This document discusses the Erasmus+ program "Maths in Art" which aims to improve math teaching and learning through international collaboration between schools. It describes the partner schools involved which are located in 7 countries. The program consists of units where students will use math to study elements in the arts and cultures of the partner countries. Calculations are provided to find population and area information for cities participating in the program. Additional information is given about interesting places to visit in these cities that can be uncovered by solving linear equations.

1. Introduction
This projec t aros e from the joint des ire of m aking learning
and teac hing Maths m ore effec tive. Ac c ording to in depth data
analys is our s tudents are afraid of this s ubjec t, they lac k learning
m otivation and find Maths very diffic ult. Finally, Maths tes t
res ults are below national and European average level. That's
why we c reated our projec t to im prove the level of key
c om petences - es pec ially Maths - through ac c ess to high quality
innovative educ ation and adopting teac hing and learini g to the
s urrounding reality.
Math is an im portant tool for other s ubjec ts and everyday life,
s o s tudents need to know it well. Es pecially s tudents with
learning diffic ulties, refugees and Rom anies to get c hanc es to
integrate. Good c om mand of key c om pete nces will help them to
bec om e full m em bers of their s oc iety. W e as pire to m ake our
s tudents aware of the im portance of Maths and s how the beauty
and univers ality of this s ubject. Each s c hool tried its bes t but only
wide international c oalition of differ ent s c hools: private and s tate
ones and prim ary and s ec ondary teac hers will enable us to find
innovative and highly effec tive approach in Maths teac hing and
learning.
O ur partners hips c omprises primary and s ec ondary s c hools
from s even different c ountries. W e wanted to have a m ix of
s c hools, s ituated in different areas, private and s tate ones from
Poland, Turkey, Germ any, Italy, Lithuania, Cyprus and Greec e.
"Maths in Art" projec t c onsists of:
 Getting to Know Eac h O ther Unit
 Traveling around Europe Unit
 Dis c overing Artis ts from Partner Countries Unit
 Finding Maths Elem ents in Partner Countries' Paintings Unit

2.  Finding Maths Elem ents in Partner Countries' Arc hitecture Unit
 Finding Maths Elem ents in Partner Countries' Sc ulptures Unit
 Finding Maths Elem ents in Partner Countries' Mus ic Unit
Through this projec t we will im prove bas ic s kills , fos ter
innovation in educ ation, im prove teaching and learning Maths and
foreign languages , inc rease m otivation and m orale for both s taff
and s tudents, particularly Romanies and refugees , s tudents with
s pec ial educ ational needs , and learning s tyles to work together
on the projec t, develop pers onal and s oc ial s kills and the idea of
c ooperation and res ponsibility for the c om m on work by s tim ulating
art m ethods.
Apart from the pos itive ac ademic effects, we are c onvinc ed
that this s pec ial international exc hange will als o c ontribute to a
better international and c ultural understanding, whic h is of
inc reas ing relevance in tim es of war and terror on our c ontinent.

3. Population
O rde r of ope rations
In m athem atics and c om puter programming, the order of
operations (or operator prec edence) is a c ollec tion of rules that
define whic h proc edures to perform firs t in order to evaluate a
given m athematical expression.
For exam ple, in m athematics and m os t c om puter languages,
m ultiplication prec edes addition.Thus, in the expres s ion 2 + 3 × 4,
the ans wer is 14, not 20. Brac kets, ( and ), { and }, or [ and ] —
whic h have their own rules — c an indic ate an alternate order or
reinforc e the default order to avoid c onfus ion, thus the prec eding
expres s ion c ould be c hanged to (2 + 3) × 4 to produc e 20, or 2 +
(3 × 4) to produc e 14 (the default if there are no brac kets ).
The order of operations us ed throughout m athematics,
s c ience, tec hnology and m any c om puter programming languages
is expres s ed here:
 exponents and roots
 m ultiplication and divis ion
 addition and s ubtraction
This m eans that if a m athematical expression is prec eded by
one binary operator and followed by another, the op erator higher
on the lis t s hould be applied firs t
Solv e the math tasks abov e to find out the population of the
citie s which take part in the Erasmus+ program “ M aths In Art” .
1. The population of Athens (in thous ands) is :

