21 st Century Math Projects

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2 Project Title: Making the Band Standard Focus: Patterns, Functions, and Algebra Topics of Focus: - Linear equations - Systems of - Multiple representations Time Range: 3-5 Days Supplies: Calculator, Basic Art Supplies, Dice Benchmarks: Expressions and Expressions and Expressions and Expressions and Expressions and Creating Reasoning with and Inequalities 7.EE 8.EE 8.EE 8.EE 8.EE A-CED A-REI 4a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. 8. Analyze and solve pairs of simultaneous linear equations. 8a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8c. Solve real-world and mathematical problems leading to two linear equations in two variables. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Building Functions F-BF 1. Write a function that describes a relationship between two quantities. Linear and Exponential Models Procedures: F-LE 1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. A.) Student will create an album of mathematically inspired songs. Teachers will evaluate and determine the starting cost for the project. B.) Students will complete the Making the Band Financial Document to make decisions for their album. They will construct a linear equation for Expenses based on their choices and use it to make predictions. C.) Students will receive the results of their choices in Did They Pay Off. Using the dice, some randomness will play a factor. They use these results to create a second linear equation and use it to make predictions. Based on their two equations, students will determine a break-even point.

3 D.) Students will receive a Change of Plans this will affect the slope of their equation and create a third equation. Using the new equation students will find the new break-even point. *E.) Students can present their album and sales report to the class as an oral presentation. *Extensions

4 Making the Band Step aside Bieber! Move over Gaga! Find a seat Kanye! It is the moment we have all been waiting for it s time to produce and launch your own music album! Before you get ourselves carried away, you were not picked up by Arista or Warner Brothers, but you were spotted by a new label Mathemusical Algetabulous Records^2. In this project, you will wear a number of hats and complete a few assignments along the way. The student is responsible for: 1. You will need to create album artwork for you first mathematically inspired record. Math, Math, Baby, Livin La Geometria Loca, and Loggystyle have already been major hits so you ll need to come up with your own. Based on your album, your teacher will assign you the cost for starting up your album (Either $100,000, $250,000, or $500,000). The better the album, the lower it will cost to get started. 2. You will need to complete the Making the Band Financial Form to make decisions for your album and release. You will need to total initial costs and monthly expenses and create a linear equation for your costs. 3. will be provided to determine the created from the Making the Band Financial Form decisions. You will create a second linear equation for and determine when you will finally break-even. 4. You will create a new equation based on a CHANGE OF PLANS. The change of plans will be determined based on the quality of the work up to this point. You will then need find a new break-even point. Where will you now break even? Individual grades for the project will be broken into the following components: Making the Band artwork is creative with attention to detail all assignments are completed and on time correct calculations are made, accurate linear models are written and graphed and break-even points are determined /100 pts /400 pts /500 pts Total /1000

5 Making the Band Album Art

6 Making the Band Financial Document The Start-Up Cost to Launch Your Album is Your job is to not only launch the most awesome mathematical record album in history, but also break-even with your money as fast as possible. These big wig execs want their money back FAST. You will need to make some choices. Select a make a decision in each category that you feel will help you earn back your budget. Each choice will have a different result, so think about what you think is most important to the success of you album. Who would you like to be your manager? JC is a top of the line manager. He is organized and understands the needs of the music industry. He is intelligent and is considered by many to be one of the top future executives in music. He has the connections and experience to launch a big album. He costs $3,000 a month. Babs is a good manager. She works hard and will not leave until the job is done. It takes her more time because she doesn t have the connections, but she makes up for it in hard work. She costs $2,000 a month. Jeff is a low quality manager. If you are on a budget, Jeff is your guy. He might return your calls. He might not. He ll do things when he feels like it. He costs $1,000 a month. Who is your choice as manager? How much does this cost? Is this a monthly expense or an initial cost? Who will manufacture the CD and advertise? CDExtraordinaire will give you the top quality product. They have some of the best graphic designers in the country and have a portfolio of top of the line products. They understand your needs as an artist and will work with you to translate your image to your CD. They cost $20,000. Madbeats is an up and coming CD maker. Currently they are short on staff, but they have released some nice CDs lately Their portfolio is not as polished as CDExtraordinaire, but they deliver an adequate product. They will cost $17,500. The Stuff is a CD producer that may be best avoided. If you like solid colors and basic text they may be for you. Rather than have a professional photographer, they send you to Walmart for pictures. They will be hard to contact since their phones have been recently disconnected. They will cost $12,000. Who do you choose to manufacture your album? How much does this cost? Is this a monthly expense or an initial cost?

