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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
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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