4.    3 2 2 2 5
10 10 3 4 3 2 3 2        
2. The population of Cz es tochowa (in thous ands) is :
     
22 2016 0 4 2
2 5 2 4 1 4 1 3 11B         
3. The population of Konya (in thous ands) is :
     
42 2 2 2 2
4 2 3 2 4 15 5 10 3 2 3C            
4. The population of Strovolos (in thous ands) is :
   
2 22 2 3
2 3 4 3 3D      
 
5. The population of Taranto (in thous ands) is :
   4 2 2 3
4 3 2 6 3 2 5 2 2E         
6. The population of Überlingen (in thous ands ) is :
 2 3 4 0
2 2 2 2 5 2 12345F       
7. The population of Vilnius (in thous ands) is :
   
22 2
7 1 2 4 5 1 5 3 6G          
 

5. Cities Area
Fractions: G e neral T heory
A frac tion is nothing les s than a num ber. You c an therefore
indic ate frac tions on the num ber line. A frac tion is the outc om e
(quotient) of a divis ion of two integers . Integers are whole
num bers. For that reas on you s hould never leave a dec im al
num ber in a frac tion. You c an als o s ay that a frac tion is the ratio
between two num bers. Examples are
1 4
,
2 3
and
2
5
.
Adding or Subtracting Fractions
You c an add or s ubtract fractions as long as their
denom inators are the s am e. To do s o, you keep the denom inator
c ons istent and s im ply add the num erators.
2 5 7
11 11 11
 
But you CANNO T add or s ubtract fractions if your
denom inators are unequal.
So what c an you do when your denom inators are unequal?
You m us t m ake them equal by finding a c om mon m ultiple (number
they c an both m ultiply evenly into) of their denom inators.
2 4 2 5 4 11 10 44 54
11 5 11 5 5 11 55 55 55
 
     
 
M ultiplying Fractions
Luc kily it is m uc h s im pler to m ultiply frac tions than it is to
add or divide them . There is no need to find a c om mon

6. denom inator when m ultiplying--you c an jus t m ultiply the frac tions
s traight ac ross.
To m ultiply a frac tion, firs t m ultiply the num erators. This
produc t bec omes your new num erator.
Next, m ultiply your two denom inators. This product bec omes
your new denom inator.
2 4 2 4 8
3 5 3 5 15

  

Div iding Fractions
In order to divide frac tions, we m us t first take the rec iprocal
(the revers al) of one of the frac tions. Afterwards, we s im ply
m ultiply the two frac tions together as normal.
W hy do we do this ? Bec ause divis ion is the oppos ite of
m ultiplication, s o we m us t reverse one of the frac tions to turn it
bac k into a m ultiplic ation ques tion.
2 4 2 5 10 10:2 5
:
3 5 3 4 12 12:2 6
    
M ake the calculations to find out the are as of the cities which
take part in the Erasmus+ program “ M aths In Art ” .
1. The area of Athens (in km 2
) is : 2 23 1 1
10 8 9
2 2 5
A
 
    
 
2. The area of Cz es tochowa (in km 2
) is :
2 3
3 10 2 3 4
5 3
3
10 2
B
   


3. The area of Strovolos (in km 2
) is :
23 3 9 1 1
90 4
5 10 2 9 3
C
  
      
  
4. The areas of Taranto, Überlingen and Vilnius are 210 km 2
,
59 km 2
and 401 km 2
res pec tively.
i. How m uc h bigger is the area of Taranto than the area of
Überlingen as a perc entage?
ii. How m uc h bigger is the area of Vilnius than the area of
Überlingen as a perc entage?
iii. Calc ulate the 40% of the area of Taranto, the 90% of
the area of Überlingen and the 30% of the area of
Vilnius . Sort the num bers from leas t to greates t.

