Our Maths tasks

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„Maths around us” Maths tasks

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Introduction............................................................................................................................................. 3 Maths around Lovech .............................................................................................................................. 3 Maths around Ziębice.............................................................................................................................. 9 Maths around in İzmit – Kocaeli ............................................................................................................ 16 Maths around Madrid ........................................................................................................................... 20 Maths around San Marco in Lamis ........................................................................................................ 25 Summary ............................................................................................................................................... 29

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Introduction The key linking all five partners of our project „Maths around us” was Mathematics. Our main aim was to improve Maths skills of students by perceiving Maths issues in their closest surrounding world. Students were encouraged to do their best to solve Maths tasks. There are some tasks prepared by each project country. Solving tasks students could read and find out a lot of important and interesting information about country, region and even history places project students are from.

Maths around Lovech

Task 1 The Medieval fortress of Lovech dates from the time of the Roman Empire, when the territory of today's Lovech was built and function a Roman road station, called “The Presidium". In 1187 a Peace Contract between Bulgaria and Byzantium was signed here, which recognizes the Second Bulgarian State. In the beginning of the XIV century it was a residence of the despot Ivan Alexander, elected as a King of the Bulgarians in 1331.

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Today a large part of the fortress has been restored and it is one of the landmarks of the modern town and an attraction for its visitors. In its western part, where are the foundations of bishop's church, there is a huge metal cross, that can be seen from almost all parts of the town. From the inner side of the fortress you can enjoy a beautiful panorama, covering the whole town, and behind it you can observe the Osam River that pass between the hills, as well as remains from the Roman road, crossing Lovech in distant past. From the end of 2005. The fortress is equipped with a special night lights.

WRITE WITH ROMAN NUMERALS: 118713312005Task 2 In the beginning of 2012 Litex Motors Company has officially opened its factory for production of Bulgarian cars with the brand Great Wall. The factory is situated near Lovech. It is one of the most modern companies in Europe and the only one in Bulgaria. The cars produced in the factory are intended for the market in Bulgaria and whole Europe. The productive force of Litex Motors are a fully new project with worldwide importance. The major investment belongs mainly to the Bulgarian company. The building of the factory began after signing the treaty for contribution between Litex Motors and Great Wall in the autumn of 2009. Two years later, in November 2011, the first car from the test series has been produced – it was in conformity with the highest standards for quality in the industry.After the factory opened, it began the serial production of the Bulgarian cars for our country and abroad.

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GWM is the first and only one independent Chinese automobile company which has a standard approbation of its production for selling in the EU and it is the only Chinese brand, which cars are produced in a factory in Europe – Litex Motors in Bulgaria. The way that we can measure the car’s engine efficiency is by calculating how much fuel does it need for 100 km. There is a big difference in the fuel consumption depending whether you are driving the car in a town or outside one. In the chart is presented the expenditure of the fuel for a car. Fuel consumption in the town

8,0 l/100 km

Fuel consumption out the town

5,6 l/100 km

What is the difference of the fuel consumption while driving in the city and outside it (in %).

Task 3 Lovech Municipality won a project for the restoration of old buildings with historical value. According to the work schedule the investors agreed that the facade of a building can be painted an average of 6 persons in 48 hours . The project planned to recruit 40 painters who will be distributed in 5 brigades each of them including 8 people, each brigade takes painting three walls.

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How many hours will be enough for painting of the facades, if work goes according to plan ? Task 4 Calculate the numerical value of the expressions and fill the letters in the table. You will find one of the symbols of the city and one of the most often visited landmarks of the town of Lovech.

