„Maths around us” mobility to Bulgaria and its results October 2016
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Introduction............................................................................................................................................. 3 Activities and expected results of Bulgarian mobility .............................................................................4 Results from these activities ...................................................................................................................5 Maths lesson ...........................................................................................................................................5 Tasks from the lesson ..........................................................................................................................6-7 Avisit to "Balkan" factory ........................................................................................................................8 Maths quizzes ....................................................................................................................................9-10 A visit to Sofia - the capital of Bulgaria .................................................................................................11 Interesting facts about Sofia .................................................................................................................11 An Exciting racing ..................................................................................................................................13 Devetashka cave and Krushuna Waterfalls ..........................................................................................14 The Museum of water in Lovech ..........................................................................................................15 A visit to the open air ethnographic museum Etara and the town of Gabrovo ...................................15 Troyan Monastery ................................................................................................................................17 Links ......................................................................................................................................................18 Summary ............................................................................................................................................... 18
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LOVECH
THE HOST TOWN OF MOBILITY Introduction The Mobility in Bulgaria was a part from the second stage of the project that was called “Maths in Vehicles”. Responsible for this stage was the Bulgarian team. The Mobility happened in October 2016 in the town of Lovech. The participants in the meeting were met in “Vasil Levski” school. Students stayed in Bulgarian host families during the week of mobility. They were familiar with Bulgarian history, traditions and customs, took part in different activities and had a chance to see Maths as a part of real life.
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Activities and expected results of Bulgarian mobility
Teachers and students from project countries were met at school and were familiar with Bulgarian traditions and some important facts about the history of Lovech and its region. The participants in the meeting were also familiar with Bulgarian school and Bulgarian educational system. They presented their schools and places of living. They had an official meeting with the representatives of local authorities in Lovech. Teachers and students took part in a Maths lesson. They had to solve Maths tasks connected with the topic of the stage “Maths in vehicles”. They also practiced their ICT skills during the lesson and communicated in English. Foreign guests visited Sofia - the capital city of Bulgaria where they saw the most interesting monuments of our history and culture. Students participated in a real cart racing and they had a chance to explore the close connection between such Maths aspects like speed, distance, time, weight and aerodynamic in a real practical situation. Guests also visited the exhibition of Balkan factory, where they were familiar with the development of the production of different vehicles and their improvement till present days. They took part in a quiz game prepared by their Bulgarian friends. Participant also visited the open-air ethnographic museum “Etara”. They saw different machineries mover by the water power. Students and teachers enjoyed the visit to our local natural landmarks “The Devetashka Cave” and “The Krushuna Waterfalls” At The Astronomical Observatory and Planetarium in the town of Gabrovo guests could observe different astronomical and physics objects.
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Results from these activities 1) Students gained knowledge about Bulgarian history and traditions. They learnt interesting facts about the history and vehicle industry in Lovech. They also got familiar with our school and our educational system. 2) Staying with their Bulgarian friends and their families for a week our guests could feel the atmosphere of our way of living, our traditions and tried typical Bulgarian food. They made new friends. 3) Participants took part in Maths lesson where they could apply their Maths and ICT knowledge and skills. They took some quizzes related with some technical characteristics of different vehicles, speed, time, distance, meteorological conditions and rules for safety. Students learnt more about the application of vehicles in everyday life, took part in workshops and in a car racing. 4) All communication during the mobility was in English. Students communicated in English with their new friends and during the stay with the host families, so they improved their language knowledge and skills in real conversations and which is the most important they became more self-confident in speaking English. 5) By working in groups and international teams students developed social skills. They had to make decisions together, to respect the opinion and the ideas of the others and to support each other 6) During the mobility teachers had a chance to share ideas, experience and good practices.
MATHS LESSON On 17th October the guests from the four countries attended a lesson in Maths at the host school. The lesson was presented by the students from the 7th grade and their Maths teacher Mrs. Marinova. All the tasks were connected with the topic of the meeting in
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Bulgaria – “Maths in vehicles” and also with the places that were chosen to be visited during the stay in Bulgaria – Krushuna Waterfalls, Devetaki Cave, The monument of Vasil Levski, The archeological and ethnographic museum in the open “Etara”. During the lesson students worked in international teams. They communicated in English, practiced their ICT skills, did sums, made decisions and had fun together. TASKS FROM THE LESSON
TASK 1: The Sunrise Travel Transport Company is hired to transport participants to an Erasmus + project on "Vehicle Mathematics" on a specific route. The company has two types of buses - "Mercedes" with 35 seats and "Setra" with 52 seats. The chart shows the maximum number of passengers that can be transported by the company with the available buses of both types. 1) Find the number of buses of each type at your disposal; 2) How many passengers are most likely to be transported
TASK 2: From the town of Lovech to the village of Krushuna a cyclist moves at a speed of 15 km / h and returns 5 km / h more slowly, which is why he travels 1 hour more. Find the distance between Lovech and Krushuna?