7. Interesting places to visit
Line ar e quation: G e neral T heory
In m athem atics, an equation is a s tatem ent of an equality
c ontaining one or m ore variables . Solving the equation c ons ists of
determ ining whic h values of the variables m ake the equality true.
How we solv e an e quation
1. If there are fr ac tions, we m ultiply both s ide with the lowes t
c om mon m ultiple.
2. W e have to rem ove the brac kets
3. W e c ollec t like term s
4. Divide both s ides with the fac tor of the unknown.
Solv e the e quations above to find out informations of
inte resting places to v isit of the citie s which take part in the
Erasmus+ program “ M aths In Art ” .
T he Parthenon (Athe ns, G reece)
The Parthenon is a form er tem ple, on the Athenian Ac ropolis,
Greec e, dedic ated to the goddes s Athena, whom the people of
Athens c ons idered their patron. Construction began in 447 BC
when the Athenian Em pire was at the peak of its power. It was
c om pleted in 438 BC although dec oration of the building
c ontinued until
3 200
8
2 4
x x
x

   BC.
It is the m os t im portant s urviving building of Clas sical

8. Greec e, generally c onsidered the z enith of the Doric order. Its
dec orative s culptures are c ons idered s om e of the high points of
Greek art. The Parthenon is regarded as an enduring s ym bol of
Anc ient Greec e, Athenian dem ocracy and wes tern c ivilisation, and
one of the world's greatest c ultural m onuments. The Greek
Minis try of Culture is c urrently c arrying out a program me of
s elec tive res toration and rec onstruction to ens ure the s tability of
the partially ruined s tructure.
Black M adonna (Cz estochowa, Poland)
The Blac k Madonna of Cz ęstochowa, als o known as O ur Lady
of Cz ęs tochowa, is a revered ic on of the Virgin Mary hous ed at
the Jas na Góra Monas tery in Cz ęs tochowa, Poland. Several
Pontiffs have rec ognised the venerated ic on, beginning with Pope
Clem ent XI who is s ued a Canonic al Coronation to the im age on
 2 4500 100 1
2 3 3 6
xx x  
  
via the Vatic an Chapter.
M e vlana M useum
The Mevlana Mus eum (Mevlana Müz es i), als o known as the
Green Maus oleum or Green Dom e, is the original lodge of the
Mevlevi W hirling Dervishes, a m ys tical Sufi Mus lim group. It
c ontaines the tom b and s hrine of the Mevlana, or Rum i, which
rem ains an im portant plac e of pilgrim age.
History of M e v lana M useum (G reen M ausoleum)
Sultan 'Ala' al-Din Kayqubad, the Seljuk s ultan who had
invited Mevlana to Konya, offered his ros e garden as a fitting
plac e to bury Baha' ud-Din W alad (or Bahaeddin Veled), the
father of Mevlana, when he died in 1231. W hen Mevlana him s elf
died on Dec em ber 17, 1273, he was buried next to his father.
Mevlana's s uc cessor Hüs amettin Çelebi built a m aus oleum
(Kubbe-i-Hadra) over the grave of his m as ter. The Seljuk
c ons truction, under arc hitect Behrettin Tebrizli, was finished in
1274. Gürc ü Hatun, the wife of the Seljuk Em ir Suleym an
Pervane, and Em ir Alam eddin Kays er funded the c ons truction.
The c ylindrical drum of the of the dom e originally res ted on
four pillars . The c onic al dom e is c overed with turquoise faience.

