Maths in buldings results 3rd stage by Ewa Nenkin

„Maths around us” “Maths in buildings” and its results

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Introduction............................................................................................................................................. 3 Project aims ............................................................................................................................................. 3 The third stage “Maths in buildings” ....................................................................................................... 4 Activity 1 Our unique houses .................................................................................................................. 5 Activity 2 Turkish famous houses .......................................................................................................... 11 Activity 3 Proverb dictionaries about home.......................................................................................... 18 Activity 4 Building stories ...................................................................................................................... 24 Activity 5 Smart furniture from the past ............................................................................................... 33 Activity 6 Maths topics .......................................................................................................................... 42 Evaluation .............................................................................................................................................. 63 Summary ............................................................................................................................................... 63

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Introduction The key linking all five partners of our project „Maths around us” was Mathematics. Our main aim was to improve Maths skills of students by perceiving Maths issues in their closest surrounding world. Students were encouraged to do their best to solve Maths tasks and to find similarities and differences between the environments of five participated schools by using a wide range of different ICT applications with English language as language of communication between partners. The project was divided into five parts:     

“Maths in kitchen” with Italian school responsible “Maths in vehicles” with Bulgarian school responsible “Maths in buildings” with Turkish school responsible “Maths in nature” with Polish school responsible “Maths in games” with Spanish school responsible

Project aims The project priority was to develop maths, ICT, English and social skills by solving a wide range of tasks. Students awareness of maths existing everywhere increased and all time maths accompanies humans’ life. Teachers tried to design such tasks where finding solution or understanding the topic needed to use ICT applications free and available on the Internet and needed to work in group or pair work. Working on tasks needed to use English language. All games, presentations, interviews, maths tasks, lessons students prepared in English. During motilities they also communicated and solved all tasks using this language. Before and after the project they solved English diagnostic test. Most of them achieved A2 level as it was expected. One of the project purpose was to develop ICT skills which are very important in contemporary world. Students were familiarized with a wide range of applications. They are free and can be easily found on the Internet. The list of apps used in the project: tagxego, smilebox, match memory game, hotpotatoes, issue, tools educator, you tube, comiclife, iMovie, moviemaker, doc.google, shapecollag, quizlet, dropbox, same quizy, symbaloo, proprofs, answergarden, socrative, kahoot, monkeyjam, blog, google maps, easly.ly, fodey, pikochart, webpage, edycaplay, blubbr, prezi, tondoo, padlet. Social and cooperation skills Doing project activities our students developed social skills. They mainly worked in pairs or in a groups enriching cooperation skills. During mobilities our students cooperated in international groups using English as language of mutual cooperation. All results of our mutual work were uploaded to eTwinning platform, our blog and our facebook

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The third stage “Maths in buildings” In this part of the project students did tasks connected with buildings, maths and presented in English on etwinning, blog and facebook. They chose the oldest house or the one that seems to be the most traditional or interesting in their neighbourhood in their street, or in village then they visualised it taking photos or drawings, they made an interview with the people living there in English and presented their work via ICT apps. The pupils in groups chose a region in Turkey which is famous for its typical traditional houses (there are many towns with different specific houses) and made a research about them on the internet. Then they made a model of the houses there using waste material and give basic information about them - their location, their date of building, their colour in common etc. The photos of the models and the information were shared on the web ( blog, etwining space,etc) Each country prepared a dictionary including proverbs, literary expressions and quotations about “home”. The dictionary was written in English and in their mother tongue. (For example one of the famous sayings of Atatürk : “Peace at home, peace in the world.”, or a well-known sentence like “There is no place like home.” ) Pupils made a research about the interesting stories or surprising facts of historical buildings. Each country found and chose such an interesting story, tale or legend and prepared a poster, presentation or description via ICT. Re-designing of a piece of old furniture : In old Turkish houses, there were some decorative objects or different furniture that no longer exist ( for example in some old houses there used to be a small pool in the living room, or there used to be a turning shelf between kitchen and living room, you put the plates and food there and turned it, then they could take it from the living room and this was used when men and women were sitting in different rooms The pupils made a research about them and they re-designed (in a more modern way) it. They created the model of it in their Technology and design “Smart Furniture From The Past”, etc. ). Maths topics students coped with during this stage were:    

Roman and Arabic numbers, golden proportion, geometric shapes, cylinders, Pythagorean theorem, Platonic solid, scale and Maths mosaics, similar triangles.