−32 . (−2)−3 . (−1)0 đ??ś= (−2)−5 . 91 . (−1)2 (32 )3 . 22 đ?‘‚= 92 160. 27 đ?‘‰= 5. 29 E=

514 .517 530

+2

R-11,5=1-8 E=15%.(-25+5.20) 0,6-D=10

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37 . 57 =15đ??ť 22đ??śâˆ’3 = 128 2.(E+7,5)=-3,4 V=((-3).5-2.(-4)).3 O=(-3).(-2)-(-3+35):8 L=3.|4| − |−7| + 2. |−4| B=|−0,5| − 0,5. |12| R=|−51|: |−3 + 6| đ??ź = −|−6,5| + 3,5.2 15,8-D= -13,6+36,4 1

G-4=−5 − 3 2

E=(-18+4).2-3 -4

36

8

7

4,5

11,25

-9,4

7

5

-9,2

-21

2

13

-5,5

17

0,5

-7

-4,5

-31

http://bulgariatravel.org/en/object/114/pokritiya_most_lovech http://en.wikipedia.org/wiki/Covered_Bridge,_Lovech

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Task 5 The Shopska salad is a Bulgarian salad, created as a product of “BALKANTOURIST” in the middle of 1950s. It is prepared with tomatoes, cucumbers, roasted peppers, onion, fresh parsley and grated white brined cheese. The taste of the salad is improved with a dressing from plant fat (oil or olive oil) and possibly, with wine or apple vinegar. Over the grated cheese it is decorated with a stem of fresh parsley, black olives or a small hot pepper. From Bulgaria the recipe is distributed in the kitchen of the neighboring Serbia and Macedonia. It was widely spread in Romania as well and is known as “ salată bulgărească” (Bulgarian salad). The Shopska salad is popular not only in the Balkans but also in the Czech Republic and Slovakia (šopský salát) attending in the menu of the catering facilities, slightly modified (without roasted peppers, and sometimes without onions), and in Slovakia it is served with sugar. Necessary ingredients for 3 portions • 400 gr. red tomatoes • 2 green peppers • 250 gr. cucumbers • 3 stems of onion (1) head, small onions) • 1 sprig parsley • 3 olives • 200 gr. cheese • 1pinch of salt • 1 tablespoon vinegar • 2 tablespoons olive oil

What quantity of the products it is necessary for 12 portions of Shopska salad?

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Maths around Ziębice

Task 1 The oldest building in our town is St. George's Church. It's been built at the beginning of 13th century.

On the northern wall, next to the cross and sculptures, two stone boards were placed. On the boards we can read the names of soldiers who were killed in World War I. Under the tower there is a board written in German with the information that the boarded we founded by local parish.

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Now the question of the task 1 Look at the picture below and answer the question: What year was that board founded?

Remember! MDCCXCI are Roman numbers and you have to change them into Arabic numbers! Can you do this?????

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Task 2 This is additional activity for the eager students. On building of the first public hospital in Ziębice (now it is a kindergarten) there is a date of when it was built. MDCCXCI Now the question: What year was it? Copy these links please we prepared the slideshows about Ziębice for you http://secure.smilebox.com/ecom/openTheBox?sendevent=4e4449774d4455314f444e384f544 9324e7a4d304d6a6b3d0d0a&sb=1 and http://secure.smilebox.com/ecom/openTheBox?sendevent=4e4449774d4459794d444a384f54 49324e7a4d304d6a6b3d0d0a&sb=1 More information about our town you can find: http://www.ziebice.pl/asp/en_start.asp?typ=14&menu=60 Task 3 The Town Government in Ziębice wanted to collect money which it needed to build the town hospital. So the government decided that: -

each person from Ziębice who wanted to buy a plot had to pay 2 silver coins and 6 fenigs for every 100 thalers they paid for the plot every foreigner needed to pay 4 silver coins per 100 thalers

The question is: How much money did the Town Government earn when a guy from Ziębice bought a plot and paid 6340 thalers for it and how much money did the Town Government earn when a foreigner bought a plot and paid 8244 thalers?

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The Thaler (or Taler or Talir) was a silver coin used throughout Europe for almost four hundred years Task 4 Some information: In Ziębice you can visit Museum of Household Equipment. It is very small but interesting. There are: Biedermeier palour, etnogtaphical hall, Baroque study, collection of irons, sculpture, the weapon collection and collection of glass. More information in English : http://www.muzeumziebice.pl/gb/historia.aspx the iron collection

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Instruction of the task: All dates in the Arabian numerical system write in the Roman numerical system: The beginning of our museum starts in 1930 _____. In 1931 _____ the first hall was created in two rooms of the Town Hall. Our collection has grown pretty fast. In years 1934-1937 __________ we received a huge donation from a widow, the wife of Silesian artist Joseph Langer. Now we've got the biggest iron collection in Europe, the oldest iron is from 1655 _____. Click on the link and find out more of the museum objects: http://www.proprofs.com/quiz-school/story.php?title=what-is-it_3 Write what in your opinion is object number 1 …………………….. Object number 2……………………………. Object nr 3………………………………….. Object number 4……………………………. Object number 5…………………………….