9. Several s ec tions were added until
200 1 300
3
3 15 5
x x x  
  
Selim I dec orated the interior and perform ed the woodc arving of
the c atafalques.
A dec ree by Ataturk in Septem ber 1925 dis s olved all Sufi
brotherhoods in Turkey. O n April 6, 1926, another dec ree ordered
that the Mevlana m aus oleum and dervis h lodge be turned into a
m us eum. The m us eum opened on Marc h 2, 1927.
Spec ial perm ission granted by the Turkis h government in
1954 allowed the Mawlawi dervis hes of Konya to perform their
ritual danc es for touris ts for two weeks eac h year. Des pite
governm ent oppos ition the order has c ontinued to exis t in T urkey
as a religious body. The tom b of Rum i, although officially part of a
m us eum, attracts a s teady s tream of pilgrim s.
M ünster St. Nikolaus (Überlingen, G ermany)
In the interior, the c athedral hous es valuable works of art,
above all the high altar c arved by Jörg Zürn from 1613 to 1616.
The Überlinger Müns ter is dedic ated to St. Nic holas , the
patron of s ailors , fis hermen, m erchants, pilgrims and travelers.
The c ons truction of the larges t Gothic c hurch in the
Bodens eeregion began in the c hoir area i n 1350; The c om pletion
of the im pres sive five-aisled bas ilica took plac e in
150 1 7 1
9 5 10 18
x x 
   .
The owner was the c ounc il of the c ity. Thus , the Churc h als o
tes tifies to the piety and pros perity of the im perial c ity of
Überlingen.
The Cathedral Tower, with its height of 66 m eters, not only
dom inates the c ity, but is als o vis ible as a landm ark from a
dis tanc e. O riginally, the c hurch was to have two towers . The
s ec ond tower, however, rem ained in the s tate of the 1420s ; The
"O s anna", poured in 1444, is the larges t bell of the
Müns tergeläut, weighing alm ost nine tons .
W ith num erous works from around 1300 to the early 20th
c entury, the c hurch has a ric h interior. The num erous fres coes

10. and s c ulptures from the Middle Ages , s uc h as the very high
quality "Annunc iation of the Virgin Mary" (c . 1300), or the grac eful
s eat of St. Nic holas (c . 1325/50) in the c entral boat.
In s pite of a profound res toration in the 19th c entury, whic h
inc luded num erous m inorities, a s eries of altars and altarpiec es
dating from the 15th to the 18th c entury were donated by the
c itiz ens of Überlingen. Als o noteworthy are the late -Gothic pulpit
(c irc a 1550) and the apos tle c yc le (c irca 1560) on the long -door
arrows , as well as the m onum ental fresco of the Las t Judgm ent by
Jakob Carl Stauder (1720) above the c hoir arc h.
The m os t fam ous work of the Überlinger Müns ters - the high
altar c arved by Jörg Zürn (around 1582 -1635 / 6) and his
works hop in 1613-1616 ris es in the c hanc el. W ith a height of
around ten and a width of around five m eters , this Marienaltar is
one of the larges t after-middle-aged c arvings in Germ any. It was
c reated after a devas tating plague epidem ic on behalf of the c ity
and was partly financ ed by private foundations. Stylistically, this
artis tically s ignificant work is at the trans ition from the late
Renais sance to the Baroque.
The c hurc h has two organs : the s m all Marienorgel, built in
1761 by W ürz burg c ourt organist Johann Philipp Seuffert, and the
large Nikolaus orgel from the Überlinger organ works hops Mönc h
and Pfaff from the year 1968. Both ins trum ents s ound at c hurch
s ervic es, but als o at c onc erts all year in the c athedral Take plac e.
Kykkos M onastery
Kykkos Monas tery, whic h lies 20 km wes t of Pedoulas , is one
of the wealthies t and bes t -known m onasteries in Cyprus .
The Holy Monas tery of the Virgin of Kykkos was founded
around the end of the 11th c entury by the Byz antine em peror
Alexios I Kom nenos (1081–1118). The m onastery lies at an
altitude of 1318 m eters on the north wes t fac e of Troödos
Mountains . There are no rem ains of the original m onas tery as it
was burned down m any tim es .
The firs t Pres ident of Cyprus , Arc hbishop Makarios III s tarted
his ec c lesiastical c areer there as a m onk in
500 20 200 13
0
20 8 10 20
x x x  
   
He rem ained fond of the plac e and returned there m any
tim es . His reques t to be buried there m aterialised after his death

11. in 1977. His tom b lies 3 km wes t of Kykkos m onas tery and
rem ains a popular vis itor des tination.
M use o Naz ionale Arche ologico (Taranto, Italy)
The National Arc haeological Mus eum of Taranto is loc ated in
a building nam ed as Convent of S. Pas quale or of the Alc antarini
m onks .
The building was erec ted s hortly after the m id -18th c entury, and
bec am e hom e to the m us eum in
100 190 150 1
3 24 5 8
x x x  
  