TASK 3: A car departs at 8 am from city A and arrives in town B at 11am and 15pm making a break on the route in town C. Using the information in the chart, the answer sheet against each of the letters A), B) , C) and D) write the answer to the question
a) How many hours did the car reach C? b) How many minutes did he spend in town C? c) How many kilometers is the distance from A to C? d) At what average speed is the distance from A to C?
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TASK 4: On Saturday, Tsveti and Polly took a walk for a stroll to the monument of Vasil Levski, the fortress of Hissarya and back to meet Bashbunar at the tap. The graphs of the movement of the two girls are shown in the drawing Analyze the graphs and fill in the table:
Time of movement in hours
Passed distance in km
Average speed in km/h
Цвети Поли TASK 5: The distance between the town of Lovech and the architectural and ethnographic complex "Etara" is 68 km, and the village A is situated just in the middle of the road between Lovech and Etara. The town of Gabrovo is situated between the settlements A and Etara and the distance between village A and Gabrovo is 26 km. Find out how many kilometers are there from Etara to Gabrovo?
ANSWERS:
a) 60
b) 34
c) 8
d) 42
TASK 6: Misho moves on foot with 4,2km / h. The road that runs for 25 minutes is equal to a) 1500 m b) 1750 m c) 1950 m d) 175 m
TASK 7: Motorcyclist travels from A to B for 2 h at a speed of 70 km / h. How fast does a car travel that travels this distance in 100 minutes? a) 140 km/h
b) 100 km/h
c) 90 km/h
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d) 84 km/h
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A VISIT TO “BALKAN” FACTORY Students and teachers visited the showroom of “Balkan” factory. It has long traditions in production of different kinds of vehicles – planes and cars in the past and bicycles till present days. The participants got familiar with the stages of the production, materials, output and export. They learned more about the speed limits that are determinate by Bulgarian and the other partners’ countries legislation and some rules of safe cycling. Students also took some Math quizzes related with some technical characteristics of different vehicles, speed, time, distance, meteorological conditions. Visiting the exhibition of the factory students had the opportunity to observe both mathematical and physical laws and aspects of solving motion tasks, the application of vehicles in everyday life, in industry, sports and even in space science. Working in groups students had to analyze and identify all the improvements of different vehicles from the past to the present days in terms of design, technical characteristics and the most important how safer are they nowadays.
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MATHS QUIZZES
1. 2. 3.
Which vehicle is moved by the human muscular power? Which vehicle moves using the lifting force of the wings? The weight of the car directly affects the …….. consumption.
1.
A car has traveled 340 km in 2 hours. How many kilometers will it take in 3 hours if it moves the same way?
2.
Reactive airplane travels 1000 meters in 10 seconds. The airplane speed in km / h is:
1. 2. 3.
An unsportsmanlike behavior of the pilot. Danger, overtaking is forbidden, "Decrease speed". All pilots must immediately cease the race and return to the start line. End of session, training or race.
4.
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DO YOU KNOW THE RULES FOR CYCLING?
1.
2.
3.
4.
Is it a legal requirement to wear a helmet? Yes No Does a bike need to have lights? Yes No Does a bike need to have reflectors at night-time? Yes, a bike must have a front and rear reflector Yes, but only a red rear reflector No Is it a legal requirement to ride with a bell? Yes No
5.
A cyclist is allowed to ride across a zebra or children's crossing? Yes No 6. Cyclists can ride in bus lanes? Yes No 7. Can cyclists ride two abreast? Yes No, they must stick to single file unless overtaking 8. What is the minimum passing distance in this scenario? 1 m. 1.5 m. 2 m. 2.5 m.
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A VISIT TO SOFIA – THE CAPITAL OF BULGARI On 19th October the partners from the project countries visited the capital of Bulgaria – Sofia. Sofia is one of the oldest cities in Europe, founded some 2500 years ago. Thanks to its central location in the heart of the Balkans it was even briefly the capital of the Roman Empire. These days however there are only few remnants of these great times but it’s not difficult to find them right in the center of the city. The city with different architectural styles - neorenaissance, neoclassical or Soviet architecture. And all these styles create an unique place. Students and teachers visitd the main tourist attractions in the city and also participated in a real cart racing in the Ring Mall of Sofia. At the beginning of the racing the students were familiar by qualified instructors about the rules of the racing and the rules of their personal safety. They were informed abot the characteristics of the truck, layouts, speed limits. On a digital display the students could see their own statistic about speed, time and passed distance. They had to calculate their final results by solving Maths tasks and to announce the winners. It was an unforgettable experience for all paricipants. Bulgarian studentns had prepared a brochure with intersting facts about Sofia for their foreign friends.