7 Who would you like to produce and record you album? Jen understands high quality music. She has received 120 Grammy nominations for her work with dozens of platinum artists. She understands the nuisances of songs and how to improve them even the slightest bit. If you want her on your team you can expect to pay $5,000. Troy has a good ear for music and he gets what will sell. He hasn t had a great deal of success in the industry, but he thinks it is because of bad luck. He is easy to work with and will help complete a quality track. Troy will cost $2,500. Ruby enjoys music, but she is not good at her job. She accidentally has recorded over music of past clients. She understands how to record the music, but she will not help enhance the quality. She will work hard for you, she needs her job. Ruby will cost $1,000. Who would you hire as your record producer? How much does this cost? Is this a monthly expense or an initial cost? What type of travel and tour plan would you like? Tour of the World An elaborate tour around the globe will certainly give you worldwide exposure. Bouncing from Paris to Rome to New York playing your music in the best arenas will be like living a dream. The dream will come with cost. You will need to pay $10,000 a month for travel. Born in the USA Touring around the Midwest United States may not bring the exposure, but will certainly help your sales. You will play in decent arenas. Not the best, but they are nice. The travel will run about $5,000 a month. City Plan There is no place like home. You can play in the local music clubs. Travel will be a minimum since it will be your car and gas. This will cost $300 a month. What travel option do you choose? How much does this cost? Is this a monthly expense or an initial cost?

8 What type of lodging and accommodations suit your style? Galloway Suites Hopping from luxury suite to luxury suite will feel like royalty. You will always get a wonderful night of sleep on special mattresses customized for your body type. These wonderful nights will run up a cost of $6,000 a month. The Best Inn A hotel with all the basic amenities. No pampering, no goodies. You have a job to do and that is your focus. These hotel stays will cost $3,000 a month. Crackles The walls may be leaking, the thunder may shake your room, and you may be surrounded in rats, but you are on the road for your music. The sleepless nights may leave you disoriented and tired, but you need to save some money. These hotel stays will cost $1,500 a month. Which type of hotel do you select? How much does this cost? Is this a monthly expense or an initial cost? Number CRUNCH Zone Upfront Expenditure Cost ($) Monthly Expenditure Cost ($) Start-Up Cost Create a linear equation that will model your cost? What do the variables represent in your equation?

9 Making the Band Graph Paper Follow-Up Interpret you y-intercept and your slope, what do they mean?

10 Predictions (Use your cost equation to answer the following questions) Determine when your total costs will be the following amounts. $250,000 $600,000 $1,000,000 Explain how you determined those answers. Determine when your total expenses after the following amounts of time. 1 Year 2 Years 5 Years 10 Years Explain how you determined those answers.

11 Did they pay off? Use the following formulas to determine how much money you will earn in based on the decisions that you made yesterday on the Making the Band Financial Document. Manager Cost Per Month Check Your Choice Generated Per Month JC $3,000/mo. $3,000x Babs $2,000/mo. $1,000x Jeff $1,000/mo. $200x Roll of the Die (x) Total Monthly Monthly because of your manager? Are you satisfied with your choice? Why or Why not? Advertiser and Manufacturer Cost Check Your Choice Generated Per Month CDExtraordianaire $20,000 $10,000x Madbeats $17,500 $10,000x The Stuff $12,000 $300x Roll of the Die (x) Total Monthly Monthly because of your manufacturer? Are you satisfied with your choice? Why or Why not? Producer Cost Check Your Choice Generated Per Month Jen $5,000 $1,800x Troy $2,500 $800x Ruby $1,000 $200x Roll of the Die (x) Total Monthly Monthly because of your producer? Are you satisfied with your choice? Why or Why not?

12 Travel and Tour Plan Tour of the World Born in the USA Cost Per Month $10,000/mo. $5,000/mo. Check Your Choice Generated Per Month $5,000x $2,000x City Plan $300/mo. $500x Roll of the Die (x) Total Monthly Monthly because of your tour plan? Are you satisfied with your choice? Why or Why not? Hotel Galloway Suites Cost Per Month Check Your Choice Generated Per Month $6,000/mo. $100x The Best Inn $3,000/mo. $50x Crackles $1,500/mo. $0x Roll of the Die (x) Total Monthly Monthly because of your hotel type? Are you satisfied with your choice? Why or Why not? Calculate your total monthly : Analysis Create a linear equation that will model your? What do the variables represent in your equation? Sketch the graph of your on the Making the Band Graph Paper that you used for expenses. Label your lines.

13 Predictions (Use your equation to answer the following questions) Determine when your total will be the following amounts. $250,000 $600,000 $1,000,000 Explain how you determined those answers. Determine when your total after the following amounts of time. 1 Year 2 Years 5 Years 10 Years Explain how you determined those answers. Break-Even When do you expect to break-even? (Have more than expenses?)

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15 Change of Plans After presenting your results to your teacher, your equations will be changing. Ultimately your success comes down your skills after all. If the previous assignments have been error-free and accurate then you will draw a slip from the (x>1) basket. If the previous assignments have had mistakes then you will draw a slip from the (x<1) basket. Remember the equations that you have used from the previous days. Expense Your Slip of Paper is You will multiply the your slip of paper. New

16 Making the Band Change of Plans Graph Paper

17 Change of Plans Predictions (Use your new equation to answer the following questions) Determine when your total will be the following amounts. $250,000 $600,000 $1,000,000 Explain how you determined those answers. Determine when your total after the following amounts of time. 1 Year 2 Years 5 Years 10 Years Explain how you determined those answers. Break-Even When do you expect to break-even with the new equation? (Have more than expenses?) How different is this result from the first break-even point?

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