Arts Count ebook by Alma Suto

Editor: María de la Piedad Gracia Santolaria Graphic preparation and formatting: Alma Suto Translated: Gema Hernández López, María de la Piedad Gracia Santolaria, Muriel Martin, Ivana Rako Vuksan, Anamarija Ivkošić, Ines Garac and Martina Andreasson

Content Introduction.............................................................................. 2 Task 1 ........................................................................................ 2 Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Task 2 ........................................................................................ 2 Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Task 3 ........................................................................................ 2 Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Task 4 ........................................................................................ 2 Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Task 5 ........................................................................................ 2

Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Task 6 ........................................................................................ 2 Croatian school ..................................................................... 2 French school ....................................................................... 2 Spanish school ...................................................................... 2 Swedish school ..................................................................... 2 Tasks in Croatian ...................................................................... 2 Zadatak 1 ............................................................................. 2 Zadatak 2 .............................................................................. 2 Zadatak 3 .............................................................................. 2 Zadatak 4 .............................................................................. 2 Zadatak 5 ............................................................................. 2 Zadatak 6 .............................................................................. 2 Tasks in French ......................................................................... 2 Tâche 1 ................................................................................ 2 Tâche 2 ................................................................................ 2 Tâche 3 ................................................................................ 2 Tâche 4 ................................................................................ 2 Tâche 5 ................................................................................ 2 Tâche 6 ................................................................................ 2

Tasks in Spanish ........................................................................ 2 Târea 1 ................................................................................. 2 Târea 2 ................................................................................. 2 Târea 3 ................................................................................. 2 Târea 4 ................................................................................. 2 Târea 5 ................................................................................. 2 Târea 6 ................................................................................. 2 Tasks in Swedish ....................................................................... 2 Uppgift 1 .............................................................................. 2 Uppgift 2 .............................................................................. 2 Uppgift 3 .............................................................................. 2 Uppgift 4 .............................................................................. 2 Uppgift 5 .............................................................................. 2 Uppgift 6 .............................................................................. 2 Meeting Task ............................................................................ 2 Photo Marathon ................................................................... 2 Photo Marathon in Croatian ................................................ 2 Photo Marathon in France ................................................... 2 Photo Marathon in Spanish .................................................. 2 Photo Marathon in Swedish ................................................. 2

Introduction In this ebook, you will find a compilation of the activities carried out by the students of four schools participating in an Erasmus+ Strategic School Partnership: Osnovna skola Zmijavci, in Zmijavci, Croatia. Collège Jean Monnet, in Épernay, France. Trönningeskoland, in Halmstad, Sweden. IES Carmen y Severo Ochoa, in Luarca, Spain.

The project our schools developed over two years was called Arts Count! and its main objective was to improve the studentsâ&#x20AC;&#x2122; communicative and mathematical skills through art. All the activities in this ebook were designed with this goal in mind and progressively increased in complexity as the project went along. Cross-curricular tasks help the students make better sense of what they are learning, thus, each task invoked the use of the English language, an artistic discipline and a mathematical element. Other desired collateral benefits were the improvement of the studentsâ&#x20AC;&#x2122; ICTs skills, and as a result, digital programmes and applications were required to complete the tasks. Nowadays, most jobs are performed in a collaborative environment; therefore, we thought it important that our students learn and get used to this way of working as soon as possible. As such, the tasks had to be carried out in groups, with the students applying different cooperative learning techniques. The target students were secondary education students, between 12 and 15 years old. In completing these activities, students went on a journey exploring the culture of four countries while improving their English, maths, arts and ICTs skills. But not only that, they were also meant to make the students aware of the fact that we are all different, but we are all the same.

Task 1 Cooperative Learning Techniques In order to carry this task out it should be used the jigsaw technique. First, each member of the group will be assigned a part of the task. Once all the members of the group have finished their part, they have to share the information. The members of the group in charge of the parts that involve mathematical operations will explain the others the steps they have followed to find the solution or answer to the problem or question proposed. This way, although each student has been working on just one of the parts, when they share the information and the results, all of them acquire some knowledge about the parts that they havenâ&#x20AC;&#x2122;t been working on. Finally, the students make the puzzle, they put together the different parts according to the teacherâ&#x20AC;&#x2122;s instructions about how to do it. This activity has been designed to be part of an oral exhibition recorded on a video. Maths elements indeks 1.

2. 3. 4. 5. 6. 7. 8.

Relative positions of two or more straight lines Concept polygon Classification of polygons according to the numbers of sides Concept mosaic Calculation of the area of plane figures Concept polyhedral Polyhedral plane development of two buildings Calculating the volumen of such buildings

Croatian school Introduction The search for mathematical explanations of nature and the universe has always occupied mathematicians, and also the artist who believed that this is the only way they can achieve ideal beauty, apropos perfectly harmonised art piece. The old Egyptians discovered the "Golden section" (the Golden ratio), so called the Divine proportion, which is still considered as the perfect proportion in nature. We can get a Golden section by dividing a line into 13 pieces, a then we divide them in a proportion 8:5, which is total 1.618. That`s how we get a proportion in which the smaller size relates to the bigger one, as well as the bigger one relates to the entirety or a : b = b: (a+b). We will show the connection between Art and Math on these art pieces: Zobnica, Diocletian`s palac and Ivan Piceljs `s painting: From the map Ulm`s variations. Usable item: Zovnica1 1. Write a short history of the item and learn where it was used. 2. Which geometric shapes were used for making zovnica? 3. If the length of zovnica is ? cm, the wight is ? cm, calculate a total amount of material needed to make zovnica. Links were you can find answers to the questions: https://hr.wikipedia.org/wiki/Pravokutnik https://www.mathsisfun.com/geometry/

Building: the floor plan of Diocletian`s palace2 1. Write a short history of Diocletian`s palace.

Traditional handmade woollen (ethno) bag The ancient palace built by the Roman emperor Diocletian at the turn of the fourth century AD. Today it forms about half of the old town and city center of Split, Croatia. Since November 1979 the palace has been on the UNESCO`s list of World Heritage Sites in Europe. 2

2. Learn of which geometrical shapes floor plan is comprised , and which shapes are repeated. 3. Find the use of Golden section inside the palace. 4. Find the connection between the Diocletian`s palace and weaving workshops (??) Links were you can find answers to the questions: http://splitculture.hr/dozivljaj/povijest/dioklecijanova-palaca http://www.visitsplit.com/en/448/diocletian-palace

Ivan Piceljs `s painting: From the map Ulm`s variations3 1. Write a short biography about Ivan Picelj. 2. Comment the painting from geometrical point of view: -Which geometrical shapes are present in the painting? -Find parallel lines in the painting. -Learn and find the Golden section inside the painting. Links were you can find answers to the questions: http://www.galerijadivila.hr/hr/autori/ivan-picelj.html https://en.wikipedia.org/wiki/Ivan_Picelj

Ulm Variation, screen-printing, 2006

French school Introduction: While studying a famous building, a painting and an object we use in our daily life, we are also going to study the different geometric shapes which are a part of these pieces of art, their particularities as well as how beautiful they are! Usable item: The Costes armchair by Philippe STARCK The objective: Create a document to introduce the artist as well as his piece of art The type of document: a slide using openOffice or libreOffice The information you have to mention: Who is the designer? What is his job experience? A description using maths: - work on the particularity of this armchair, its name, why it's interesting, its geometric shapes - draw the centre of gravity of the triangle which is created with its 3 feet pictures to illustrate your work. http://www.cotemaison.fr/chaine-d/deco-design/philippe-starck-lachaise-costes_24673.html https://www.centrepompidou.fr/cpv/resource/cEbz7E5/rk4erog https://www.mathsisfun.com/geometry/solid-geometry.html

Criteria of success: My answer is: Complete

My opinion (YES / NO) /4

Correctly written (spelling, grammar) Clear

Precise

Well presented

Building: The Louvre Pyramid

My teacher

The objective: Create a document which introduces the Louvre Pyramid. The type of document: a slide using openOffice or libreOffice The information you have to mention: Where is it located? When was it created? Why was it created? Who decided to build it? Who built it? What was it built for? … A description using maths: the solid. - vocabulary of the solid, geometric shapes, dimensions, the different materials used, the result, ... - how to find the pyramid height once we know the length of one side of the lozenge (use Pythagoras) and then the pyramid volume pictures to illustrate your work. http://www.lexpress.fr/culture/art/10-choses-a-savoir-sur-la-pyramide-du-louvre_752571.html http://www.mathovore.fr/les-pyramides-et-cones-cours-maths-39.php https://www.mathsisfun.com/geometry/solid-geometry.html

Victor Vasarely `s painting: «CHEYT PYR» 4 The objective: create a document to introduce the artist as well as his piece of art The type of document: a slide using openOffice or libreOffice The information you have to mention: Who is the artist? Which techniques did he use? A description using maths: - work on the different geometric shapes, its dimensions, colors, the result.... pictures to illustrate your work. http://www.fondationvasarely.fr/vasarely.php http://www.vasarely.com/site/site.htm https://www.mathsisfun.com/geometry/solid-geometry.html

ZE TOIT TERRASSE, by Vasarely. Photo by Yann Artus-Bertrand

Spanish school Introduction Geometry, part of mathematics that is responsible for studying the properties and measurements of a figure, also plays an important role in the artistic field. In fact, geometric shapes allow us to create high expressive compositions and of great artistic value, as occurs in the works of the works of art for this task: the mosaics in the Jewish quarter of Toledo, the leaning towers of Madrid and José María Yturralde’s painting.

Design piece: Mosaic5 Give a simple definition of a mosaic. Find out where this mosaic is. Which is the main figure that has been used to build this mosaic? If the side of one of the rhombus is 5 cm. and the DIAGONAL MAYOR is 6 cm., calculate the area of the following figure, made out of six rhombus. You can find the answers to these questions on these links. - English http://gwydir.demon.co.uk/jo/tess/grids.htm http://www.mathwords.com/a/area_rhombus.htm

Mosaic from the Jewish Quarter in Toledo. Made of small pieces of coloured ceramic, called tesserae

Relevant Building6 The first leaning skycrapers built in the world were the two leaning towers in Madrid, which form the so called “Puerta de Europa”. What other name have they got? A polyhedron is a geometrical figure limited by four or more flat polygons. Find out whether each of the towers is a polyhedron, and, if it is so, find out which polygons are on every face. In order to do this, you can use its plane development. Given that their bases are squares, with 34,5 metres on every side, and their height is 114 metres, find the volume of each of the towers. You can find the answers to these questions on these links. http://www.mathsisfun.com/geometry/polyhedron.html http://ths.teh.k12.ca.us/ourpages/auto/2014/9/18/46105644/----1-7%20Page%2071%2012-23.pdf http://www.mathsteacher.com.au/year7/ch09_polygons/06_polyhedra/prism.htm

Famous painting by the Spanish artist José María Yturralde7 1. Write a short biography of the Spanish artist José María Yturralde, just a few relevant details about him, where he is from, what type of artist he is,… 2. Comment on the painting from a geometrical point of view: Relative positions of two or more straight lines. Define a polygon. Which polygons can you see. Classify them according to the number of sides they have. You can find the answers to these questions on these links. http://www.sangakoo.com/en/unit/relative-positions-between-straight-lines https://quizlet.com/403996/polygon-vocabulary-flash-cards/ http://www.yturralde.org/n-obra-en.html

6 The Gate of Europe. Twin towers with a height of 114 m and an inclination of 15 º. Designed by the American architects Philip Johnson and John Burgee. They were constructed between 1989 and 1996. They are located in Paseo de la Castellana, in Madrid 7 Impossible Figure, painting by José María Iturralde, acrylic on wood, 1970

Swedish school Introduction In this task, you are going to work with some objects that are special for Sweden within the fields of painting, architecture and design. The chosen works of art can be found in or close to our region. You are going to explore how mathematics can be used in painting, architecture and design. Various mathematic calculations affect for example the aesthetics of a painting, the pattern of a design or the construction and functions of a building or monument. Relevant Building: Öresundsbron/ The Øresund Bridge 8 This 16-kilometer long bridge connects Sweden and Denmark and the two main cities of the Øresund region: Malmö and Copenhagen. The bridge came as the long-awaited solution to problems that Sweden and Denmark struggled with for hundreds of years. It has brought the two countries closer together in many ways, such as making it easier for people of both countries to work in and commute to the other country, as well as facilitating trading between the two countries. Before, you would have to take the ferry to cross the sea. Seen from above, the bridge seems to disappear into the ocean, which is actually the case since it also consists of a tunnel. 1. When did the Øresund Bridge open to the public? 2. What is the average speed of the train if you travel between Kastrup Airport in Copenhagen and Hyllie Station in Malmö? The distance between Kastrup and Hyllie is 27.5 km. 3. The bridge has two pylons. Describe what a pylon is. You can find the answers to these questions using the following links: 8

The Øresund Bridge - The Øresund Bridge is an approximately 16 km long road and rail link between Sweden and Denmark, connecting Malmö and Copenhagen. It was designed by the Danish bridge architect Georg Rotne and was constructed between 1993 and 2000.

https://www.oresundsbron.com/en/node/6738 http://physics.tutorvista.com/motion/speed.html http://www.csgnetwork.com/csgtsd.html http://global.britannica.com/technology/pylon-architecture https://www.youtube.com/watch?v=rxFWgHichcM

Check out this video, the first five minutes!

Design piece: “Berså” by Stig Lindberg.9 “Berså” is one of Gustavsberg Porcelain Factory’s most well-known patterns, created by designer Stig Lindberg in 1960. It has been sold in large numbers and the motif with green leaves has become an icon representing Stig Lindberg. 1. The Green leaves are placed symmetrically. Symmetry is a term that is used in art as well as in science. Symmetry is often used in art in order to create balance in the motif so that it is pleasant to look at. Explain what symmetry is. 2. On a 20x20 cm napkin, see in picture above, the branch is seen two times as two parallell branches, per side/per part. A napkin has four such parts which means it will be 40x40 cm when opened up. How many branches like the ones above and how many green leaves will be on a tablecloth that is 140x250 cm? Show how you solve the problem using pictures and calculations. You can find the answers to the questions using these links. http://lyk-peir-mytil.les.sch.gr/mart/ https://www.mathsisfun.com/geometry/symmetry.html http://dictionary.reference.com/browse/symmetry http://www.haelmedia.com/OnlineActivities_txh/mc_txh4_001.html

Famous painting “Composition with geometry” by the Swedish artist Esaias Thorén10 Write a short biography of the Swedish artist Esaias Thorén just a few relevant details about him, e.g. where he is from, what type of artist he, etc. Find out some facts about Halmstadgruppen that he was part of. What geometrical shapes can you find in this painting? 9 Berså is one of Gustavsberg Porcelain Factory’s most well-known patterns, created by designer Stig Lindberg in 1960. It has been sold in large numbers and the motif with green leaves has become an icon representing Stig Lindberg. 10 Composition with geometry painting by Esaias Thorén, oil on panel. (year unknown)

Calculate the area of some different forms: * A square: How large is the area of a square if a side is 4 cm? * The largest circle: How large is the area of the circle if its radius is 0.8cm? * What percent of the whole triangle is the top triangle? Explain/show how you have calculated your answers. You can find the answers to the questions using these links. http://www.mjellbykonstmuseum.se/omwebbplatsen/english/thehalmstadgroup.4.31d9bb9f1285e3aab 5780007238.html http://www.mathsisfun.com/area.html http://www.mathsisfun.com/geometry/area.html

Task 2 Programming and carrying out of the task. This task has to be carried out by working with several groups. It has two different parts. Part 1 The first part of this task consists of writing a short story inspired either by the artistic photograph by Darko PuhariÄ&#x2021; or by the painting by Vasilije Jordan, both works contain mathematical elements. Each group will work with three other groups and the four groups will have to create the story by turns: 1. The first Group will write the introduction. 2. Once this group has finished their part, the next group will write the plot. 3. After that, the third group will write the climax of the story. 4. Finally, the last group will write the conclusion, the end of the story. Prior to this, all of you have to talk about the artwork youâ&#x20AC;&#x2122;ve been assigned and decide what you are going to write: What? Who? Where? When? Since the story has to be written by the four groups, you have to agree on the plot, the characters, where and when the action takes place, how the story ends, etc. Each part of the story, that is each paragraph, has to have about 50 words, font Arial 14. The coordinator of each group will be in charge of writing the part of the story they are responsible of ( and which has been developed and written by all the members of the group). Parte 2 Each group will make a drawing, collage or photograph based on one of the short tales written previously and it has to contain the mathematical elements shown on the artwork that inspired the story. It has to be presented on a A4 paper sheet. If it is a photograph, it will have digital format.

Evaluation Criteria For the story: • Correct use of the language. • Coherence and cohesion. • Originality and creativity. • Work group. For the drawing, collage or photograph: • Originality and creativity. • Use of mathematical elements. • Artistic quality. • Work group. Cooperative Learning Techniques For the story writing two techniques are used: pens in the middle for the brainstorm of ideas and then the story is written by using the write around technique. The drawing, photo or collage is made with the jigsaw technique. Maths elements index 1. 2. 3. 4. 5. 6. 7.

Protactor Horizontal line Square and triangle Relative positions of two or more straight lines Circular sector Rectangles Outer ring

Croatian school Croatian painting - Vasilije Jordan: Harmica 11 Vasilije Josip Jordan is a Croatian painter. He was born in Zagreb in 1934. He graduated from the Art Academy in Zagreb and received a lot of art awards. His paintings are surrealistic, presenting secrets and mysteries of everyday life. Jordan’s work is connected with renaissance-baroque tradition and consistent in figuration. He uses the techniques of old masters, mostly in oil and tempera. He is also interested in the magic of old photographs. One of those memories of the earliest photographs is this painting, called Harmica, which is also the old name of the main square in Zagreb. The painting shows the balanced classical composition of the accentuated perspective. The painting was installd as a curtain in the National Theatre in Zagreb in 1999. Croatian photograph - Darko Puharić12 Darko Puharić is a Croatian photographer who worked on a digitalisation of the material from the Vinkovci Town Museum. This photo dating from 2011 shows a vase that belongs to Vučedol culture (Vučeol Orion found in 1978). It is considered the oldest European calendar. You can clearly see 4 zones, each divided in 12 sign fields. 4 zones depict 4 sessons, and the sign fields probably present weeks. Each sign is a certain constellation, placed on a vase as it appears chronologocally in the sky. This first European calendar was made in 3000 BC. it is believed that Večedol people made notes about their mathematical and astronomical knowledge on ceramics which they also used as an abacus. The fact they understood the concepts of calendar and drawing chessboards says a lot about their logical understanding of Pythagorean theorem which was yet to be introduced. 11

Vasilije Jordan, Harmica, oil on canvas

Darko Puharic, Calendar Orion. The vessel with a calendar found in 1978 in Vinkovci (The first European calendar) Photography, Darko Puharić, 2011

French school Le pont de l'Europe by Gustave Caillebotte13 Gustave Caillebotte, (born on 19 August 1848 and dead on 21 February 1894) was a French painter, member and patron of the artists known as Impressionists, although he painted in a much more realistic manner than many other artists in the group. Caillebotte was noted for his early interest in photography as an art form. He may be considered part of the first movement after Impressionism: NeoImpressionism. Caillebotte aimed to paint reality as it existed and as he saw it, hoping to reduce the inherent theatricality of painting. Cropping and "zooming-in", techniques that commonly are found in Caillebotte's oeuvre, also may be the result of his interest in photography, but may just as likely be derived from his intense interest in perspective effects. A large number of Caillebotte's works also employ a very high vantage point. Caillebotte painted many domestic and familial scenes, interiors, and portraits. Many of his paintings depict members of his family. There are scenes of dining, card playing, piano playing, reading, and sewing all executed in an intimate, unobtrusive manner that portrays the quiet ritual of upper-class indoor life. His country scenes focus on pleasure boating on the leisurely stream as well as fishing and swimming, and domestic scenes around his country home. Caillebotte is best known for his paintings of urban Paris, such as The Europe Bridge (Le Pont de l'Europe) (1876). Many of his urban paintings were quite controversial due to their exaggerated, plunging perspective.

The Europe Bridge, painting by Gustave Caillebotte, oil on canvas, 1876

Ze Toit Terrasse de Vasarely, photo by Yann Arthus-Bertrand14 Yann Arthus-Bertrand (born 13 March 1946 in Paris) is a French photographer, journalist, reporter and environmentalist. He is especially well known for his book Earth from Above (1999). He became a reporter and an international photographer, specialized in great reports on adventures, sports, animals and in pictures taken from the above for the National Geographic, Figaro Magazine, Paris Match and GĂŠo. He also took a part in 10 Paris-Dakar rallyes. Every year, he made a book on the Roland-Garros tennis tournament, took pictures at the Annual Agricultural Exhibition in Paris and also made a film about Dian Fossey and her gorillas. He also published books about the relationship between animals and humans. He founded the Altitude Agency in 1991, which was the world's first press agency and images bank specializing in aerial photography. In 1994 he started a thorough study on the state of the Earth sponsored by UNESCO. As part of the study, he made a picture inventory of the world's most beautiful landscapes, taken from helicopters and hot-air balloons. In 2000, his "Earth from Above" free exhibitions were set up in big cities. In 2004, he took a picture for the operation called 10,000 hearts for a red ribbon (10 000 CĹ&#x201C;urs pour un Ruban Rouge), to raise funds for the AIDS association in Mali. Around 6,000 people create the shape of a heart which could be seen from the sky. On 1 July 2005, he founded the international environmental organization Good Planet, and set up the program Action Carbone. He was elected member of the Fine Arts Academy in 2006 thanks to his pictures. In April 2007 he started directing a film originally called Boomerang, later re-titled Home. The film was produced by Luc Besson and financed by the PPR group (a French multinational company). It was Arthus-Bertrand's intention to show the state of our planet and the challenges humanity faces. 14

Ze Toit Terrasse, by Vasarely. Photo by Yann Artus-Bertrand

Spanish school Chema Madoz 15was born in Madrid, 57 years ago. He is one of the most prestigious Spanish photographers, known worldwide. His works are created taking skilful imagination games as a starting point. He uses perspective and different textures to create his extremely personal photographs: you always have to look at them twice, the first one to see what you think you are seeing, the other one to understand the elements you can see. In his works, always in black and white, things are never what they seem to be. An example of this is the photograph on the right. It is a minimalist image, created from a protractor, resting on a horizontal line, dividing the space in two unequal parts, following the rule of the two thirds. By keeping the original texture of the elements in the image, the photographer plays with the scale, making the protractor appear as if it were the sun. In the mid-twentieth century, there are some different groups and trends that try to renew the Spanish art scene. One of them is Equipo Crónica. It appeared in Valencia in 1964. It was originally formed by Manuel Valdés, Rafael Solbes y Juan Antonio Toledo, although Toledo left the group soon. Their works are made in group16. Solbes and Valdés gave a thought to the idea they wanted to convey first, and then they painted together, using well known images taken from the mass media, as well as from the Art History. In this picture, (La factoría y yo, 1970), we can see, skilfully combined, three master works from three artistic genius: Velázquez (Retrato del infante don Carlos. 1626), Andy Warhol (Ten-Foot 15

Transportador (protractor), photography by Chema Madoz, 2007

La Factoría y yo by Equipo Crónica, acrylic on canvas, 1970

Flowers.1967) and Roy Lichtenstein (Preparedness, 1968). As we can see, taking a work from the XVIIth century and two from the XXth century, Equipo Crónica succeeds in creating a totally balanced composition in spite of the chaos given by the mixture of colours, shapes and textures.

Swedish school The Swedish painter Sven Jonson 17was born in 1902 to a fisherman's family in Söndrum outside Halmstad. In 1929, Jonson formed the Halmstad Group together with Axel and Erik Olson, Waldemar Lorentzon, Esaias Thorén, and Stellan Mörner. The Halmstad Group is made up of the most famous Swedish surrealist painters. Surrealistic artworks are often inspired by dreams. Jonson´s surrealism is characterised by barren landscapes in light, yellow and brown shades, often with small human figures to exemplify man's smallness in the universe. Architectural elements and vast distances to the horizon with mile long shadows, arches and arcades are all typical elements of Jonson's work of this period. During the second half of the 1930s Jonson mirrors the fear of a new World War in a series of visions of a destroyed world. During the 40´s Jonson took part in Söndrumskolonin (the Söndrum Colony) a grouping of artists in Halmstad´s coastal area. In the early 1960s Jonson painted labyrinthine cathedrals where he referred back to the cubism of the 20s. During the latter part of the 1960s and the 1970s, the blue shades of sea and sky returned to dominate his work; also reflecting his lifelong interest in space, planets, and celestial constellations. This can be seen in the painting “Stjustjärnan” (The Big Dipper: see above). Sven Jonson passed away in 1981. Sven Jonson, "Sjustjärnan"/ The Big Dipper Source: http://www.mjellbykonstmuseum.se/omwebbplatsen/english/thehalmstadgroup/svenjonson.4.293aa03 e12928a822b180006724.html

The Star by Sven Jonson, oil on canvas, (year unknown)

The photograph below was taken by the Swedish press photographer Hans Runesson18 in 1977. It was taken in the stairway of a building that was going to be torn down during a protest that was trying to save the building. Hans Runesson was born in 1947 in Växjö in southern Sweden. He is famous for his black and white photos, especially “A Woman Hitting a Neo-Nazi With Her Handbag”, taken during a demonstration of the Nordic Reich Party supporters in Växjö in 1985. The woman with the handbag in that picture was of Polish-Jewish origin and her mother had been in a concentration camp during World War II. The photograph was selected as the Swedish Picture of the Year in 1985 and later as the Picture of the Century by the magazine Vi and the Photographic Historical Society of Sweden. In 2013-14 a miniature statue was made of the woman, based on the photograph. The statue was placed at Varberg Fortress in Varberg in the south of Sweden in November 2015.

Untitled, photography by Hans Runesson 1977. The photo shows a woman in a stairway of a building that is to be torn down.

Task 3 Objectives - Understanding the traditions of the other countries through their traditional tales. - Encouraging the artistic creation while keeping in mind some mathematical premises. Final Production - Production, either on paper or on a digital format, of a graphic story/storyboard of the former creation. Steps 1. Each group of students will be given a story, legend or popular tale. 2. Then, the students will make a script with dialogues adapting the story, legend or popular tale. 3. From this script, the students will create a storyboard in no more than two papers (paper, A4 format, or digital). The graphic story can be made as follows: -By using a program as Pixton, Tondoo, Comic Life, Bitstrips or other online resources. -Drawn by hand. -Making a collage. -By using any other program or technique they know. - The graphic story must have up to 12 vignettes and has to include, at least, five of the following mathematical elements: 1. Oval bubbles (for the speeches, for example). 2. Rectangles (for the narratorâ&#x20AC;&#x2122;s voice, for example). 3. Circles. 4. Concentric circles. 5. Symmetry. 6. Acute angles. 7. Parallels. 8. Perpendiculars. 21

9. Equilateral triangles. 10. Squares. - If the comic is made by hand, the mathematical elements have to be made by using the specific drawing tools required such as ruler, set-square, compass, etc. - The students have to provide, together with the comic, a list of the mathematical elements they have used and they have to say specifically in which vignette and where in the vignette they have used them. The graphic stories which haven't been made by using digital tools must be scanned. Cooperative learning techniques: First, there should be a few minutes of a brainstorm of ideas by using the pens to the middle technique, followed by a discussion and a final agreement on what they are going to do. Then, the students have to write the script and the dialogues by using the writearound technique. For the graphic story they have to use the team jigsaw technique. Evaluation and Qualification Criteria -

Use of English. Adequacy between the script and the original story. Creativity and originality. Use of the geometrical elements. Artistic quality. Group work.

Croatian school The Croatian Legend The Lake Fairy19 The legend says that the dance of fairies above Blue lake starts during the full moon. It is believed that the one who dances in a fairy round will cross the border between the worlds- become a fairy. Many people wanted that and lots of young lives were lost in the depths of the lake. Once upon a time, during the early dawn, a young man decided to go to the lake. There he saw a beautiful girl in the the shade of pines. It was a fairy. During the fairy round she did not notice dawn approaching so she was left alone at the lake. She knew that the dazzle of the sun undoes fairy magic and that just one touch of the sun's rays would turn her into its reflection. Abandoned and in fear,the fairy was hiding and didn't realise that the young man saw her. However, he recognised the sorrow in her eyes and decided to help her. Sheltering her from the sun, the young man led her to a cave located by the lake. The fairy remained there waiting for the full moon â&#x20AC;&#x201C; the time when moonlight would illuminate the lake and she would dance again and hence return to her world. But young man fell in love with her and decided to do everything to become part of her world, even do the fairy dance. One night, while the fairy was still sleeping, the young man noticed moonlight shining upon the lake and the water stirring up.He ran to the lake hoping this night his dream of becoming a fairy would come true. However, he accidentally tripped and fell into the lake. He disappeared into the depths of the lake. Soon the dance and singing started and the sleepy fairy headed to the lake. She was happy to see her sisters fairies, but she impatiently looked for him. However, dark clouds covered the sky and moonlight illuminating the surface of the lake soon disappeared together with the fairy round. The fairy was left alone again. Completely heart-broken, the fairy waited for her loved one, but nobody saw the young man anymore. While some believe the fairy stayed in the 19

The Lake Fairy, the legend from Imotski, English version by group students, proofread by an English teacher Anamarija Ivkosic

darkness of the Fairy cave, others think that she let herself down to the first sunbeams to touch her.

