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© 21st Century Math Projects Project Title: World Traveler Standard Focus: Patterns, Functions & Algebra Time Range: 2-3 Days Supplies: Calculator, Lab for extension Topics of Focus: - Defining and Using Functions - Inverse Functions - Currency Conversion Benchmarks : Functions 8.F Seeing Structure in Expressions A-SSE 1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 1. Interpret expressions that represent a quantity in terms of its context.★ Interpreting Functions F-IF 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Interpreting Functions F-IF 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Interpreting Functions F-IF 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Building Functions F-BF 4. Find inverse functions. Building Functions F-BF 4a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Procedures: A.) Student will complete “Money Changers” which will practice the type of problems and develop the thinking necessary to complete the project. B.) Students will complete “World Traveler” where they develop functions and inverse to convert currency. Students will track spending and remaining conscious of a budget. Extension*C.) In “World’s Fair” students represent different countries and offer different goods. They must research to find the price of 5 goods in their country. They must also write a function to convert currency from US Dollars to the currency in their country and an inverse to change it back. Half of the class, will be “shoppers” while the others are “sellers”. In the middle of the class period, these roles can switch. Shoppers are responsible for buying items from at least 8 different countries. The sellers should help the shoppers with the calculations. Google has exchange rates. X-Rates.com is also useful. © 21st Century Math Projects Money ChangerS Until Paypal takes over the world, currency conversion is an essential part of international travel. Like languages, currencies were developed and used in smaller communities and have continued on to the present day. Everything pretty much stayed the course until 1995 when the European Union elected to use the euro. This allowed most European countries to skip that conversions and just talk money. Currency conversion happens to be a mathematical function! In this assignment, these conversions will be converted using functions. Practice 1. Greta soon will be traveling to the UK over spring break. The conversion of US Dollars to British Pounds is a ratio of 1 dollar to 0.6330 pounds. This can be modeled by the function, f(x) = 0.6330x, where x represents the number of dollars to be converted. a.) If Jamie converted $1000 to British Pounds, how many pounds will she get? b.) Greta will return home soon and needs to convert her currency back. Find f -1(x) and define it. If she converts 150 pounds, how many dollars will she get back? 2. Arnold is taking a trip to Japan for an internship. The conversion of US Dollars to Japanese Yen is a ratio of 1 dollar to 78.76 yen. Then can be modeled by the function, g(x) = 78.76x, where x represents the number of dollars to be converted. a.) If Arnold exchanged $5000 to Yen, how many yen will he receive? b.) After his paid internship, Arnold returns with 500,000 yen. Find g-1(x) and define it. If he all of his yen, how many dollars will he get receive? © 21st Century Math Projects 3. The following currency conversion table is missing some values! Define a function for the known values, find its inverse and use it to solve for the unknown. … you get _____ of these USD For 1 of these… MXN CNY EUR AUD 1 13.1884 c 0.7993 0.9618 a 1 0.4819 0.0606 0.0728 0.1574 2.0751 1 d 0.1511 1.2510 b 7.9510 1 e 1.0398 13.7297 6.6159 0.8311 1 . MXN → USD EUR → MXN USD → CNY CNY → EUR EUR → AUD Answers a= b= c= d= e= © 21st Century Math Projects World Traveler Jessica is about to take a trip of a lifetime. Four weeks in four different countries. All of the tickets are bought, all the hotels are booked. She is bringing with her $4000 to spend and her goal is to spend less than $1000 in each country. THE PROBLEM IS after she gets off the airplane, she has to swap her money. After she does this, keeping track of $1000 is pretty difficult and she has no idea how much she spent in each country. Your job is to help her figure out if she stayed within her goal. Before she left, Jessica printed off the current exchange rates from the US Dollar. This didn’t help her one bit when she was trying to exchange pounds for dirhams. Jessica’s Trip Week Country Currency Value of One US Dollar British Pound 1 USD : .63 GBP Dirham 1 USD : 3.67 AED 1 United Kingdom 2 United Arab Emirates 3 South Korea Won 1 USD : 1135.68 ROK 4 Brazil Real 1 USD : 2.027 BRL Answer the following questions in complete sentences. Show all work. 1. Which currency(ies) have a value higher than the dollar? 