Task 5 is connected with Bolko I – The duke of Ziębice

Bolko I the Strict also known as the Raw or of Jawor ] 1252/56 – 9 November 1301 He was a Duke of Lwówek and Jawor since 1278, sole Duke of Lwówek since 1286, Duke of ŚwidnicaZiębice since 1291. Write Roman number: Energetic Duke of Ziębice Bolko I founded the special society in Ziębice in Ziebice in 1241 _____ The main aim of the society was teaching the youth how to use bows and crossbows in the case of a future war. To join this society you needed to come from Ziębice and not lose the inhabitant's laws. Instruction: Calculate the unknown numbers and match them with ones on the list to reveal the original Polish name of that organization.

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2

2,55 : O = 2,55 7  R = 6,3 2  2,8)  W  8 (4 5 T :1,3 = 3 3 2 9  2  B = 4 1 1 4 30 A-26 C + 3 2= 4 0 3 E  2 W  1,5  2,4  2,52

O= R= W= T= B= A= C= E= W=

2 K =4 R:9=-6 2 4 O  - 1 1 U   2 0 3 1 2 ( ) K  0 5 5 1 4

8

K= R= O= U= K= - 54

6,2

-2

3,9

0,7

2,55

1 6

0,9

-2

- 16

5

1

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The painting shows the building of St. George’s church Task 6 In our town there's a beautiful park with dinosaur statues. It's been founded in 1894 _____ (type it in the roman numerical system). It has a surface of 18 ha (hectares). Type the size in ars (a) and squared meters (m2)

18ha- _____a 18ha- _____m2

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Maths around in İzmit – Kocaeli

Task 1 The oldest building in our city is Mosque of Orhan. It's been built at the beginning of 13th century. It is constructed by Orhan Gazi ( Orhan Gazi; was the second sultan of the nascent Ottoman Empire ) 683 years ago.

AND NOW THE QUESTION OF THE TASK - 1 In what year was The Orhan Mosque built ? If Orhan Gazi live at the moment, How is he ? ( Please, search his birth year  )

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Task 2 The most famous sweet in our town is “Pişmaniye” and it includes only Flour, Butter, Sugar and water ( Some kinds of them include chocolate ). You can see the recipe of Pişmaniye below; 1 Kg sugar 0,5 lt water 2 Kg Flour 1 Kg Butter With these materials, you can take 4 kgs Pişmaniye

AND NOW THE QUESTION OF THE TASK - 2 If you want to make 250 gr Pişmaniye, Can you say me the recipe list ? Task 3

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9 cm

This is “Turgut Özal” bridge in İzmit City Center. The height of the tower is 9 cm on the picture and the ratio of the picture is 1/1500 AND NOW THE QUESTION OF THE TASK - 3 Can you say me that the how many meters the tower in real? Task 4 Some information:

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In İzmit you can visit Museum of “Gayret Frigates” and “Hızır Submarine”. They are a museum now. The Hızır Submarine is 470 tones with 120 tones fuel and It can go 1200 miles in normal condition with this fuel. The Gayret Submarine is 5.000 tones with 950 tones fuel and It can go 3400 miles in normal condition with this fuel. AND NOW THE QUESTION OF THE TASK - 4 If the 1 liter fuel is 1,00 €, Can you say me that the cost of 1 miles for Frigate and Submarine? Task 5

In our city there's a beautiful lake. It is a surface of 47 kilometer square and it has approximately 112.000.000.000 meter cube water 112.000.000.000 m3 = ………………. tone 112.000.000.000 m3 = ………………. Km3