French school The French Tale The Vase Of Soissons20 According to Gregory of Tours (ca. 538–594), a Gallo-Roman historian and bishop, the sacred hard-stone carved vase was of marvelous size and beauty. It was stolen together with other holy ornaments from a church, in the pillage that followed the Battle of Soissons of 486, a battle which was won by the French king Clovis I. At that time, he had not yet converted to Christianity. Saint Remigius, the bishop of Reims, sent messengers to Clovis, begging that if the church might not recover any other of the holy vessels, at least the sacred vase might be restored. He wanted to get it back so much. Clovis agreed to do so and therefore he claimed the vase as his rightful part of the booty, when it came to share all they had robbed in the church. He even asked Saint Remigius to come to Soissons to get the sacred vase back. At Soissons, all the soldiers agreed to give the vase back to Saint Remigius. Only one greedy soldier disagreed and smashed the vase with his battle-axe. Clovis at first did not react to this and gave the broken vase to Remigius. But he never forgot this incident. A year later, however, Clovis saw the soldier again, took the man's axe and threw it on the ground, pretexting his armament wasn’t correct. The man bent down to pick up his axe, and Clovis smashed his skull with his own axe, commenting "Just as you did to the vase at Soissons!” Today’s popular version, which remains in French history books, is “Remember the vase at Soissons!” (Souviens-toi du vase de Soissons !”)

The Vase of Soissons, traditional tale from Soissons, English version by Muriel Martin

The Spanish Popular Tale

Spanish school

The Legend Of The Kissing Bridge (Cambaral, The Pirate)21 In the Middle Ages the Cantabric Seas were dominated by pirates. One of the most famous and feared, was called Cambaral, who ravaged the Spanish travellers. It was the terror of the passengers not only because he took over the ships and stole their belongings, but because he used to conclude their work torturing and killing the crew. In addition, he kidnapped the beautiful maidens and then traded with them in the markets. The Government tried to stop him many times, but it was in vain, because Cambaral defeated all fleets. Since his capture seemed impossible, Hidalgo, Lord of the fortress of Luarca, and his men decided to lay an ambush for him. They would pretend to be fishermen. Thus, they sailed offshore and they trusted that as soon as the pirates saw them they would attack them. As the pirates didn't know that they had been set a trap, they fell into it and found themselves with dozens of people perfectly armed and prepared for the attack. Cambaral was taken prisoner and taken to the fortress of la Atalaya, where he was locked in a dungeon. While celebrating the victory, the Lord's daughter (a beautiful kindhearted young woman) asked permission to visit the prisoner and heal his wounds before bringing him to justice. And that's how, while she was healing him, both felt the powerful boost of love. They decided to run away while her father was sleeping. They gathered and escaped to the port, but at the very last moment, Hidalgo, who had been informed of the flight, caught them. They then realised it was impossible to escape, so they hugged and put their lips together in a last kiss. Hidalgo, unable to stand what he thought was a betrayal, drew his sword and beheaded them with a single stroke. Both of their heads fell into the river while their bodies remained tightly embraced.

Cambaral the Pirate , tradicional tale from Luarca, English version by Gema HernĂĄndez LĂłpez and MarĂa de la Piedad Gracia Santolaria

Later on, the Kissing Bridge was built in the same place where this terrible event happened. It is said that, nowadays, at midnight, when the full moon shines, love words coming out from the sea can be heard and that if you look at the horizon, you can see two floating heads joined in a kiss.

Swedish school The Swedish Tale The Black Jewel Case and the Red One22 A Swedish folk-tale from the south of the Småland region in the south of Sweden. A mean and spiteful widow with a like-minded daughter marries a friendly and good-natured man with a daughter. When the man dies, the woman pushes his daughter into the well of the farm. However, the girl doesn’t drown. She sinks to the bottom of the well, the ground opens and when she wakes up she is lying on an underground meadow. She gets a job as a maid on a farm and she does an excellent work. She is friendly towards the animals that in return help her with the tests that the woman who owns the farm puts her through. At the end of the year, the girl asks to end her employment on the farm. The woman offers the girl to choose one of twelve jewel cases in her attic as payment for her job. On the cats’ advice, the girl chooses the smallest, black case. Once back on her own farm, her step-mother obliges her to live in the poultry-house with the chickens. After cleaning the poultry-house and putting the case on its’ place, she opens it and finds it full of jewelry made of gold, pearls and jewels. The jewel case spreads a golden light on the walls and ceiling and the poultry-house becomes more magnificent than the most splendid royal hall. 22

The black jewell case and the red one, traditional tale from Sweden, English version by Martina Andreasson. Author unknown.

The step-mother then pushes her own daughter into the well, hoping she will bring back an even more magnificent jewel case. The daughter gets a job on the same farm, but she doesn’t treat the animals with the same kindness as the other girl so they don’t help her with the farm owner’s tests. At the end of the year she demands payment and is offered to go get a jewel case from the attic. Without anyone’s help she picks the red, biggest and most magnificent jewel case. Back with her mother she opens the red jewel case and it is full of snakes and toads. A flame from the jewel case sets the house on fire. Both the step-mother and her daughter die in the fire, only he poultry house and the girl are unharmed.

Task 4 Multimedia recreation of a poem 1. The students will work in groups. They will have to make a multimedia recreation of a poem by a foreign author, putting together images, music and the reciting of the poem. The images have to include mathematical elements such as spirals, symmetries and modular arithmetic art images that will contribute, somehow, to a better understanding of the poem. Procedure: 1) Each group of students will be given a poem. 2) The multimedia outcome, the video, canâ&#x20AC;&#x2122;t be longer than three minutes and it must consist of the following: a. The recitation of the poem in English and in the mother tongue, arranged consecutively or merged freely. b. Images or video sequences, original or manipulated, that include mathematical elements such as spirals, symmetries and modular arithmetic art images which will contribute, somehow, to a better understanding of the poem. c. Music to enhance the emotions and feelings the text shows. The students have to compose their own music using, for example, Music Maker Jam. If thatâ&#x20AC;&#x2122;s not possible, then, they have to use a piece of instrumental music by an artist from the same country as the poem theyâ&#x20AC;&#x2122;re working with. Assessment Criteria The following criteria will be considered for the assessment and qualification of the task: - The reciting in English and in the mother tongue (pronunciation, intonation, rhythm). The adaptation of the music, images and mathematical elements to the content of the poem. Quality of image and sound. Cooperative Learning Technique: Group Investigation - Steps

1) Students are assigned or decide which part of the task they are going to be responsible of. Then, they establish deadlines to finish the different parts of the task, which are: 1. Collecting images for the video. 2. Selecting the most suitable images containing mathematical elements and deciding their sequence for the video. 3. Reciting and recording the poem. 4. Composing/Choosing the music for the video. 5. Editing the video. 2) All the students contribute to each part of the task and the student in charge of each part makes sure that everyone does his/her part in time. 1. All the students collect images with mathematical elements to illustrate the poem. 2. All the students contribute to the reciting of the poem in English and in the mother tongue, in order to be recorded. 3. All the students compose/choose some music to go with the video. 3) Students come together as a group, share what they have and make decisions. 1. All the students take part in the selection of the music, of the images and in the decision about their sequence in the video. 2. Editing the video is normally a one person task at the computer, and itâ&#x20AC;&#x2122;s the same about the recording of the reciting in English, but all the students have to contribute to this part of the task too. 4) Each student will make an individual report in which they will place on record the following: - A list of the mathematical elements that were shown on the images they compiled. - The audio file with the music they composed / the name of the song and artist they chose to go with the video. - An assessment of the performance of the coordinators of each part of the task. Maths elements index 1. Spirals 2. Symmetries 3. Modular artihmetic art images

Croatian school The Croatian Poem I wish you loved me by Jure KaĹĄtelan 23 I wish you loved me, I was a flower in your hair, if you're night, I'll be the dawn and flashing light in the dew. I wish you loved me and all days would be a song. if you are a spring, I will be too In the bedrock a clear fountain.

I wish you loved me, poem by Jure Kastelan, English version by pupil Petra Tolic, proofread by an English teacher Ivana Rako Vuksan

French school The French Poem Euclidians by EugĂ¨ne Guillevic24 Parallels We go, the space is large, We see each other, We want to talk. But what we tell The other already knows it, Because since the beginning Erased, forgotten, It has been the same adventure. In dreams we meet each other, We love each other, we complete each other, We don't go any farther Than in the other and in ourselves. Perpendicular Easy is to say That I arrive at the right moment. But it's also for me That the other arrives at the right moment.

Euclidians, poem by EugĂ¨ne Guillevic. English version Muriel Martin

Spanish school The Spanish Poem Tough You May Not Know by Luís García Montero25 As the light of a dream, That can’t enlighten the world but still exists, This is how I’ve lived Illuminating That part of yourself that you don’t know, The life you’ve led together with my thoughts... And though you may not know, I’ve seen you Going through the door without denying, Asking for an ashtray, looking over the books, Responding to the desire of my lips With your whisky lips, Following my steps to the bedroom. We have also talked In bed, slowly, many evenings This bed of love that you don’t know, The same bed that gets cold As you leave. Though you may not know, I invented you with me We planned a thousand projects, we walked along Every city you love, We remembered songs, we chose abdications Both learning to live Between reality and thinking. Being spied in the shadow of your schedule Or in the night of a club by my surprise. 25

Though You May Not Know, poem by Luís García Montero. English version by Gema Hernández López and María de la Piedad Gracia Santolaria

I’ve lived this way, As the light of a dream You don’t remember when you wake up.

Swedish school The Swedish Poem Kissing Wind by Hjalmar Gullberg26 He came like a wind What does the wind care about prohibitions? He kissed your cheek He kissed all the blood to your skin It should have stopped there You belonged to another, just borrowed One night in the lilacs’ time And month of the golden chains He kissed your ear, your hair What does the wind care if he’s allowed to or not? On the eyes he kissed you blind Of course you didn't want at first, to answer his desire But soon your arms were around his neck In the month of the golden chains From your mouth he has kissed The last of your resistance Your mouth lay quiet With half open lips against his There comes a wind and it goes And your whole world falls apart For a breeze from lilacs’ spring And the golden chains’ clusters 26Kissing

wind, poem by Hjalmar Gullberg. English version by Martina Andreasson.

Task 5 Reading Contemporary Theatrical Texts And Writing A Theatrical Scene The students will work in groups. Each group will be assigned and then read an excerpt from a playwright by a contemporary author. Next, the students will write a scene which will be the continuity of the text they have been given. Finally, they will make a photograph which shows a situation of the scene they have written. Process of execution: 1) The students will be working on an excerpt from a play by a contemporary author. Conditions of the text: a) The topic is free, as long as the text deals with one of the contemporary human affairs. b) The length of the text will be of 3 or 4 pages. c) A contextualization of the excerpt has to be provided, 5 or 6 lines that summarises the plot of the play and the moment the excerpt takes place. d) The text will be in English. 2) Each group is assigned one excerpt. The students have to read the text and then write a scene that gives continuity to it. This scene will be at least 1 page long, 2 pages maximum, written with Arial, size 12, spacing 6 points, single. If they want (depending on the text it can be even necessary) they can add one or more characters. The text has to have stage directions (for example those describing how a character moves on the stage, sounds, changes in lighting, etc.) 3) Once the scene is written, each group will have to make a photograph which shows an instant of the scene they have created. All the members of the group must appear on the picture. They will have to wear the costumes that fit the most and the set must also go with the scene they are depicting. This set has to contain the following geometrical elements: - Ovals. - Spirals of two or three centres. - Star polygons of a minimum of five points.

The geometrical elements have to be made by the students, using the right tools. They also have to have a relevant place on the setting of the picture, for example, they can be part of a painting as decorative item, or be part of the pattern of the costumes, of a lamp. The picture can be in colour or black and white and it has to have a digital format. Assessment criteria Writing of the dramatical scene: - Correct use of the English language. - Range and breadth of vocabulary. - Coherence with the excerpt the scene gives continuity to. - Creativity. Photograph: - Technical quality. The image is clear, not blurry, and itâ&#x20AC;&#x2122;s well focused. - Adequacy of the costumes and the setting to the content of the scene, attention to details. - Use of the geometrical elements and perfection in their design. - Dramatization (the gestures, the facial expressions show the right emotion. Cooperative Learning Technique In order to write the scene, and as a brainstorm of ideas, the â&#x20AC;&#x153;pens in the middle techniqueâ&#x20AC;? will be used. The students discuss what they are going to write. All the members of the group have to contribute with ideas about the following: - The key element that connects the scene they have read and the scene they are going to write. Something that triggers the action again, it can be a new character bursting into the stage, something that happens unexpectedly, for example. - The number of characters that are going to take part (this will depend on the number of members of the group) - What happens and how the scene is going to end. - When and where the action takes place. It can be the same setting or a different one.

Then, they come to an agreement about all these items. They also decide the order of intervention of the different characters, the stage directions to point out the movements of the characters on the stage, if any, or sounds, changes in lighting, etc. and they proceed with the writing of the scene. Finally, the revision and the edition of the text will be carried out by all the members of the group too. For the picture, everyone in the group collaborates with everything, but, one or two members of the group (depending on the groups) will be responsible of each of these parts: - Costumes and atrezzo. - Setting and decoration. - Photographic material and edition of the picture. Manufacture of the geometrical elements. The picture will be handed in together with a report saying who coordinated the parts of the task mentioned before and the opinion of their group mates about the performance of their duties as coordinators. The coordinatorsâ&#x20AC;&#x2122; job will be rated from 1 to 5, being 1 the lowest and 5 the highest mark.

Croatian school The Croatian Excerpt Drivers forever By Miro Gavran27 Characters:

Francek, 48 years old Štefa, his wife, 47 Žaklina, their daughter, 23 Bruna, their neighbour, 46 Nikica, 38 Nena, his wife, 48 Jure, 28 The play is about two friends, Franvek and Nikica, who work as drivers for government Ministers. As soon as they get the job, they and their families start behaving as they were wealthy Ministers themselves: spending too much money, preparing parties, even arranging work positions or doing other favours through acquaintances. Later on, Francek and Nikica enroll in an illegal operation trying to blame everything on Jure, their young colleague. In the meantime, Jure starts a relationship with Žaklina, and she gets pregnant so, in the end, Jure becomes Francek's son-in-law. He forgives him for the hoax and convince him to leave the position of Minister driver so the two of them can start their own transport business. This excerpt is from the beggining of the play and depicts how the characters enjoy the life of luxury. It is interesting, and even funny, how people change when they get their hands on some money. 3rd scene (living room, hosts and guests met to have dinner together) FRANCEK: People, let's raise our glassses. Welcome to our home, I am so glad you are here tonight. Special welcome to our new colleague, Jure. I propose a toast to our young friend and to our old irreparable wives. Cheers! EVERYONE: Cheers! NENA: Listen, we might be old, but we aren't irreparable. You are wrong there. FRANCEK: What do you mean?

An excerpt from the play Drivers forever, by Miro Gavran english version by Ivana Rako Vuksan

NENA: I was at doctor Glumicic's yesterday. The plastic surgeon. I arranged everything. When you see me in two months – you won't recognize me. ŠTEFA: Are you really going to plastic surgery? Come on. ŽAKLINA: Tell us all, aunt Nena. What are you having? FRANCEK: I would never do it, It' s dangerous and against the nature. NENA: Well, listen, in the west it is normal for every woman after they turn twenty to fix their teeth, chin, nose, waist, double chin and thighs. Only those who don't have money oppose it. FRANCEK: Either way, I am against it. Nikice, how did you let her do it? NIKICA: You think she asked? ŠTEFA: Come on guys, don't interrup her. Tell us Nena, what procedures have you arranged? NENA: Everything. Global correction. ŽAKLINA: So called overall. NENA: I am having face lifting, eyelids correction… ŽAKLINA: What correction? NENA: Eyelids correction, I have to do it, look at my eyelids! FRANCEK: Come on. NENA: You should do the same with yours. FRANCEK: Hmm. NENA: Then, the lip correction. FRANCEK: What is wrong with your lips? NENA: They aren't pursed enough. It can be fixed easily with a little implant. Then liposuction – here, on my thighs. So I get rid of my fat. NIKICA: But you have no cellulite. NENA: Then, buttock correction. FRANCEK: What does that mean? NENA: There is a little surgery for lifting butts, get it? I have to take care of my stomack and my butt. And those stretch marks after my second childbirth. NIKICA: Oh, I'm going to throw up. Stop talking about it. FRANCEK: man, you won't recognize her after all those corrections. She'll look like Michael Jackson. Maybe she'll find even younger boyfriend. ŠTEFA: You can tease your wives. You like us attractive but you are too cheap to invest in our looks. Hej, how much does everything cost? NENA: Nothing. Forty thousand. FRANCEK: Kunas? NIKICA: Euros, my friend. Forty thousand euros. ŠTEFA: Tell us more about it.

FRANCEK: Do we really have to listen to it? ŠTEFA: No, you don't. But, we want to hear it. That's why we're going to Žaklina's room, and you stay here and talk about football.We'll have dinner in half an hour – ok? FRANCEK: Great. NIKICA: I am sick and tired of hearing about those plastic nonsense. NENA: Ok, let's go to Žaklina's room. ŽAKLINA: Come, Nena and tell us everything, in details. NENA: Ok, girls. (Ladies go to Žaklina's room. Men are alone.) FRANCEK: Are you seriously letting her do that? NIKICA: What can I do? She stucks on it. I think it is menopause. I oppose everything. FRANCEK: If your wife does it – mine will want it too, I'm positive. I saw her little eyes sparkle when Glumičić was mentioned. NIKICA: Hmm, it is the way it is nowadays. We are distinguished people. Our wives must look perfect. Jure must be annoyed with all this. You don't get them either, do you? JURE: Aaa, no… I would never do it – but women care about their appearance a lot. And we, the men, are to blame. FRANCEK + NIKICA: Why is that? JURE: Because we created the male civilization which emphasizes the importance of female beauty.For centuries – even the artists, painters and poets stress appearance as the most important aspect. Nobody mentions the richness of women's soul. Get it? NIKICA: Well… They like it too. And, you see her first and after that you meet her soul. FRANCEK: That's right. JURE: I'm just saying, it is our fault. And now, when the plastic surgery appeared, women see it as the solution of all their problems – prolonging their youth and staying interesting to their partners and the neighbourhood. FRANCEK: I don't like it at all. (Silence.) FRANCEK: However, let's propose the deal to Jure, while the ladies aren't here.

French school The French Excerpt Christmas Eve At The Police Station By Jean-Pierre Martinez28 Synopsis: During Christmas eve, three police officers are on guard duty and the only people at the police station are a few lonely people they arrested. Then, the Minister of the Interior arrives at this police station to pay tribute to the devoted police officers. Obviousy, nothing is going to happen as planned... Characters: Police Captain Cop 1 Cop 2 Cop 3 Chief of Staff Collaborator Tramp Mythomaniac Drag Queen Paranoaic Characters in this scene: cop 1, cop 2, cop 3 (man or woman, gay style) and Mister Dumortier (collaborator) Setting: A creepy office in a very old police station. In a corner, a pathetic christmas tree supposed to give a happy note to this creepy atmosphere, which looks like a bad crime series. Two scruffy cops, both holding a gun in a holster, are playing cards at a desk. Cop 3 arrives followed by a man. He's carrying a bottle. Cop1: Shit, no, not him... Cop 2: Good evening, Mister Dumortier, how are you? Collaborator: Good evening, good evening... I'm stopping by just to wish you a merry Christmas. I don't bother you, do I? 28

Christmas eve at the police station, excerpt from a play by Jean-Pierre Martinez, English version by Muriel Martin

Cop 1: Well you never bother us, Mister Dumortier..... We were talking about you.... Actually, we were talking about rats in general.... Cop 2: We are fortunate to have watchful citizens like you who are willing to help the police in its noble mission. Cop 3: If there were more people like you Mister Dumortier, I'm sure, our city wouldn't have to invest in a video surveillance system. Cop 2: So, Mister Dumortier, who are you going to rat on today? An alleged polygamist? A welfare cheater? An undocumented orphan? Collaborator: Just a friendly call. I'm just coming as a neighbour to pay tribute to our local devoted police, whose great leader is yourself. Cop 1: Well, as far as I can see, you haven't come empty-handed.... Collaborator: I know what it's like to spend a lonely Christmas, far from one's family, mine doesn't want to see me any-more. So, if I can give some solace to the soldiers who are protecting our country from the dangers lurking from the inside.... Taste it, and tell me what you think about it.... He puts his bottle on a desk. Cop 1: Tell me, it's home-made, isn't it? The label is hand-written like on Bonne Maman jam jars. Cop 2 (reading over his shoulder): Chestnut alcohol... Cop 3: I didn't know it was possible to make alcohol from chestnuts... Collaborator: We can make alcohol from anything, you know. During the war, my grandfather used to make alcohol with potato peels and old leather soles. Cop 3: Oh my god, 53 degrees... It must be good... As an antiseptic I mean. Collaborator: I inherited some bottles from granddad before he was shot at the Liberation. You weren't even born when it was distilled... Cop 2: You do know that it's striclty forbidden to make alcohol at home, Mister Dumortier. We could put you under arrest because you didn't comply with the rule about alcohols.... Dumortier seems to be worried. Cop 3: My colleague is joking, you know... Cop 1: Anyway, the statute of limitations has expired, hasn't it? Unfortunately, we won't be able to toast with you. You know: never when we are on guard duty! Collaborator: Then, you will drink it on New Year's Day. If you are not on duty again, of course... Well, I must go.... You may have a lot of people to arrest and put to prison. Cop 3: Indeed, at Christmas eve, right here, it's like being at the theater. It's always full. I escort you to the door, Mister Dumortier?

Collaborator: I already know the way, but anyway... Cop 2: You are almost at home, aren't you? Cop 1: Thanks for the bottle. Dumortier is ready to leave but he changes his mind. Collaborator: I take advantage to inform you that the guy next door hasn't bought his breathalyzer yet. Do you want his license plate? Cop 2: We are quite busy at the moment of this holiday period and moreover we haven't got enough colleagues on guard duty. So, what about coming back for a New Year's gift! Collaborator: Of course, I will. Have a nice evening then... The man leaves, followed by Cop 3. Cop 1: After that, we are going to think that people don't like the police... Cop 2: That's true. We're always complaining because people don't like us and yet... We can't help thinking it's a little bit weird, to like the police that much I mean. Cop 1: We were wise enough not to drink with him, he would have been pleased to rat us on to the Inspectors of our Police, for drinking at work. He uncorks the bottle, as the other cop takes 2 glasses out of a cupboard, then he fills them. They give a toast. Cop 1: Well., er ... Merry Christmas. Cop 2: Yes indeed, Merry Christmas to you too. They drink their glasses in one sip. Cop 1: Not bad... Cop 2: 53 degrees. Cop 1: That's really strong. Cop 2: We will have to ask him for its composition. Cop 1: Yep, there are not only plums in this. Cop 2: He said it was chestnut... (a moment) I wonder whether his grandfather didn't use to add some Destop to enhance the taste of the fruit. Cop 1: Can you believe it. This liquor is older than us... Cop 2: Maybe, his granddad used to make it in his cellar during the curfew with whatever he could find. Cop 1: His own way to stand up to the occupying forces. Cop 2: Well, pour us some more. At least, the krauts won't get this one... The other cop fills the 2 glasses again, which they drink in one sip. Cop 1: I don't know if there is some Destop in it, but it's true it unblocks our pipes.

Spanish school The Spanish Excerpt Pic- Nic by Fernando Arrabal29

Picnic or Picnic on the Battlefield is a play written by Fernando Arrabal in 1947 and it was performed for the first time in 1952. It is a clear denouncement of war. Even nowadays it’s being performed all over the world, “to show the absurdity of deaf war”, according to Arrabal. SYNOPSIS: The play tells in an absurd way, how a married couple decides to go to the battlefield in order to visit their son, a soldier, and offer him to have a picnic in the middle of the battle. Later on, an enemy soldier gets there and he joins the picnic. Then, they start to talk about the war, concluding that none of them wants to be there and they try to find solutions to end up with this absurd war. They feel very happy about their ideas about how to put the war to an end and having the intention of going back home, but … [The selected extracts belong to the beginning and the end of the play and they are connected so that they make up a synthesis of the original text] CHARACTERS: ZAPO MISTER TEPÁN MISTRESS TEPÁN ZEPO Set: Battlefield. There is a wire fence from one side of the stage to the other. Nest to this wire fence there are some sand bags. (The battle is all the rage. Gunfire, explosions, bursts of machine gun can be heard. ZAPO, alone on the stage, is tuck among the bags. He’s really scared. The combat stops. Silence. ZAPO takes some wool an a pair of knitting needles

An excerpt from the play Pic-Nic, by Fernando Arrabal. English version by Gema Hernández López and María de la Piedad Gracia Santolaria

out of a basket. He begins knitting a jersey, which is already quite advanced. Suddenly, the campaign phone that is next to ZAPO starts ringing.) ZAPO.- Hello?... Hello? …At your command, captain … Certainly, I’m the sentinel of the 47 high point …All quiet at the front, captain … Excuse me, captain, when does the next battle begin?... What about the bombs? When shall I throw them?... And, where shall I throw them on? Forwards or backwards? … But, don’t get mad at me. I’m not saying this to bother you … Captain, I feel so lonely. Couldn’t you send me a comrade? Even the goat would help… (The captain tells him off) At your command … At your command, captain. (ZAPO hangs up the phone. He grumbles.) (Silence. Mr and Mrs TEPÁN come on the stage. They’re carrying some baskets, as if they were going to spend a day in the country. They talk to their son, ZAPO, who is hiding among the bags and with his back to them, doesn’t see what’s going on) MR. TEPÁN.- (Ceremoniously) Son, stand up and kiss your mother on her forehead. (ZAPO, relieved and surprised, stands up and kisses his mother on her forehead showing great respect. He wants to say something but his father interrupts him) And now, kiss me. (He kisses his father on his forehead.) ZAPO.- But daddy, mummy, why have you taken the risk of coming here, to such a dangerous place? You must go immediately. MR. TEPÁN.- Do you, by any chance, want to teach your father a lesson about wars and dangers? This is just a pastime for me. Without going any further, I have stepped out of the underground many, many times when it was on the move. MRS. TEPÁN.- We have thought you would be bored, this is why we have come to see you. So much war must be very boring. ZAPO.- That depends. MR. TEPÁN.- I know perfectly well what’s going on. At the beginning you enjoy it because it’s something new. Killing and throwing bombs and wearing a helmet, which makes you look so elegant, it’s nice, but, in the end, it will annoy you. ZAPO.- I’m so sorry. You’ve got to go. It’s not allowed to come to war unless you are a soldier. MR. TEPÁN.- I don’t give a dam. We are not here in the front to make war. We just want to have a picnic with you making the most of the Sunday.

MRS. TEPÁN.- Precisely, I have prepared a really good meal. I’ve made a Spanish omelette, which you love so much, some ham sandwiches, red wine, a salad and cakes. ZAPO.- Fine, whatever, but if the captain comes, I’ll say I didn’t know anything. He’ll get really angry, you’ll see. He doesn’t like at all people paying visits in the middle of the war. MR. TEPÁN.- Don’t worry, I’ll tell him just a couple of things to that captain. MRS. TEPÁN.- Well, let’s have our lunch. MR. TEPÁN.- Yes, let’s do it, I’m so hungry. That smell of gunpowder whets my appetite. MRS. TEPÁN.- We can eat right here, sitting on the blanket. ZAPO.- Shall I keep my rifle with me while I’m eating? MR. TEPÁN.-No rifles here. It’s really bad-mannered sitting by the table with a rifle. (Pause) But you’re so dirty, my son … How did you get like that? Show me your hands ZAPO.- (Ashamed, he shows his hands) I’ve had to crawl on the ground because of the manoeuvres. MRS. TEPAN: Well, you may come in ZAPO.- Yes, mum (They start eating) MRS. TEPAN.- Well, my son, have you killed much? ZAPO.- When? MRS. TEPAN.- These days ZAPO.- Where? MRS. TEPAN.- In this war. ZAPO.- Not much. I’ve killed a little. Almost nothing. MRS. TEPAN.- I’ll play a record . (She puts a record in the gramophone. The three of them, sitting on the floor, listen) MR. TEPAN.- This is music, oh yes. (The music goes on playing. An enemy soldier enters: ZEPO. He is dressed like ZAPO. The only difference is the colour of the suit, ZEPO’s is green and ZAPO’s is grey. ZEPO, ecstatic, listens to the music giving his back to the TEPAN family. The music ends. When standing up, ZAPO discovers ZEPO. They both raise their hands in terror. Mr. and Mrs. TERAN look at them in surprise.) MR. TEPAN.- What’s the matter? (ZAPO reacts. He doubts. Finally, he points at ZEPO with his rifle.) ZAPO.- Hands up! (He ties his hands and feet) ZAPO.- Well, what shall we do with the prisoner?