The s truc ture has been expanded and res tored in s everal
s tages , s tarting in 1903 when Guglielm o Calderoni redes igned the
faç ades . Carlo Ces chi is the arc hitect res ponsible for the
Northern wing, built between 1935 and 1941.
The new dis play foc us es on the m os t s ignificant objec ts in
the m us eum c ollections and on the c ontexts from whic h they were
exc avated. The vis itor, proceeding from the s ec ond to the firs t
floor, will follow the his tory of Taranto and its territory in a
c hronological s equence: Prehistory and Proto-history, Greek
Period, Rom an Age, Late Antiquity and Middle Age. In the
exhibition the dynam ic interrelations with the pre -Roman native
populations are not neglec ted as well.
O n the firs t floor, whos e opening is gradually in progres s, a
large s pac e is given to the exc eptional finds from the 4th -3rd
c entury nec ropolis, from the funerary m onuments to the tom bs
with gold objec ts , in a path winding as far as the period of the
Rom anization.
In the room s dedic ated to Rom an Taranto, the m agnificence
of the c ity after Rom an c onquest is illus trated through the
s c ulpted furniture, s tatues and m os aic floors of the private and
public buildings of the im perial age.
In the c orridors of the c lois ter, the his tory of the Mus eum and
of the form ation of the c ollec tions is illus trated; the dis play
c ontains m aterial whic h joined the m us eum c ollections through
ac quis itions and beques ts, inc luding the paintings given by
Bis hop Gius eppe Ricciardi.

12. G e diminas' T ower (Vilnius, Lithuanian)
Gedim inas ' Tower (Lithuanian: Gedim ino pilies bokš tas) is
the rem aining part of the Upper Cas tle in Vilnius , Lithuania.
The firs t wooden fortifications were built by Gedim inas ,
Grand Duke of Lithuania. The firs t bric k c as tle was c om pleted in
200 7 40
1
5 10 6
x x 
  
by Grand Duke Vytautas . The three-floor tower was rebuilt in 1930
by Polis h arc hitect Jan Borows ki. Som e remnants of the old c as tle
have been res tored, guided by arc haeological res earch.
It is pos s ible to c lim b to the top of the hill on foot or by
taking a funic ular. T he tower hous es a m us eum exhibiting
arc haeological findings from the hill and the s urrounding areas.
The m us eum has m odels of Vilnius c as tles from the 14th to the
17th c enturies, arm ament, and ic onographic m aterial of the O ld
Vilnius . It is als o an exc elle nt vantage point, from where the
panoram a of Vilnius ' O ld Town c an be adm ired.
Gedim inas ' Tower is an im portant s tate and his toric s ymbol
of the c ity of Vilnius and of Lithuania its elf. It was depic ted on the
form er national c urrency, the litas , and is m e ntioned in num erous
Lithuanian patriotic poem s and folk s ongs . The flag of Lithuania
was re-hois ted atop the tower on O c tober 7, 1988, during the
independenc e m ovement that was finaliz ed by the Ac t of the Re -
Es tablishment of the State of Lithuania on Marc h 11, 1990.[1]
A rec ons truction of the Royal Palac e of Lithuania was
c om pleted in 2009, and is loc ated near the bas e of the hill upon
whic h Gedim inas' Tower s tands.

13. Travel to the partner school town
M ap scale
Map s c ale refers to the relations hip (or ratio) between dis tance on a
m ap and the c orresponding dis tance on the ground. For exam ple, on
a 1:100000 s c ale m ap, 1c m on the m ap equals 1km on the ground.
How T o M e asure Distances on a M ap
1. Find the s c ale for the m ap you're going to us e - it m ight be
a ruler-looking bar s c ale or a written s c ale, in words or
num bers.
2. Us e a ruler to m eas ure the dis tanc e between the two
plac es . If the line is quite c ureved, us e a s tring to
determ ine the dis tance and then m eas ure the s tring.
3. If the s c ale is a repres entative frac tion (and looks like
1/100,000 or 1:100,000), m ultiply the dis tanc e of the ruler
by the denom inator, giving dis tance in the ruler units .
4. If the s c ale is a word s tatement (i.e. "O ne c entimeter
equals one kilom eter") then determine the dis tance.
5. For a graphic s c ale, you'll need to m eas ure the graphic and
divide the s c ale into the m eas ured units on the ruler.
6. Convert your units of m eas urement into the m os t
c onvenient units for you (i.e. c onvert 63,360 inc hes to one
m ile)