You can find more information about city in this link below http://kocaeli.bel.tr/Files/English/PDFs/turizmson.pdf You can watch more information about city in this link below www.youtube.com/watch?v=2kqIS2WNIoY

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Maths around Madrid

Scale 1 : 00 12 This is the name of the official centrepoint of Spain. It is, above all, a crossroads with people forever passing through on their way elsewhere. In early times, the Puerta del Sol (the Gate of the Sun) was the eastern gate of the city and from here passed a road through the peasant hovels of the outer ‘suburbs’ en route to Guadalajara, to the northeast. The name of the gate appears to date from the 1520s, when Madrid joined the revolt of the Comuneros against Carlos I and erected a fortress in the east-facing arch in which the sun was depicted. The fort was demolished around 1570. The main building on the square houses the regional government of the Comunidad de Madrid. The Casa de Correos (Post office House), as it is called, was built as the city’s main post office in 1768. The clock was added in 1856 and on New Year’s Eve people throng the square to wait impatiently for the clock to strike midnight, and at each gong swallow a grape – not as easy as it sounds!

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On the footpath outside the Casa de Correos is a plaque marking Spain’s Kilometre Zero , the point from which Spain’s network of roads is measured. The semicircular junction owes its present appearance in part to the Bourbon king Carlos III (r 1759–88), whose equestrian statue (complete with his unmistakable nose) stands in the middle. Just to the east of Carlos III, the statue of a bear nuzzling a madroño (strawberry tree) is the city’s symbol. QUESTION 1: How many meters long are Puerta del Sol, if we tell you that the photo’s scale is 1:1200? If you wonder how is this place, just click here to watch it on line COCIDO MADRILEÑO Cocido Madrileño - or simply cocido - is probably one of Spain's national dishes. Cocido is based on a vast cauldron, which simmers away all day, hardly bubbling. In the old days households made it every day, for poached meat used to be the hallmark of the middle-class kitchen. From this pot comes a series of magnificent things. Now we still eating this delicious dishes, and one of the most famous restaurants in Madrid where you can eat a cocido is Lhardy (nearby Puerta del Sol). One of the Lhardy's anecdotes is that in 1847, Queen Elizabeth II escaped own palace and went to dinner with their ladies Lhardy service. But she didn't be the only royal member who has visited this restaurant, because the King Alfonso XII went undercover multiple times, coinciding Lhardy salons with friends and characters of Madrid life.

We are sure that you wish to know how to cook a cocido. So this is the ingredients to cook one for 8 people: INGREDIENTS 9 oz dried chickpeas soaked overnight 1 lb cured brisket of beef or silverside in one piece 9 oz salt pork belly, streaky bacon in one piece or fresh pork belly. 1 lb 4 oz knuckle gammon bone, with some meat attached

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1 1/2 lb beef marrow bone, sawn accross 1/2 boiling chicken 1 pig's trotter, split 1 whole garlic bulb 2 bay leaves 8 black peppercorns, crushed 1 small onion, studded with 2 cloves 1 1/2 lb Savoy cabbage, quartered 2 carrots, in big pieces 2 leeks, short lengths 1 lb new potatoes 2 chorizos, or other smoked sausage 1 morcilla or 7 oz black pudding.

QUESTION 2: Which are the ingredients for 100 people? EL ESCORIAL The Escorial is a vast building complex located in San Lorenzo de El Escorial, near Madrid. The building is the most important architectural monument of the Spanish Renaissance. Construction of El Escorial began in 1563 and ended in 1584. Due to the huge amount of time it takes to build the monastery, there is a typical phrase that says "You're slower than building ecorial" The project was conceived by King Philip II, who wanted a building to serve the multiple purposes of a burial place for his father, Holy Roman emperor Charles V; a Hieronymite monastery; and a palace. The first architect, Juan Bautista de Toledo, designed the ground plan on a gridiron scheme, recalling the grill on which San Lorenzo, the patron of the building, was martyred. After Toledo's death, Juan de Herrera took up work on the project. Although Herrera was influenced by the styles of Sebastiano Serlio and Giacomo Barozzi da Vignola, the final product was uniquely Spanish. The building complex, severe in its lines, has four principal stories with large towers at each corner. Today, the Escorial is a UNESCO World Heritage Site and it is one of Spain’s most visited landmarks.