MRS. TEPAN.- We can invite him for lunch. What do you think? MR. TEPAN.- It is all right with me ZAPO (to ZEPO).- So what? Would you like to have lunch with us? ZEPO.- Well… MR. TEPAN.- We have brought some good red wine ZEPO.- Then, all right. MR. TEPAN.- You just make yourself at home. You can order whatever you want ZEPO.- All right MR. TEPAN.- Well, then, what about you? Have you killed much? ZEPO.- When? MR. TEPAN.- These days ZEPO.- Where? MR. TEPAN In this war. ZEPO.- Not much. I’ve killed a little. Almost nothing. MRS. TEPAN (to ZEPO).- If you want, we can untie you. ZEPO.- No, it is all right, I am fine. MR. TEPAN.- Do not be shy with us. If you want to be untied, please tell us. MRS. TEPAN.- Just make yourself comfortable. ZEPO.- Well, if you insist, you can untie me. But just to please you. MR. TEPAN.- Son, untie him. (ZAPO) unties him.) MRS. TEPAN.- This is fantastic! Mr. prisoner is so nice we are going to have a great day in the country. ZEPO.- You do not have to call me “Mr. prisoner”, just “prisoner” MRS. TEPAN.- Won’t you mind? ZEPO.- Not at all MR. TEPAN.- Indeed, we must admit that you are a very modest man MRS. TEPAN.- This is the best thing about going out to the country on a Sunday. You always meet nice people (Pause) And you, why are you an enemy? ZEPO.- I do not know of those things. I am not a very cultivated man. MR. TEPAN.- Then we can do something: stop the war ZEPO.- How? MR. TEPAN.- It is very easy. You tell all the soldiers in our army that the enemy soldiers do not want to make war and you tell your friends the same. And everybody can go back home. ZAPO.- Wonderful!! ZAPO.- How come we did not think of something like this before, to end with this war stuff?

ZEPO.- Listen, if we stop the war, what will happen with the generals and the corporals? MRS. TEPAN.- We will give them some of their arms to keep them quiet. ZEPO.- Very good idea MRS. TEPAN.- You see, Everything is fixed ZEPO.- It will be a great success ZAPO.- How happy my friends will be! MRS. TEPAN.- How about dancing a pasodoble to celebrate? ZEPO.- Good idea ZAPO Yes, mum, play it again ( Mrs. TEPAN plays the record. Expectation. Nothing is heard) MR. TEPAN.- We cannot hear anything MRS. TEPAN.- ( Goes to the gramophone) Oh, I have made a mistake. Instead of a record, I had placed a beret.

Swedish school The Swedish play Beyond the riot by Johanna Emanuelsson30 Contextualization It is early morning and the lively big city starts to wake. The fruit stands are being built up, the low paid employees at the hamburger place are heating up the frying oil, the decision makers are opening the board meeting. Some of the citizens are dissatisfied with the conditions, others are very pleased, most of them continue in a rut. But this is not an ordinary day. Today alarming reports are starting to appear. Today everything will reach a critical point. Today the riot will come. Nobody knows how it all started or if there’s someone behind it, or how it will end. But one by one they are forced to take a stand. Do they really want everything to change? SCENE 33. By the fruit stand at the larger square Suddenly the square is starting to get crowded, Maurits is coming back. Moritz: Oh, what a lot of people! And my son is back! Do you see my son, now the customers are coming too! Didn’t you find the woman? Maurits: Shut up! Stop staring! Start selling! Moritz can’t stop looking at the huge crowd of people that is gathering at the square. Moritz: Guess who I am? Maurits: Can you stop with your stupid riddles, I’m telling you to start selling! What is it that you don’t get? We haven’t sold a frickin’ fruit all day and now, when the sun is setting, a lot of people are coming, and you’re just standing there staring? Sell fruit for God’s sake! Moritz: What did she say? Maurits: What? Moritz: The woman, the ordinary woman? What did she say? Everything is in constant change, isn’t it? Maurits: Can you stop talking in riddles? Moritz: Everything is in constant change… I’m a grown up. Maurits: So? Moritz: Yes I am, I’m a grown up. 30

Beyond the riot, play by Johanna Emanuelsson. English version by Martina Andreasson

Maurits: And what do you mean by that? Moritz: That I do what I want. Look, those are people who do what they want, aren’t they? They do exactly what they want to do. And they don’t want more. That’s exactly what they want to do, nothing more, and that’s exactly what they are doing. Maurits: What are you talking about? Moritz: I don’t exist. I’m invisible. Ever since you were little I’ve just been a faceless father, you have always been bossing me around. ‘Do that, do that, do that!’ You always decide everything, always, always. ‘Read a book to me dad, give me a hug dad, give me 300 bucks dad, shut up at the parent meeting dad, I will hit you if you don’t help me buy a car dad, ever since mum died you have been a worthless dad’. I don’t exist! Maurits: Now you’re exaggerating a bit, aren’t you? Moritz: There is a limit for everyone. There is. Even for the limitless. There is a limit for how much a man is able to take, then it’s enough. It’s enough. Sell your own bananas! Moritz leave the fruit stand. Maurits: Where are you going?! Moritz: find happiness! With big eyes, Maurits is watching his father leave. SCENE 35. At the hamburger place Evin and Mirja have armed themselves with spatulas and oven mittens. Rojda stands paralyzed on the greasy floor. Evin: Are you not going to arm yourself Rojda? Here, take a potato masher! Rojda stays put. Suddenly, someone knocks on the glass door. Mirja: Shall I open? Evin: No! Evin goes to open the door. Evin: What? Li sneeks in. Evin: we’re closed! Mirja: It’s not open today! Evin: Get out! Li: There’ something going on out here! Haven’t you noticed? Evin: Of course we have noticed! What do you want? Li: I had a dream. Mirja: and?

Li: It was a dream that told me that if a qualitative change shall take place, the quantitative change has to cross a critical point. It’s the dialectics of nature. Evin and Mirja look at each other. Li: Sorry, I was just about to break up with my girlfriend, I was finally going to have the courage to leave her and then I do it and feel totally euphoric and scared at the same time and I leave that café and on the street this is what I run into! Li looks around at what is now a rather messy hamburger place. Mirja: We’re about to get organized here. Evin: yeah, exactly. Li: Get organized? Suddenly there is another knock on the glass door. Evin opens. Evin: What is it this time?! Elfriede sneeks in. Elfriede: I saw that there are some people in here. I didn’t really know where to go. I was going to write a play and then… you know…so it felt kind of meaningless in the middle of all this… Mirja: Welcome. Elfriede: There are things going on outside. Evin: You don’t say... Take a spatula. Evin handles over a spatula to Elfriede. Elfriede: Thanks. Outside the hamburger place more and more people are gathering. Mirja: We have some more spatulas if you want some. Evin: And maybe we can use some of the bigger saucepans as helmets too? Rojda who has been quiet for a long time suddenly bursts out: BUT FOR HEAVEN*S SAKE! Get real! Evin: What? Rojda: get real! It’s time to put out the evening menus. Mirja: Now?! Rojda: It’s time to work! What exactly do you think is going on out there? Not a thing! Come on! We’re going to work! Mirja: Work? Li: You’re not going out? Elfriede: Are we not going to join? Rojda: Join what?! Elfriede: The riot! Rojda: It’s a hamburger line!

Evin: It’s a riot! Rojda: No! We’re going to work! We’re going to fry burgers! Mirja: It’s time! Don’t you get that? It’s time, Rojda. Rojda: I’m the work manager here, aren’t I?! I’m the one who gives orders here! Mirja: But we’re not going to work anymore Evin: We’re going to riot. Rojda: You can’t be sure on anything yet! It could be anything going on out there! Li: It’s a whole lot of people anyway…? Rojda: But forget about them! Evin: What do you mean ‘forget about them’? Mirja: What’s wrong with you?! Rojda: Nothing?! I’m just trying to fix this extraordinary situation! Evin: Are you going to chicken out? (are you afraid) Elfriede: Come on! Rojda: ah, you can’t just…What the…?! Evin: I’m going out now anyway! Mirja: Me too! Elfriede: Me too! Li: What if it’s dangerous? Mirja, Evin and Elfriede grab some hamburger stuff that they think can be used as weapons. Evin: Are you coming or not? Rojda: Stop this nonsense now, you guys?! Mirja: We don’t have time to stand here and argue about it! Evin: Let’s go! Li: Ok, wait for me! Evin, Mirja, Li and Elfriede leave the hamburger place. Rojda: Hey! Wait! Stop! You can’t just…hey! Rojda stands still, looking with big eyes on her leaving friends. SCENE 36. In the very stuffy board room There is almost no oxygen left around the conference table. The sound from a screaming crowd is drowning the thoughts of the decision makers.

Task 6 Making of a Short Film The students, in groups, will make a short film which will be a remake of a scene from a contemporary film. The film will be about 5 minutes long. Process of execution. The students will work in groups. Each group will be assigned a scene of a film. The scene will be in its original version language with English subtitles and will be about five minutes long. 1. Once the students have seen the clip, they will write the literary part of the film script, by following these steps: a) Agreement on the main idea, the core of the scene. b) Development of the main idea: they will write a synopsis, a very short summary of the scene. Example of synopsis: A teenage boy accidentally travels 30 years into the past where he inadvertently interferes with his mother and father’s first meeting. While trying to find a way back to the future, he must try to make his mismatched parents fall in love or he will never be born. a) Making of the narrative part of the script: the description of the atmosphere and the characters that take part in the scene in a very concise way. Taking into account that each member of the group has to perform one of the characters that appear on the scene, they can adapt it to their own needs, this means they can add or take out one or more characters or change their gender if necessary. They also have to assign the characters. Example of the narrative part of the script: The scene takes place in the sitting-room of John’s house. Characters: John, 24-year-old blogger and youtuber, he’s a kind man. He’s in love with Helen. Helen, mysterious young woman. She has an affair with John, but she’s hiding something. Mark, John’s friend, he’s been acting weird lately. Mrs. Spencer, Helen’s boss. A determined woman who doesn’t like when people oppose her. a) Writing of the shooting script. It will include the type of shots and angles, the

dialogues and the stage directions about the mood of the dialogue. It will contain other technical details such as sounds, music, etc. It will be one page or one and a half pages long. Format of the script including all the sections. 2. Next, the students will agree on the location of the setting, the costumes, Shot

Dialogue

Image

Music/sounds/tone of voice John with a pitiful voice, Helen, angry and sad.

John: “Please, don’t Close up of both go!” characters. Helen: “Leave me Angle at eye alone! I don’t trust level. you anymore” atrezzo, etc. The decoration will include the following geometrical elements: The students will make 6 to 8 patterns of a continuous curve (called LINK) by connecting tangent circumference arcs.

These patterns will be made on cardboard or acetate. Then, the links will be cut out and used as templates. These templates will be used to make an abstract artwork out of linked curves that will be coloured the way they like.

The students will use it as part of the decoration.

They will rehearse according to their needs. 3. After that, the students will record the scene. - Before that, they have to agree on how many takes there are going to be, there should be at least 5 takes, and on which shots will be recorded at each take. - It’s advisable to keep the format of the original scene. In order to do so, they will keep in mind the shots according to their framing: close ups, mid shots, wide shots, etc. or according to the angle: eye level, low or high angle, bird’s eye, etc. 4. Finally, they will edit the short film. They will put the different sequences they have recorded in the right order; they will add the opening and closing credits with the names of the participants, the title of the film and all the information they want. If they decided not to live record the dialogues, then they can be added during the editing process. The music can be the same as in the original scene, if there was any, or it can be music created by the students, using the Music Maker Jam, for example. Both the title credits and the music have to go with the narrative style. 5. In order to “get their film known”, the students will have to make a film poster, which will help to catch people’s attention and communicate, with just a glance, the essence and the mood of the film. Poster requirements: - Size: A3 - Content (title, members of the group and slogan) - Geometrical elements (all or some of those that have been used for the setting) - It can be made by hand (free technique) or using an online tool (https://www.canva.com/create/posters/ for example) or computer programme. In order to design the poster for their film, the students will follow these steps: 1. Each member of the group will make a draft, A4 paper size, with the minimum content: title, slogan, etc. If they have used an online programme, they can print them or show them to their group mates. 2. They will discuss the different drafts and select the parts that they like best one by one (they will decide which title is the best, which slogan they like most, etc.) 3. They will make the poster. 4. They will have to hand out/send the final poster and all the drafts.

Cooperative Learning Technique In order to write the drama scene, the “pens-in-the-middle” technique will be used for the brainstorming of ideas part. First, they will have to decide what they are going to write about. Each and every member of the group has to contribute ideas for the: 1. Main idea, the core of the sequence. 2. The characters that take part in the sequence. 3. Development of the main idea: - Beginning. - Climax. - Closing. 4. Contribution of every character to the development of the story. Then, they will have to agree on each of these points and they will write the synopsis and the narrative part of the script After that, they will write the dialogues, including the stage directions with the mood of the dialogue. The writing of the synopsis, the script with all the parts required and the dialogues have to be written by the whole group. To carry out the recording of the scene, all the members of the group will work together on everything and contribute equally, but there will be a coordinator for each of the following parts: - Costumes and atrezzo. - Setting and decoration. - Recording and editing equipment (camera, digital programme, etc.). - Geometrical elements. The students will write a report with the names of the coordinators of the different parts mentioned before and an assessment about how they have carried out their duties, grading their performance as coordinators from 1 to 5, with 1 being the lowest and 5 the highest. For example: Juana, recording and editing equipment: 4 points. In the end, each group’s products must be the technical script, the short film and the film poster.

Croatian school The Crotian film scene belongs to Hrvoje Hribar’s 2005 film “What Is a Man Without a Moustache?”. Time frame: 26:12- 34:13.

French school The French film scene belongs to Patrick Leconte’s 1979 film “Les Bronzés font du ski”. Time frame: 1:10:56 – 1:14:21

Spanish school The Spanish film scene belongs to Pedro Almodóvar’s 1988 film “Mujeres al borde de un ataque de nervios”. Time frame: 01:01:37- 01:10:13.

Swedish school The Swedish film scene belongs to Felix Herngrens 2013 film “Hundraåringen som klev ut genom fönstret och försvann”/ ”The hundred year old who climbed out of the window and disappeared” Time frame: 1:13:00 – 1:16:30

Cooperative Learning Techniques In order to carry this task out it should be used the jigsaw technique. First, each member of the group will be assigned a part of the task. Once all the members of the group have finished their part, they have to share the information. The members of the group in charge of the parts that involve mathematical operations will explain the others the steps they have followed to find the solution or answer to the problem or question proposed. This way, although each student has been working on just one of the parts, when they share the information and the results, all of them acquire some knowledge about the parts that they havenâ&#x20AC;&#x2122;t been working on. Finally, the students make the puzzle, they put together the different parts according to the teacherâ&#x20AC;&#x2122;s instructions about how to do it. This activity has been designed to be part of an oral exhibition recorded on a video. Maths elements indeks 1.

2. 3. 4. 5. 6. 7. 8.

Tasks in Croatian Zadatak 1 Cooperative Learning Techniques Tehnika slagalice. Indeks matematičkih elemenata 1.

2. 3. 4. 5. 6. 7. 8.

Položaji dvaju ili više pravaca Koncept poligon. Razvrstavanje poligona prema broju stranica Koncept mozaik. Izračun površine geometrijskih likova Koncept poliedar Poliedarski prikaz dviju zgrada Izračun volumena tih zgrada

Uvod Potraga za matematičkim objašnjenjima prirode i svemira oduvijek je zaokupljala matematičare, ali i umjetnike koji su vjerovali da jedino na taj način mogu stvoriti idealnu ljepotu, odnosno savršeno skladno umjetničko djelo. Stari Egipćani otkrili su „zlatni rez“, tzv. Božansku proporciju, kojeg i danas smatramo savršenim razmjerom u prirodi, Zlatni rez dobivamo tako da dužinu podijelimo na 13 dijelova, a njih zatim podijelimo u dnosu 8 : 5, što iznosi oko 1.618. Tako dobivamo razmjer u kojem se manja veličina odnosi prema većoj kao veća prema cjelini, odnosno a : b = b :( a + b ) . Vezu umjetnosti i matematike prikazat ćemo na sljedećim umjetničkim djelima: Zobnica, Dioklecijanova palača i slika Ivana Picelja: Iz mape Ulmske varijacije.

Uporabni predmet: Zovnica31 1. Napišite kratku povijest predmeta i saznajte gdje se koristio. 2. Koji geometrijski likovi su korišteni u izradi zobnice? 3. Ako je dužina zobnice ? cm, a širina ? cm, izračunajte ukupnu površinu materijala potrebnog za izradu zobnice. Linkovi na kojima možete pronaći odgovore na ta pitanja. https://hr.wikipedia.org/wiki/Pravokutnik https://www.mathsisfun.com/geometry/

Građevina: Tlocrt Dioklecianove palače 32 1. Napišite kratku povijest Dioklecijanove palače 2. Istražite koje likove sadržava tlocrt, koji likovi se ponavljaju? 3. Pronađite primjenu zlatnog reza unutar palače. 4. Istražite poveznicu Dioklecijanove palače i radionica ovčjih tkanja ( ?? ) Možete pronaći odgovore na ta pitanja na ovim linkovima: http://splitculture.hr/dozivljaj/povijest/dioklecijanova-palaca http://www.visitsplit.com/en/448/diocletian-palace

Tradicionalna vunena ručno tkana (etno) torba Dioklecijanova palača - antička palača u Splitu koju je 300. godine sagradio rimski car Dioklecijan. Palača je na UNESCO-vom popisu mjesta svjetske baštine u Europi. 32

Slika hrvatskog umjetnika Ivana Picelja: Iz mape Ulmske varijacije 33 1.Napišite kratak životopis hrvatskog umjetnika Ivana Picelja, 2. Komentar na sliku sa geometrijskog stajališta: - koji likovi su prisutni na slici? - pronađite usporedne pravce na slici - istražite postoji li zlatni rez unutar slike Možete pronaći odgovore na ta pitanja na ovim linkovima: http://www.galerijadivila.hr/hr/autori/ivan-picelj.html https://en.wikipedia.org/wiki/Ivan_Picelj

Zadatak 2 Planiranje i izvršavanje zadatka Ovaj zadatak izvršit će nekoliko grupa i to u 2 dijela. 1. Dio Prvi dio zadatka sastoji se od pisanja priče inspirirane fotografijom Darka Puharića ili slikom Vasilija Jordana, koje obje sadrže matematičke elemente. Svaka grupa radit će s tri druge grupe tako da se izmijenjuju u pisanu i to tako da će prva grupa napisati uvod, iduća zaplet, treća grupa će nastaviti pisanje vrhunca priče, a posljednja će završiti priču. Prije samog pisanja sudionici moraju razgovarati o umjetničkom djelu koje im je dodjeljeno i odlučiti o čemu će pisati odgovarajući na pitanja: Tko? Što? Kada? Gdje? Budući da priču pišu četiri grupe, one se moraju dogovoriti o sadržaju priče, likovima, mjestu i vremenu radnje i slično. Svaki dio priče treba imati 50 riječi napisanih fontom Arial 14. Koordinator svake grupe zadužen je za pisanje ulomka priče svoje grupe (u pisanju priče moraju sudjelovati svi članovi). 33

Ulmske variacije, slikani sitotisk, 2006

2. Dio Svaka grupa napravit će crtež, kolaž ili fotografiju koja se temelji na jednoj od napisanih priča te mora sadržavati matematičke elemente kao i početna slika koja je inspirirala priču. Rad treba biti na A4 papiru. Ako je fotografija bit će u digitalnom obliku. Kriteriji ocjenjivanja Za priču: • Uporaba jezika • Povezanost i smislenost • Originalnost i kreativnost • Grupni rad Za crtež, kolaž ili fotografiju: • Originalnost i kreativnost • Uporaba matematičkih elemenata • Umjetnički kriterij • Grupni rad Uporaba strategija kooperativnog učenja Prvi dio zadatka uključuje korištenje tehnika pisanja u krug, izdvajanje misli na papir tehnikom olovka u sredini. Za crtež će se koristiti tehnika slagalice. Indeks matematičkih elemenata 1. Kutomjer 2. Horizontalne crte 3. Kvadrat i trokut 4. Položaj dvaju ili više pravaca 5. Kružni sektor 6. Pravokutnici 7. Vanjski prsten

Hrvatski slikar - Vasilije Jordan: Harmica 34 Vasilije Josip Jordan hrvatski je slikar, rođen 1934. godine u Zagrebu. Diplomirao je 1958. na Akademiji u Zagrebu, te je dobitnik mnogih nagrada za slikarstvo. Njegove slike su nadrealne i govore o tajnama i zagonetkama ljudske svakodnevice. Vezan je uz renesansno-baroknu tradiciju, dosljedan u figuraciji, slika tehnikom starih majstora, uglavnom u ulju i temperi, ali je ujedno zaokupljen magičnim svijetom starih fotografija. Jedno od takvih sjećanja na najranije fotografije Zagreba je i ova slika, Harmica, što je staro ime glavnog zagrebačkog trga, na kojoj je vidljiva uravnotežena klasična kompozicija naglašene perspektive. 1999. godine postavljena je kao zastor HNK u Zagrebu.

Hrvatski fotograf - Darko Puharić35 Darko Puharić, hrvatski je fotograf koji je radio na digitalizaciji građe iz fundusa Gradskog muzeja Vinkovci. Na ovoj fotografiji iz 2011. g. nalazi se posuda iz vučedolske kulture (Vučedolski Orion pronađen 1978.g.) , koja se ujedno smatra i najstarjim europskim kalendarom. Na posudi se jasno vide četiri pojasa, od kojih je svaki podijeljen na 12 polja sa znakovima. Četiri pojasa dočaravaju četiri godišnja doba, a polja su vjerojatno tjedni. Svaki znak predstavlja neko zviježđe, raspoređeno prema vremenu kad se pojavljuje na noćnom nebu. To je, dakle, prvi europski kalendar, a nastao je oko 3000. g. prije Krista. Smatra se da su Vučedolci svoje matematičke i astronomske spoznaje bilježili na keramici te da su šahovnice osim kao kalendare koristili i kao tablice množenja. Razumijevanje kalendara i crtanje šahovnica govori o njihovu logičnom shvaćanju budućega Pitagorinog poučka. 34

Vasilije Jordan, Harmica, ulje na platnu

Darko Puharić, Kalendar Orion. Posuda s kalendarom pronađena je 1978. godine u Vinkovcima. Fotografija, Darko Puharić, 2011

Zadatak 3 Ciljevi - Razumijevanje tradicije drugih zemalja upoznavanjem tradicionalnih priča iz zemalja partnera. - Poticanje umjetničkog stvaralaštva, uzimajući u obzir neke matematičke elemente. Konačan proizvod Izrada, na papiru ili digitalnom obliku, stripa i scenarija prema tradicijskim pričama iz zemalja partnera Koraci 1. Svaka grupa studenata će dobiti legendu ili popularnu priču. 2. Učenici prvo trebaju napraviti sažetak priče s dijalozima koji su prilagođeni priči, legendi ili popularnoj priči. 3. Zatim će učenici stvoriti scenarij na najviše dvije stranice (papir A4 format, ili digitalni oblik). Grafički prikaz (strip) priča može se izraditi: - Pomoću programa Pixton, Toondoo, Comic Life Bitstrips ili drugih online alata za izradu stripa - Crtanjem rukom - Izradom kolaža. - Korištenjem bilo kojeg drugog programa ili tehnike. Grafička priča (strip) može imati najviše 12 scena, a mora sadržavati barem pet od sljedećih matematičkih elemenata: 1. Ovalni oblačići (za govor, na primjer). 2. Pravokutnici (za pripovjedačev tekst, na primjer). 3. Krugovi. 4. Koncentričnim krugovima. 5. Simetrija. 6. Oštre kutove. 7. Paralele. 8. Okomica. 63

9. Jednakostraničan trokut. 10. Kvadrat. - Ako je strip je ručno crtan, matematički elementi moraju biti nacrtani pomoću pribora za tehničko crtanje: ravnalo, trokuti, šestar, itd - Učenici uz strip trebaju priložiti popis matematičkih elemenata koje su koristili i u kojoj sceni je korišten pojedini matematički element .. Stripovi koji nisu izrađeni pomoću digitalnih alata moraju biti skenirani. Uporaba strategija kooperativnog učenja Prvi dio zadatka uključuje korištenje tehnika pisanja u krug, izdvajanje misli na papir tehnikom olovka u sredini i konačni sporazum o stripu. Učenici će pisanje scenarija raditi tehnikom pisanja u krug, ovisno o broju scena svaki učenik iz grupe osmislit će nekoliko scena. Za crtanje stripa učenici će koristiti tehniku slagalica. Procjena i Kriteriji ocjenjivanja - Uporaba jezika - Povezanost između stripa i orginalne priče - Originalnost i kreativnost - Uporaba geometrijskih elemenata - Umjetnički kriterij - Grupni rad

Hrvatska Legenda Jezerska vila 36 Legenda kaže da ples vila nad Modrim jezerom počinje za vrijeme punog mjeseca. Nakon što bi ugledali ples prelijepih vila, ljude bi dugo pratili nemirni snovi i čežnja da im se pridruže. Vjeruje se i da će onaj tko zapleše u vilinskom kolu prijeći granicu svijetova -pretvoriti se u vilenjaka. Mnogi su to željeli te je mnogo mladih života izgubljeno u dubinama jezera. 36

Jezerska Vila, legenda iz imotske krajine, prilagodba teksta Anamarija Ivkosic

Jednom davno, za vrijeme prvoga proljetnoga dana jedan je mladić, željan tišine koje pruža smirujući prizor jezera, začuo tih, jedva čujan plač. Misleći da u ranoj zori neće biti nikoga uz jezero, on ugleda prekrasnu djevojku u sjeni borova. Bila je to vila. Tijekom plesa s ostalim vilama nije ni primijetila prikradanje zore te se odjednom zatekla sama na jezeru. Znala je da blještavilo sunca poništava vilinsku čaroliju te da bi je samo jedan dodir sunčeve zrake pretvorio u njegov odsjaj. Napuštena i u strahu, vila se skrivala i nije slutila da ju je mladić ugledao. Međutim, mladić je prepoznao tugu u njenim očima i odlučio joj je pomoći. Zaklonivši ju od sunca, mladić ju je poveo stazama zasjenjenim stablima do pećine koja se nalazila uz jezero. Vila je tu danima boravila iščekujući vrijeme punog mjeseca - vrijeme kada će mjesečina obasjati jezero, a ona će ponovno zaplesati kolo s ostalim vilama i tako se vratiti u svoj svijet. Međutim, mladić se zaljubio u vilu i razmišljao je kako će učiniti sve kako bi postao dio njezinog svijeta. Čekao je puni mjesec znajući da se čovjek može pretvoriti u vilenjaka ako zapleše u vilinskom kolu. Jedne noći, dok je vila još spavala, mladić je ugledao kako mjesečina obasjava jezero te kako se voda uzburkala. Potrčao je prema jezeru nadajući se da će se tu noć njegov san ostvariti – da će postati vilenjak. Međutim, u brzini se spotaknuo i upao u jezero te nestao u dubini virova koji su uzburkali vodu. Nijedna vila nije ništa primijetila. Ubrzo se kolo zavrtilo, pjesma je započela, a još sanjiva vila pošla je prema jezeru. Bila je sretna ugledavši svoje sestre vile, ali je pogledom nestrpljivo tražila mladića. Međutim, tamni oblaci prekrili su nebo te je nestalo mjesečine nad površinom jezera. Tako nestade i vilinskog kola, a ona vila ponovno ostade sama. Potpuno slomljenog srca vila je još dugo čekala, ali mladića više nitko nije vidio. Dok neki misle da je vila zauvijek ostala u mraku Vilinske pećine, drugi vjeruju da se prepustila prvim zrakama sunca da je dotaknu. Ipak, priča o njihovoj ljubavi još uvijek živi u mnogim sjećanjima.

Zadatak 4 Multimedijska obrada pjesme Učenici će na Twinspace-u razmijeniti informacije o izvođačima modernih pjesama u njihovoj zemlji. Nakon razgovora u upoznavanja popularne glazbe zemalja partnera, učenici će po grupama (grupe će se formirati kao i kod zadatka „Priče inspirirane slikama “ ) napraviti playlistu na web stranicama kao što su Spotify, Amazon Music, Project Playlist, Stracks, Plurn, YouTube i Webjay. Ove stranice omogućuju kategoriziranje, uređivanje i slušanje liste online. Playlista mora sadržavati po pet pjesama iz svake zemlje. Svaka grupa će morati napisati naziv i izvođača pjesme, iz koje je zemlje, kad je puštena u eter, kratki opis o bendu ili izvođaču pjesme, žanr, tekst pjesme, navesti instrumente koji izvode glazbu te napisati o čemu pjesma govori. Nakon prvog dijela, učenici se dijele u grupe. Učenici će morati napraviti multimedijsku obradu pjesme stranog autora, kombinirajuči slike, glazbu i recitaciju pjesme na izvornom i na engleskom jeziku. Slike moraju sadržavati matematiče elemente kao što su spirala. simetrija te standardne artimetičke slike ili skulpture ( slično kao Piceljeve slike) koje će nekako pridonijeti razumjevanju pjesme. Postupak: 1. Svaka grupa će dobiti pjesme drugih zemalja partnera koja mora biti na izvornom materinjem i na engleskom jeziku. (svaka zemlja šalje po dvije pjesme) 2. Konačni video ne smije bit duži od 3 minute, a mora sadržavati: A) recitaciju pjesme na materinjem i na engleskom jeziku, poredane jedna iza druge ili drugačije uklopljene( jedna rečenica na materinjem pa jedna na engleskom i sl.) PAŽNJA! Da bi učenici razmijenili recitacije pjesme, moraju kontaktirati jedni druge preko Twinspace-a. Učenici će snimiti recitaciju pjesme (koristeći npr. Audacity) i poslati učeniku koji ga je kontaktirao. Recitaciju na engleskom jeziku snimaju svi učenici iz grupe ( mogu snimati dio po dio, ne moraju svi sve)

B) slike, izvorne ili obrađene moraju sadržavati matematičke elemente kao što su spirala, simetrija i standardne artimetičke slike i moraju pridonijeti boljem razumijevanju pjesme C) glazba koja će naglasiti emocije i osjećaje koje se izražavaju u tekstu ( kao glazbu u pozadini može se izabrati jedna od pjesama s playliste) Po tri videa iz svake zemlje partnera će biti objavljeni na blogu. Procjena i Kriteriji ocjenjivanja Za procjenu zadatka sljedeći kriteriji će se uzeti u obzir: -recitacija na materinjem jeziku (dikcija, ritam) -recitacija na engleskom jeziku (izgovor, intonacija, ritam) -adaptacija glazbe, slika i matematičkih elemenata do sadržaja pjesme -kvaliteta slike i zvuka Tehnika kooperativnog učenja 1. Bira se po jedan učenik koji će biti odgovoran za pojedini dio zadatka. Zatim se određuju rokovi za pojedini dijelove zadatka. Dijelovi su: 1. Pronaći učenika na TwinSpace-u koji će snimiti i poslati recitaciju na materinjem jeziku 2. Skupiti slike koje će se koristiti u videu 3. Izabrati najprikladnije slike koje sadrže matematičke elemente i odrediti njihov redoslijed za video 4. Recitacija i snimanje pjesme na engleskom jeziku 5. Biranje glazbe za video 6. Uređivanje videa 2. Svi učenici u grupi moraju sudjelovati na zadatku dok učenik koji je odgovoran za svoj dio zadatka mora provjeravati da li svi jednako sudjeluju i jesu li izvršili svoj zadatak na vrijeme. 1. Svi učenici moraju kontaktirati drugog učenika na TwinSpace-u i zamoliti da mu se snimi i pošalje recitacija na materinjem jeziku. 2. Svi učenici skupljaju slike koje sadržavaju matematičke elemente.