SIGHTSEEINGS AND INTERESTING FACTS ABOUT SOFIA
Sofia is Bulgaria’s capital and its largest city. Founded thousands of years ago, today the city continues to develop as the country’s cultural and economic centre. At present, the city has a population of 1,250,000. Sofia is located in the western part of the country, on The Sofia Plain and on the lower slopes of Mount Vitosha. Sofia preserves many valuable monuments to its long and storied past. Visitors exploring the city’s streets can see remnants of The Eastern Gate from the days when Sofia was Serdika and Sredets, dating from the 2nd-4th centuries CE. These remains are exhibited in the underpass connecting the Presidential Palace and The Ministerial Council, surrounded by shops selling traditional Bulgarian souvenirs and rosewater.
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The gold-domed Alexander Nevsky Cathedral was built in the early 20th century The Alexander Nevsky Cathedral is a cross-domed basilica featuring an emphasized central dome. The cathedral's gold-plated dome is 45 m high, with the bell tower reaching 53 metres The temple has 12 bells with total weight of 23 tons, the heaviest weighing 12 tons and the lightest 10 kilograms. The interior is decorated with Italian marble in various colours, Brazilian onyx, alabaster, and other luxurious materials. The central dome has the Lord's Prayer inscribed around it, with thin gold letters.[ Built in Neo-Byzantine style, it serves as the cathedral church of the Patriarch of Bulgaria and is one of the largest Eastern Orthodox cathedrals in the world, as well as one of Sofia’s symbols and primary tourist attractions. The St. Alexander Nevsky Cathedral in Sofia occupies an area of 3,170 square metres and can hold 10,000 people inside. It is the second biggest cathedral located on the Balkan Peninsula after the Cathedral of Saint Sava in Belgrade. The early Byzantine Church of St Sophia was built in the 6th century on the place of an ancient Roman theatre and several earlier churches. The Hagia Sophia Church is now one of the most valuable pieces of Early architecture in South-eastern Europe. The present building is a cross basilica with three altars. The floor of the church is covered with complex Early Christian ornamental or flora and fauna-themed mosaics. The Hagia Sophia Church stands in the middle of an ancient necropolis and many tombs have been unearthed both under and near the church. Some of the tombs even feature frescoes.
The National Assembly of Bulgaria was established in 1879 with the Constitution of Bulgaria. The National Assembly of Bulgaria is the unicameral parliament and body of the legislative of the Republic of Bulgaria. It was established in 1879 with the Tarnovo Constitution. The National Assembly’s main building has been proclaimed a monument of culture for its historic significance. Situated in downtown Sofia, it was designed in Neo-Renaissance style by Konstantin Jovanović, a Serbian-Bulgarian architect who received his education in Vienna and Switzerland and whose other works include the Parliament of Serbia building. It was constructed between 1884 and 1886 by Friederich Wilhelm Gustav Liebe, a young builder from Saxony who was only 22 years old when construction began.
The St. Clement of Ohrid University of Sofia or Sofia University is the oldest higher education institution in Bulgaria, founded on 1 October 1888. The university’s edifice was constructed between 1924 and 1934 with the financial support of the brothers Evlogi Georgiev and Hristo Georgiev, whose sculptures are now featured on its façade, and has an area of 18,624 m² and a total of 324 premises.
The National Gallery for Foreign Art in Sofia is the only one of its kind in the Balkans. It presents a unique collection of Christian sculpture of the Indian province of Goa which can be found only in Great Britain and Portugal. Here is the Poetic Reality collection which no other museum has, etc. The Gallery is unique with the character of its collection – the art of distant lands, of exotic tribes and nations, of old and new ages coexists with the modern European tendencies, with traditional and religious pictorial principles in the chronological span of a millennium. The most valuable exhibits of the Gallery funds are displayed on four floors, housed in 19 rooms, with a total exhibition area of approximately 3,200 square metres. The Gallery holds over 10,000 museum items – graphic works, paintings, sculptures, fine arts.
The Bulgarian Academy of Sciences s the National Academy of Bulgaria, established in 1869. The Academy is autonomous and has a Society of Academicians, Correspondent Members and Foreign Members. It publishes and circulates different scientific works, dictionaries and journals, and runs its own publishing house.