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QUESTION 3: This is the floor of the monastery. With the measures that we give, calculates the perimeter of the real building. 30m

150m

200m

200m LAS MENINAS A portrait of the Infanta Margarita, daughter of Felipe IV (1605-1665), surrounded by her servants or “family” in a hall of Madrid’s Alcázar Palace. This, the most famous of Velázquez’s works, offers a complex composition built with admirable skill in the use of perspective, the depiction of light, and the representation of atmosphere. There have been innumerable interpretations of this subject and later references to it. The most numerous emphasize a defense of the nobility of painting versus craft. Velázquez portrays himself, painting the painting itself, on the left of the canvas, thus affirming the supremacy of the art of painting. The Infanta Margarita (1651-1673), wears white and appears in the center of the composition, surrounded by her ladies in waiting, the “meninas” María Agustina de Sarmiento and Isabel de Velasco, along with two court buffoons, María Bárbola and Nicolasito

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Pertusato, and a mastiff. Behind her, the duenna Marcela de Ulloa converses with the quartermaster, José Nieto, who is in the doorway. The King and Queen, Felipe IV and María de Austria (1634-1696) are reflected in the mirror at the back of the room, leading to series of extraordinarily complex spatial relations.

Question 4: Searching the date of creation of this painting and express it in Roman numbers. https://www.museodelprado.es/en MADRID’S FOOTBALL TEAMS There are 4 important teams in Madrid: Real Madrid, Atlético de Madrid, Rayo Vallecano and Getafe. As you know the soccer in the Spanish culture is essential. Many fans go to the bars to watch the games and share some drinks between goal and goal. If the capacity of their stadiums is the following: Stadium Santiago Bernabéu (Real Madrid)

Capacity 81044

Vicente Calderón (Atlético de Madrid)

54960

Teresa Ribero (Rayo Vallecano)

14.505

Coliseum Alfonso Pérez (Getafe)

17000

Question 5: If the population of Madrid is 3,234 millions. Sum the capacity of the four stadiums, and give us the percentage of “madrileños” that they are?

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Maths around San Marco in Lamis

Task 1

Convent Shrine “Santa Maria di Stignano” www.santuariostignano.it/ www.lavalledeglieremi.it/gli-eremi The Convent Shrine “Santa Maria di Stignano” is located in the beautiful valley of Stignano, not far from San Marco in Lamis (FG) nestled in the mountains, in the countryside, in the silence and peace. An ancient legend tells that St. Francis returning from the East has passed for this valley and has blessed its fruit; it was MCCXVI ___________. With painstaking work, the convent of Santa Maria was restored in the year of jubilee MM__________. Check the Roman numerals, with corresponding numbers Arab The Convent Shrine holds groups for meeting, spiritual retreats, short stays, workshops, summer camps. The structure has got 80 beds. If you book 2/5 of all the beds you earn € 480. If you book all the beds, how much can you earn?

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Task 2 LE “FRACCHIE” di San Marco in Lamis

San Marco in Lamis is known for the traditional Procession of the “fracchie”, a popular religious festival very impressive and very unusual. It dates back about three centuries and takes place every Holy Friday to evoke the Passion of Christ. Every year it draws a large number of foreigners. The “fracchie” are made from a lengthwise split trunk and filled with dry branches, twigs and bits of wood, it is a bonfire of conical shape, which ends with a protruding arm. The fracchia is transported on trolleys. The wood is held together by two large circles of iron, and is drenched with flammable substances. The fracchia lights from the widest part, it is weighted with a ballast of sand bags in the rear to avoid that it does not fall forward or slides on the carriage. At the bottom there is a pole with at its top Our Lady of Sorrow image. In 2012 Poste Italiane published a collection of stamps entitled to "The Italian folklore", dedicated to the rites of the fire, “the Fracchie of San Marco in Lamis”. To learn more you can visit: http://www.foggiatoday.it/cronaca/francobollo-fracchie-sanmarco-in-lamis.html

Or www.foggiatoday.it/.../san-marco-in-lamis

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TASKS -

Keeping in mind that the maximum length is 8m, what is the reproduction scale of fracchia in the picture? People from San Marco build 5/7 of the fracchia in 20 days, how many days do they need to complete the job?