3. Svi učenici sudjeluju u recitaciji pjesme. 4. Svi učenici biraju glazbu koja će se snima uz video. 3. Učenici rade u grupama, iznose svoje prijedloge i zajedno odlučuju: 1. koja je najbolja recitacija na materinjem jeziku 2. svi učenici sudjeluju u biranju glazbe, slika te njihova redoslijeda za video 3. obično jedan učenik uređuje video na računalu, kao što je slučaj i s recitacijom i njenim snimanjem, ali svi učenici moraju pridonijeti i ovom dijelu zadatka. Indeks matematičkih elemenata 1. Spirale 2. Simetrije 3. Slike ili skulpture modularne aritmetike

Hrvatska pjesma Jure Kaštelan: Volio bih da me voliš Volio bih da me voliš, da budem cvijet u tvojoj kosi, Ako si noć, ja ću biti zora i blijesak svjetlosti u rosi. Volio bih da me voliš i da svi dani budu pjesma. Ako si izvor, i ja ću biti u živoj stijeni bistra česma.

Volio bih da me voliš, stihovi Jure Kaštelana.

Zadatak 5 Čitanje suvremenih dramskih tekstova i pisanje dramskog prizora Kao i obično, učenici rade u grupama. Svakoj grupi bit će dodijeljen ulomak iz drame pisca iz jedne od zemalja partnera. Zatim će učenici trebati napisati nastavak prizora kojeg su dobili. Na kraju, trebaju napraviti fotografiju koja prikazuje prizor kojeg su napisali. Tijek zadatka: 1)Svaka škola treba izabrati ulomak iz drame suvremenog autora iz njihove zemlje. Uvjeti odabira: a) Tema je slobodna ukoliko je o suvremenim ljudskim pitanjima. b) Tekst treba biti 3 ili 4 stranice dug sa sažetkom i popisom likova c) Ulomak treba biti lokaliziran, u 5-6 redaka sažeti radnju dramskog teksta te ulomak smjestiti u djelo. d) Tekst treba prevesti na engleski. 2) Svaka će škola poslati odabrani ulomak francuskoj koordinatorici do 15. prosinca. Francuska koordinatorica će proslijediti tekst ostalim partnerima. 3) Svaka škola dodijeljuje svakoj grupi jedan od ulomaka zemlje partnera. Učenici moraju pročitati tekst i napisati prizor koji će biti nastavak zadanom ulomku. ovaj prizor treba biti dug barem 1 stranic, a maksimalno 2, napisan Ariel fontom, veličina fonta 12, razmak 6 točaka, jednostruki prored. Ako žele (ili to tekst zahtijeva) mogu dodati jednog ili dva lika. Tekst mora sadržavati i didaskalije (npr kako se lik kreće scenom itd.) 4) Kad napišu prizor, svaka grupa će napraviti fotografiju koja prikazuje trenutak prizora koji su stvorili. Svi se članovi grupe moraju pojaviti na ovoj fotografiji. Moraju nositi prikladne kostime i scena mora odgovarati prizoru. Scena treba sadržavati sljedeće geometrijske elemente: - oval (elipsu) - ovoid (oblik jajeta, oval) - spitale s dva ili tri centra - zvjezdaste mnogokute s minimalno pet vrhova

Geometrijske elemente moraju izraditi učenici, ne smiju ih naći ni isprintati s internet. Također, ti elementi moraju imati svrhu na sceni, npr. biti dio slike ili uzorak na kostimu, lampi, nešto razrađeno, ne samo bezveze nabačeno na zid. Slika može biti u boji ili crno-bijela i mora biti u digitalnom formatu. Rok za izvršenje zadatka je 28. veljače kad će svaka škola poslati napravljene tekstove i slike francuskom koordinatoru, hrvatskom koordinatoru te koordinatoru projekta, npr. Španjolska će poslati tekst i sliku na zadani hrvatski, francuski te švedski ulomak (znači 3 ulomka i 3 fotografije). Svi uradci bit će na Twinspaceu i blogu. Kriterij ocjenjivanja Pisanje dramskog prizora: - točna uporaba engleskog jezka - razina i širina vokabulara - povezanost s polaznim ulomkom - kreativnost Fotografija: - tehnička kvaliteta- čistoća i focus - povezanost kostima i scene sa sadržajem prizora, posvećivanje pažnje detaljima - korištenje geometrijskih elemenata i savršenstvo u dizajnu istih - dramatizacija (jesu li geste i izrazi lica u skladu s emocijama) Tehnike suradničkog učenja Prije pisanja prizora učenici će koristiti tehniku “olovka u sredini” da skupe ideje. Razgovarat će o tome što će pisati. Svi članovi grupe doprinose idejama o: Ključnom elementu koji povezuje polazni tekst i njihov prizor. To treba biti nešto što opet pokreće radnju, možda novi lik koji se pojavljuje na sceni, nešto neočekivano... Broj likova u prizoru (ovisi o broju članova grupe) Gdje se odvija radnja. Može se zadržati zadano mjesto ili odabrati neko drugo.

Zatim se učenici dogovore o ovim točkama. Također moraju smisliti redosljed pojavljivanja likova, te kako će se kretati na pozornici, zatim zvukove, promjene osvjetljenja i slično. Na kraju će svi provjeriti sve i urediti tekst zajednički. Za izradu slike, svi sudjeluju u svemu, ali jedno ili dvoje će biti zaduženi za: kostime i rekvizite pozornicu i dekoracije fotografski material i uređenje slike izradu geomerijskih elemenata Sliku (footgrafiju) treba predati s izvješćem o tome tko je koordinirao gore spomenute dijelove zadatka i mišljenje članova grupe o uspješnosti njihova rada. Ocjenit će ih od 1 do 5 (1 je najniža, 5 najviša ocjena). Npr. Joaquín i Carmen: kostimi i rekviziti, 5 points.

Hrvatski ulomak Miro Gavran: Vozači za sva vremena38 Likovi:

Francek, 48 godina Štefa, njegova supruga, 47 Žaklina, njihova kći, 23 Bruna, njihova susjeda, 46 Nikica, 38 Nena, njegova supruga, 48 Jure, 28 Predstava je oko dva prijatelja, Franceka i Nikice, koji rade kao vozači za državne ministre. Čim su dobili posao, oni i njihove obitelji počeli su se ponašati kao da su bogati ministri: trošiti previše novca, pripremati zabave, čak i zapošljavaju ili to rade preko poznanika. Kasnije, Francek i Nikica u tajnoj operaciji pokušavaju okriviti sve o Juri, njihovom mladom kolegi. U međuvremenu, Jure započinje odnos sa Žaklinom, a ona zatrudni tako da na kraju, Jure postaje Franceku zet. On mu oprašta za prijevare i uvjeri ga da napusti položaj ministrova vozača tako da bi njih dvojica mogla pokrenuti vlastiti posao s prijevozom. Ovaj ulomak je s početka predstave i opisuje kako su likovi uživali u luksuznom životu. Zanimljivo je, pa čak i smiješno, kako se ljudi mijenjaju kada dobiju nešto novca. 3. scena (Dnevni boravk, domaćini i gosti sastali su se na večeri) FRANCEK: Ljudi, idemo dižimo čaše. Dobro došli u moj dom, tako mi je drago da ste ovdje večeras. Posebna dobrodošlica za našeg novog kolegu Juru. Ja nazdravljam našem mladom prijatelju i našim starim nepopravljivim ženama. Živjeli! SVI: Živjeli! NENA: Slušaj, mogu biti stara, ali nisam nepopravljiva. U krivu ste tamo. FRANCEK: Kako to misliš? NENA: Jučer sa bila kod liječnika Glumičića . Plastični kirurg. Dogovorila sam sve. Kad me vidite za dva mjeseca - nećete me prepoznati. ŠTEFICA: Jel stvarno ideš na plastične operacije? Ajde. 38

Isječak iz drame Vozači za sva vremena, Mira Gavrana.

ŽAKLINA: Recite nam svima, teta Nena. Što ima? FRANCEK: Nikad ne bih to učinio, to je opasno i protiv prirode. NENA: Pa, slušaj, na zapadu je normalno za svaku ženu nakon navršene dvadesete popraviti zube, bradu, nos, struk, podbradak i bedra. To ne rade samo oni koji nemaju novca. FRANCEK: Bilo kako bilo, ja sam protiv toga. Nikice, kako si dopustio da to učini? NIKICA: Misliš da je pitala? ŠTEFICA: Hajde dečki, nemojte je prekidati. Reci nam Nena, koje postupke ćete raditi? NENA: Sve. Globalna korekcija. ŽAKLINA: Tako se zove sve. NENA: Imam face lifting, korekciju kapaka ... ŽAKLINA: Što korekcija? NENA: Korekcija kapaka, moram to učiniti, pogledajte moje kapke! FRANCEK: Hajde. NENA: ti bi trebala učiniti isto i s svojim. FRANCEK: Hmm. NENA: Onda, korekcija usana. FRANCEK: Što nije u redu s tvojim usnama? NENA: One nisu dovoljno napućene. To može biti lako uz malo implantata. Zatim liposukcija - ovdje, na mojim bedrima. Tako ću se riješiti moje debljine. NIKICA: Ali nemaš celulita. NENA: Onda, korekcija stražnjice. FRANCEK: Što to znači? NENA: Tu je mali kirurški zahvat za podizanje dupeta, shvaćaš? Moram se pobrinuti za moju stomak i moju guzu. A i strija od mog drugog poroda. NIKICA: Oh, ja ću povratiti. Prestani govoriti o tome. FRANCEK: čovječe, nećeš je prepoznati nakon svih tih korekcija. Ona će izgledati kao Michael Jackson. Možda će pronaći još mlađeg dečka. ŠTEFICA: možete zafrkavati svoje žene. Volite da su lijepe, ali ste spreviše škrti ulagati u naš izgled. Hej, koliko sve košta? NENA: Ništa. Četrdeset tisuća. FRANCEK: kuna? NIKICA: eura, prijatelju. Četrdeset tisuća eura. ŠTEFICA: Reci nam više o tome. FRANCEK: Da li mi stvarno to moramo slušati? ŠTEFICA: Ne, ne. No, želimo čuti. Zato ćemo u Žaklininu sobu, a vi ostanite ovdje i razgovarajte o nogometu. Mi ćemo večerati za pola sata - ok?

FRANCEK: Odlično. NIKICA: Ja sam bolestan i umoran od rasprava o tim plastičnim glupostima. NENA: Ok, idemo do Žaklinine sobe. ŽAKLINA: Dođite, Nena spričaj nam sve u detalje. NENA: Ok, djevojke. (Žene odlaze u Žaklininu sobu. Muškarci su sami.) FRANCEK: Jesi li je ozbiljno pustitio da to učini? NIKICA: Što mogu učiniti? Mislim da je menopauza. Protivim se. FRANCEK: Ako to tvoja žena uradi - moja će željeti također, ja nisam protiv. Vidio sam joj u učima iskru kad se spominje Glumičić. NIKICA: Hmm, to se danas tako radi. Mi smo ugledni ljudi. Naše žene moraju izgledati savršeno. Jure moraju li biti ljute na sve ovo. Vi ne bi ih bilo, zar ne? JURE: Aaa, ne ... nikad ne bih to učinio - ali žene brinu o svom izgledu puno. A mi, muškarci smo krivi. FRANCEK + NIKICA: Zašto je to tako? JURE: Zato što smo stvorili mušku civilizaciju koja naglašava važnost ženske ljepote. Već stoljećima - čak i umjetnici, slikari i pjesnici naglašavaju izgled kao najvažniji aspekt. Nitko ne spominje bogatstvo ženske duše. Zar ne? NIKICA: Pa ... Oni to vole previše. A, prvo vidite njen izgled, a nakon toga upoznajete njezinu dušu. FRANCEK: Tako je. JURE: Samo kažem, to je naša krivnja. I sada, kada je tu plastična kirurgija, žene vide kao rješenje svih njihovih problema - - produljenje svoje mladosti i ostati zanimljiva za njihove partnere i susjede. FRANCEK: Ne sviđa mi se to uopće. (Tišina.) FRANCEK: No, idemo predložiti posao Juri, a dame nisu ovdje.

Zadatak 6 Izrada kratkog filma Učenici će izraditi kratki film koji će zapravo biti nova verzija scene filma iz zemlje partnera. Tijek zadatka 1 – Studenti rade u grupama. Svakoj grupi dodijelit će se scena iz suvremenog filma iz zemlje partnera. Scena treba biti u originalnoj verziji s titlovima na engleskom i oko 5 minuta duga. Scena će biti lokalizirana – smještena u film, uz kratak sažetak filma. 2 – Nakon što učenici pogledaju odabranu scenu, napisat će novi dijalog, mijenjajući postojeći kako god žele (što ne znači da ga moraju potpuno promijeniti). Ovo je književni dio filmskog scenarija. Imajući na umu da svaki član grupe mora glumiti nekog lika iz scene, mogu ga prilagoditi svojim potrebama. To znači da mogu dodati ili izbaciti neki lik /likove ili im promijeniti spol. 3 – Zatim će se učenici dogovoriti oko podjele likova, lokacije, kostima, rekvizita itd. što sve može biti prilagodjeno okolnostima i potrebama, te tko će snimati scenu. Uvježbavat će prema potrebi. Dekoracija mora uključivati naredne elemente: 6 - 8 primjera niza zakrivljenih linija koje će se dobiti spajanjem obodnih lukova.

Ovi ukrasi nek budu napravljeni na kartonu ili acetatnoj foliji. Zatim ih treba izrezati I koristiti kao predloške za izradu apstraktnog umjetničkog djela zakrivljenih linija koje će obojati po želji. Učenicima će to biti dio ukrasa.

4 - Prije snimanja, učenici trebaju izraditi knjigu snimanja gdje će bilježiti kadar svake snimke te zvukove, glazbu itd.manja, učenici trebaju izraditi knjigu snimanja gdje će bilježiti kadar svake snimke te zvukove, glazbu itd. Primjer knjige snimanja: Shot

Dialogue

Image

John: “Molim te ne idi!” Helen: “Ostavi me samu! Više ti ne vjerujem”

Krupni plan s oba lika.

Music/sounds/tone of voice John sažaljivim glasom, Helen, ljuta I tužna.

5- Nakon navedenog će učenici snimati. Poželjno je zadržati format originalne scene: paziti na plan – krupni plan, srednji plan, total I kut snimanja- kamera u razini pogleda, gornji ili donji rakurs. Ova stranica može pomoći: http://www.skwirk.com/p-c_s-54_u-251_t-647_c-2411/camera-shots-anglesand-movement-lighting-cinematography-and-mise-en-scene/nsw/camerashots-angles-and-movement-lighting-cinematography-and-mise-en-scene/skillsby-text-type-film/film-overview 6- Na kraju, treba urediti film – sastaviti snimljene kadrove u pravi redoslijed, dodati uvodnu I završnu špicu s imenima sudionika, ime filma I druge informacije. Ako učenici ne snime zvuk uzivo, mogu naknadno dodati prilikom montaže, Mogu zadržati originalnu glazbu ili je sami snimiti koristeći npr. Music Maker Jam.Sve dodano mora biti u skladu s filmskom pričom.

7- Da bi reklamirali film, učenici trebaju napraviti filmski plakat, koji će privući gledatelje I prenijeti srž i atmosferu filma. Izgled plakata: A3 Sadržaj: ime, sudionici grupe, slogan) Geometrijski elementi (svi ili neki od onih koji su korišteni za scenu za snimanje) Može biti izrađen ručno (slobodna tehnika) ili korištenjem kompjuterskog programa ili alata npr. https://www.canva.com/create/posters/ Postupak izrade plakata: Svaki član grupe će izraditi skicu na A4 papiru s minimalnim sadržajem (ime, slogan) te je pokazati ostalim članovima grupe. Na temelju razgovora odabrat će najbolje dijelove (najbolji slogan, najbolje ime i slično). Izradit će poster. Poslat će finalnu verziju plakata I skice od kojih je nastao. Tehnike suradničkog učenja Za pisanje prizora učenici će koristiti tehniku “olovka u sredini” da skupe ideje. Razgovarat će o tome što će pisati. Svi članovi grupe doprinose idejama o: Ideji i smislu djela Likovima Razvoju ideje kroz djelo : Početku, vrhuncu i završetku Ulozi svakog pojedinog lika u prizoru Nakon toga će razgovarati o prikupljenim idejama i napisati synopsis (sažetak filmske priče) i sažetak scenarija (sažet opis atmosphere djela i likova koji sudjeluju). Zatim će pisati dijalog, uključujući upute za set snimanja i atmosferu. U pisanje svakog dijela zadatka trebaju sudjelovati svi članovi grupe. Snimanje također trebaju raditi svi članovi i podjednako doprinijeti uratku, ali treba odabrati koordinatora za svaki dio: Kostime i rekvizite Set i scenografiju Snimanje i montažu (kamera, programi…) Geometrijske elemente.

Učenici će napisati izvješće s imenima koordinatora i ocjenu o njihovu radu, ocjenjujući koordinatore ocjenom od 1 do 5 (1 najniža, 5, najviša). Npr. Juana, snimanje i uređivanje opreme: 4 boda Učenici će staviti film na internet i poslati link film ate plakat, sinopsis, prepričani scenarij i scenarij.

Primjer. sinopsisa: Tinejdžer slučajno otputuje 30 godina u prošlost gdje se nepovratno umiješa u očevo i majčino upoznavanje. Dok pokušava pronaći put do budućnosti, mora pokušati spojiti roditelje ili se nikada neće roditi. Primjer prepričanog scenarija: Radnja se događa uJohnovu dnevnom boravku. Likovi: John, 24ogodišnji bloger i youtuber, ljubazan čovjek, zaljubljen u Helen. Helen, tajanstvena mlada žena, u vezi je s Johnom, ali nešto skriva Mark, Johnov prijatelj, čudno se ponaša u zadnje vrijeme Gđa. Spencer, Helenina šefica, odlučna žena koja ne želji da joj se suprostavljaju Hrvatski filmski ulomak je dio filma Hrvoja Hribara iz 2005.g. “Što je muškarac bez brkova?”. Dio filmskog ulomka je od: 26:12- 34:13 minute.

Tasks in French Tâche 1 Techniques d'apprentissage coopératif Technique du puzzle. Maths elements indeks 1. Positions

relatives de deux lignes droites, voire plus. 2. Concept du polygone. 3. Classification des polygones selon le nombre des côtés. 4. Définition de la mosaïque. 5. Calcul de l'aire de figures planes. 6. Concepte du polyèdre. 7. Développement plat des édifices de forme polyédre. 8. Calcul du volume de ces édifices.

Introduction: à travers une œuvre architecturale, un tableau et un objet de la vie courante nous allons observer toutes les formes géométriques qui les composent et font ainsi leur particularité et surtout leur beauté ! Le fauteuil Costes de Philippe STARCK objectif : réaliser une fiche de présentation de l'artiste et de son oeuvre dans le cadre du projet « arts count ! » sous quelle forme : une diapo d'un fichier de présentation openOffice ou libreOffice. 79

Contenu : - Qui est-le designer? Son parcours? - Description mathématique de l'objet : - observer la particularité de cette chaise, - son nom, son intéret, formes géométriques - tracer le centre de gravité du triangle défini par - les trois pieds. - photos d'illustration http://www.cotemaison.fr/chaine-d/deco-design/philippe-starck-la-chaise-costes_24673.html https://www.centrepompidou.fr/cpv/resource/cEbz7E5/rk4erog https://www.mathsisfun.com/geometry/solid-geometry.html

Critères de réussite : Ma réponse est Complète

Mon avis (oui/non) /4

Ecrite correctement (orthographe, grammaire) Claire

professeur

/2 /1

Concise

Bien présentée

La Pyramide du Louvre objectif : réaliser une fiche de présentation de la Pyramide du Louvre dans le cadre du projet « arts count ! » sous quelle forme : une diapo d'un fichier de présentation openOffice ou libreOffice. Contenu :

où se situe t-elle ? Quand a t-elle été réalisée ? Pourquoi ? À la demande de qui ? Par qui ? Dans quel but ?... Description mathématique : solide. vocabulaire du solide, figures géométriques qui la compose, dimensions, matières, effet... calcul de la hauteur de la pyramide connaissant la longueur d'un coté de losange (penser à Pythagore) puis le volume de la pyramide photos d'illustration

http://www.lexpress.fr/culture/art/10-choses-a-savoir-sur-lapyramide-du-louvre_752571.html http://www.mathovore.fr/les-pyramides-et-cones-cours-maths39.php https://www.mathsisfun.com/geometry/solid-geometry.html

« CHEYT PYR » de Victor Vasarely 39 objectif : réaliser une fiche de présentation de l'artiste et de son oeuvre dans le cadre du projet « arts count ! » sous quelle forme : une diapo d'un fichier de présentation openOffice ou libreOffice. Contenu : Qui est l'artiste? Quelle technique à t-il développée ? Description mathématique du tableau : - observer les différentes figures géométriques du plan et de l'espace, dimensions, couleurs, effet obtenu.. photos d'illustration http://www.fondationvasarely.fr/vasarely.php http://www.vasarely.com/site/site.htm https://www.mathsisfun.com/geometry/solid-geometry.html

ZE TOIT TERRASSE, par Vasarely. Photo prise par Yann Artus-Bertrand

Tâche 2 Programmation et mise en œuvre de la tâche. Cette tâche doit être réalisée par différents groupes. Elle comporte 2 parties différentes. Partie 1 La première partie de cette tâche consiste à écrire une nouvelle inspirée soit d’une photo de Yann Arthus-Bertrand ou d’une peinture de Gustave Caillebotte, les 2 œuvres d’art contenant des éléments mathématiques. Chaque groupe travaillera avec 3 autres groupes et les 4 groupes devront créer la nouvelle à tour de rôle : 1. Le 1er groupe écrira l’introduction. 2. Une fois l’introduction terminée, le groupe suivant se chargera d’écrire l’intrigue. 3. Après l’intrigue, le 3ème groupe écrira le climax de la nouvelle. 4. Pour finir, le dernier groupe rédigera la conclusion, la fin de la nouvelle. Auparavant, tous les élèves du groupe devront discuter de l’œuvre d’art qui leur aura été assignée et devront décider de ce qu’ils vont écrire : Quoi ? Qui ? Où? Quand ? Comment ? Etant donné que la nouvelle doit être écrite par 4 groupes, vous devez vous mettre d’accord sur l’intrigue, les personnages, où et quand l’action se déroule, comment la nouvelle finit ; etc. Chaque partie de l’histoire, c’est à dire chaque paragraphe, doit contenir 50 mots environ, tapée en Arial 14. Le coordinateur de chaque groupe sera chargé d’écrire la partie de l’histoire dont ils sont responsables (et qui a été développée et écrite par tous les membres du groupe). Partie 2 Chaque groupe réalisera un dessin, un collage ou une photo basée sur l’une des nouvelles écrite dans la partie 1 et qui devra contenir les éléments mathématiques inclus dans l’œuvre d’art inspirée de l’histoire. Votre travail devra être présenté sur une feuille de papier A4. Si c’est une photo, il devra être dans un format digital.

Critères d’évaluation Pour la nouvelle : • Utiliser correctement la langue. • Cohérence et cohésion. • Originalité et creativité. • Travail de groupe. Pour le dessin, collage ou la photographie: • Originalité et créativité. • Utiliser les éléments mathématiques. • Qualité artistique. • Travail de groupe. Les techniques d’apprentissage coopératif utilisées La réalisation de la première partie de la tâche telle que décrite, suppose une adaptation de la technique du « chacun son tour » qui devra être précédée d’un brainstorming sur les idées, en ayant recours à la technique du « crayon au milieu du groupe ». Le dessin, le collage ou la photo doit être fait en utilisant la technique du puzzle. Index des éléments mathématiques 1. 2. 3. 4. 5. 7.

Transportador de ángulos Ligne horizontale Carré et triangle Positions relatives de deux lignes droites voire plus. Rectangles Cercles

Le pont de l'Europe by Gustave Caillebotte40 Gustave Caillebotte, (born on 19 August 1848 and dead on 21 February 1894) was a French painter, member and patron of the artists known as Impressionists, although he painted in a much more realistic manner than many other artists in the group. Caillebotte was noted for his early interest in photography as an art form. He may be considered part of the first movement after Impressionism: NeoImpressionism. Caillebotte aimed to paint reality as it existed and as he saw it, hoping to reduce the inherent theatricality of painting. Cropping and "zooming-in", techniques that commonly are found in Caillebotte's oeuvre, also may be the result of his interest in photography, but may just as likely be derived from his intense interest in perspective effects. A large number of Caillebotte's works also employ a very high vantage point. Caillebotte painted many domestic and familial scenes, interiors, and portraits. Many of his paintings depict members of his family. There are scenes of dining, card playing, piano playing, reading, and sewing all executed in an intimate, unobtrusive manner that portrays the quiet ritual of upper-class indoor life. His country scenes focus on pleasure boating on the leisurely stream as well as fishing and swimming, and domestic scenes around his country home. Caillebotte is best known for his paintings of urban Paris, such as The Europe Bridge (Le Pont de l'Europe) (1876). Many of his urban paintings were quite controversial due to their exaggerated, plunging perspective.

Le Pont de lâ&#x20AC;&#x2122;Europe, peinture de Gustave Caillebote, huile sur toile, 1876

Ze Toit Terrasse de Vasarely, photo de Yann Arthus-Bertrand41 Yann Arthus-Bertrand (né le 13 mars 1946 à Paris) est un photographe, reporter, réalisateur et écologiste français. Il est très connu grâce à son livre La Terre vue du ciel, paru en 1999. Il devient journaliste, reporter, photographe international spécialisé dans les grands reportages d'aventure, de sport, de nature, d'animaux et dans la photographie aérienne pour National Geographic, Figaro Magazine, Paris Match et Géo. Il couvre dix rallyes Paris-Dakar, réalise chaque année le livre du tournoi de Roland-Garros et photographie le salon de l'agriculture annuel de Paris. Il réalise également un reportage sur Dian Fossey et ses gorilles. Il publie aussi des ouvrages traitant de la relation entre l'homme et l'animal. En 1991, il crée l'agence Altitude, qui était la première agence de presse et banque d'images de photographie aérienne dans le monde. En 1994, avec le parrainage de l'Unesco, il entreprend de faire l'inventaire des plus beaux paysages du monde vus du ciel. Ce projet, intitulé La Terre vue du ciel, a comme credo : « Témoigner de la beauté du monde et tenter de protéger la Terre ». L'exposition de ses photos « grand format » en plein air a été vue depuis dans une centaine de pays par plus de 200 millions de visiteurs en 2000. En 2004, il réalise au Mans un cliché pour l'opération « 10 000 Cœurs pour un Ruban Rouge », au profit de la lutte contre le SIDA au Mali. Près de 6 000 personnes forment un cœur vu du ciel. Le 1er juillet 2005, il fonde Good Planet, une organisation environnementale internationale et met en place le programme Action Carbone. Il est élu membre de l'Académie des Beaux-Arts en 2006 à l'occasion de la création d'une nouvelle section consacrée à la photographie. En avril 2007, il commence à diriger un film qui devait s’appeler Boomerang, renommé Home. Ce film a été produit par Luc Besson et financé par le groupe français PPR, c’était l’intention d’Arthus-Bertrand de montrer l’état de la planète et les challenges auxquels les humains doivent faire face.