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Activity 1 Our unique houses Each country team chose very interesting or old house ,made a research about it and presented the house by means of ICT.

Example 1 https://youtu.be/L-kO1wwk2Oo

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Example 2 https://youtu.be/HuOXXWsPa58 https://www.youtube.com/watch?v=6hTdA6MeVoc&feature=youtu.be

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Example 3 https://youtu.be/wlvMNa8ZEBQ

Example 4 Here our students are analysing the structure of a palace using the application geogebra which permit them to draw the plant of the palace itself and find its area. Moreover the Maths teacher explains to the students the basic notions of pressure, structural collapses and their connection to earthquakes

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( a real current problem in this period in Italy) The activity will be made in different stages: 1) use of a Cartesian plane to find all the vertexes of the rooms 2) their transcription on geogebra 3) connection of the points through segments and drawing of the rooms 4) calculation of area and weight of the architectural structures of the palace 5) calculation of pressure for square cm. 6) calculation of the effects of an earthquake

MY HOUSE: FROM ITS ORIGINS TO TODAY 1) Which era does this building go back to? This house where I live with my husband, my children and my mother goes back to the late 20s, so it reflects the prevailing style at that time: Art Nouveau. It's a building consisting of ground floor, two floors, attic and basement rooms and has got very high vaults and very large rooms. It is located where today it is the centre of our village, opposite to the Municipal park but, at the time of its construction there were very few homes in that area and the park was a public one, mostly used for football matches and military parades. 2) By whom was it built? It was built by a certain Angelo Coco who, after having lived there for a while, moved to the nearby town of San Severo and decided to rent it. So, from that moment this building suddenly changed its destination of use: in the period of the World War II it became barracks and after that a hotel, a school and finally it was rented to families for residential purposes. In

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the basement rooms there are some wells of spring water and, in the past, in these premises they made and sold ice since in that time there were no refrigerators. 3) How long have you and your family been living here? My maternal grandfather Mr. Giovanni Napolitano bought this building in the early 50s. After a few years it became his home and then, when my mother (his daughter) got married with my father it became her house. After my parents' marriage, the basement rooms were used as consulting room of my father who was a surgeon. From 50s onwards this property underwent several renovations, while maintaining its original style. The cherry wood entrance door was masterfully realized by local craftsmen in the 20s. In the staircase there is an impressive cast iron railing in Art Nouveau style, that ends with a statue of a young woman. The same is the railing on the balconies. The main facade presents at the centre also two little balconies with masonry columns. The bearing walls are made of stone and are 80 centimetres wide so that the house is cool even during the hot summer days. From the balconies you can enjoy a view that embraces much of the country and the surrounding hills.

Example 5 A very old house

Today, our reporters Mauro and David, went to visit one of the oldest houses in Valdemorillo. They have talked to her owner and asked her some questions:

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How many years have you been living here? I´ve been living here since I was born and I inherited it when my parents death Have you reformed the house since you live here? No, and we haven’t thought about that because we are very old. How many meters have this house? The house is only 60 m2. What is the thing you like the most about your house? I like the comfort of living in a small house. You would change something in your house? I would make it bigger. You live all the year in this house or you just come on weekends and vacations? I live here for all the year. Which materials is the house built with? The house is mainly built with bricks and cement and the floor is made of wood. How many rooms does it have? It has two bedrooms and one bathroom. How many people live in the house and which is your relation with them? Here we only live my husband and me.

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Activity 2 Turkish famous houses Students chose Turkish typical and famous house or houses made researches, and created models of these house.

Example 1 Harran is 44 kilometres southeast of Şanlıurfa. The area was first inhabited in the Early Bronze Age III.