2. Write four functions that represents the exchanging Dollars with each of the different foreign currencies. USD → GBP 3. USD → AED USD → ROK USD → BRL Write four inverse functions that convert the foreign currency back into Dollars. GBP → USD AED → USD ROK → USD BRL → USD © 21st Century Math Projects Welcome to United Kingdom 4. When Jessica lands in the United Kingdom she exchanges all $4,000 into pounds. The exchange office also charges her 5 pounds for processing. How many pounds does she have? Jessica currently has __________________ 5. After taking a week-long tube pass, a hearty batch of fish and chips, and a coach ride to see Stonehenge, Jessica still has 1820 pounds. How many total pounds did she spend in the UK? In United Kingdom, Jessica spent __________________ Jessica currently has __________________ اإلم ارات دول ة ف ي ب كم مرح با ال م تحدة ال عرب ية 6. After landing in Dubai in the United Arab Emirates Jessica goes to an exchange booth. She exchanges all of her pounds into dirhams and is charged a 10 dirham processing fee. How many dirhams does she have? (You’ll need to convert pounds back to dollars before you can convert to dirhams) Jessica currently has __________________ 7. After visiting Dubai, the revolutionary 21st century Masdar City, and visiting the Gold Souk, Jessica loses track of her money! She looks in her pocket and has six 1000 dirham notes, three 500 dirham notes and three 100 dirham notes! How much money did she spend in UAE? In UAE, Jessica spent __________________ Jessica currently has _________________ © 21st Century Math Projects 한국 에 오신 것을 환영합니다 8. Jessica then flies to South Korea. In exchange for her dirham, she is handed 2,300,000 won! She’s rich! The exchange advertises a processing fee of 100,000 won, did they do the math correct or was Jessica cheated? Jessica currently has __________________ 9. While in South Korea, Jessica is able to catch a show at the Nanta Theater and relax at the Samcheong-dong Bukchon. When she counts up her won she sees that she only has 1,100,000. She spent over a million won! How many total won did she spend in South Korea? In South Korea, Jessica spent __________________ Jessica currently has __________________ Bem-vindo ao Brasil 10. She flies to Brazil and exchanges her won for Real. The exchange does not charge a processing fee! How many reals should Jessica receive? Jessica currently has __________________ 11. In Brazil, Jessica is about to watch a friendly futbol game between Brazil and Spain, and enjoy a night about town in Rio. She looks in her pocket and only has 200 reals! How many reals did she spend in Brazil? In Brazil, Jessica spent __________________ Jessica currently has __________________ © 21st Century Math Projects A HomeComing 12. Upon returning home Jessica is able to exchange her money back to US dollars (thankfully!). She is given $73.67 after a $25 processing fee. Was this math done correctly? 13. Backtrack Jessica’s spending. How many US Dollars did she spend in each country? Trip Finances Country Total Local Currency Spent United Kingdom pounds United Arab Emirates dirhams South Korea won Brazil reals Equivalent US dollar amount 14. Did Jessica meet her goal and spend less than $1000 a week in each country? 15. Why do you think it important to understand the exchange rate? If a friend plans to travel out of the country what suggestions could you make to help make their trip go smoother? EXTENSION Using the conversion table, develop a function that coverts British Pounds into Brazil Reals. © 21st Century Math Projects World’s Fair You are going to participate in an unprecedented World’s Fair in your own classroom! Students will each represent a country, develop currency conversion functions and research and sell goods. You will play two different roles in this Fair – a seller and a shopper. As a seller, you will identify and price five items from a country of your choice. As a shopper you will have $500 of U.S. money to spend in the different countries and must keep track of your money along the way. Complete this page to prepare