ZE TOIT TERRASSE, par Vasarely. Photo prise par Yann Artus-Bertrand

Tâche 3 Objectifs Comprendre les traditions d’autres pays grâce à leurs histoires traditionnelles. Encourager la création artistique tout en gardant à l’esprit quelques principes mathématiques. Production finale Production, soit sur papier ou sous forme digitale, d’une histoire graphique type bande dessine basée sur l’histoire traditionnelle. Étapes Les professeurs de chaque pays choisiront 1, voire 2 histoires traditionnelles (mythes, légendes ou histoires populaires) de leur ville, région ou pays. Elles seront traduites en anglais simple (au cas où il n’y aurait pas de version anglaise existante) et devra comporter environ 400 mots. Les histoires seront échangées. Le délai pour envoyer les versions anglaises des histoires au coordinateur espagnol est fixé au 28 mars. Le coordinateur espagnol enverra toutes les histoires aux autres coordinateurs avant le 30 mars. Chaque pays recevra donc 3, voire 6 histoires, soit 1 ou 2 par pays partenaire. Par groupe, les étudiants inventeront le script comprenant les dialogues adaptés d’une des histoires, légendes ou histoires populaires des autres pays. A partir du script, les élèves créeront la bande dessinée qui devra tenir sur 2 feuilles maximum, au format A4, ou sous format digital. La bande dessinée peut être réalisée comme suit : - en utilisant un logiciel tel que Pixton, Tondoo, Comic Life, etc. - en dessinant à la main. - en faisant un collage. - en utilisant tout autre logiciel ou technique que vous connaissez. La bande dessinée doit comporter un maximum de 12 vignettes et doit inclure au moins 5 des éléments mathématiques ci-dessous : 86

Des bulles ovales (pour les dialogues, par exemple). Des rectangles (pour la voix du narrateur, par exemple). Des cercles. Des cercles concentriques. De la symétrie. Des angles aigus. Des parallèles. Des droites perpendiculaires. Des triangles équilatéraux. Des carrés. - Si la bande dessinée est faite à la main, les éléments mathématiques doivent être réalisés à l’aide des outils mathématiques adéquats, tels que la règle, l’équerre, le compas, … - Les élèves doivent fournir, avec la bande dessinée, la liste des éléments mathématiques qu’ils ont utilisés et doivent mentionner dans quelle vignette et où dans la vignette, ils ont été incorporés. Les bandes dessinées qui n’ont pas été faites sur un support digital, doivent être scannées de manière à être téléchargées sur le blog et le Twinspace au cas où elles seraient choisies. Les techniques d’apprentissage cooperatif : Tout d’abord, il faut commencer par un bref brainstorming de quelques minutes, en utilisant la technique du « crayon au milieu », suivi d’une discussion et d’un accord général sur ce que les élèves vont créer. Ensuite, les élèves doivent écrire le script et les dialogues en utilisant la technique du « chacun son tour ». Pour la bande dessinée, ils doivent utiliser la technique du puzzle par équipe. Mise en commun Chaque partenaire choisira une bande dessinée par pays. Par exemple, les Croates devront choisir la meilleure bande dessinée illustrant l’histoire

espagnole mais aussi celle illustrant l’histoire française et l’histoire suédoise, parmi celles réalisées par leurs élèves. Ensuite les coordinateurs enverront ces 3 travaux au coordinateur espagnol avant le 1er Mai. Le 2 mai, le coordinateur espagnol enverra les 3 bandes dessinées basées sur l’histoire de chaque pays à tous les partenaires. Ensuite, chaque pays devra choisir la meilleure représentation graphique parmi les 3 qu’ils auront reçues. Le délai pour l’élection est fixé au 5 mai. Par exemple, les français recevront les histoires graphiques basées sur leurs mythes, etc... qui ont été faites par les élèves croates, suédois et espagnols et devront choisir celle qu’ils préfèrent. Ces 4 histoires graphiques (une par pays) seront téléchargées sur le blog et sur TwinSpace. Évaluation et critères de Qualification Utilisation de l’anglais. Adéquation entre le script et l’histoire originale. Créativité et originalité. Utilisation des éléments géométriques. Qualité artistique. Travail de groupe.

Notre Legende Francaise Le Vase De Soissons42 Selon Grégory de Tours (vers 538–594), un évêque et historien gallo-romain, le vase sacré en pierre sculpté, était de grande taille et de grande beauté. Il avait été volé, de même que d'autres reliques précieuses, dans une église pendant les pillages qui suivirent la bataille de Soissons en 486, une bataille qui avait été remportée par le roi français Clovis I, qui à cette époque ne s'était pas encore converti au Christianisme. Saint Rémi, l'évêque de Reims, envoya un messager à Clovis, le suppliant de rendre à l'Eglise, ce vase sacré, à défaut des autres trésors pris pendant le pillage. Il voulait absolument récupérer ce vase. Clovis accepta de le lui rendre et, de ce fait, déclara devant ses soldats que ce vase lui revenait de droit comme part du butin. Quand le moment du partage arriva, Clovis demanda même à Saint Rémi de venir à Soissons pour récupérer lui-même le vase sacré. A Soissons, tous les soldats étaient d'accord pour rendre le vase à Saint Rémi. Seul un des soldats ne fût pas d'accord et frappa le vase avec sa hache de guerre. Tout d'abord, Clovis ne réagit pas et donna le vase cassé à Saint Rémi. Mais il n'oublia jamais cet incident. Un an plus tard, il vit le soldat à nouveau, il prit la hache du soldat et la jeta par terre, prétextant que son équipement n'était pas correct. L'homme se baissa pour la ramasser et Clovis lui fracassa le crâne avec sa propre hache, en lui disant : “Ainsi, as-tu fait au vase de Soissons.” De nos jours, la version populaire qui demeure dans nos livres d'histoire française, est “Souviens-toi du vase de Soissons !”

Le Vase de Soissons, légende de Soissons

Tâche 4 Creation Multimedia D’un Poeme 1- Les élèves travailleront en groupes. Ils devront faire une nouvelle création multimédia d’un poème d’un auteur étranger, en mettant des images, de la musique et en récitant le poème, à la fois dans sa langue d’origine et en anglais. Les images doivent comporter des éléments mathématiques tels que les spirales, les symétries de même que des images artistiques d’arithmétique modulaire qui contribueront en fait à mieux comprendre le poème. Mise en oeuvre: 1)Chaque groupe d’élèves recevra un poème d’un des pays partenaires (sauf de leur pays). Le poème doit être en anglais et dans la langue maternelle du pays. 2) La réalisation multimédia, la vidéo, ne doit pas durer plus de 3 minutes et doit contenir : a.La récitation du poème dans la langue maternelle et en anglais, récités à la suite ou fusionnés à votre guise ; b.Les images ou les séquences de la vidéo, originales ou modifiées, qui comporteront les éléments mathématiques tels que les spirales, les symétries et les images artistiques d’arithmétique modulaire qui contribueront à mieux comprendre le poème. c.La musique qui servira à susciter les émotions et sentiments convoyés par le texte du poème. Cela peut être une des chansons des playlists qu’ils auront été faites avant. Evaluations et critères : Les critères suivants seront étudiés pour évaluer la réalisation et la qualification de la tâche :

La récitation dans la langue d’origine (diction, rythme). La récitation en anglais (prononciation, intonation, rythme). L’adaptation de la musique, des images et des éléments mathématiques au contenu du poème. La qualité de l’image et du son. Technique d’Apprentissage Coopératif : Recherche par groupe - Les étapes : 1) On assigne aux élèves ou ils choisissent eux-mêmes la partie de la tâche dont ils vont être responsables. Ensuite, ils définissent le délai pour finir les différentes parties de la tâche à savoir : 1La recherche d’images pour la vidéo. 2La sélection des meilleures images contenant les éléments mathématiques et définir la séquence de la vidéo. 3La récitation et l’enregistrement du poème en anglais. 4Le choix de la musique pour la vidéo. 5La création de la vidéo. 2) Tous les élèves doivent participer à chaque partie de la tâche et l’élève en charge de chaque partie doit s’assurer que chacun fait son travail en temps et en heure. 1. Tous les élèves doivent chercher des images comprenant les éléments mathématiques qui illustreront le poème. 2. Tous les élèves contribuent à la récitation du poème en anglais pendant son enregistrement. 3. Tous les élèves choisissent de la musique pour accompagner la vidéo. 3) Les élèves, en tant que groupe, partagent leurs trouvailles et prennent les décisions ensemble. 1. Tous les élèves prennent part à la sélection de la musique, des images et des endroits de la séquence vidéo où ils seront mis.

2. Normalement, la réalisation de la vidéo sur PC doit être faite par une seule personne, de même que l’enregistrement de la récitation en anglais, mais tous les élèves doivent aussi participer à cette tâche. 4) Chaque élève rédigera un rapport individuel dans lequel il indiquera : - la liste des éléments mathématiques qui font partie des images qu’ils ont choisies, - le fichier audio avec la musique qu’ils ont composée / le titre de la chanson et le nom de l’artiste qu’ils ont choisis pour cette vidéo, - une évaluation de la performance des coordinateurs de chaque étape de la tâche. Index des éléments mathématiques 1. 2. 3.

Spirales Symétries Réseaux modulaires

Le poème français Euclidiennes de Eugène Guillevic43 Parallèles

On va, l’espace est grand, On se côtoie, On veut parler. Mais ce qu’on se raconte L’autre le sait déjà, Car depuis l’origine Effacée, oubliée, C’est la même aventure. En rêve on se rencontre, On s’aime, on se complète. On ne va plus loin Que dans l’autre et dans soi. Perpendiculaire Facile est de dire Que je tombe à pic. Mais c'est aussi sur moi Que l'autre tombe à pic.

Euclidiennes, poème de Eugène Guillevic

Tâche 5 Lire Des Pieces De Theatre Contemporaines Et Ecrire Une Scene Comme d'habitude, c'est un travail de groupe. On donnera à chaque groupe un extrait d'une pièce de théâtre d'un auteur d'un des pays partenaires. Ensuite, les élèves écriront une scène qui continuera le texte qu'on leur aura donné. A la fin, ils prendront une photo de la mise en scène d'une partie de leur écrit. Procede De Realisation : Chaque établissement choisira un extrait d'une pièce de théâtre d'un auteur contemporain de leur pays. Conditions du texte : Le sujet est libre du moment que le texte parle de thèmes contemporain sur l'être humain. La longueur du texte sera de 3 ou 4 pages. Il faudra fournir le contexte de l'extrait entre 5 ou 6 lignes qui résumeront l'intrigue de la pièce et le moment où se passe l'extrait. Le texte sera traduit en anglais. 2) Chaque partenaire distribue un des extraits des autres pays aux groupes. Les élèves le liront et écriront une suite, en 1 voire 2 pages maximum, écrit en Arial 12, espace 6, simple interligne. S'ils le veulent (selon l'extrait) ils pourront ajouter un ou plusieurs personnages. Des explications scéniques peuvent être ajoutées si nécessaire (par exemple, comment un personnage évolue sur la scène, etc.) 3) Une fois la scène écrite, chaque groupe devra prendre une photo qui montre un moment de la scène qu'ils auront créée. Tous les membres du groupe doivent être sur la photo. Ils devront porter des costumes adéquats et les décors doivent aussi être en adéquation. Les décors devront contenir les éléments géométriques suivants : - formes ovales. - Ovoïdes. 94

- Spirales de 2 ou 3 centres. - Etoiles à 5 branches minimum Les éléments géométriques doivent être réalisés par les élèves, ils ne doivent pas les imprimer d’Internet, mais utiliser les outils adéquats. Ils doivent être placés à des endroits appropriés sur la photo, par exemple, ils peuvent faire partie d’une peinture tenant lieu de décor, ou faire partie d’un costume, d’une lampe, …., quelque chose d’élaboré et pas seulement une forme sur un mur. La photo peut être en couleur ou noir et blanc, et au format numérique. Critères d’évaluation L’écriture d’une scène de théâtre : Anglais correct. Étendue du vocabulaire. Cohérence de la suite écrite avec l’extrait donné Créativité. Photographie : Qualité : l’image est claire, pas floue, et bien cadrée. Adéquation des costumes et des décors au contenu de la scène, attention aux détails. Utiliser les éléments géométriques et la perfection dans leur réalisation. Mise en scène (les gestes, les expressions montrant les émotions) Technique d’apprentissage de groupe Afin d’écrire la scène, et pour faire le brainstorming d’idées, on utilisera la technique du “crayon au centre”. Les élèves discutent de ce qu’ils vont écrire et tous les membres doivent contribuer en donnant des idées comme suit : L’élément clé qui va relier la scène qu’ils ont lue à la scène qu’ils vont écrire. Quelque chose qui relance encore l’action, cela peut être un nouveau personnage débarquant sur la scène, quelque chose d’inattendu …. Le nombre de personnages (cela dépendra du nombre de personnes dans le groupe) Ce qui va se passer et comment la scène va finir.

Où l’action se passe. Cela peut être au même endroit ou un endroit différent. Ils parviennent ensuite à un accord sur tous ces sujets. Ils décident aussi de l’ordre d’apparition des différents personnages, les instructions scéniques pour expliquer les déplacements des personnages sur la scène, s’il y a lieu, ou les sons, les jeux de lumières, etc. et ils commencent à écrire leur scène. A la fin, tous les membres du groupe corrigeront et éditeront le texte. Pour la photo, chacun doit participer mais 1 ou 2 personnes du groupe (selon les groupes) sera responsable : - des costumes et des accessoires. De la scène et du décor. Du matériel de photo et de l’impression de la photo. De la création des éléments géographiques. La photo sera remise avec un rapport détaillant qui a collaboré dans les tâches mentionnées ci-avant, et donnant aussi l’opinion de leurs camarades de groupe sur la réalisation des tâches dont ils étaient responsables. Le travail des coordinateurs sera évalué de 1 à 5, 1 étant la plus petite note et 5 la plus haute. Extrait de la pièce française Réveillon au poste44 Jean-Pierre Martinez La nuit de Noël, deux inspecteurs sont de garde, avec pour seule compagnie quelques naufragés du réveillon. C’est alors que le Ministre de l’Intérieur débarque dans leur commissariat, pour rendre hommage au dévouement des forces de l’ordre. Évidemment, rien ne va se passer comme prévu… Personnages : Commissaire Flic 1 44

Réveillon au poste, extrait de la pièce de théâtre de Jean-Pierre Martinez

Flic 2 Flic 3 Chef de Cabinet Collabo Clodo Mytho Travelo Parano Décor: Un bureau glauque dans un commissariat sans âge. Dans un coin, un sapin de Noël pathétique supposé apporter une touche de gaîté dans cette ambiance de mauvaise série télé. Deux flics débraillés, portant chacun une arme dans un holster, terminent une partie de poker sur un bureau. Le premier abat ses cartes. Un homme entre à la suite du Flic 3. Il a une bouteille à la main. Flic 1 – Oh putain non, pas lui… Flic 2 – Ah, bonsoir Monsieur Dumortier, comment allez-vous ? Collabo – Bonsoir, bonsoir… Je passe en coup de vent vous souhaiter un joyeux Noël. J’espère que je ne vous dérange pas ? Flic 1 – Mais vous ne nous dérangez jamais, Monsieur Dumortier. Flic 1 – Justement nous parlions de vous… Enfin, nous parlions des cafards en général… Flic 2 – Heureusement qu’il existe des citoyens vigilants comme pour vous pour assister la police dans sa noble mission. Flic 3 – S’il y avait plus de gens comme Monsieur Dumortier, c’est sûr, la municipalité n’aurait même plus besoin d’investir dans la vidéosurveillance. Flic 2 – Alors Monsieur Dumortier, qui venez-vous dénoncer aujourd’hui ? Un polygame présumé? Un fraudeur aux allocations familiales ? Un orphelin sans papier ? Collabo – Simple visite de courtoise. Je viens en voisin pour rendre hommage au dévouement des forces de l’ordre, dont vous êtes le bras armé. Flic 1 – Mais je vois que vous n’êtes pas venu les mains vides… Collabo – Je sais ce que c’est que de passer Noël tout seul loin de sa famille, la mienne ne veut plus me voir. Alors si je peux apporter un peu de réconfort

aux soldats qui protègent notre pays contre les dangers qui le menacent de l’intérieur. Tenez, vous m’en direz des nouvelles… Il pose sa bouteille sur un bureau. Flic 1 – Ah mais dites-moi, c’est de la fabrication artisanale, on dirait. C’est écrit à la main, comme sur les pots de confiture Bonne Maman. Flic 2 (lisant par dessus son épaule) – Alcool de châtaignes… Flic 3 – Je ne savais pas qu’on pouvait faire de l’alcool avec des châtaignes… Collabo – On peut faire de l’alcool avec tout, vous savez. Pendant la guerre, mon grand-père en faisait même avec des épluchures de pommes de terre et de vieilles semelles en cuir. Flic 3 – Ah oui, 53 degrés, quand même… Ça ne doit pas être mal… Comme antiseptique, en tout cas. Collabo – Pépé m’en a laissé quelques bouteilles en héritage avant d’être fusillé à la Libération. Quand celle-ci a été distillée, vous n’étiez même pas encore nés… Flic 2 – Vous savez que c’est strictement interdit de fabriquer de l’alcool chez soi, Monsieur Dumortier. Nous pourrions vous mettre en garde à vue pour infraction à la législation sur les vins et spiritueux… Dumortier semble inquiet. Flic 3 – Mon collègue plaisante, évidemment… Flic 1 – D’ailleurs, il y a prescription, n’est-ce pas ? Hélas, nous ne pourrons pas trinquer avec vous. Vous savez ce que c’est : jamais pendant le service ! Collabo – Vous la boirez à ma santé pour le Jour de l’An, alors. Si vous n’êtes pas de garde encore une fois… Allez, je me sauve… Vous devez avoir des tas de gens à mettre en prison… Flic 3 – C’est vrai que les jours de réveillon, ici, c’est comme au théâtre. On affiche souvent complet. Je vous raccompagne, Monsieur Dumortier ? Collabo – Je connais le chemin, mais bon… Flic 2 – Vous êtes presque de la maison, pas vrai ? Flic 1 – Et encore merci pour la bouteille ! Dumortier s’apprête à tourner les talons, mais se ravise. Collabo – J’en profite quand même pour vous signaler que mon voisin de palier n’a pas encore acheté son éthylotest. Vous voulez le numéro de sa plaque d’immatriculation ? Flic 2 – Nous sommes un peu débordés pendant cette période de fêtes. Et en sous-effectif. Mais revenez donc nous voir pour les étrennes…

Collabo – Je n’y manquerai pas. Et bonne soirée quand même… L’homme s’en va, suivi du Flic 3. Flic 1 – Et après, on va dire que les gens n’aiment pas la police… Flic 2 – C’est vrai, on se plaint toujours d’être mal aimés, et pourtant… On ne peut pas s’empêcher de trouver ça un peu louche, d’aimer la police à ce point. Flic 1 – On a bien fait de ne pas trinquer avec lui, il aurait été foutu de nous dénoncer aux bœufs-carottes pour avoir picolé pendant le service. Il débouche la bouteille, pendant que l’autre sort deux verres, aussitôt remplis. Ils trinquent. Flic 1 – Bon ben … Joyeux Noël, alors. Flic 2 – C’est ça, joyeux Noël toi-même. Ils vident leurs verres cul-sec. Flic 1 – Ah oui, quand même… Flic 2 – 53 degrés. Flic 1 – Ça ramone. Flic 2 – Faudra qu’on lui demande la composition exacte. Flic 1 – Ouais, il n’y a pas que de la prune là dedans. Flic 2 – Il a dit que c’était de la châtaigne… (Un temps) Je me demande si le grand-père ne rajoutait pas un peu de Destop pour rehausser le goût du fruit. Flic 1 – Tu te rends compte, cette liqueur est plus vieille que nous… Flic 2 – Le pépé devait fabriquer ça dans sa cave pendant le couvre-feu avec ce qui lui tombait sous la main. Flic 1 – Sa façon à lui de résister à l’occupant. Flic 2 – Allez, ressers-nous une tournée, va. C’est toujours ça que les boches n’auront pas… L’autre remplit à nouveau les deux verres, qu’ils vident encore cul sec. Flic 1 – Je ne sais pas s’il y a du Destop là dedans, mais c’est vrai que ça débouche la tuyauterie.

Tâche 6 Réaliser un court métrage Les élèves, en groupes, devront réaliser un court métrage qui sera le remake d'une scène d'un film d'un pays partenaire. Le court métrage durera environ 5 minutes. Procédé de réalisation Les élèves travailleront en groupe. Chaque groupe recevra une scène d'un film contemporain de l'un des pays partenaires. La scène sera dans sa version originale, sous titrée en anglais et durera 5 minutes environ. Il faudra fournir un texte pour expliquer le contexte de la scène, un résumé de l'intrigue en quelques lignes et le moment où se déroule la scène. 1- Une fois que les élèves auront visionné la scène, ils réécriront le dialogue de la scène, en suivant les étapes suivantes : A- se mettre d'accord sur l'idée principale, le cœur de la scène, B- développer l'idée générale : ils écriront le synopsis, un bref résumé de la scène Exemple de synopsis : Un adolescent voyage dans le passé par accident et arrive 30 ans en arrière. Par inadvertance, il interfère dans la première rencontre entre son père et sa mère. Alors qu'il essaie de trouver un moyen de retourner dans le futur, il doit aussi arriver à ce que ses parents, mal assortis, tombent amoureux, sinon il ne verrait jamais le jour. A)L'écriture du script : la description de l'atmosphère et des personnages qui apparaissent dans cette scène de manière très détaillée. Prenant en compte que chaque membre du groupe doit avoir un rôle dans cette scène, ils peuvent l'adapter selon leurs propres besoins, ils peuvent donc ajouter ou retirer l'un ou plusieurs des personnages, ou même changer leur sexe si nécessaire. Ils doivent également faire la distribution des rôles. Exemple de script détaillé : La scène se passe dans le salon de John. Personnages : 100

John, un blogger et youtuber de 24 ans, c'est un gentil garçon. Il est amoureux d'Helen. Helen, une jeune femme mystérieuse. Elle sort avec John, mais elle cache quelque chose. Mark, l'ami de John, depuis peu, il se comporte de manière étrange. Mrs. Spencer, la patronne d'Helen. Une femme déterminée qui déteste lorsque les gens s'opposent à elle. B)Ecriture des prises de vue du script. Il comprendra le type de prises de vue et d'angles de vue, les dialogues et les directions scéniques concernant l'humeur des personnages dans les dialogues. Il comprendra aussi d'autres détails techniques tels que les bruits, la musique, etc,... Elle fera une page de long, voire une et demie. Format du script incluant toutes les sections. Prise de Dialogue Image vue 1 John: “Je t'en prie, ne Close up sur les t'en va pas !” deux Helen: “Laisse moi personnages. tranquille ! Je ne te fais Angle au niveau plus confiance.” des yeux.

Musique/bruits /ton de la voix John avec une voix pleine de pitié, Helen, en colère et triste.

3- Ensuite, les élèves devront s'entendre sur la distribution des rôles, sur le lieu de la scène les costumes, accessoires, etc. Les décors devront inclure les éléments géométriques suivants : Les élèves réaliseront 6 à 8 formes d'une courbe continue (appelée LINK) en connectant des arcs.

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Ces formes seront réalisées sur du carton ou acétate. Ensuite, les liens seront découpés et utilisés en tant que gabarits. Ces gabarits seront utilisés pour faire une œuvre d'art abstraite contenant des courbes reliées, qui seront coloriées à leur convenance.

Les élèves s'en serviront pour le décor. Ils répéteront selon leurs besoins. 4- Après, les élèves enregistreront la scène : -

Avant ça, ils doivent se mettre d'accord sur le nombre de prises qu'ils devront faire, il devrait y avoir au moins 5 prises, et ils doivent aussi se mettre d'accord sur quelles prises seront enregistrées à chaque fois.

Il est préférable de garder le même format de la scène originale. Afin d'y parvenir, ils devront garder en mémoire les prises de vue et les angles.

5 – A la fin, ils feront le montage du court métrage. Ils mettront les différentes séquences qu'ils ont enregistrées dans le bon ordre ; ils ajouteront le générique de début et de fin avec le nom des participants, le titre du film et toutes les informations qu'ils veulent. S'ils ont choisi de ne pas enregistrer les dialogues en live, alors ils peuvent les ajouter pendant le montage du film. La musique peut être la même que dans la scène originale, s'il y en avait une, ou elle peut être créée par les élèves en utilisant Music

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Maker Jam par exemple. Le générique et la musique doivent être en accord avec le genre narratif. 6- Afin “de faire connaître leur film”, les élèves devront créer l'affiche de leur film, qui devra attirer l'attention des gens et communiquer, en un coup d’œil, l'essence et l'humeur du film. Recommendations pour l'affiche : - Format : A3 - Contenu (titre, membres du groupe et slogan) - Éléments géométriques (tous ou plusieurs utilisés pour les décors) ElIe peut être réalisée manuellement (technique libre) ou grâce à des outils numériques (https://www.canva.com/create/posters/ par exemple) ou des logiciels informatiques. Afin de réaliser l'affiche de leur film, les élèves suivront les étapes suivantes: 1- Chaque membre du groupe réalisera une esquisse, papier format A4, avec un minimum de contenu : titre, slogan, etc. S'ils ont utilisé un logiciel, ils peuvent l'imprimer ou le montrer aux autres membres du groupe. 2- Ils discuteront des différentes esquisses et choisiront les parties qu'ils préfèrent, une par une (quel titre est le meilleur, puis le slogan, ….). 3- Ils réaliseront l'affiche. 4- Ils devront rendre/envoyer l'affiche définitive avec tous les esquisses du groupe. La scène du film français est extraite du film de Patrick Leconte “Les Bronzés font du ski” (1979). Extrait : 1:10:56 – 1:14:21

Technique d'apprentissage coopératif Afin d'écrire la scène, on utilisera la technique du “crayon au milieu” pour le brainstorming pour trouver les idées. Tout d'abord, ils devront se mettre d'accord sur ce qu'ils vont écrire. Chaque membre du groupe doit contribuer à l'apport d'idées. 1- idée principale de la séquence.

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2- les personnages qui sont dans la séquence. 3- développement de l'idée principale : * le début * le climax * la résolution 4- Contribution de chaque personnage au développement de l'histoire. Ensuite, ils devront se mettre d'accord sur chacun de ces points et ils écriront le synopsis et la narration du script. Après, ils écriront les dialogues, en incluant les indications scéniques avec le ton des dialogues. La rédaction du synopsis, du script contenant toutes les informations requises, tout devra être écrit par le groupe tout entier. Pour enregistrer la scène, tous les membres du groupe travailleront ensemble sur toutes les tâches et y contribueront de manière égale, mais il y aura un coordinateur pour chacune des parties suivantes : 1. les costumes et les accessoires, 2. la scène et les décors 3. l'enregistrement et le matériel de montage (caméra, logiciel, etc.), 4. les éléments géométriques Les élèves rédigeront un rapport comprenant le nom des coordinateurs des différentes parties mentionnées ci-avant, de même qu'une évaluation sur la façon dont ils ont mené leur tâche, en graduant leur travail en tant que coordinateur de 1 à 5, 1 étant la plus petite note et 5 la plus haute. Par exemple : Marie, enregistrement et montage : 4 points A la fin, les produits de chaque groupe comprendront le script détaillé, le court métrage et l'affiche du film.

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Tasks in Spanish Târea 1 Técnica de aprendizaje cooperativo aconsejada Para realizar esta tarea hay que utilizar la técnica del “rompecabezas”. En primer lugar, se asignará a cada miembro del grupo una parte de la tarea. Una vez que todos los miembros del grupo han acabado de hacer su parte, se comparte la información con los demás. Los miembros del grupo encargados de las partes que implican operaciones matemáticas, explicarán al resto del grupo los pasos que han seguido hasta hallar la solución o respuesta a la problema o pregunta planteados. De esta manera, aunque cada uno haya trabajado una parte, al compartir la información con el resto del grupo, todos adquieren conocimiento de las partes sobre las que no ha trabajado. Finalmente, se da forma al “puzzle”, se ensamblan las piezas según el formato que el profesor haya elegido. Esta actividad ha sido diseñada para formar parte de una exposición oral grabada en vídeo. Índice de elementos matemáticos 1. 2. 3. 4. 5. 6. 7. 8.