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Beehive house is a building made from a circle of stones topped with a domed roof. The name comes from the similarity in shape to a straw beehive. Throughout history, man has always adapted to natural landscapes and to making good use of resources. The beehive houses of Harran are a perfect example of this. They first appeared around 3000 years ago and although now days, most are used as tourist exhibitions, they are still a marvelous insight into life during history. Used up until the 1980s, the traditional method of constructing them with bricks and mud, was with an aim to be cool in summer, yet warm in winter. The circle shape also deflected the blast of strong winds and torrential rainfall. Although the beehive houses in Turkey are specific to the region of Harran, their designs were used all over the world including Africa and Scotland.

https://www.youtube.com/watch?v=HL4EBHNQdXs&list=UUJablhPP_EccMlqzGkIjv5g&index =95

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Example 2

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Example 3

https://youtu.be/nBmbyncGfiQ

Example 4 Cumalikizik is a village in the Yıldırım district, province of Bursa, located 10 kilometers east of the city of Bursa, at the foot of Mount Uludağ, Turkey. Its history dates back to the period of the founding of the Ottoman Empire. The village is now included in the border district of Yıldırım, as a neighborhood. Cumalikizik was founded as a waqf village. The history of the place was well protected, they are still intact the architectural structures of the Ottoman period. For this, Cumalikizik has become a popular tourist destination, though still unspoiled. A group of similar villages, located nearby, among the foothills of Mount Uludağ and valleys, were called Kızık in turkish. The name comes from one of the twenty-four clans of the Oghuz Turks, even the villagers are called Kızık. similar villages, although less well preserved, are Değirmenlikızık, Derekızık, and Hamamlıkızık. The name comes from the local spas Hamamlıkızık (hamamli), who had their headquarters there. Cumalikizik name comes from "Friday" (Cuma, in turkish), the day when the people of the Islamic religion gather for the celebration of worship. The ethnographic museum of Cumalikizik, located in the village square, shows different historical objects of the site. Every year, in June, takes place the raspberry festival. The famous Cumalikizik houses are made of wood and brick. Most of the houses is threefold. The windows of the upper floors are usually equipped with a grate and with a bay window. The handles and the doors on the main entrance doors are iron work. The cobbled streets are very narrow, without sidewalks, but the center is present a typical medieval gutter for the discharge of rain and water in general.

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BURSA Bursa is since 1968 the center of the automotive Industry production in Turkey, [in fact, there are establishments of Tofaş Fiat, the Oyak Renault and Peugeot Karsan, as well as a lot of industries that produce automotive components, such as Bosch and Magneti Marelli. The textile and food industries are equally strong, with Coke's presence, Pepsi Cola and other beverage brands, as well as fresh and canned food industries. Bursa was then a great center for the production and processing of silk, and in the twenty-first century is the most important center in Turkey for textiles, but the city is also known for its fertile land cultivated with olive trees and for its agricultural activities, that in the last decades of the last century and the beginning of the current you are seen subtract space for the benefit industrial and demographic expansion. The city is a major tourist destination for Europeans than for Arabs, who visit especially in the summer, to climb the mountain and enjoy temperatures in their unknown country. The Bursa spas have been used for medicinal purposes since Roman times; in the twenty-first century, apart from the annexes to the hotel hamam or public ones, the dell'Uludağ University has a spa therapy center. Bursa (ancient Prusa), is a Turkish city of 2,787,539 inhabitants located south of the Sea of Marmara and resting on the slopes of Mount Uludağ, 2,543 meters high and home to the most important station for winter sports in Turkey.Administratively, Bursa is one of the metropolitan municipalities of Turkey, the fourthlargest and one of the most industrialized and culturally active city in the country. The metropolitan municipality is made up of the urban areas of Gemlik districts, Gürsu, Kestel, Mudanya, Nilüfer, Osmangazi and Yıldırım. The very center of town and right is included in the Osmangazi district.Bursa was the capital of the Ottoman state between 1326 and 1365. The city is frequently cited as "Yeşil Bursa" (meaning "Green Bursa") because of the many parks and gardens that permeate the urban fabric and of the vast and diverse forests They extend into the surrounding region. The mausoleums of early Ottoman sultans are located in Bursa and numerous buildings dating back to the Empire period characterize still today the city.