your store. You will need to create a sign with the goods and their cost in your currency. Country Currency Exchange Rate from U.S. Dollars to _____ Use the exchange rate to write functions to convert to and from U.S. Dollars. From U.S. Dollars To U.S. Dollars Identify five items to sell from your country. You may find the price in your currency, but you may only find the price in U.S. Dollars. Use your exchange function to price the item in your currency. Item Description Cost in Your Currency Cost in U.S. Dollars © 21st Century Math Projects Seller’s Log Country: Currency: For each sale, record the item(s) you have sold and the amount of money you have earned. Item(s) Sold Earnings © 21st Century Math Projects Shopper’s Log For each country you visit, convert the amount of U.S. Dollars you have remaining into the currency of the country, record the item(s) you have bought and the cost in the currency. Calculate the Cost in U.S. Dollars and subtract it from the money you have left. Country / Currency Amount of U.S. Dollars Remaining in the Country’s Currency Item(s) Sold Cost in Currency Amount Remaining in Currency Cost in U.S. Dollars U.S. Dollars Remaining $500 © 21st Century Math Projects Thank you for being my Math Friend! If you liked this 21st Century Math Project You might like others. (Click the logo) Math it Up. Boomdiggy. © 21st Century Math Projects Money ChangerS Until Paypal takes over the world, currency conversion is an essential part of international travel. Like languages, currencies were developed and used in smaller communities and have continued on to the present day. Everything pretty much stayed the course until 1995 when the European Union elected to use the euro. This allowed most European countries to skip that conversions and just talk money. Currency conversion happens to be a mathematical function! In this assignment, these conversions will be converted using functions. Practice 1. Greta soon will be traveling to the UK over spring break. The conversion of US Dollars to British Pounds is a ratio of 1 dollar to 0.6330 pounds. This can be modeled by the function, f(x) = 0.6330x, where x represents the number of dollars to be converted. c.) If Jamie converted $1000 to British Pounds, how many pounds will she get? 633 pounds d.) Greta will return home soon and needs to convert her currency back. Find f-1(x) and define it. If she converts 150 pounds, how many dollars will she get back? 236.97 2. Arnold is taking a trip to Japan for an internship. The conversion of US Dollars to Japanese Yen is a ratio of 1 dollar to 78.76 yen. Then can be modeled by the function, g(x) = 78.76x, where x represents the number of dollars to be converted. c.) If Arnold exchanged $5000 to Yen, how many yen will he receive? 393,800 d.) After his paid internship, Arnold returns with 500,000 yen. Find g-1(x) and define it. If he all of his yen, how many dollars will he get receive? 6348.40 © 21st Century Math Projects 3. The following currency conversion table is missing some values! Define a function for the known values, find its inverse and use it to solve for the unknown. … you get _____ of these USD For 1 of these… MXN CNY EUR AUD 1 13.1884 c 0.7993 0.9618 a 1 0.4819 0.0606 0.0728 0.1574 2.0751 1 d 0.1511 1.2510 b 7.9510 1 e 1.0398 13.7297 6.6159 0.8311 1 . MXN → USD EUR → MXN USD → CNY CNY → EUR EUR → AUD Answers a= 0.0758 b= 16.5092 c= 6.3547 d= 0.1258 e= 1.2032 … you get _____ of these USD For 1 of these… MXN CNY EUR AUD 1 13.1884 6.3547 0.7993 0.9618 0.0758 1 0.4819 0.0606 0.0728 0.1574 2.0751 1 0.1258 0.1511 1.2510 16.5092 7.9510 1 1.2032 1.0398 13.7297 6.6159 0.8311 1 © 21st Century Math Projects World Traveler Jessica is about to take a trip of a lifetime. Four weeks in four different countries. All of the tickets are bought, all the hotels are booked. She is bringing with her $4000 to spend and her goal is to spend less than in each country. $1000 THE PROBLEM IS after she gets off the airplane, she has to swap her money. After she does this, keeping track of $1000 is pretty difficult and she has no idea how much she spent in each country. Your job is to help her figure out if she stayed within her goal. Before she left, Jessica printed off the current exchange rates from the US Dollar. This didn’t help her one bit when she was trying to exchange pounds for dirhams. Jessica’s Trip Answer Week 1 2 3 4 Country United Kingdom United Arab Emirates South Korea Brazil Currency British Pound Dirham Won Real the Value of One US Dollar 1 USD : .63 GBP 1 USD : 3.67 AED 1 USD : 1135.68 ROK 1 USD : 2.027 BRL following questions in complete sentences. Show all work. 1. Which currency(ies) have a value higher than the dollar? Just the British Pound. 