Posiciones relativas de dos o más rectas. Concepto de polígono. Clasificación de los polígonos según el número de lados. Definición de mosaico. Cálculo del área de figuras planas. Concepto de poliedro. Desarrollo plano de dos edificios poliédricos Cálculo del volumen de dichos edificios

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La geometría, parte de las matemáticas que se encarga de estudiar las propiedades y las medidas de una figura, juega también un importante papel en el ámbito artístico. De hecho, las formas geométricas nos permiten crear composiciones de alto valor expresivo y artístico, tal y como ocurre en las obras protagonistas de esta tarea: los mosaicos de la judería de Toledo, las torres inclinadas de Madrid y la pintura de José María Yturralde

Pieza de diseño: Mosaico45 1. Define de una forma muy sencilla qué es un mosaico. 2. Investiga a qué lugar puede pertenecer el mosaico de la figura. 3. ¿Cuál es la figura básica que se ha utilizado para construir el mosaico? 4. Si el lado de uno de los rombos midiera 5 cm, y la diagonal mayor midiera 6 cm, calcula el área de la figura siguiente formada por la composición de seis rombos: Podrás encontrar solución a las respuestas en las siguientes direcciones URL: http://guiametoledo.com/rutas-por-toledo/el-greco-y-la-juderia/ http://www.significados.com/mosaico/ https://matematicasmartinrivero.files.wordpress.com/2010/04/mosaicos.pdf

Mosaico de la Judería de Toledo. Hecho con pequñas piezas de cerámica de colores llamadas teselas

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Obra arquitectónica relevante46 Los primeros rascacielos inclinados que se construyeron en el mundo fueron las dos torres inclinadas de Madrid que conforman la llamada Puerta de Europa. 1. ¿Qué otro nombre reciben? 2. Un poliedro es un cuerpo geométrico limitado por cuatro o más polígonos planos. Investiga si cada una de las torres son poliedros y en ese caso investiga qué polígonos conforman cada una de sus caras. Para ello ayúdate de su desarrollo plano. 3. Si sus bases son cuadrados de 34.5 metros de lado y su altura es de 114 metros. Halla el volumen de cada una de las torres. Podrás encontrar solución a las respuestas en las siguientes direcciones URL: http://recursostic.educacion.es/secundaria/edad/4esomatematicasB/semejanza/kio_cidead.pdf https://matematicasiesoja.files.wordpress.com/2013/10/c3a1reas-y-olc3bamenes-de-cuerposgeomc3a9tricos.pdf

Pintura de un famoso artista: José María Yturralde47 1. Realiza una pequeña biografía del artista español José María Yturralde. Incluye, simplemente algunos detalles importantes tales como de dónde es, qué tipo de artista es,… 2. Analiza el cuadro anterior desde un punto de vista geométrico: • Posiciones relativas de dos o más rectas • Definición de polígono • Polígonos que observas y clasifícalos según su número de lados. Podrás encontrar solución a las respuestas en las siguientes direcciones URL: http://www.yturralde.org/index-es.html http://iesdefuentesauco.centros.educa.jcyl.es/sitio/upload/10_Tema_10_1.pdf

46 La Puerta de Europa. Torres gemelas de 114 m de altitud y una inclinación de 15º. Diseñadas por los arquitectos norteamericanos Philip Johnson y John Burgee. Fueron construídas entre 1989 y 1996. Se encuentran en el Paseo de la Castellana, en Madrid. 47 Figura imposible, obra pictórica de José María Iturralde, acrílico sobre madera, 1970

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Târea 2 Programación y realización de la actividad Para realizar esta tarea, tenéis que trabajar en grupos. Consta de dos partes.  Parte 1 La primera parte de la tarea consiste en escribir un relato inspirado en la foto artística de Chema Madoz o en el cuadro creado por Equipo Crónica, ambos tienen en común la presencia de elementos matemáticos. Cada grupo trabajará con otros tres grupos y entre todos los grupos tendréis que elaborar el relato, trabajando por relevos: 1. Empezará un grupo escribiendo la introducción. 2. Una vez este grupo haya finalizado, el siguiente grupo deberá continuar el relato, desarrollando parte de la historia. 3. Cuando terminen, seguirá el tercer grupo, que seguirá con el desarrollo de la trama. 4. Por último, el grupo que quede, escribirá el final de la historia. Previamente los componentes de todos los grupos tenéis que comentar la obra con la que os corresponde que trabajar y decidir qué vais a escribir: ¿Qué? ¿Quién? ¿Dónde? ¿Cuándo? La historia la tenéis que escribir entre cuatro grupos y tenéis que planear entre todos el argumento, los protagonistas, dónde y cuando tiene lugar la acción, cómo acaba, etc. Cada parte de la historia debe constar de aproximadamente 50 palabras en Arial 14. El coordinador de cada grupo se encargará de escribir la parte del relato que les corresponda (y que ha sido acordada y escrita por todos los miembros del grupo).  Parte 2 En esta segunda fase, cada grupo tiene que realizar, a partir de uno de los relatos escritos, un dibujo, collage o fotografía, que contenga los elementos geométricos que aparecían en la obra que inspiró ese relato. La presentación será en un formato A4, si se trata de una creación en papel, y la fotografía hay que presentarla en formato digital. Criterios de Evaluación 108

Para la Historia: A. Uso correcto de la lengua. B. Coherencia y cohesion. C. Originalidad y creatividad. D. Trabajo en grupo. Para el dibujo, collage o fotografía: 5. Originalidad y creatividad. 6. Utilización de los elementos geométricos. 7. Calidad artística. 8. Trabajo en grupo. Técnicas de aprendizaje cooperativo aplicadas. La realización de la primera parte de la tarea, tal y como aparece descrita, supone una adaptación de la técnica del “folio giratorio”, que va precedida de una “lluvia de ideas” mediante la técnica de “lápices al centro”. El dibujo, fotografía o collage, se debe hacer utilizando la técnica del “puzzle”. Chema Madoz 48 Chema Madoz , nació en Madrid hace 57 años y es uno de los fotógrafos españoles de mayor prestigio internacional. Sus obras son creadas a partir de hábiles juegos de imaginación, en los que emplea perspectivas y texturas para elaborar sus personalísimas fotografías, las cuales tienes que mirar dos veces, una para ver lo que crees ver y otra para entender los elementos de lo que ves. Con este artista, que trabaja siempre en blanco y negro, nada es lo que parece. Ejemplo de ello es la fotografía que mostramos a la derecha.

Transportador, fotografía de Chema Madoz, 2007.

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Imagen minimalista, originada a partir de un transportador de ángulos que reposa sobre una recta horizontal que divide el espacio en dos partes desiguales (regla de los tercios) Manteniendo la textura original de los elementos de la imagen, el fotógrafo juega con la escala haciendo que el transportador adopte el papel del sol.

A mediados del siglo XX, surgen en España diferentes grupos y tendencias con el propósito de renovar el panorama artístico español. Equipo Crónica 49es uno de ellos. Nace en Valencia en 1964, formado en su origen por Manuel Valdés, Rafael Solbes y Juan Antonio Toledo (pero este último abandonó pronto el grupo). Sus obras son realizadas en equipo. Solbes y Valdés reflexionaban primero sobre lo que se proponían y después pintaban conjuntamente, utilizando imágenes conocidas, tanto de los medios de comunicación de masas como de la historia del arte. En este cuadro (La factoría y yo, 1970), se integran magistralmente tres obras de tres genios de la pintura: Velázquez (Retrato del infante don Carlos. 1626), Andy Warhol (Ten-Foot Flowers.1967) y Roy Lichtenstein (Preparedness, 1968). Como vemos, a partir de una obra del s. XVII y otras dos del s. XX, el Equipo Crónica consigue formar una composición totalmente equilibrada dentro del caos generado por la mezcla de colores, direcciones y texturas.

La Factoría y yo, de Equipo Crónica, acrílico sobre lienzo, 1970.

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Târea 3 Objetivos A. Comprender las costumbres de los otros a partir de sus narraciones tradicionales. B. Impulsar la creación plástica y literaria. Planificación de la actividad y productos finales 1. Cada grupo de alumnos será asignado una historia, leyenda o relato popular. 2. A continuación, los alumnos tiene que escribir un guión con diálogos adaptando la historia, leyenda o relato popular que les ha sido asignado. 3. A partir de este guión los alumnos tienen que elaborar una historia gráfica con una extensión no superior a dos páginas.(En papel formato A4 o formato digital) La historia gráfica se puede hacer de las siguientes maneras: - Mediante el uso de un programa de creación de “comics” online, tal como Pixton , Tondoo, Bitstrips u otros recursos online. - Dibujado a mano. - Mediante el uso del programa Comic Life. - Realizando un collage. - Cualquier otro método o herramienta que conozcan. - La historia gráfica debe tener un máximo de 12 viñetas y ha de incluir, al menos, cinco de los siguientes elementos matemáticos: 1. Burbujas ovales (por ejemplo para los bocadillos) 2. Rectángulos (por ejemplo, para la voz del narrador) 3. Círculos 4. Círculos concéntricos 5. Simetrías 6. Ángulos agudos 7. Paralelas 8. Perpendiculares 111

9. Triángulos equiláteros 10. Cuadrados _ Si la historia gráfica se dibuja a mano, los elementos matemáticos hay que hacerlos utilizando las herramientas adecuadas (regla, cartabón, compás…) _ Junto con el cómic, deberá entregarse una lista de todos los elementos matemáticos que se hayan utilizado, señalando claramente en qué viñeta y en qué lugar concreto de la viñeta aparece cada uno. _ Las historias gráficas que se hayan realizado a mano deben escanearse. Técnicas de trabajo cooperativo En primer lugar, tendrá que haber una tormenta de ideas, utilizando la técnica “lápices al centro”, seguida de una discusión entre los miembros del grupo, antes de tomar la decisión final de lo que se vaya a realizar. Después, se utilizará la técnica del folio giratorio para escribir el diálogo. Para crear la historia gráfica, se utilizará la técnica del puzzle en equipo. Criterios de evaluación y calificación  Uso de la lengua inglesa.  Adecuación entre el guión y el relato original.  Creatividad y originalidad  Utilización de los elementos geométricos.  Calidad artística.  Trabajo en grupo.

El relato popular español LA LEYENDA DEL PUENTE DEL BESO (EL PIRATA CAMBARAL)50 En la Edad Media los mares cantábricos estaban dominados por piratas. Uno de los más famosos y temidos que asolaba a los viajeros españoles se llamaba Cambaral. Era el terror de los pasajeros no solo porque se apoderaba de las naves y robaba todas sus pertenencias, sino porque solía concluir su labor torturando y asesinando a los tripulantes. Además, raptaba a las bellas doncellas para después comerciar con ellas en los mercados. 50

El pirata Cambaral , relato tradicional de Luarca de autor anónimo.

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Muchas veces el Gobierno tomó cartas en el asunto, pero fue inútil, porque Cambaral derrotaba a todas las flotas. En vista de que parecía imposible su captura, Hidalgo, el señor de la fortaleza de Luarca, decidió tenderle una emboscada con sus hombres fingiendo ser pescadores. Así, salieron a esperarlos a la mar y confiaron en que en cuanto los piratas los vieran, intentarían asaltarlos. Los piratas, no conociendo la trama, picaron y se encontraron con decenas de personas perfectamente armadas y preparadas para el ataque. Cambaral fue hecho prisionero y conducido a la fortaleza de la Atalaya, donde fue encerrado en unas mazmorras. Mientras se celebraba la victoria, la hija del señor (una bella joven de muy buen corazón) pidió permiso para poder entrar a curarle las heridas antes de llevarlo ante la Justicia. Y así fue cómo, mientras se las curaba, ambos sintieron el poderoso influjo del amor. Tomaron la decisión de fugarse mientras el padre estaba durmiendo. Se reunieron y escaparon hacia el puerto, pero en el último momento Hidalgo, al que habían puesto al corriente de la fuga, los sorprendió. Ellos, viendo imposible su huida, se abrazaron y juntaron sus labios como si fuera su último beso. Hidalgo, incapaz de soportar esa traición, sacó una afilada espada y les cortó de un solo tajo ambas cabezas, las cuales cayeron al agua del puerto, mientras sus cuerpos se quedaron fuertemente abrazados. Tiempo después en ese mismo lugar se levantó el Puente del Beso. Muchos dicen que hoy en día, a la media noche, cuando brilla la luna llena, se escuchan todavía palabras amorosas que provienen del mar; y que mirando al horizonte pueden verse flotando dos cabezas unidas en un beso.

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Târea 4 RECREACIÓN MULTIMEDIA DE UN POEMA Los alumnos trabajarán en grupos. Realizarán una recreación multimedia de un poema de un autor extranjero contemporáneo, integrando para ello imágenes, música y el recitado bilingüe del texto. Las imágenes tienen que incluir elementos matemáticos tales como, espirales, simetrías y redes modulares que contribuya n, de alguna manera, a un mejor entendimiento del texto. Proceso de realización: 1) A cada grupo se le asignará un poema de un país extranjero con el fin de que realicen colectivamente la tarea. (El poema estará en la lengua materna y en inglés) 2) El producto multimedia que elaboren los alumnos no puede superar los tres minutos de duración y debe constar, al menos, de los siguientes elementos: a) El recitado en lengua original y en inglés del poema, dispuestos de forma consecutiva o intercalados libremente. b) Imágenes o secuencias de vídeo, originales o manipuladas, que c) incluyan elementos matemáticos tales como, espirales, simetrías y d) redes modulares que contribuyan, de alguna manera, a un mejor entendimiento del texto y sirvan para ambientar la temática y las referencias del poema recitado. e) Música que ayude a realzar las emociones y sentimientos que el texto expresa. Cada alumno compondrá su propia música utilizando, por ejemplo, Music Maker Jam. Criterios de evaluación: A la hora de evaluar y calificar las tareas se tendrán en cuenta los siguientes criterios: - Uso de la lengua inglesa en la primera parte de la tarea (información acerca de los intérpretes, relación de los instrumentos utilizados y resumen del contenido de las letras) - El recitado en su lengua original (dicción, ritmo). - El recitado en lengua inglesa (pronunciación, entonación, ritmo). - La adecuación de la música, las imágenes y los elementos matemáticos al contenido del poema. 114

- Calidad de imagen y sonido. Técnica de aprendizaje cooperativo Equipo de investigación. Indicaciones: 1. En primer lugar, es tarea de todos decidir qué miembro del grupo es responsable de cada una de las partes de la tarea. A continuación los responsables establecen los plazos para la realización de las distintas partes de la tarea, que son: 1. Búsqueda de un alumno del centro asociado que corresponda, a través del TwinSpace, para pedirle que recite y grabe el poema en su lengua materna. 2. Recopilación de imágenes que contengan elementos matemáticos para el vídeo. 3. Selección de las imágenes más apropiadas y su secuenciación en el vídeo. 4. Recitado y grabación del poema en inglés. 5. Composición de la música para el vídeo. 6. Edición del vídeo. 2. Todos los miembros del grupo contribuyen a cada una de las partes de la tarea y el alumno responsable se asegura de que todos hacen su parte a tiempo. 1. Cada uno de los miembros del grupo contacta con un alumno diferente del centro asociado correspondiente a través del TwinSpace y le pide que recite el poema, lo grabe en su lengua materna y le envíe el archivo de audio. 2. Cada uno de los miembros del grupo recopila imágenes con elementos matemáticos para ilustrar el poema. 3. Todos contribuyen al recitado del poema en inglés para su grabación. 4. Cada uno de los miembros del grupo compondrá música para acompañar al video. 3) El grupo de reúne, comparten lo que cada uno aporta y toman las decisiones correspondientes: 1. Deciden qué grabación del poema en lengua materna es la mejor. 2. Entre todos deciden qué composición musical es la más apropiada, qué imágenes son las idóneas y cuál es la mejor manera de secuenciarlas en el vídeo.

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3. Editar el video suele ser la tarea de una sola persona al ordenador, lo mismo ocurre con la grabación del poema en inglés, pero todos los miembros del grupo deberán contribuir a estas partes de la tarea.

4) Para comprobar que todos los miembros del grupo hicieron su parte de las distintas sub-tareas, todos y cada uno deberán entregar un informe en el que hagan constar: Con quién contactaron en el TwinSpace para la grabación del poema en lengua materna. La relación de los elementos matemáticos que aparecían en las imágenes que recopilaron. El archivo de audio con la pieza musical que compusieron para acompañar el vídeo. Una valoración de la labor de los distintos coordinadores. Enviarán este informe de forma individual por correo electrónico adjuntando la grabación del poema en lengua materna que aportó, las imágenes escogidas por él/ella y el enlace o archivo de la música compuesta. Índice de elementos matemáticos 1. Espirales 2. Simetrías 3. Redes modulares

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El poema español Aunque tú no lo sepas de Luís García Montero51 Como la luz de un sueño, que no raya en el mundo pero existe, así he vivido yo iluminando esa parte de ti que no conoces, la vida que has llevado junto a mis pensamientos. Y aunque tú no lo sepas, yo te he visto cruzar la puerta sin decir que no, pedirme un cenicero, curiosear los libros, responder al deseo de mis labios con tus labios de whisky, seguir mis pasos hasta el dormitorio. También hemos hablado en la cama, sin prisa, muchas tardes esta cama de amor que no conoces, la misma que se queda fría cuanto te marchas. Aunque tú no lo sepas te inventaba conmigo, hicimos mil proyectos, paseamos por todas las ciudades que te gustan, recordamos canciones, elegimos renuncias, aprendiendo los dos a convivir entre la realidad y el pensamiento. Espiada a la sombra de tu horario o en la noche de un bar por mi sorpresa. Así he vivido yo, como la luz del sueño que no recuerdas cuando te despiertas

Aunque tú no lo sepas, poema de Luís García Montero

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Târea 5 Lectura De Textos Teatrales Contemporáneos Y Elaboración De Una Escena Teatral. Por grupos, los alumnos leerán fragmentos de obras de teatro de dramaturgos contemporáneos. Después, los alumnos escribirán una escena que de continuación al texto que les haya correspondido. Finalmente harán una fotografía que represente una situación de la escena escrita por ellos mismos. PROCESO DE REALIZACIÓN: 3) Los alumnos trabajarán con un fragmento de una obra de teatro de 4) un autor contemporáneo. Condiciones del texto: a) La temática es libre, siempre y cuando el texto trate alguno de los asuntos propios del ser humano contemporáneo. b) La extensión del texto será de 3 o 4 páginas. c) El fragmento debe ir acompañado de una contextualización (5-6 líneas que sinteticen el argumento de la obra y el momento al que pertenece el fragmento proporcionado). d) El texto estará traducido al inglés. 5) Se asigna a cada grupo un texto teatral. Los alumnos deben leer el fragmento y escribir una escena que de continuación al mismo. Esta escena tendrá una duración mínima de una página, máximo 2 páginas con fuente Arial, tamaño 12, espaciado 6 puntos e interlineado sencillo. Pueden, si lo desean, añadir algún personaje más, en algunos casos será necesario habida cuenta del número de alumnos en el grupo y de los personajes que parecen en el fragmento. En el texto, tendrán que aparecer las acotaciones necesarias (por ejemplo aquellas que indiquen el desplazamiento de un personaje por el escenario, etc.) 6) Cada grupo deberá hacer una fotografía que represente un instante de la escena creada por ellos mismos. Todos los componentes del 118

grupo deben aparecer en la misma. Tendrá que usarse el vestuario adecuado a la escena y el escenario que corresponda, en el que deberán aparecer los siguientes elementos geométricos: - Óvalos. - Espirales de dos o tres centros. - Polígonos estrellados de un mínimo de cinco puntas. Los elementos matemáticos tiene que ser elaborados por los alumnos según las indicaciones correspondientes y utilizando las herramientas adecuadas y deberán tener un lugar destacado en la imagen, por ejemplo, pueden formar parte de un cuadro como elemento decorativo, o del estampado del vestuario, o de una lámpara. La fotografía puede ser en color o blanco y negro y debe tener formato digital. Criterios de evaluación - Elaboración de la escena dramática:  Uso adecuado de la lengua inglesa, corrección morfosintáctica.  Riqueza de vocabulario.  Coherencia con el fragmento al que da continuidad la escena.  Creatividad. - Fotografía:  Calidad técnica. La imagen es nítida y está bien enfocada.  Adecuación del vestuario y el escenario al contenido de la obra y esmero en la elección de los mismos.  Uso de los elementos matemáticos propuestos y perfección en su diseño.  Dramatización (los gestos, las expresiones faciales muestran las emociones pertinentes)

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Técnica de aprendizaje cooperativo Para escribir la escena dramática, se aplicará a modo de lluvia de ideas, la técnica “lápices al centro”. Los alumnos debaten sobre lo que van a escribir. Todos y cada uno de los miembros del grupo tienen que aportar ideas acerca de los siguientes puntos:  El elemento que sirve de conexión entre la escena que han leído y la escena que van a escribir. Algo tiene que servir de resorte para poner la acción en marcha de nuevo, puede ser la aparición repentina de un personaje, algo que sucede inesperadamente,…  El número de personajes que van a intervenir (se pueden añadir o quitar en función de los miembros del grupo)  Qué sucede durante la escena y cómo acaba.  Dónde tiene lugar la acción, puede ser el mismo escenario o un escenario distinto. Posteriormente se ponen de acuerdo sobre cada uno de estos puntos. Deciden también entre todos el orden de intervención de los personajes y la necesidad de acotaciones para explicar los movimientos de los personajes obre el escenario, si los hay, o por ejemplo sonidos, cambios de luz, etc. y proceden a la redacción de la escena. Por último, las acotaciones, la revisión del texto y la edición del mismo se llevarán a cabo, también, entre todos los miembros del grupo.

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Para la fotografía, todos colaboran en todo, pero se nombrará a uno o dos miembros del grupo (depende de los grupos) responsable de cada una de los siguientes apartados: Vestuario y atrezzo. Escenario, la decoración del mismo. Material fotográfico y edición de la fotografía. Elementos geométricos. La fotografía deberá ir acompañada de un informe en el que figure quién coordinó cada uno de las apartados anteriores y una valoración por parte de sus compañeros del desempeño de su

obligación, calificando su trabajo del 1 al 5, siendo 1 la calificación más baja y 5 la más alta. El texto español Pic–Nic52 de Fernando Arrabal. Picnic o Picnic en el campo de batalla es una obra escrita por Fernando Arrabal en 1947 y estrenada en 1952. Es un claro alegato frente a la guerra. Aún en estos días se sigue representando en todo el mundo, "para evidenciar lo absurdo de la guerra sorda", según Arrabal. SINOPSIS: La obra cuenta de manera absurda, como un matrimonio decide ir a la guerra a visitar a su hijo, un soldado, y proponerle un día de campo en la mitad de la batalla. Luego aparecerá un soldado enemigo el cual se unirá a éste picnic de manera amistosa y empezarán a comentar lo que pasa en la guerra, llegando a la conclusión que ninguno de ellos quiere estar ahí, buscan soluciones para acabar con esa absurda guerra; felices con sus ideas y con la intención de regresar a casa, son asesinados por culpa de la batalla que empieza a hacer furor en donde ellos se encontraban. [Los fragmentos seleccionados pertenecen al principio y el final de la obra, y están enlazados de forma que constituyen una síntesis del texto original] PERSONAJES ZAPO SEÑOR TEPÁN SEÑORA TEPÁN ZEPO Decorado: Campo de batalla. Cruza el escenario, de derecha a izquierda, una alambrada. Junto a esta alambrada hay unos sacos de tierra. (La batalla hace furor. Se oyen tiros, bombazos, ráfagas de ametralladora. ZAPO, solo en escena, está acurrucado entre los sacos. Tiene mucho miedo. 52

Un fragmento de la obra de teatro Pic-Nic, de Fernando Arrabal.

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Cesa el combate. Silencio. ZAPO saca de una cesta de tela una madeja de lana y unas agujas. Se pone a hacer un jersey que ya tiene bastante avanzado. Suena el timbre del teléfono de campaña que ZAPO tiene a su lado.) ZAPO.-Diga... Diga... A sus órdenes mi capitán... En efecto, soy el centinela de la cota 47... Sin novedad, mi capitán... Perdone, mi capitán, ¿cuándo comienza otra vez la batalla?.. Y las bombas, ¿cuándo las tiro?.. ¿Pero, por fin, hacia dónde las tiro, hacia atrás o hacia adelante?.. No se ponga usted así conmigo. No lo digo para molestarle... Capitán, me encuentro muy solo. ¿No podría enviarme un compañero?.. Aunque sea la cabra... (El capitán le riñe.) A sus órdenes... A sus órdenes, mi capitán. (ZAPO cuelga el teléfono. Refunfuña.) (Silencio. Entra en escena el matrimonio TEPÁN con cestas, como si vinieran a pasar un día en el campo. Se dirigen a su hijo, ZAPO, que, de espaldas y escondido entre los sacos, no ve lo que pasa.) SR. TEPÁN.- (Ceremoniosamente.) Hijo, levántate y besa en la frente a tu madre. (ZAPO, aliviado y sorprendido, se levanta y besa en la frente a su madre con mucho respeto. Quiere hablar. Su padre le interrumpe.) Y ahora, bésame a mí. (Lo besa en la frente.) ZAPO.-Pero papaítos, ¿cómo os habéis atrevido a venir aquí con lo peligroso que es? Iros inmediatamente. SR. TEPÁN.- ¿Acaso quieres dar a tu padre una lección de guerras y peligros? Esto para mí es un pasatiempo. Cuántas veces, sin ir más lejos, he bajado del metro en marcha. SRA. TEPÁN.-Hemos pensado que te aburrirías, por eso te hemos venido a ver. Tanta guerra te tiene que aburrir. ZAPO.-Eso depende. SR. TEPÁN.-Muy bien sé yo lo que pasa. Al principio la cosa de la novedad gusta. Eso de matar y de tirar bombas y de llevar casco, que hace tan elegante, resulta agradable, pero terminará por fastidiarte. […] ZAPO.-Perdonadme. Os tenéis que marchar. Está prohibido venir a la guerra si no se es soldado. SR. TEPÁN.-A mí me importa un pito. Nosotros no venimos al frente para hacer la guerra. Sólo queremos pasar un día de campo contigo, aprovechando que es domingo.

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SRA. TEPÁN.-Precisamente he preparado una comida muy buena. He hecho una tortilla de patatas que tanto te gusta, unos bocadillos de jamón, vino tinto, ensalada y pasteles. ZAPO.-Bueno, lo que queráis, pero si viene el capitán, yo diré que no sabía nada. Menudo se va a poner. Con lo que le molesta a él eso de que haya visitas en la guerra. […] SR. TEPÁN.-No te preocupes, ya le diré yo un par de cosas a ese capitán. […] SR. TEPÁN.- Bueno, vamos a comer. […] SR. TEPÁN.-Sí, vamos, que tengo un apetito enorme. A mí, este tufillo de pólvora, me abre el apetito. SRA. TEPÁN.-Comeremos aquí mismo, sentados sobre la manta. ZAPO.- ¿Como con el fusil? SR. TEPÁN.-Nada de fusiles. Es de mala educación sentarse a la mesa con fusil. (Pausa) Pero qué sucio estás, hijo mío… ¿Cómo te has puesto así? Enséñame las manos. ZAPO.- (Avergonzado, se las muestra.) Me he tenido que arrastrar por el suelo con eso de las maniobras. […] SRA. TEPÁN.-Bueno, pueden pasar. […] ZAPO.-Sí, mamá. (Se ponen a comer). SR. TEPÁN.-Qué, hijo mío, ¿has matado mucho? ZAPO.- ¿Cuándo? SR. TEPÁN.-Pues estos días. ZAPO.- ¿Dónde? SR. TEPÁN.-Pues en esto de la guerra. ZAPO.-No mucho. He matado poco. Casi nada. […] SRA. TEPÁN.-Voy a poner un disco en el gramófono. (Pone un disco. Los tres, sentados en el suelo, escuchan). SR. TEPÁN.-Esto es música, sí señor. (Continúa la música. Entra un soldado enemigo: ZEPO. Viste como ZAPO. Sólo cambia el color del traje. ZEPO va de verde y ZAPO de gris. ZEPO,

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extasiado, oye la música a espaldas de la familia TEPÁN. Termina el disco. Al ponerse de pie, ZAPO descubre a ZEPO. Ambos se ponen manos arriba llenos de terror. Los esposos TEPÁN los contemplan extrañados.) SR. TEPÁN.- ¿Qué pasa? (ZAPO reacciona. Duda. Por fin, muy decidido, apunta con el fusil a ZEPO). ZAPO.- ¡Manos arriba! (Le ata las manos y los pies) […] ZAPO.-Bueno, ¿y qué hacemos ahora con el prisionero? SRA. TEPÁN.-Lo podemos invitar a comer. ¿Te parece? SR. TEPÁN.-Por mí no hay inconveniente. ZAPO.-(A ZEPO). ¿Qué? ¿Quiere comer con nosotros? ZEPO.-Pues... SR. TEPÁN.-Hemos traído un buen tintorro. ZEPO.-Si es así bueno. SR. TEPÁN.-Usted haga como si estuviera en su casa. Pídanos lo que quiera. ZEPO.-Bueno. SR. TEPÁN.- ¿Qué?, ¿y usted, ha matado mucho? ZEPO.- ¿Cuándo? SR. TEPÁN.-Pues estos días. ZEPO.- ¿Dónde? SR. TEPÁN.-Pues en esto de la guerra. ZEPO.-No mucho. He matado poco. Casi nada. […] SRA. TEPÁN.- (A ZEPO.) Si quiere usted, le soltamos las ligaduras. ZEPO.-No, déjelo, no tiene importancia. SR. TEPÁN.-No vaya usted ahora a andar con vergüenzas con nosotros. Si quiere que le soltemos las ligaduras, díganoslo. SRA. TEPÁN.-Usted póngase lo más cómodo que pueda. ZEPO.-Bueno, si se ponen así, suéltenme las ligaduras. Pero sólo se lo digo por darles gusto. SR. TEPÁN.-Hijo, quítaselas. (ZAPO le quita las ligaduras) […] SRA. TEPÁN.-Qué bien, con lo simpático que es el señor prisionero, vamos a pasar un buen día de campo.

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ZEPO.-No tiene usted que decirme «señor prisionero», diga «prisionero» a secas. SRA. TEPÁN.- ¿No le va a molestar? ZEPO.-No, en absoluto. SR. TEPÁN.-Desde luego hay que reconocer que es usted modesto. […] SRA. TEPÁN.-Esto es lo agradable de salir los domingos al campo. Siempre se encuentra gente simpática. (Pausa.) Y usted, ¿por qué es enemigo? ZEPO.-No sé de estas cosas. Yo tengo muy poca cultura. […] SR. TEPÁN.-Pues entonces podemos hacer una cosa: parar la guerra. ZEPO.- ¿Cómo? SR. TEPÁN.-Pues muy sencillo. Tú le dices a todos los soldados de nuestro ejército que los soldados enemigos no quieren hacer la guerra, y usted le dice lo mismo a sus amigos. Y' cada uno se vuelve a su casa. ZAPO.- ¡Formidable! […] ZAPO.- ¿Cómo no se nos habrá ocurrido antes una idea tan buena para terminar con este lío de la guerra? […] ZEPO.-Oiga, pero si paramos así la guerra, ¿qué va a pasar con los generales y los cabos? SRA. TEPÁN.-Les daremos unas panoplias para que se queden tranquilos. ZEPO.-Muy buena idea. SR. TEPÁN.- ¿Veis qué fácil? Ya está todo arreglado. ZEPO,-Tendremos un éxito formidable. ZAPO.-Qué contentos se van a poner mis amigos. SRA. TEPÁN.- ¿Qué os parece si para celebrarlo bailamos el pasodoble de antes? ZEPO.-Muy bien. ZAPO.-Sí, pon el disco, mamá. (La SRA. TEPÁN pone un disco. Expectación. No se oye nada.) SR. TEPÁN.-No se oye nada. SRA. TEPÁN.- (Va al gramófono.) ¡Ah!, es que me había confundido. En vez de poner un disco, había puesto una boina.