Example 5

https://youtu.be/v8hOFOnWpLo

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Activity 3 Proverb dictionaries about home Example 1 Home´s Dictionary A casa vieja, portada nueva - Old house, new cover Cada uno en su casa y Dios en la de todos - Everyone in his house and God in everyone's Abre la puerta a la pereza y entrará a tu casa la pobreza - Open the door to laziness and poverty will enter your house Con regla y compás, en tu casa vivirás; sin compás y sin regla, ni en tu casa ni fuera de ella With ruler and compass, in your house you will live; without compass and without rule, neither in your house nor outside it El uno por el otro y la casa sin barrer - The one on the other and the house without sweeping

En casa del músico, todos saben cantar - At the musician's house, everyone knows how to sing El que a mi casa no viene, de la suya me echa – Who does not come to my house, kicks me off from her´s En la casa del ahorcado, nombrar la soga es pecado - In the house of the hanged, naming the rope is an offense En casa de viejo, no faltará un buen consejo - In an old man's house, a good advice will never lack Como en casa en ningún sitio – Nowhere like home En casa del herrero, cuchillo de palo - In the blacksmith's house, wooden knife En casa del pobre, la alegría dura poco - In the house of the poor, joy lasts little En casa que no entra el sol, pronto entrara el doctor - At home that does not enter the sun, soon the doctor will enter No hay que empezar la casa por el tejado - Do not start the house on the roof No tirar la casa por la ventana - Do not throw the house out the window Hogar, dulce hogar – Home, sweet home

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Example 2

https://youtu.be/6XhmOHTU8fQ Example 3

DICTIONARY

of Turkish Proverbs and “Maths around us” 2015-1-PL01-KA219-016511_1

Expressions Peace at home,peace in the world: Yurtta sulh , Cihanda sulh

Doctor gets into the home that never gets sunlight: Güneş girmeyen eve doktor girer.

Home is the place in which there is heart: Ev, kalbin olduğu yerdir.

The value of home is understood barely when it becomes evening: Evin kıymeti, ancak akşam olunca anlaşılır.

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Everyone is landlord at his own home: Herkes evinde ağadır.

Confused guest hosts the home owner: Şaşkın misafir, ev sahibini ağırlar.

Buy a home which is been built, buy a vineyard which is been planted: Evi yapılmış,bağı dikilmiş al.

God helps the people who buy a home and marry: Ev alanla evlenene Allah yardım eder

Don’t buy a home, take a neighbour: Ev alma, komşu al

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Home owner has got a home, tenant has got one thousand home: Ev sahibinin bir evi, kiracının bin evi var.

The calculation at home is not suitable for the market: Evdeki hesap çarşıya uymaz.

Housewife is a person who makes the house a real home: Evi ev eden avrat.

It may be a home without a bride, it may not be a home that death didn’t entered in it: Gelin girmedik ev olur, ölüm girmedik ev olmaz.

There is no place like home: İnsanın evi gibisi yoktur.

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A clever thief suprises the master of the house: Yavuz hırsız ev sahibini bastırır.

Charity begins at home: Önce can ,sonra canan.

Men make houses, women make homes: Yuvayı dişi kuş yapar.

They put the nightingale into a golden cage,it still moaned for its home: Bülbülü altın kafese koymuşlar yinede vatanım demiş.

The liar's house burned but nobody believed it: Yalancının evi yanmış, kimse inanmamış.

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The plumber's house always leaks: Terzi kendi söküğünü dikemezmiş.

Example 4 In the house where there is a good doctor or a rich priest, you do not feel neither hunger nor thirst. God lord, protect our house from trouble, so that lowyer nor doctor will never set foot. When the cat is away, the mice will play. Everyone loves justice at home other Rich or poor you are, welcome to my home. My home, my home, little on that you are, you seem an abbey Home of the thief is not steal.

Example 5 https://youtu.be/fpLONiVlp-s Polish poem by Aleksander Fredro about Paweł and Gaweł in English Johnny and Tommy who lived in the same house and had some problems with it. This poem is well known in Poland. Translated in English: https://issuu.com/ewanenkin/docs/johny_and_tommy_02aa6b86c3b0a8