2. Write four functions that represents the exchanging Dollars with each of the different foreign currencies. USD → GBP USD → AED USD → ROK USD → BRL Y = 0.63x Y = 3.67x Y = 1135.68x Y = 2.027 x where x is USD where x is USD where x is USD where x is USD 3. Write four inverse functions that convert the foreign currency back into Dollars. GBP → USD AED → USD ROK → USD BRL → USD Y = x/0.63 or Y = .272x Y = 0.00088x Y = .49x Y = 1.59x Where x is GBP Where x is AED Where x is ROK Where x is BRL © 21st Century Math Projects Welcome to United Kingdom 4. When Jessica lands in Great Britain she exchanges all $4,000 into pounds. The exchange office also charges her 5 pounds for processing. How many pounds does she have? 2515 Jessica currently has __________________ 5. After taking a week-long tube pass, a hearty batch of fish and chips, and a coach ride to see Stonehenge, Jessica still has 1820 pounds. How many total pounds did she spend in the UK? 695 In United Kingdom, Jessica spent __________________ 1820 Jessica currently has __________________ اإلم ارات دول ة ف ي ب كم مرح با ال م تحدة ال عرب ية 6. After landing in Dubai in the United Arab Emirates Jessica goes to an exchange booth. She exchanges all of her pounds into dirhams and is charged a 10 dirham processing fee. How many dirhams does she have? (You’ll need to convert pounds back to dollars before you can convert to dirhams) $2888.89 10,602.23 7. Jessica currently has __________________ After visiting Dubai, the revolutionary 21st century Masdar City, and visiting the Gold Souk, Jessica loses track of her money! She looks in her pocket and has six 1000 dirham notes, three 500 dirham notes and three 100 dirham notes! How much money did she spend in UAE? 2802. 23 dirham 7800 dirham In UAE, Jessica spent __________________ Jessica currently has _________________ © 21st Century Math Projects 한국 에 오신 것을 환영합니다 8. Jessica then flies to South Korea. In exchange for her dirham, she is handed 2,300,000 won! She’s rich! The exchange advertises a processing fee of 100,000 won, did they do the math correct or was Jessica cheated? $2125.34 should be 2,413,706.81 she was cheated. 2,300,000 won 9. Jessica currently has __________________ While in South Korea, Jessica is able to catch a show at the Nanta Theater and relax at the Samcheong-dong Bukchon. When she counts up her won she sees that she only has 1,100,000. She spent over a million won! How many total won did she spend in South Korea? 1,200,000 won In South Korea, Jessica spent __________________ 1,100,000 won Jessica currently has __________________ Bem-vindo ao Brasil 10. She flies to Brazil and exchanges her won for Real. The exchange does not charge a processing fee! How many reals should Jessica receive? $968.58 -> 1963.32 real Jessica currently has __________________ 11. In Brazil, Jessica is about to watch a friendly futbol game between Brazil and Spain, and enjoy a night about town in Rio. She looks in her pocket and only has 200 reals! How many reals did she spend in Brazil? 1763.32 real 200 reals In Brazil, Jessica spent __________________ Jessica currently has __________________ © 21st Century Math Projects A HomeComing 12. Upon returning home Jessica is able to exchange her money back to US dollars (thankfully!). She is given $73.67 after a $25 processing fee. Was this math done correctly? $98.67, Yes the math is correct 13. Backtrack Jessica’s spending. How many US Dollars did she spend in each country? Trip Finances Country Great Britain United Arab Emirates South Korea Brazil 14. Total Local Currency Spent 695 pounds 2802. 23 dirhams 1,200,000 won 1763.32 reals Equivalent US dollar amount 1103.17 763.55 1056.64 869.92 Did Jessica meet her goal and spend less than $1000 a week in each country? She spent more than $1,000 in Great Britain and South Korea. 15. Why do you think it important to understand the exchange rate? If a friend plans to travel out of the country what suggestions could you make to help make their trip go smoother? Answer Vary EXTENSION Using the conversion table, develop a function that coverts British Pounds into Brazil Reals. f(x) = 3.2336x Where x represents the number of pounds. (Can be solved with composition of functions) © 21st Century Math Projects