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Târea 6 Realización de un corto cinematográfico. Los alumnos, en grupos, elaborarán un corto cinematográfico, de una duración aproximada de unos cinco minutos, que recreará una escena correspondiente a una película. Procedimiento: 1- Los alumnos trabajarán en grupos. Se asignará a cada uno de los grupos una escena correspondiente a una película contemporánea. La escena estará en versión original con subtítulos en inglés y tendrá una duración de aproximadamente cinco minutos. 2- Una vez que los alumnos hayan visto la escena, deberán escribir la parte literaria del guión cinematográfico y lo harán siguiendo los siguientes pasos: A. Acuerdo acerca de la idea central, el núcleo de la secuencia. B. Desarrollo de la idea. Para ello, escribirán una sinopsis, un resumen muy breve de la historia. Ejemplo de sinopsis: A teenage boy accidentally travels 30 years into the past where he inadvertently interferes with his mother and father’s first meeting. While trying to find a way back to the future, he must try to make his mis-matched parents fall in love or he will never be born. C. Realización de la parte narrativa del guion. En esta fase se describe el ambiente y los personajes que forman parte de la escena de forma muy concisa. Teniendo en cuenta que a cada miembro del grupo le corresponde interpretar a uno de los personajes que aparecen en la escena, podrán adaptar la misma a sus necesidades, es decir, pueden añadir o quitar algún personaje o cambiar el género de alguno de ellos si es preciso. Se asignarán los personajes según acuerdo entre todos los miembros del grupo. Ejemplo de parte narrativa del guion: The scene takes place in the sitting-room in John’s house. Characters: 126

John, 24-year-old blogger and youtuber, he’s a kind man. He’s in love with Helen. Helen, mysterious young woman. He has an affair with John, but she’s hiding something. Mark, John’s friend, lately he’s been acting in a weird way. Mrs. Spencer, Helen’s boss. A determined woman who doesn’t like people to oppose her. D. Escritura del guion técnico. Incluirá los planos, los tipos de plano según la cámara y el ángulo y los diálogos. Figurarán las acotaciones donde se indicará el tono del diálogo. También incluirá otros detalles técnicos tales como sonidos, música, etc. Tendrá una extensión de una página y media, aproximadamente. Formato del guion que incluye todos los apartados: Shot Dialogue Image 1

John: “Please, don’t go!” Helen:”Leave me alone! I don’t trust you anymore”

Close up of both characters. Angle at eye level.

Music/sounds/t one of voice John with a pitiful voice, Helen, angry and sad.

3- A continuación, se pondrán de acuerdo en la localización del escenario, el vestuario, atrezzo, etc. y quién llevará a cabo la grabación. El decorado deberá incluir los siguientes elementos geométricos:

ENLACES Para la realización de esta propuesta se realizarán previamente de seis a ocho enlaces sucesivos en un boceto previo sobre un soporte rígido que puede ser una cartulina o en el mejor de los casos un acetato. Durante esta operación es

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necesario que los trazados sean lo más precisos posibles para que las circunferencias tengan unas transiciones suaves y continuas sin aparición de ninguna arista. Posteriormente se recortarán con cuidado las curvas de manera que se obtienen unas plantillas que servirán para trazar una composición abstracta de circunferencias enlazadas que se colorearán libremente.

*Imágenes obtenidas del blog “ @RTEFACTO” 4- Posteriormente, procederán a la grabación de la escena. - Previamente, los alumnos tienen que acordar el número de tomas que van a hacer, que serán un mínimo de cinco, y los planos que grabarán en cada una de ellas. Es aconsejable conservar el formato de la escena original, para ello se tendrán en cuenta los planos utilizados: primeros planos, medios, cortos, generales, etc. según el encuadre o planos normales, picados, cenitales, etc. según el ángulo. 5- Finalmente, procederán a la edición y el montaje del corto utilizando un programa tipo movie maker o similar . Mediante este proceso, los alumnos ordenarán las secuencias rodadas para crear la película. Se añadirán los títulos de créditos tanto al principio como al final de la película, que recogerán los nombres de los participantes, el título del corto y toda la información que consideren necesaria. Es el momento también de añadir los diálogos, si se optó por descartar el sonido en directo y la música, que puede ser la de la escena original, si la tuviera,o una pieza compuesta por

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ellos mismos utilizando el Music Maker Jam, por ejemplo. Tanto los títulos de créditos como la música tienen que estar ligados al estilo de la narración. 6- Para dar publicidad a su “película”, los alumnos deberán elaborar un cartel de cine, cuya función será captar la atención y comunicar a un golpe de vista la esencia y el tono de la película que han hecho. Los elementos básicos de carácter plástico a través de los que se expresará el cartel son: la composición, la imagen, el color y la tipografía. Requisitos del cartel: - Dimensión: A3 - Contenido (título, miembros del grupo y frase promocional/slogan) - Elementos geométricos - Herramientas utilizadas (digital por ejemplo utilizando esta herramienta https://www.canva.com/es_es/crear/posters/ , a mano, en este último caso, técnica libre) Para diseñar el cartel promocional los alumnos deberán seguir estos pasos: 1. Cada miembro realizará un boceto en tamaño folio con el contenido mínimo del mismo. 2. Puesta en común de los trabajos realizados y selección, uno a uno, de los componentes del cartel definitivo. Decidirán qué título, eslogan son los más indicados, etc. 3. Realización del cartel. 4. Envío del mismo y de los bocetos realizados por cada uno de los miembros del grupo. Si se ha hecho mediante ordenador, envío del archivo. Si se ha hecho a mano, hay que escanearlo para después enviarlo. La escena española pertenece a la película de 1988 “Mujeres al borde de un ataque de nervios”, de Pedro Almodóvar. Metraje: 01:01:37- 01:10:13.

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Técnica de aprendizaje cooperativo Para escribir la escena dramática, se aplicará a modo de lluvia de ideas, la técnica “lápices al centro”. En primer lugar, tendrán que debatir sobre lo que van a escribir. Todos y cada uno de los miembros del grupo tienen que aportar ideas acerca de los siguientes puntos: 1. Idea central, el núcleo de la secuencia. 2. Los personajes que participan en la escena. 3. Desarrollo de la idea central: - Comienzo de la escena. - Clímax. - Fin de la escena. 4- Contribución de cada uno de los personajes al desarrollo de la historia. A continuación, se tendrán que poner de acuerdo en cada uno de estos puntos y procederán a la redacción de la sinopsis y de la parte narrativa del guion Posteriormente, deberán llevar a cabo la escritura de la parte dialogada, que Irá acompañada de acotaciones donde se indique el tono del diálogo. Estas últimas partes de la tarea, junto con el guion que incluye todos los apartados, han de realizarse entre todos los miembros del grupo. Para la grabación de la escena, todos colaboran en todo, pero se nombrará a uno o dos miembros del grupo (depende de los grupos) responsable de cada una de los siguientes apartados: - Vestuario y atrezzo. - Escenario, la decoración del mismo. - Material de grabación, edición y montaje de la película. - Elementos geométricos. La película deberá ir acompañada de un informe en el que figure quién coordinó cada uno de los apartados anteriores y una valoración por parte del resto de los compañeros del desempeño de su obligación, calificando su trabajo del 1 al 5, siendo 1 la calificación más baja y 5 la más alta. Por ejemplo: Juana, material de grabación, edición y montaje: 4 puntos.

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Tasks in Swedish Uppgift 1 Metod för kooperativt lärande För att genomföra denna uppgift ska “jigsaw”-metoden användas. Först tilldelas varje medlem i gruppen en del av uppgiften. När alla medlemmar i gruppen gjort klart sina delar ska de dela med sig av informationen. Medlemmarna som är ansvariga för delarna som innehåller matematiskt arbete ska förklara för de andra vilka steg de har följt för att komma fram till lösningen av problemet/frågan. På så sätt lär de alla sig något om samtliga delar i uppgiften, även de delar som de inte arbetat med själva. Till sist gör eleverna the puzzle, de sätter ihop de olika delarna enligt lärarens instruktioner. Denna aktivitet har utformats för att bli del av en muntlig redovisning, inspelad på video. Index över matematiska element 1. Relativa positioner av två eller flera räta linjer 2. Polygonbegrepp 3. Klassificering av polygoner efter antal sidor. 4. Mosaikbegrepp 5. Uträkning av area av plana figurer. 6. Begreppet polyhedral 7. Polyhedral plan utveckling av två byggnader. 8. Räkna ut volymen av sådana byggnader. Introduktion till uppgiften I denna uppgift kommer du att arbeta med några föremål som är speciella för Sverige inom måleri, arkitektur och design. De utvalda föremålen finns nära oss. Du ska utforska hur matematik kan användas inom måleri, arkitektur och design. Olika matematiska beräkningar påverkar till exempel en målnings 131

estetik, en designs mönster, eller konstruktionen och funktionen av en byggnad eller ett monument. Relevant byggnad: Öresundsbron53 Denna 16 kilometer långa bro sammankopplar Sverige och Danmark och de två största städerna i Öresundsregionen: Malmö och Köpenhamn. Bron kom som en efterlängtad lösning på problem som Sverige och Danmark haft i hundratals år. Den har fört de båda ländrna närmare på många sätt, så som att underlätta för människor att arbeta i och pendla till det andra landet, samt att underlätta handeln länderna emellan. Tidigare var man tvungen att ta färjan för att korsa sundet. Sett från ovan verkar bron försvinna ner i havet, vilket faktiskt är fallet då den också består av en tunnel. 1.När öppnades bron för trafik? 2.Vilken medelhastighet har tåget när du reser mellan Kastrup flygplats och Hyllie (Malmö)? Avståndet mellan Hyllie och Kastrup är 27,5 km. 3.Bron har två pyloner. Beskriv vad en pylon är. Du kan hitta svaret på frågorna på dessa länkar: https://www.oresundsbron.com/en/node/6738 http://physics.tutorvista.com/motion/speed.html http://www.csgnetwork.com/csgtsd.html http://global.britannica.com/technology/pylon-architecture https://www.youtube.com/watch?v=rxFWgHichcM

Titta på de första minuterna av denna film om Öresundsbron!

Design: “Berså” av Stig Lindberg.54 “Berså” är en av Gustavsbergs porslinsfabriks mest välkända mönster, skapat av designern Stig Lindberg 1960. Den har varit en riktig storsäljare och mönstret är fortfarande eftertraktat. Motivet med gröna blad har blivit en ikon för Stig Lindberg.

Öresundsbron är en circa 16 km lång väg- och järnvägslänk mellan Sverige och Danmark. Den designades av den danske broarkitekten Georg Rotne och konstruerades mellan 1993 och 2000. 54 Berså av Stig Lindberg. Berså är en av Gustavsbergs porslinsfabriks mest kända monster, skapat av Stig Lindberg 1960. Den har sålts i stora antal och motivet med de gröna löven har blivit en ikon som representerar Stig Lindberg.

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1.De gröna löven är symmetriskt placerade. Symmetri är en term som används både inom konst och vetenskap. Inom konst används ofta symmetri för att skapa balans i motivet så att det blir behagligt att titta på. Förklara vad symmetri är. 2.På en 20x20 cm stor servett förekommer kvisten på bilden ovan två gånger som två parallella kvistar, per sida/del. En servett har fyra sådana delar och blir alltså 40x40 cm utvecklad. Hur många kvistar som den ovan och hur många gröna löv förekommer på en duk som är 140x250 cm? Visa hur du löser uppgiften med bilder och beräkningar! Du kan hitta svar på frågorna på dessa länkar: http://lyk-peir-mytil.les.sch.gr/mart/ https://www.mathsisfun.com/geometry/symmetry.html http://dictionary.reference.com/browse/symmetry http://www.haelmedia.com/OnlineActivities_txh/mc_txh4_001.html

Känd målning: “Composition with geometry” av den svenska konstnären Esaias Thorén55 1. Skriv en kort biografi om den svenska konstnären Esaias Thorén, bara några relevanta fakta om honom, var han kommer ifrån, vilken slags konstnär han är… Ta reda på några fakta om Halmstadgruppen som han var med i. 2. Vilka geometriska former kan du hitta i tavlan? 3. Räkna ut area av några olika former: * Kvadraten: Hur stor är arean av kvadraten om sidan är 4 cm? * den största cirkeln: Hur stor blir cirkelns area om radien är 0.8 cm? * Hur många procent av hela triangeln utgör topptriangeln? Förklara/visa hur du räknar ut uppgifterna. Du kan hitta svar på frågorna på dessa länkar: http://www.mjellbykonstmuseum.se/omwebbplatsen/english/thehalmstadgroup.4.31d9bb9f1285e3aab 5780007238.html http://www.mathsisfun.com/area.html http://www.mathsisfun.com/geometry/area.html

Geometrisk komposition, målning av Esaias Thorén, olja på pannå. (årtal okänt)

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Uppgift 2 Kooperativa lärtekniker För berättelseskrivningen används två tekniker: Pennan i mitten för att brainstorma idéer, berättelsen skrivs sedan med Skriva-runttekniken. Teckningen, fotot eller kollaget görs med pusseltekniken. Index över matematiska element 1. 2. 3. 4. 5. 6. 7.

Gradskiva Horisontal linje Kvadrat och rektangel Relativa positioner av två elelr flera räta linjer Cirkelsektor Rektanglar Ytterring

Den svenska konstnären Sven Jonson 56 föddes 1902 i en sjömans- och hantverksfamilj i Söndrum utanför Halmstad. 1929 bildade han Halmstadgruppen tillsammans med Axel och Erik Olson, Waldemar Lorentzon, Esaias Thorén och Stellan Mörner. Halmstadgruppen är de mest kända svenska surrealistiska konstnärerna. Surrealistiska konstverk är ofta inspirerade av drömmar. Jonsons surrealism karaktäriseras av ödsliga landskap i ljust gula och bruna toner, ofta med små människogestalter för att visa på hur liten människan är i universum. Arkitektoniska element, vidsträckta horisonter med milslånga skuggor, valvbågar och arkader är typiska kännetecken för Jonsons måleri under denna period. Under andra hälften av 1930-talet speglade Jonson skräcken inför ett nytt 56

Sjustjärnan av Sven Jonsson, olja på duk, (årtal okänt)

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världskrig i en serie visioner av en raserad värld. Under 40-talet var Jonson delaktig I Söndrumskolonin, en grupp av konstnärer vid Halmstads kust. Vid 1960-talets början gjorde han en serie bilder med labyrintiska katedraler där han till viss del återkopplade till 20-talets kubism. På 60- och 70- talet dominerade himlens och havets blå färgskala hans verk. Detta visar även på hans livslånga intresse för rymden, stjärnbilder och planeter. I bilden här intill syns detta tydligt: blå toner och stjärnbilden Karlavagnen, vilken gett tavlan namnet ”Sjustjärnan”. Sven Jonson dog 1981. SVEN JONSON, "SJUSTJÄRNAN" Källa: http://www.mjellbykonstmuseum.se/omwebbplatsen/english/thehalmstadgroup/svenjonson.4.293aa03 e12928a822b180006724.html

Detta fotografi togs av den svenska pressfotografen Hans Runesson 57 1977. Det togs i trapphuset till ett hus som skulle rivas, under en protest där man försökte rädda byggnaden. Hans Runesson föddes 1947 i Växjö i södra Sverige. Han är känd för sina svartvita foton, särskilt ”Kvinnan med handväskan” som visar hur en kvinna av polsk-judiskt ursprung är på väg att slå en nazist i huvudet under en nazistisk demonstration i Växjö 1985. Kvinnans mamma hade suttit i koncentrationsläger under andra världskriget. 1985 utsågs fotografiet till årets bild, och några år senare utsågs det till århundradets bästa bild av tidskriften Vi och Svensk Fotohistorisk Förening. 2013-14 gjordes en liten skulptur av kvinnan baserad på fotografiet. Statyn sattes upp i november 2015 vid Varbergs fästning i Varberg.

Utan titel, fotografi av Hans Runesson 1977. Fotot visar en kvinna i tapphuset till en byggnad som ska rivas.

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Uppgift 3 Syfte att förstå andra länders traditioner genom deras folksagor att uppmuntra det konstnärliga skapandet med några matematiska förutsättningar i åtanke. Slutproduktion Produktionen, på papper eller i digitalt format ska vara en serie baserad på en legend/folksaga. Steg Varje grupp kommer få en av de andra samarbetsländernas legend eller folksaga Eleverna ska sedan anpassa legenden till ett manus med dialoger. Utifrån manuset ska eleverna göra en serie på max två papper (format A4, eller digitalt) Serien kan göras enligt följande: Genom att använda ett program som Pixton, Tondoo, Comic Life, Bitstrips eller andra internetresurser. Rita för hand Göra ett collage Genom att använda något annat program eller tekniker de känner till Serien får ha max 12 rutor och måste innehålla minst fem av följande matematiska termer: Ovala bubblor (t.ex. till pratbubblor) Rektanglar (till berättarröst) Cirklar Koncentriska cirklar Symmetri Spetsiga vinklar Parallella linjer Lodräta linjer, linjer som korsas Liksidiga trianglar 136

kvadrater Om ni arbetar för hand måste ni använda linjaler, gradskivor etc. till de matematiska figurerna. Ni måste göra en lista på vilka av de matematiska termerna ni använt och ni måste tala om i vilken serieruta och var i rutan de har använts Handgjorda serier scannas för att kunna läggas upp på bloggen och Twin space. Kooperativa lärtekniker 1 – i gruppen ska ni börja med att brainstorma idéer muntligt genom tekniken ”pens to the middle” = alla lägger ifrån sig pennorna mitt på bordet, ingen skriver, alla diskuterar med alla. Varje elev måste säga något. De ska sedan komma fram till ett gemensamt beslut om hur och vad de ska göra. 2 – alla i gruppen hjälps åt att skriva, turas om. Alla i gruppen måste ha skrivit. ”writearound”- tekniken 3 – När ni börjar arbeta på serien ska ni använda ”jigsaw”-tekniken, vilket innebär att var och en är ansvarig för att göra en liten del – Vem gör vad? Sedan sätts det ihop till en helhet. Ni blir bedömda på: Den engelska ni använder i serien Att ert manus passar till folksagan Kreativitet och originalitet Hur ni använt de geometriska elementen (matematiska termerna) Konstnärlig kvalitet Grupparbete Den svenska folksagan DET SVARTA SKRINET OCH DET RÖDA58 En stygg och illvillig änka, med en likasinnad dotter, gifter sig med en vänlig och beskedlig man med en dotter. Mannen avlider och kvinnan knuffar hans dotter i gårdens brunn. Men flickan drunknar inte. Hon sjunker till brunnens 58

Det svarta skrinet och det röda, folksaga från Sverige, engelsk översättning av Martina Andreasson. Författare okänd.

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botten, jorden öppnar sig och när hon vaknar ligger hon på en underjordisk äng. Hon söker arbete som lagårdspiga och sköter sina sysslor utmärkt. Hon är vänlig mot djuren som i gengäld hjälper henne i de prov som flickans matmoder ställer henne inför. När året är slut ber hon att få sluta sin tjänst. Matmodern erbjuder flickan att som lön för sitt arbete välja ett av tolv skrin i hennes vindskammare. På katternas inrådan väljer flickan det minsta, svarta, skrinet. Väl hemma på sin egen gård hänvisar hennes styvmor flickan att bo i hönshuset. Efter att ha städat hönshuset och ställt skrinet på sin plats öppnar hon det och finner att det är fullt av smycken av guld, pärlor och ädla stenar. Skrinet sprider även ett gyllene sken på väggar och tak och hönshuset blir grannare än den finaste kungasal. Styvmodern knuffar då ner sin egen dotter i brunnen i hopp om att hon ska hämta hem ett ännu grannare skrin. Dottern får jobb på samma gård, men då hon inte behandlar djuren med samma vänlighet som sin styvsyster så hjälper de henne inte i matmoderns prov. Vi årets slut kräver hon sin lön och erbjuds att hämta ett skrin i vindskammaren. Utan hjälp från någon väljer hon det stora röda som är störst och grannas av alla. Hemma hos sin mor öppnar hon skrinet som innehåller ormar och paddor. En eldslåga från skrinet sätter huset i brand. Både styvmodern och hennes dotter avlider i branden. Bara hönshuset och flickan klarar sig.

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Uppgift 4 Multimediarekreation Av En Dikt 1. Eleverna ska arbeta i grupper. De ska göra en multimediarekreation av en dikt av en utländsk författare, där de ska sätta ihop bilder, musim och recitation av dikten. Bilderna måste innehålla matematiska element så som spiraler, symmetri och aritmetiska konstbilder, som på något sätt bidrar till en bättre förståelse av dikten. Procedur: - Varje grupp elever får en dikt. - Multimediaprodukten, videon, får inte vara längre än tre minuter och måste innehålla följande: a. Recitation av dikten på engelska och på ursprungsspråket, i följd eller sammansatta i fri ordning. b. Bilder eller videosekvenser, original eller manipulerade, som innehåller matematiska element så som spiraler, symmetrier och aritmetiska konstbilder som på något sätt bidrar till en bättre förståelse av dikten. c. Musik för att förstärka de känslor som texten visar. Eleverna måste komponera sin egen musik, genom att använda t.ex. Music Maker Jam. Om det inte är möjligt får de istället använda ett stycke instrumentalmusik från en artist som kommer från samma land som dikten de jobbar med. Bedömningskriterier Följande kriterier kommer användas för bedömning av uppgiften: - Recitationen på engelska och på originalspråket (uttal, intonation, rytm). E. Musiken, bilderna och de matematiska elementens anpassning till diktens innehåll. F. Kvalitet på ljud och bild. Kooperativa lärtekniker: Grupputredning - Steg 1) Eleverna tilldelas eller bestämmer vilken del av uppgiften de ska vara ansvariga för. Sedan sätter de upp deadlines för när de olika delarna av uppgiften ska vara klara. Delarna är:

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9. Samla bilder till videon 10. Välja ut de mest passande bilderna som innehåller matematiska element och bestämma var i videon de ska vara med. 11. Recitera och spela in videon. 12. Komponera/välja ut musik till videon. 13. Redigera videon. 2) Alla eleverna bidrar till samtliga delar av uppgiften och den elev som är ansvarig för respective del ser till att de andra gör sin del i tid. 1. Alla eleverna samlar bilder med matematiska element för att illustrera dikten. 2. Alla eleverna bidrar till att recitera dikten på engelska och på modersmålet, för att spelas in. 3. Alla eleverna komponerar/väljer ut musik till videon. 3) Eleverna samlas som grupp, delar med sig av vad de har och tar beslut. 1. Alla eleverna deltar i att välja ut musik, bilder och i beslutet om dess sekvens i videon. 2. Att redigera videon är normalt ett enmansjobb vid datorn och så är det med inspelningen av recitationen på engelska också, men alla eleverna måste bidra till dessa delar av uppgiften också. 4) Varje elev ska göra en individuell rapport där de ska ha med följande: - En lista över de matematiska element som finns i de utvalda bilderna. - Ljudfilen med musiken de komponerat/namnet på den sång och artist de valt att använda i videon. - En utvärdering av hur varje elev skött den del av uppgiften som de varit ansvariga för.

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Den svenska dikten Kyssande vind59 Av: Hjalmar Gullberg Han kom som en vind. Vad bryr sig en vind om förbud? Han kysste din kind, han kysste allt blod till din hud. Det borde ha stannat därvid: du var ju en annans, blott lånad en kväll i syrenernas tid och gullregnens månad. Han kysste ditt öra, ditt hår. Vad fäster en vind sig vid, om han får? På ögonen kysstes du blind. Du ville, förstås, ej alls i början besvara hans trånad. Men snart låg din arm om hans hals i gullregnens månad. Från din mun har han kysst det sista av motstånd som fanns. Din mun ligger tyst med halvöppna läppar mot hans. Det kommer en vind och går: och hela din världsbild rasar för en fläkt från syrenernas vår och gullregnens klasar.

Kyssande vind, dikt av Hjalmar Gullberg. Engelsk översättning av Martina Andreasson.

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Uppgift 5 Läsa Och Skriva Manus Av Samtida Teaterpjäs Som vanligt ska eleverna jobba i grupp. Varje grupp tilldelas ett utdrag från en pjäs av en författare från ett av samarbetsländerna. Eleverna ska läsa detta och ska sedan skriva fortsättning på den scen de läst. Detta görs såklart på engelska. Slutligen ska eleverna arrangera och ta ett foto som visar en situation från den scen de själva skrivit. Utförande: 1. Varje skola väljer ett utdrag från en pjäs av en samtida författare från sitt land. Villkor för texten: a) Ämnet är fritt så länge det rör ”Human affairs” vilket kan förklaras som ”saker som människor gör, tänker på, bryr sig om” b) Texten ska vara 3-4 sidor lång c) En liten sammanfattning av utdraget ska bifogas, där man förstår handlingen i pjäsen och var det utspelar sig. d) Texten ska översättas till engelska. 2. Varje skola ska skicka sitt utdrag till den franska koordinatorn senast 15 december. Den franska koordinatorn skickar sedan alla pjäser till de andra koordinatorerna. 3. Varje skola ska ge varje elevgrupp ett utdrag från de andra länderna (en pjäs per grupp, variera land mellan grupperna). Eleverna ska läsa texten och sedan skriva en scen som är fortsättning på det de läst. Denna scen ska vara minst 1 A4 lång, max 2 sidor och skrivas i Arial strl. 12 med enkelt radavstånd. Om de vill/behöver kan de lägga till karaktärer till pjäsen. Texten ska innehålla information om hur karaktärerna rör sig över scen (t.ex. ”Oliver går iväg för att öppna dörren”) alltså inte som repliker utan ren information. (t.ex. En kyrkklocka hörs klämta i fjärran…) 4. När scenen är skriven ska varje grupp ta ett foto som visar ett ögonblick från scenen de skrivit. Alla gruppmedlemmar måste vara med på fotot. De ska ha på sig passande kläder/utklädnad och 142

platsens utseende måste passa till scenen. De måste ha med följande geometriska element på fotot, t.ex. i bakgrunden, detalj på kläder m.m. - Ovaler - Spiraler med 2 eller 3 ”centrum” - Stjärnpolygoner med minst fem spetsar/uddar De geometriska elementen måste tillverkas av eleverna, de får inte leta upp och skriva ut från internet. De måste använda lämpliga verktyg t.ex. linjal. Formerna ska ha relevant placering t.ex. vara del av ett mönster på dräkterna, del av en tavla i bakgrunden etc. inte bara vara uppsatt på väggen. Fotot kan vara svartvitt eller i färg och måste vara av digitalt format. Deadline för uppgiften är 28 februari. Då ska varje skola skicka in uppgiften till den franska koordinatorn, den kroatiska koordinatorn och projektets koordinator. Varje skola ska skicka en text och ett foto per samarbetsland. (en av den franska pjäsen, en av den spanska, en av den kroatiska). Allt kommer laddas upp på TwinSpace och bloggen (artscount.blogspot.se). Bedömningskriterier Skrivandet av scenen: - korrekt användning av engelska - Vokabulär (variation, nivå etc.) - Stämma överens med utdraget som deras egen scen bygger på - kreativitet Fotografi: - teknisk kvalitet: bilden är klar, inte suddig, och är välfokuserad - Kostymernas och bakgrundens lämplighet i förhållande till scenens innehåll/handling. Att tänka på detaljer. - Hur de geometriska elementen har använts och hur välgjorda de är - Dramatisering (miner, gester, ansiktsuttryck som visar rätt känslor för scenen)

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Kooperativ lärstrategi För att skriva scenen och för att brainstorma idéer ska tekniken ”pennorna i mitten” användas. (lägg allas pennor i mitten och diskutera hur ni ska göra innan ni skriver) Eleverna diskuterar vad de ska skriva. Alla i gruppen måste bidra med idéer om följande: - Nyckelelement som kopplar samman scenen de läst med scenen de ska skriva. Något som triggar igång handlingen igen, t.ex. en ny karaktär som kommer inspringande, något oväntat händer… - Antalet karaktärer/roller som ska finnas med (detta beror på antalet medlemmar i gruppen) - Vad händer och hur ska den egenskrivna scenen sluta. - Var handlingen utspelar sig. Det kan vara samma som i utdraget de läst eller en ny plats. Efter att de diskuterat dessa saker ska de komma överens och fatta beslut. De ska också bestämma i vilken ordning de olika rollerna griper in/dyker upp, direktiv för vad som händer på scenen för att förklara hur karaktärerna förflyttar sig på scen, eller t-.ex. ljud, förändringar i ljus etc. Sedan fortsätter de med att skriva scenen. När texten är klar ska alla gruppens medlemmar läsa igenom den och granska den, göra eventuella ändringar. Till fotografiet ska alla i gruppen samarbeta med alla förberedelser. Varje elev (alt. två elever tillsammans) har ansvar för ett av nedanstående moment och kontrollerar att samtliga i gruppen bidrar till momentet. - Kostymer/dräkter/utklädnad samt rekvisita - Plats och dekoration - Fotografisk utrustning samt redigering av bilden - Tillverkning av de geometriska elementen Fotot ska lämnas in tillsammans med en rapport där gruppen beskrivit vem som varit ansvarig för vilket moment samt deras åsikt om hur insatsen varit för de som ansvarat för de olika momenten. Deras insats ska bedömas från 1-5 där 1 är det lägsta och 5 det högsta betyget. T.ex. Joakim och Karin: kostymer och rekvisita, 5 poäng.