Activity 4 Building stories Example 1

https://youtu.be/LtPjyjOvI9Q

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Example 2

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Example 3

Exmple 4

https://youtu.be/LtPjyjOvI9Q Example 4 El Palacio de Linares

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José de Murga y Reolid y Raimunda de Osorio y Ortega, Marqueses de Linares, compraron en 1874 un solar en la intersección de la Calle Alcalá con el Paseo de Recoletos, de más de 3.000 metros cuadrados, para levantar su futura vivienda. Tras fallecer los marqueses, y ante la ausencia de descendencia, el palacio lo heredó la ahijada de éstos, Raimunda. Casi un siglo más tarde, en el 1992, el edificio se reabrió como la Casa de América. En estas grabaciones se podían escuchar voces que hablaban de forma nítida y clara. La primera, masculina gritaba ““¡Fuera,no… aquí no!”, la segunda, quizás la que más angustia producía, era de una niña, que con voz quebrada susurraba, “Mamá… yo no tengo mamá”. La última, la de una mujer mayor, decía varias frases, entre ellas, la más reveladora de todas era “Mi hija Raimunda… nunca oyó decir mamá”. Las supuestas psicofonías pronto quedaron en entredicho, se trataba de una farsa de la doctora para promocionar su libro pero sin embargo, no podemos obviar la oscura vida que tuvieron los Marqueses de Linares y la tenebrosa leyenda que se cernió sobre ellos. ¿qué misterio ocultaban los marqueses? Cuenta la leyenda que después de haberse casado, José y Raimunda descubrieron con estupor que en realidad eran hermanos. Ella era fruto de una aventura amorosa del padre del Marqués con una vendedora de tabaco de Lavapiés.

Example 5

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Activity 5 Smart furniture from the past Old fashioned furniture can be also used nowadays but can be used in different way. Students made research, chose furniture or things and described their new function.

Example 1

https://youtu.be/ha5ppJyAk0E Example 2 Jaquard: A machine for sewing typical Spanish costumes My grandmother talk me about a very special machine to saw the typical Spanish costumes at XIXs The saw machine use these cartoon forms with holes. These holes serve to guide the threads and form the drawings that then decorate the fabric.

The re-use that we imagine for that cards is to use them for redecorating your room!! As a picture or to cover your headboard!!

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Example 3

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Example 4

Example 5 Nutcracker from our museum This is a nutcracker in shape of a crocodile made of brass. From 19th century.

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This is our crocodile. We named it Freddy. But it isn't a nutcracker. Freddy is paperweight. Our master-crocodile. We made it of salt dough and painted.

BAKING TINS In our museum there are many beautiful baking tins from the past.

We changed using plasticine, toothpicks, glue.

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Our object originally served to bake muffins, after changing its purpose it holds soft-boiled eggs. Unique scissors The object I have choosen are scissors for cutting the umbilical cord. In our muzeum this scissors are done in steel. As the name suggests, they are designed to cut the umbilical cord. I did my model by white clay. I changed a lot of elements, because I don't have manual skills. My model simpler then original scissors and feet were looks like stand. They look like crane but they are imperfect. My scissors serve as hangers for keys. The beak is the place where the keys are hung. Feet are used as something to attach the structure. What I did is unideal but I believe that the hardness I put in making it pay off.

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Activity 6 Maths topics Roman and Arabic numbers Links to quizzes with Roman and Arabic numbers for students from partner countries: http://www.roman-numerals.org/quizzes.html http://do-skoly.cz/en/courses/math/m-1/roman-arabic-numbers/test.aspx http://www.factmonster.com/math/roman-numeral-game.html There are examples of Roman numbers on buildings in Ziębice: http://issuu.com/ewanenkin/docs/roman_numbers_on_buildings_in_zi__b and link to our presentation: https://issuu.com/ewanenkin/docs/roman_numbers Do you want to know more about our partner countries? If yes start this quiz: http://partnersquizes.3-2-1.pl/test1.htm

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Golden ratio presentation:

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Platonic solids The Platonic solids were known to the ancient Greeks, and were described by Plato in his Timaeus ca. 350 BC. In this work, Plato equated the tetrahedron with the "element" fire, the cube with earth, the icosahedron with water, the octahedron with air, and the dodecahedron with the stuff of which the constellations and heavens were made (Cromwell 1997). Predating Plato, the Neolithic people of Scotland developed the five solids a thousand years earlier. The stone models are kept in the Ashmolean Museum in Oxford (Atiyah and Sutcliffe 2003).

