thoughts/Arguments 0 1 2 3 4 5 Total Points (out of 30): _________ Ratings are determined as follows: 5 All complete and correct 4 Most complete and correct 3 Some incomplete or some incorrect 2 Some incomplete and incorrect 1 Most incomplete and incorrect 0 All incomplete and incorrect Follow-Up Activities: As a follow-up, the students could look up insurance rates from different companies for the car they choose and determine from which insurance company to purchase an insurance policy. Submitted By: Name: Rebecca Skutt School District: West Ottawa Public Schools School: West Ottawa High School Address: 1024 136th Avenue, Holland MI 49424 Email: thsrls01@westottawa.k12.mi.us How Much Does That Car Cost??? 5