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Den svenska pjäsen Bortom upproret av Johanna Emanuelsson60 Det är tidig morgon och den myllrande storstaden börjar vakna till liv. Fruktstånden monteras upp, de lågavlönade anställda på hamburgerkedjan värmer frityroljan, beslutsfattarna öppnar sitt styrelsemöte. Vissa av invånarna är missnöjda med tillvaron, andra är synnerligen belåtna, de flesta kör i gamla hjulspår. Men det här är ingen vanlig dag. Idag börjar det dyka upp oroväckande rapporter. Idag kommer allt att ställas på ända. Idag kommer upproret. Ingen vet hur det började, eller om någon ligger bakom, eller hur det ska sluta. Men en efter en tvingas karaktärerna ta ställning. Vill de verkligen att allt ska förändras? Scen 33. Vid fruktståndet på det större torget Plötsligt börjar torget fyllas med folk, Maurits kommer tillbaka. Moritz: Vad mycket människor! Och min son är tillbaka! Ser du min son, nu kommer kunderna också! Hittade du inte kvinnan? Maurits: Håll käften! SLuta glo! Börja sälj! Moritz kan inte sluta titta på det stora havet av människor som håller på att bildas på torget. Moritz: Gissa vem jag är? Maurits: Kan du sluta med dina jävla gåtor, börja sälj, säger jag! Asså vad är det du inte får in i din tjocka skalle?! Vi har inte sålt en jävla fruktjävel på hela dan och nu, i skymnings-tid dräller det in massor av människor, och då står du bara där och glor?! Sälj frukt för i helvete! Moritz: Vad var det hon sa? Maurits:Va? Moritz: Kvinnan, den helt vanliga kvinnan? Vad sa hon? Allt är i ständig förändring… inte sant? Maurits: Kan du sluta snacka i gåtor säger jag! Moritz: Allt är i ständig förändring… jag är en vuxen människa. Maurits: Jaha? Moritz: Ja det är jag, jag är en vuxen människa. 60

Bortom upproret, pjäs av Johanna Emanuelsson. Engelsk översättning av Martina Andreasson.

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Maurits: Och vad menar du med det? Moritz: Att jag gör det jag vill. Titta där, det där är människor som gör det dom vill, inte sant? Dom gör precis det dom vill. Och dom vill inte mer. Det är precis det dom vill göra, inget mer och det är precis det dom gör. Maurits: Vad pratar du om? Moritz: Jag finns inte. Jag syns inte. Ända sen du var liten har jag bara varit en ansiktslös papa, jämt kört med mig. Gör det, gör det, gör det! Alltid ska du bestämma allt, jämt, jämt, jämt. Läs en bok pappa, ge mig en kram pappa, ge mig 300 spänn pappa, håll käften på föräldramötet pappa, jag slår dig om du inte hjälper mig att köpa en bil pappa, ända sen mamma dog har du varit en usel människa pappa, pappa, du är värdelös pappa. Jag finns inte! Maurits: Nu överdriver du väl lite grann? Moritz: Det finns en gräns för alla människor. Det gör det. Även för dom mest gränslösa. Det finns en gräns för hur mycket skit en människa är beredd att ta, sen tar det stopp. Sen tar det stopp. Sälj dina egna bananer! Moritz lämnar fruktståndet. Maurits: Vart ska du?! Moritz: Finna lyckan! Maurits ser storögt efter sin far. Scen 35. På hamburgerkedjan Evin och Mirja har beväpnat sig med stekspadar och grytlappar. Rojda står paralyserad på det fettglansiga golvet. Evin: Ska du inte vara med och rusta upp, Rojda? Här, ta en potatis-mosare. Rojda står kvar. Plötsligt knackar någon på glasrutan. Mirja: Ska jag öppna? Evin: Nej, det ska du inte! Evin går och öppnar dörren. Evin: Vad? Li smiter in. Evin: Det är stängt! Mirja: Vi har inte öppet! Evin: Stick! Li: Det är nånting här ute! Det pågår grejer! Har ni inte märkt det?!

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Evin: Det är väl klart som fan att vi har märkt att det pågår grejer! Vad vill du? Li: Jag hade en dröm. Mirja: Jaha? Li: Det var en dröm som handlade om att för en kvalitativ förändring plötsligt ska äga rum så måste den kvantitativa förändringen överskrida en kritisk gräns. Det är naturens egen dialektik. Evin och Mirja ser på varandra. Li: Förlåt. Alltså jag skulle bara, jag skulle bara göra slut med min tjej, jag skulle äntligen ta modet till mig att lämna min tjej och så gör jag det och känner mig helt euforisk och rädd på samma gång och så lämnar jag det där jävla caféet och så kommer jag ut på gatan och så är det det här jag möter! Li ser sig omkring på den nu ganska stökiga hamburgerrestaurangen. Mirja: Vi håller på att ordna upp lite här. Evin: Ja, precis. Mirja: Vi håller på att organisera upp oss lite. Li: Organisera upp er? Plötsligt knackar det på glasrutan igen. Evin öppnar. Evin: Vad är det nu då?! Elfriede smiter in. Elfriede: Jag såg att det var lite människor här inne. Jag visste inte riktigt vart jag skulle ta vägen. Jag skulle skriva en pjäs och så… ah, ni kanske fattar, så det kändes rätt så meningslöst mitt i allt detta liksom… Mirja: Välkommen. Elfriede: Det pågår grejer här utanför. Evin: No shit. Ta en stekspade. Evin räcker en stekspade till Elfriede. Elfriede: Tack. Utanför kedjan samlas allt fler och fler människor. Mirja: Vi har några fler stekspadar om man vill ha. Evin: Sen kanske man kan använda vissa av dom större kastrullerna som hjälmar också? Rojda som har stått tyst under en längre stund flippar plötsligt. Rojda: MEN FÖR I HELVETE! Skärp er! Evin:Va? Rojda: Skärp er för fan! Det är dags att ställa fram kvällsmenyerna!

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Mirja: Nu?! Rojda: Det är dags att jobba! Vad fan tror ni det är som händer där ute egentligen?! Inte ett skit! Kom igen nu! Vi ska jobba! Mirja: Jobba? Li: Ska ni inte gå ut? Elfriede: Ska vi inte gå med? Rojda: Gå med i vad?! Elfriede: Upproret! Rojda: Det är en hamburger-kö! Evin: Det är ett uppror! Rojda: Nej! Vi ska jobba! Vi ska steka hamburgare! Mirja: Det är dags! Fattar du inte det? Det är dags, Rojda. Rojda: Det är väl jag som är arbetsledare här, inte sant?! Det är jag som ger order i den här arbetsgruppen! Mirja: Men vi ska inte arbeta mer/ Evin: /vi ska göra uppror. Rojda: Ni kan inte vara säkra på nånting ännu! Det kan ju vara vad som helst som pågår därute! Li: Det är en väldig massa folk i alla fall…? Rojda: Men skit i dom! Evin: Vaddå skit i dom?! Mirja: Vad är det med dig?! Rojda: Inget?! Jag försöker bara styra upp den här extraordinära och nyuppkomna situationen! Evin: Fegar du?! Elfriede: Kom igen nu! Rojda: Men herregud, det är väl inte bara till att… Va fan?! Evin: Jag tänker gå ut nu i alla fall! Mirja: Jag med! Elfriede: Jag med! Li: Det kanske kan vara farligt? Mirja, Evin och Elfriede plockar på sig de hamburger-grejer som de tror att de kan använda som vapen. Evin: Ska du med eller inte?! Rojda: Men lägg av nu! Hörrni?! Mirja: Vi har inte tid att stå här och dividera!

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Evin: Vi går! Li: Okej. Vänta på mig! Evin, Mirja, Li och Elfriede lämnar hamburgerkedjan. Rojda: Hallå! Vänta! Stopp! Ni kan väl inte bara… Hallå…! Rojda star kvar. Hon ser storögt efter sina kamrater. Scen 36. I det nu väldigt kvava styrelserummet Syret är snart slut runt konferensbordet. Rop och skrik från folkmassorna överröstar beslutsfattarnas tankar.

Uppgift 6 Göra en kortfilm Eleverna ska göra en kortfilm som kommer vara en nyinspelning av en scen ur en film från ett av samarbetsländerna. Genomförande Eleverna ska arbeta i grupp. Varje grupp tilldelas en scen från en film från ett av samarbetsländerna. Klippet kommer att vara i originalversion med engelsk textning och kommer vara ca fem minuter långt. En sammanfattning av scenen kommer delas ut; några rader som summerar handlingen och om ögonblicket då scenen utspelar sig. 1. När eleverna har tittat på filmklippet ska de skriva om dialogen från scenen genom att följa dessa steg: A. Huvudidé, sekvensens kärna. B. Utveckling av huvudidén: de ska skriva ett sammandrag, en väldigt kort sammanfattning av scenen. Exempel på sammandrag: En tonårspojke färdas av misstag 30 år tillbaka i tiden där han oavsiktligt avbryter sina föräldrars första möte. Medan han försöker hitta ett sätt att ta sig tillbaka till framtiden måste han försöka få sina föräldrar att bli kära i varandra, annars kommer han aldrig bli född. 149

C. Skriva den berättande delen av manuset: en kort beskrivning av stämningen och av karaktärerna som är med i scenen. Eftersom alla elever ska spela en varsin roll i scenen kan de anpassa rollerna efter behov. Detta innebär att de kan lägga till eller ta bort roller eller ändra deras kön om så behövs. De måste också bestämma vem som ska spela vilken roll. Exempel på den berättande delen av manus: Scenen utspelar sig i vardagsrummet i Johns hus. Roller: John, 24-årig bloggare och youtubare, han är en snäll man. Han är kär I Helen. Helen, gåtfull ung kvinna. Hon har ett förhållande med John men hon döljer något… Mark, Johns vän. Han har betett sig underligt på sistone… Fru Spencer, Helens chef. En bestämd kvinna som inte gillar när folk säger emot henne.

D. Skriva ett inspelningsmanus. Det ska innehålla information om de olika tagningarna och bildsnitt, dialoger och scendirektiv om stämningen för dialogen. Det ska även innehålla andra tekniska detaljer t.ex. ljud, musik etc. Den ska vara en eller en och en halv sida lång. Format för inspelningsmanus Tagnin Dialog g 1 John: “Snälla, gå inte!” Helen:”Låt mig va! Jag litar inte på dig längre!”

Bildsnitt Närbild på båda karaktärerna

Musik/ljud/röst läge John med ynklig röst, Helen, arg och ledsen.

2- Eleverna ska sedan bestämma plats för handlingen, kostymer, rekvisita etc. Dekorationen ska innehålla följande geometriska element:

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Eleverna ska göra sex till åtta mönster av en kontinuerlig kurva genom att koppla samman tangenters omkretsbågar. Dessa mönster görs på kartong. Sedan ska mönstret klippas ut och användas som mallar. Mallarna ska användas för att skapa ett abstrakt konstverk av sammanlänkade kurvor som ska färgläggas på valfritt sätt.

Eleverna ska använda det som en del av dekorationen I sin scen. De ska öva efter behov. 3- Efter detta ska eleverna spela in scenen. - Det är klokt att hålla samma format som originalscenen. För att göra det behöver de komma ihåg vilka bildnsitt tagningarna hade: närbilder, halvbilder, helbilder etc. eller enligt vinkeln: ögonhöjd, låg eller hög vinkel, fågelperspektiv etc. Den här sidan kan vara till hjälp: http://www.skwirk.com/p-c_s-54_u-251_t-647_c-2411/camera-shots-angles-and-movement-lightingcinematography-and-mise-en-scene/nsw/camera-shots-angles-and-movement-lighting-cinematographyand-mise-en-scene/skills-by-text-type-film/film-overview

4 - Slutligen ska de redigera sin kortfilm. De ska sätta ihop de olika tagningarna de har filmat i rätt ordning; de ska lägga till öppnings och sluttexter med namn på gruppmedlemmarna, titeln på filmen och all information de vill ha med (t.ex. musik de använt etc.). Om de bestämmer sig för att inte spela in dialogreplikerna när de filmar kan dialogen spelas in separat och läggas till som ljudfil när de redigerar sin film. Musiken kan vara

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samma som i originalscenen, om där var någon, eller så kan den skapas av eleverna, t.ex. genom att använda Music Maker Jam. Både öppningstexter och musik måste passa till berättarstilen. 5- För att göra sin film känd måste de tillverka en filmaffisch som fångar folks uppmärksamhet och som kommunicerar det viktigaste innehållet I filmen och filmens stämning. Krav för affischen: - Storlek: A3 - Innehåll (titel, gruppmedlemmar och slogan) - Geometriska element (alla eller några av dem som har använts till scensättning.) - Den kan göras för hand (valfri teknik) eller med hjälp av ett digitalt redskap/program (t.ex. https://www.canva.com/create/posters/) För att designa sin filmaffisch ska de arbeta enligt följande steg: 1. Varje gruppmedlem ska göra en skiss, på A4 papper med allt innehåll: titel, slogan etc. Om de har använt ett datorprogram kan de skriva ut dem, eller visa sina gruppmedlemmar. 2. De ska diskutera de olika skisserna och välja ut de delar de gillar mest en efter en. (de ska bestämma vilken titel som är bäst, vilken slogan de gillar mest etc.). 3. Tillverkning av affischen på A3 4. De ska lämna in/skicka affischen och alla skisser. Den svenska filmscenen är hämtad ur Felix Herngrens film “Hundraåringen som klev ut genom fönstret och försvann” från 2013. Tidsram: 1:13:00 – 1:16:30 Kooperativa lärstrategier För att skriva manuset ska tekniken “pennan I mitten” användas till brainstorming av idéer. Först ska de bestämma vad de ska skriva om. Varje gruppmedlem måste bidra med idéer om följande: 1. Huvudidé, sekvensens kärna.

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2. Vilka roller/karaktärer som är med i sekvensen. 3. Utveckling av huvudidén: - Början. - Klimax. - Avslutning. 4- Varje karaktärs bidrag till handlingens utveckling. (vad varje karaktärs roll är för handlingen) Sedan ska de komma överens om var och en av dessa punkter och göra sitt sammandrag (kort sammanfattning av berättelsen/handlingen) och den berättande delen av manuset, en kort beskrivning av stämningen och av karaktärerna som är med i scenen (likt de som de har fått läsa om originalscenen). Efter det ska de skriva dialogen, inklusive scendirektiv för dialogens stämning. Hela guppen måste hjälpas åt att skriva sammandraget, manuset med alla delar och dialogen. För att genomföra inspelningen av scenen måste alla gruppmedlemmarna samarbeta med allt och bidra lika mycket, men där ska vara en samordnare för varje av de följande delarna: - Kostymer och rekvisita - Plats och dekoration - Inspelning och redigeringsutrustning (kamera, digitalt program etc.). - Geometriska element. Eleverna ska skriva en rapport med namnen på samordnarna för varje del och en utvärdering om hur de har genomfört sina uppgifter genom att sätta betyg på deras insats som samordnare från 1 till 5, där 1 är det lägsta och 5 det högsta betyget. Till exempel: Juana, inspelnings- och redigeringsutrustning: 4 points. Eleverna ska ladda upp filmen och sedan skicka länken tillsammans med affischen, sammanfattningen, det berättande manuset och inspelningsmanuset.

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Meeting Task Photo Marathon Maths Photograph Contest Getting To Know Avilés

“The purpose of this activity is to be aware of the constant presence of mathematical elements around us, as well as to show its usefulness in every day life”. Rules: GROUP WORK: There will be 8 groups of 5 students, 3 of them Spanish and two other students from another country. Each group will be responsible of the material needed to make the photos. TOPIC:It has to be related to the maths world, in any of its different aspects (geometrical figures, mosaics. symmetry…) PRESENTATION: They will be delivered in a digital format, to the following address: erasmusluarca@gmail.com. DEADLINE: Wednesday, 2nd March 23:59 h. JURY: Cristina Acuña Álvarez Gema Hernández López Almudena Cobo Sancho

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PRIZE: The winning group will get a prize on 4th March, during the 3rd hour at school. CRITERIA: The following will be taken into account: 1. Originality and creativity of the photographs 2. Quality of the photographs (make sure they are not blurred or unfocused) 3. They must contain the geometric elements required. 4. Under no circumstances downloaded Internet photos will be accepted. NUMBER OF PHOTOGRAPHS: Each working group must submit 12 photographs. Pictures can be inserted into a Word document type. Three pictures will be inserted on each page. Each picture must be accompanied by a text explaining which geometrical element is shown and where it is located in the photo.

Maths Photo Contest ROUTE 1: 1. In the Niemeyer Square you can take photos in which a cylinder, a spiral or a portion of a sphere can be seen. 2. On the way to the Plaza de España (1) you will be able to perform photos where we can find parallel arcs or a network of squares. 3. In the Plaza de España (1) and facing the Town Hall, you will have to take a picture that contains a circle. 4. At the end of the Calle La Fruta (17) you will reach the Palace of Camposagrado . On the façade you will take a picture containing symmetry. 5. Next to the Church of the Franciscan Fathers (5) is the Plaza de Carlos Lobo, where you will have to shoot an octagon, and, in the facade of the Museum of Avilés Urban History, part of a prism. 6. In the Calle de la Ferrería (3) you will take a picture of a structure containing parallel and perpendicular lines.

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7. Up theCalle Palacio Ferrera (18), you should find on the facade of the Municipal Conservatory of Music the figure of an oval. 8. At the beginning of Galiana Street (24) you will find the very characteristic arches of the old town of Aviles, which you will have to shoot. 9. Down the Calle de La Cámara (14 ) you have to photograph the facade of a building containing triangles Mathematical Photography Maratón in Avilés Contest 1. In the centre of this picture we can see a cylinder surrounded by a spiral. On the right side of the photo we can see a portion of a sphere.

2. It’s a portion of a sphere in the Niemeyer Square.

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3. Curve lines situated in Plaza EspaĂąa.

4. Parallel arcs or a network of squares in a colourful bridge.

5. This photo shows part of the facade of the Municipal Conservatory of Music. In the middle of this photo you can see a window with the shape of an oval.

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6. This is an octagon near the Church of the Padres Franciscanos.

7. You can see a part of a prism on the facade of the Avilés Urban History Museum; it can be seen in the middle of this photo.

8. Characteristic arches of the old town of Avilés at the beginning of Galiana Street.

9. This is the facade of a building where triangles can be seen. It’s on La Cámara Street.

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10. A structure of parallel and perpendicular lines on la FerrerĂa Street.

11. Symmetric windows.

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Photo Marathon in Croatian Matematičko-fotografski maraton Upoznajmo Avilés

“Svrha ove aktivnosti je da postanemo svjesni prisutnosti matematičkih elemenata oko nas te da prepoznamo njihovu upotrebu u svakodnevnom životu.” PRAVILA: GRUPNI RAD: Bit će 8 grupa po 5 učenika, troje učenika iz Španjolske te dvoje učenika iz druge države. Svaka grupa je odgovorna za pribor potreban za izradu fotografija. TEMA: Tema mora biti vezana za matematiku u bilo kojem obliku (geometrijski likovi,mozaik, simetrija..) PRESENTACIJA: Prezentacije trebaju biti dostavljene u digitalnom obliku na adresu: erasmusluarca@gmail.com. ROK : Srijeda, 2.3. u 23:59 h. ODBOR: Cristina Acuña Álvarez Gema Hernández López Almudena Cobo Sancho NAGRADA: Pobjednička skupina će dobiti nagradu 4. ožujka za vrijeme trećeg školskog sata.

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KRITERIJI: U obzir će se uzimati sljedeće:  Originalnost i kreativnost fotografija  Kvaliteta fotografija (vodite računa da ne budu zamagljene ili nefokusirane)  Moraju sadržavati potrebne geometrijske elmente  Fotografije preuzete sa interneta neće biti prihvaćene ni u kom slučaju BROJ FOTOGRAFIJA: Svaka radna skupina mora predložiti 12 fotografija. Fotografije se mogu umetnuti u Word dokument. Na svakoj stranici će biti umetnute tri fotografije. Uz svaku fotografiju mora biti popratni tekst u kojem se objašnjava koji geometrijski element je prikazan na slici,te gdje je fotografija snimljena. Matematičko-fotografski maraton RUTA 1: 1. Možete fotografirati na Neimeyer trgu gdje se mogu vidjeti valjak, spirala i dio kugle 2. Možete fotografirati na putu prema trgu “Plaza de España” (1) gdje možete vidjeti paralelne lukove ili splet kvadrata. 3. Na trgu “Plaza de España” (1) , okrenuti prema Town Hall-u,trebate fotografirati dio koji sadrži krug. 4. Na dnu ulice “La Fruta” (17) doći ćete do palače Camposagrado na čijem pročelju možete fotografirati simetriju. 5. Pokraj crkve Franciscan Fathers (5) je trg Carlos Lobo, gdje trebate fotografirati osmerokut te na pročelju muzeja Avilés Urban History dio prizme. 6. U ulici Ferrería (3) možete fotografirati građevinu koja sadrži paralelne i okomite linije. 7. Duž ulice Palacio Ferrera (18), na pročelju Municipal Conservatory of Music možete pronaći ovalni geometrijski lik. 8. Na početku Galiana ulice (24) pronaći ćete vrlo karakteristične lukove starog grada Aviles koje trebate fotografirati. 9. Niz ulicu “La Cámara” (14 ) trebate fotografirati pročelje zgrade na kojoj se nalaze trokuti. 161

Photo Marathon in France Concours de Photos Avec Aspects Mathematiques La Visite D'avilés

“Le but de cette activité est d'avoir conscience de la présence constante des éléments mathématiques qui nous entourent, de même que de montrer leur utilité dans la vie quotidienne.” REGLEMENT : TRAVAIL DE GROUPE : Il y aura 8 groupes de 5 étudiants, dont 3 espagnols et 2 étudiants d'un autre pays. Chaque groupe sera responsable du matériel nécessaire pour prendre les photos. SUJET : Il doit avoir un rapport avec le monde des mathématiques, dans tous ses aspects (formes géométriques, mosaïques, symétrie,…) PRESENTATION : Les photos seront envoyées en format numérique, à l'adresse suivante : erasmusluarca@gmail.com. DELAI : mercredi 2 mars 2016 à 23:59 JURY: Cristina Acuña Álvarez Gema Hernández López Almudena Cobo Sancho

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PRIX : Le groupe vainqueur recevra un prix le 4 mars, au cours de la 3ème heure de cours. CRITERES : Les éléments suivants seront pris en compte : 1. Originalité et créativité des photographies. 2. Qualité des photographies (assurez-vous qu'elles ne soient ni floues ni mal cadrées). 3. Elles doivent comporter les éléments géométriques demandés. 4. Des photos téléchargées à partir d'Internet ne seront absolument pas acceptées. NOMBRE DE PHOTOGRAPHIES : Chaque groupe doit proposer 12 photos. Elles peuvent être insérées dans un document de type Word. Il y aura 3 photos par page. Chaque photo doit être accompagnée d'un texte qui explique quel élément géométrique est photographié et où il se trouve dans la photo. Concours Photo Avec Aspects Mathematiques ITINERAIRE 1: 1. Sur la Place Niemeyer, vous pouvez prendre une photo sur laquelle on peut voir un cylindre, une spirale ou la partie d'une sphère. 2. Sur le chemin pour se rendre à la Plaza de España (1), vous pourrez prendre des photos montrant des arcs parallèles ou un ensemble de carrés. 3. Sur la Plaza de España (1), en faisant face à la Mairie, vous devrez prendre une photo qui comporte un cercle. 4. Au bout de la Calle La Fruta (17), vous arriverez au Palais de Camposagrado. Sur la façade, vous prendrez une photo de la symétrie. 5. A côté de l’Église des Pères Franciscains (5), il y a la Plaza de Carlos Lobo, où vous devrez prendre la photo d'un octogone, et, sur la façade du Musée d'Histoire de la ville d'Avilés, un morceau d'un prisme.

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Dans la Calle de la Ferrería (3), vous prendrez la photo d'une structure qui contient des droites parallèles et perpendiculaires. 7. En haut de la Calle Palacio Ferrera (18), vous devriez trouver une forme ovale sur la façade du Conservatoire Municipal de Musique. 8. Au début de la rue Galiana (24), vous trouverez les arches très caractéristiques de la vieille ville d'Avilés, que vous devrez prendre en photo. 9. En bas de la Calle de La Cámara (14), vous devez photographier la façace d'un bâtiment qui comporte des triangles.

Photo Marathon in Spanish CONCURSO FOTOGRAFÍA MATEMÁTICA CONOCIENDO AVILÉS

“El objetivo de esta actividad es resaltar la presencia constante a nuestro alrededor de elementos matemáticos, y poner de manifiesto su utilidad en la vida cotidiana.” BASES: GRUPOS DE TRABAJO: Se harán 8 grupos de 5 alumnos/as formados por 3 alumnos/as españoles y 2 alumnos/as del resto de los países participantes en el programa. Cada grupo será responsable del material necesario para realizar las fotografías.

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TEMA: El tema de las fotografías tiene que estar relacionado con el mundo de las matemáticas, en sus múltiples manifestaciones (figuras geométricas, mosaicos, simetrías…). PRESENTACIÓN: Se entregarán en formato digital a la dirección de correo erasmusluarca@gmail.com. PLAZO MÁXIMO: Miércoles 2 de marzo hasta 23:59 h. JURADO: Cristina Acuña Álvarez Gema Hernández López Almudena Cobo Sancho PREMIO: El grupo ganador recibirá un premio el día 4 de marzo a 3ª hora. CRITERIOS DE CALIFICACIÓN: Se tendrán en cuenta los siguientes ítems: 1. Originalidad y creatividad de la fotografías. 2. Calidad de la fotografías (las fotos no estén borrosas o mal enfocadas). 3. Han de contener los elementos geométricos pedidos 4. En ningún caso se aceptarán fotos descargadas de Internet. NÚMERO DE FOTOGRAFÍAS REALIZADAS: Cada grupo de trabajo deberá entregar 12 fotografías. Las fotografías se insertarán en un documento tipo Word. En cada página se insertarán tres fotos. Cada una de ellas deberá ir acompañado de un texto dónde se explique qué elemento geométrico contiene y dónde se encuentra localizado en la foto. Concurso Fotografía Matemática RUTA 1: 1. En la Plaza del Niemeyer se podrán realizar fotos en las que aparezca un cilindro, una espiral o una parte de una esfera. 2. De camino a la Plaza de España (1) podréis realizar fotos en las que aparezcan paralelas, arcos de circunferencia o una red de cuadrados.

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3. En la misma Plaza de España (1) y mirando hacia el Ayuntamiento deberéis realizar una fotografía que contenga un círculo. 4. Al final de la calle de la Fruta (17) llegaréis al Palacio de Camposagrado. En su fachada realizaréis una fotografía que contenga una simetría. 5. En la Iglesia de los Padres Franciscanos (5), se encuentra la Plaza de Carlos Lobo, en ella deberéis fotografiar un octógono y, en la fachada del Museo de la Historia Urbana de Avilés, parte de un prisma. 6. En la calle de La Ferrería (3) realizaréis una foto de una estructura que contenga rectas paralelas y perpendiculares. 7. Subiendo por la calle Palacio Ferrera (18) deberéis encontrar en la fachada del Conservatorio Municipal de la Música la figura de un óvalo. 8. Al empezar la calle de Galiana (24) encontraréis unos arcos muy característicos del casco antiguo de Avilés que deberéis fotografiar. 9. Bajando la calle de La Cámara (14) tenéis que fotografiar la fachada de un edificio que contenga triángulos.

Photo Marathon in Swedish Matematik Och Foto Tävling Lär Känna Avilés

"Syftet med den här aktiviteten är att vara medveten om den konstanta närvaron av matematiska element runt oss, likväl som den ska visa vilken nytta den kan ha i vårt vardagliga liv". 166

REGLER: GRUPPARBETE: Det kommer vara 8 grupper med 5 personer i varje, 3 av dem kommer att vara spanska och de 2 andra kommer vara från andra länder. Varje grupp kommer vara ansvarig för materialet som behövs för att ta fotona. ÄMNE: Det måste vara relaterat till matematikvärlden, i alla dess olika aspekter (geometriska figurer, mosaik och symmetri.) PRESENTATION: De kommer levereras till följande e-postadress i ett digitalt format: erasmusluarca@gmail.com. DEADLINE: Onsdag den 2:a mars 23.59. JURY: Cristina Acuña Álvarez Gema Hernández López Almudena Cobo Sancho

PRIS: Den vinnande gruppen kommer få ett pris den 4 mars på den tredje timmen i skolan. KRITERIER: Följande kommer att beaktas: 1. Fotografiernas originalitet och kreativitet. 2. Fotografiernas kvalitet (se till att de inte är suddiga eller ofokuserade). 3. De måste innehålla de geometriska formerna som krävs. 4. Under inga omständigheter är nedladdade foton från Internet acceptabla. ANTAL FOTON: Varje arbetsgrupp måste lämna in 12 fotografier. Bilder får vara inlagda i ett Word dokument. Tre bilder läggs in på varje sida. Varje bild måste ha en förklarande text som beskriver vilket geometriskt element det är som visas och var på bilden det finns.

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