14. M ake the calculation above to find out the distances be tween
the citie s which take part in the Erasmus+ program “ M aths In
Art” .
Exercise 1
W e have an 1:5,000,000 s c ale m ap. The air (flying) dis tance
between Athens and Konya is 769Km . W hich is the m ap dis tance, in
c m , between Athens and Konya?
Exercise 2
W e have an 1:10,000,000 s cale m ap. The air (flying) dis tance
between Athens and Überlingen is 1606 km . W hic h is the m ap
dis tanc e, in c m , between Athens and Überlingen?
Exercise 3
W e have an 2,000,000 s c ale m ap and with a s tring we determ ine
the dis tanc e between Athens and Taranto. The m ap dis tance is

15. 31.5c m . W hich is the air (flying) dis tance, in kilom etres, between
Athens and Taranto?
Exercise 4
W e have an 10,000,000 s c ale m ap and with a s tring we determ ine
the dis tanc e betw een Athens and Cz ęs tochowa. The m ap dis tanc e
is 14.7c m . W hich is the air (flying) dis tance, in kilom etres, between
Athens and Cz ęs tochowa?
Exercise 5
The air (flying) dis tance between Athens and Vilnius is 1863Km and
our m ap dis tance is 20.7 c m . W hich is the s c ale of the m ap we us e?

16. Exercise 6
The air (flying) dis tance between Athens and Strovolos is 917 Km
and our m ap dis tance is 15.3 c m . W hich is the s c ale of the m ap we
us e?

17. Calculating budget (transport fares, hotels, daily
expenses in nationalcurrency and in Euro)
How to budge t for a big trip
(article from G EO RGE DUNFORD , Lonely Plane t Writer)
For s om e people budgeting is a way to get ex c ited about
a trip. They us e it as the firs t s tep in the planning and a
way to get them s elves ps yched up about a des tination.
Som e people are, of c ours e, c ertifiably ins ane.
For m os t of us , though, budgeting for a trip is like going to the
dentis t after bingeing on s ugar for a few m onths . But budgeting is
better than running out of m oney halfway through a trip and having
to m ake an em barrassed c all hom e to friends or parents . It only
takes a few s im ple s teps to s ave you a whole trip of s tres sing about
c as h flow.
Figure out how much you' ll ne e d
Start your budget with the bigges t expens es firs t – us ually this
will be your flights , but ac c ommodation als o adds up.
W ith a rough idea of how long you'll be away, you c an work out
a daily c os t bas ed on room rates and m eal c os ts. Add in a little
m ore for ac tivities, m useum entry fees , a c ouple of s ouvenir t -s hirts
and the odd c onc ert.
Allow for an oc c asional s plurge. The worst budget is a c hain at
your leg pulling you away from the bes t (if s lightly m ore expens ive)

18. travel experienc es. Sure it c an be c heaper to s elf -c ater your way
around Europe, but if you're not trying paella in Barc elona or wagyu
in Tokyo then you won't enjoy the trip.
What to spe nd be fore you le av e
Add in pre-trip c osts inc luding vis as, reliable travel i ns urance
and im m unisations. Som e travellers s kimp on travel ins urance, but if
you c an't afford travel ins urance, you c an't afford to travel. Even if
nothing goes wrong, it pays for its elf in peac e of m ind and when
s om ething does go wrong (los t luggage or c anc elled flights ) you'll
find it invaluable.
I don't like to over -invest in s pec ialised travel gear, but quality
luggage and c om fy walking s hoes always m ake for an eas ier trip.
Power adapters, a trus ty Swiss Arm y knife and a torc h m ight als o be
worth buying, but travelling light is always a good aim .
How to sav e as much as you ne e d
O nc e you've worked out how m uc h you need, then you've got a
figure you c an s ave towards . Some people m ake this num ber their
s c reensaver or put it on their fridge us ing this s aving goal as
m otivation to go to work everyday.
Have your very own telethon -s tyle c ountdown as you s ave
towards the goal. If you find s aving tough, try budgeting s oftware
like Pear Budget or Mint – the latter inc ludes c ountdown functions
for your s avings and c an s ugges t ways to c ut your expens es. If you
don't hit your s aving goal, then it m ight be tim e to go bac k and re -
vis it the budget - m aybe that Singapore Sling m ight have to be in a
m ore down-market bar.
The m os t im portant rule for your travel budg et is flexibility.
Allowing for on-the-road s plurges (and the odd belt tightening) will
take the s tress out of your trip, but will als o m ean that when you get
hom e you won't be m et with a huge c redit c ard bill. A little planning
at the s tart of the trip will s ave penny pinc hing, grouchy haggling
and worrying about being ripped off at the c os t of enjoying your trip.