Here there is a web site where you can learn more about that solids: https://illuminations.nctm.org/activity.aspx?id=3521 This is one of the interactive games we can find on internet. It is separated for different grades, so you can practice your knowledge whatever your age is: https://eu.ixl.com/math/geometry

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Another ancient way to practice your geometry and train your brain is with TANGRAM, the Chinese game that use basic regular shapes to form different figures (It is in Spanish, but it is very intuitive): http://www.matemath.com/juegos1.php?cadena=1-3

http://www.tangramgames.co.uk/tangramgameA/ (English version) And another kind of game to review 3D- shapes

CYLINDERS

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Cylinder, in mathematics, surface generated by a line moving parallel to a given fixed line and continually intersecting a given fixed curve called the directrix; each line of the family of lines forming the cylinder is called a ruling, or generator. If the directrix is a conic section (e.g., a circle or a parabola), the cylinder is called a quadric cylinder. The commonest type of cylinder is the right circular cylinder, in which the directrix is a circle and the lines forming the cylinder are all perpendicular to the plane of the circle. The solid bounded by a cylindrical surface and two parallel planes intersecting the surface in closed curves is also called a cylinder. The perpendicular distance between the planes is the altitude of the cylinder. The volume of the cylinder is equal to the product of the altitude and the area of the base (the area enclosed by either closed curve). http://www.mathopenref.com/cylinder.html During our January activities our students’ task was to design the net of cuboit as a box for a present. Students had to design the box in this way to use as little paper as they could. Then they had to calculate areas. Polish students working on tasks:

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their calculations:

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Pythagorean theory

Here is the proof of pyhteogeon theorem ( Turkey) http://www.youtube.com/watch?v=-N27KbJZlB8 Here is link Italy :https://youtu.be/POEe4KHzWt8 Polish students' notes about Pythagorean theory:

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Twierdzenie Pitagorasa Zad.1 Przyporządkuj równości odpowiednim rysunkom

III

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A. đ?&#x2019;&#x192;đ?&#x;? + đ?&#x2019;&#x17D;đ?&#x;? = đ?&#x2019;&#x201A;đ?&#x;? B.

đ?&#x2019;&#x2018; đ?&#x;? + đ?&#x2019;&#x201C;đ?&#x;? = đ?&#x2019;&#x152; đ?&#x;?

đ?&#x2019;&#x2122;đ?&#x;? + đ?&#x;?đ?&#x2019;&#x161;đ?&#x;? = đ?&#x2019;&#x203A;đ?&#x;?

Zad.2

Ile wynosi x ?

a).

b).

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Zad.3 Czy ten trójkąt jest prostokątny? a).

b).

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Maths mosaics and scale Polish presentation about maths mosaics: http://issuu.com/ewanenkin/docs/maths_mosaics1 Polish students presentation about mosaics: http://issuu.com/ewanenkin/docs/mozaiki_mariola_oliwka_wszystkie_61d11b6765cefb

â&#x20AC;&#x153;Maths around usâ&#x20AC;? 2015-1-PL01-KA219-016511_1

Scale tasks 1. On the map with the scale 1:4000000 the distance from Poznań to Warszawa is 8 cm. What is the real distance between these cities? 2. Change numerical scale 12000000 into direct reading scale. 3. Change direct reading scale 1 cm – 80 km. into numerical scale. 4. The distance from Szczawnica do Zakopane is 40 km. how many cm. on the map are in scale 1:1000000? 5. The distance from Warszawa to Paris is 1400 km. what is the map scale when the distance on the map is 7 cm? 6. Count the real distance between Adam’s house and his school if on the map with scale 1:18 000 is 8 cm? 7. The plan of Wroclaw was made in scale 1:45 000, and a plan of Ziębice in 1:20 000. Which plan is more detailed? Origami, scale and photo shop: https://www.youtube.com/watch?v=9UeHSUIpbmg&list=UUJablhPP_EccMlqzGkIjv5g&index=90

SIMILAR TRIANGLES Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other. A modern and novel perspective of similarity is to consider geometrical objects similar if one appears congruent to the other when zoomed in or out at some level. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other.

Links to leran more about similar triangles http://study.com/academy/lesson/how-to-identify-similar-triangles.html https://www.slideshare.net/sirgibey/math-9-similar-triangles-intro

https://youtu.be/GzBGSGt_dJI

“Maths around us” 2015-1-PL01-KA219-016511_1

Evaluation https://issuu.com/ewanenkin/docs/evaluacja_wszystich.pptx

Summary Maths activities were connected with activities which let project students get familiar with home national proverbs, interesting buildings in the project countries or some surprising home accessories. Project students presented their work results by means of ICT application to make them more involving and interesting. Polish summary: https://www.youtube.com/watch?v=5hPlLKWypT8&feature=youtu.be

â&#x20AC;&#x153;Maths around usâ&#x20AC;? 2015-1-PL01-KA219-016511_1