Task3 “Dolina Pozzatina”

On the road that leads to San Marco in Lamis from Sannicandro Garganico, you can visit the karst pot “Dolina Pozzatina”, one of the largest natural depression of Italy or perhaps of Europe; the bolder visitor can venture into a soft trip up to the bottomless pothole that is located on the valley below, feeling to sink into the bowels of the Earth; its quite varied vegetation is typical of the maquis and the scenery from the top and from the bottom is intoxicating in the pure nature. It’s a great karst pothole 100m deep and 400m wide. TASK During the flood of September 2014, the cavity was filled with water up to 40 m from the entrance, how many hectoliters of water were poured into the pothole? Task 4 Autochthonous Caciocavallo cheese from Gargano

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The Autochthonous Caciocavallo of Gargano is a typical cheese of Apulia, from several years it is counted among the Slow Food Presidia, its name comes from the variety of cows whose milk is produced, the autochthonous cows “Vacca Podolica”, as the term autochthonous in Italian is Podolico. It is pear-shaped with a little “head”. The crust is thin, with a pale straw to deep yellow colour in aged cheeses; you can see the same colors in the curd that rarely presents little holes. TASK The weight of an aged caciocavallo cheese usually decreases by 12%. If the weight of a caciocavallo cheese is reduced by 30 kg, what is its initial weight?

THE “PROPATO” The Propato (lu prupate – in Sammarchese language) is a typical Gargano sweet which is prepared in the town bakeries during the whole year, but in the past it was made at home. It was the cake for particular celebrations like weddings, First Communions and Baptisms, because at end of the banquet, people receive a gift, along with Propato. Propato recipe for 4 pieces Ingredients: ½ kg of sourdough 2 kg white flour 500 g of sugar 500 g of honey 6 eggs 120 ml soluble coffee 1 grated orange peel 5 g of cloves 5 g of cinnamon PROCEEDINGS Make a fountain with the flour and add sourdough, sugar, honey, eggs, the two spices, orange peel. Mix until you have an elastic ball (add the coffee) and put it to rise for at least 4-5 hours. Take back the dough and cut a loaf, extend the loaf at least to 50 cm then roll and put in a ring mold without grooves and let rise another 2-3 hours. After leavening, bake for 30- 35 minutes at 180°C until golden. The cake is almost dry and you can eat it with a wine or dry sparkling wine TASK: What are the ingredients for 10 pieces?

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Task 5MARGHERITA SALINAThe Margherita di Savoia Salina nature reserve is a protected natural area located on Tavoliere plain; it was founded in 1977, and is on Adriatic Sea. It consists of a vast expanse of calm waters divided into basins for the production of sea salt, it is the largest salina in Italy and one of the largest in the Mediterranean basin. Many years ago hereby there was the Salpi Lake: its deposits of salt were used since the Neolithic and by the Greeks and Romans, too. Human interest toward this Salina is due to economic reasons and to the therapeutic use of the red water for spa treatments. Over time the territorial trim has been modified due to the evolution of the techniques to extract salt. Important examples of industrial architecture are the structures built by Ferdinand I of Bourbon in the early nineteenth century. The Salina of Margherita is 20 km long and 5 km wide; it is the most important European Salina and produces ca. 600,000 tons of salt per year. TASK Keeping in mind that 3.5 tons of salt can be produced by1000 hectoliters of water, how many hectoliters of sea water have to evaporate per day to obtain 50 kg of salt?

Summary The key linking the project was to combine maths with interesting information about the architecture, kitchen or specific features of places where project participants live, Doing such activities students are becoming aware that maths is around us and can be found everywhere: in buildings, kitchen, nature, vehicles and games. Solving these tasks students not only will become better at maths but also will gain knowledge about many other aspects of life.

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