19. Let’s travel to the cities which take part in the
Erasmus+ program “M aths In Art”.
This is an inte ractive e xercise, s o you have to us e W orld W ide
W eb and, m aybe, other apps or touris t books , to c alc ulate the
budget for travelling from your own c ity to another “Math In Art”
m em bership c ity. Let’ s ee an exam ple.
T ransport fares
Calc ulation of the trans ports fares is a diffic ult but not bor ing
puz z le. You have to c hoos e the m eans of trans port. It is pos s ible,
that you have to us e variety of m eans bec ause, for exam ple, there is
no airport in a c ity. Als o, you have to think the expens es for getting
from a plac e to another with the loc al tran s port(museums,
interes ting plac es, etc .).
T ransport Cost
Flight 1 €120
Flight 2 ( low c os t) €70
Train €40
Underground €50 per week
Accommodation
You have to m ake a lis t of Hotels you would like to s tay. Think
about the s ervic es of eac h hotel and the extra c harges for thes e
s ervic es.
Hote l/ Apartme nt Cost (pe r day)
Hotel 1 (Center of town) €80
Hotel 2 (Near Metro Station) €70
Hotel 3 (with breakfas t) €85
Hotel 4 (near the town) €60
Food e xpe nses
W hen you're on the road, there's nothing m ore enjoyable than a

20. good m eal. Finding good food while traveling is not always eas y
— there m ay be language, navigation, or c ultural differences that
c an m ake the whole proc es s frustrating and dis appointing. Is a
great he c hallenge of finding a new plac e to eat, but think about
the expens es.
Place Cost (pe r pe rson)
Fas t Food €10
Res taurant €20
Spec ial Res taurant (with view or
fam ous )
€30
Breakfas t €6
Cost of ticke ts of muse ums, place s I would like to v isit.
W hen you vis it m us eums or other interes ting plac es and dis c over
the c ultural and his torical heritage of c ities is a lovely experience.
W hen vis iting thes e plac es, always as k if they are s pec ial rates
are available for s tudents , s eniors, or s m all gro ups. Some
dis c ounts aren’t c learly vis ible and c an be overlooked. In s om e
plac es , c harge is for free in c ertain hours .
Ente rtainment e xpenses, e tc.
O the r e xpe nse s Cost
Mobile internet €10
Shopping €100
Sights eeing tour €20
Traditional Mus ic (live), Theater, etc . €30
Currency calculator
Inte re sting Place s Cost
Plac e 1 €10
Plac e 2 €5
Plac e 3 Free
Plac e 4 12€+5€ (loc al bus )

21. A Greek traveller s tarts a journey to Europe with 3.345 Euros .
1. His firs t s top is in Cyprus where s he s pends 954 euros .
2. Next he goes to Poland where there he s pends 584 z loty.
3. After having a very good tim e in Poland , he travels to
Germ any, where there he s pends 596 euros .
4. From Germ any he goes to Italy where there s pends 1/3 of the
m oney he s pent in Cyprus .
5. Next s top is in Lithuania , where he s pends s pends 1/4 of the
expens es of Poland.
6. The trip ends in Turkey, where there he c onverts all m oney left
in turk.lires(TL)
W ork out how m uc h m oney in euros s pent in eac h c ountry and
pres ent the res ult in a table.
(1 EURO = 4, 42 ZLO TY = 3.7008 TL, 1 ZLO TY= 0,23 EURO , 1TL=
0, 2750 EURO )