The “Ivan Vazov” National Theatre is Bulgaria’s biggest theatre, as well as the oldest and most stand out and most imposing theatre in the country. This theatre is one of the major landmarks in Sofia due to its prime location and grandiose architecture. Founded in 1904 by the artists from the “Salza i Smyah” theatre, initially, it was called simply the National Theatre, but soon after it was named after the prominent Bulgarian writer Ivan Vazov. The theatre’s Neoclassical building, designed by famous Viennese theatre architects Hermann Helmer and Ferdinand Fellner, was
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finished in 1906 and opened in 1907. A theatrical school was established as part of the National Theatre in 1925. For the making of this brochure were used photos and information from “Sofia Guide” and Wikipedia
AN EXCITING RACING
THE WINNERS
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DEVETASHKA CAVE AND KRUSHUNA WATERFALLS
Devtashka cave
Krushuna waterfalls
Devetashka cave is a large karst cave about 15 km northeast of Lovech. A narrow path by the river Osam leads to the cave. The cave is a part of a beautiful public park that includes waterfall. The site is 35 m wide and 30 m high at the entrance. The cave widens after around 40 m , forming a spacious hall with an area of 2,400 m2 , a height of 60 m that can reach up to 100 m. Several large openings in the ceiling allow daylight to lighten the vast interior, due to commercial use of the site during the 1950s. Thirty-four species of mammals, four of which are included in the „Red book with protected animals and plants”and fifteen species of bats are to be found at the Devetashka cave. Krushuna waterfalls ar a seriea of beautiful waterfallsnear the town of Lovech. They are famous with their picturesque landscape. There is a tourist path leading to the cave where the river springs. Students and teachers from the projec countries visited the cave and the waterfalls and were familiar with its history, flora and fauna. The students had to solve some math tasks related with lenght, height, dept and inner volume.
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THE MUSIUM OF WATER IN LOVECH The first virtual Museum of water was visited from the participants in the project. Inside visitors could observe through a special glass how the ancient underfloor heating systems functioned. By a modern audio-visual technology the visitors could learn many interesting “water’ facts, as well as facts about the history of Lovech from the ancient times to the present.
A VISIT TO THE OPEN AIR ETHNOGRAPGIC MUSEUM “ETARA” AND THE TOWN OF GABROVO
Open Air Ethnographic museum “ETARA” is the first one of its type in Bulgaria and has the only one and unique collection of old time water-driven machinery. It is also one of the most riches and well-kept active technical collection around the European museums on the open air. All the objects are in action as they were in the past. Visiting this Ethnographic complex students and teachers could feel the atmosphere of the Bulgarian National Revival. They were familiar with the Bulgarian customs, culture and craftsmanship. They could also see the different houses with craftsman’s workshops
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and even to work in them using original instruments and following the old traditions. They could observe different geometrical shapes and find out how they are applying in real life in the past and nowadays.
A VISIT TO THE TOWN OF GABROVO Students and teachers had the opportunity to enter in the first Bulgarian school dating back from 1836. The old classroom which is a museum now keeps the history of education from those days.
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The guests also visited the Planetarium in Gabrovo. The Astronomical Observatory and Planetarium – Gabrovo was opened in 1984 in order to carry out educational, research and cultural functions. The purpose is to disseminate knowledge of astronomy and physics, to promote the achievements of cosmonauts in the cultural and educational field of “Nature Studies and Ecology”. The exact copy of the real starry sky and the movements of the space bodies provokes the imagination and the sense of the infinity of time, as well as the unique harmony of the universe.
The guests from the project countries could see different photographs, drawings, maps and other astronomical and space themes at the exhibition in the lobby. They also had to discuss some Mathematical aspects connected with space and space machines.
TROYAN MONASTERY
The foreign guests also visited the third largest monastery in Bulgaria – The Troyan Monastery and the Museum of Natural history in the village of Cherni Osam.
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LINKS A movie about Lovech and its most famous sightseeing – The Covered Bridge
https://www.facebook.com/natalia.christova/videos/g.389610561213434/10208263922421 369/ A movie about the Mobility in Bulgaria made by our Spanish partners
https://www.facebook.com/leticia.reyes.7547/videos/g.389610561213434/1021127159689 4527/
Summary All activities that were organised during the period of Mobility in Bulgaria were connected to the main topic “Maths in vehicles”. Our main aim was, through mathematical case studies, to show students how mathematics finds its application in the vehicles and the surrounding world as a whole. Students took part in all activities that we had prepared for them. They shared and respected different ideas and ways of thinking. They made calculations and solve mathematical tasks and in a friendly and pleasant environment they had fun together.
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