Piedmont is a region in northwest Italy that borders France and Switzerland. It has a varied landscape including mountains, hills, and plains. The capital and largest city is Turin. Piedmont has a strong industrial sector led by automaker Fiat and also has important agricultural industries such as winemaking and rice production. The region has a rich cultural heritage including royal palaces in Turin and the Sacred Mountains, which are UNESCO World Heritage Sites.
The legend describes knights sleeping underground in Blaník Hill who will come to the aid of the Czech people during their greatest time of need. The hill is located south of Vlašim and contains ruins of an old castle and stones on top. According to the legend, the knights and their horses sleep below and only emerge at night, leaving behind hoofprints. Two people who entered the hill experienced time passing differently outside. The knights will awake when a dry oak on the hill turns green and a spring begins to flow, signaling an important battle for Czech independence is near. Saint Wenceslas will lead the knights to victory.
Stephenie Meyer is an American author best known for her Twilight series. She was born in 1973 in Connecticut and grew up in Phoenix, Arizona with five siblings. Her first published book was Twilight in 2005, which was inspired by a dream she had about a human girl and vampire. Some of her other popular books include New Moon, Eclipse, and The Host. Meyer is married with three sons and lives in Arizona. In addition to writing, she works as a film producer and has produced adaptations of her books.
John Ronald Reuel Tolkien was an English writer, poet, and professor born in 1892 in South Africa who is best known for his classic fantasy works The Hobbit, The Lord of the Rings, and The Silmarillion. He did not immediately volunteer for the British Army when World War 1 began in 1914. Tolkien had four children with his wife - John, Michael, Priscilla, and Christopher. He is remembered as one of the most popular fantasy authors of all time known for The Lord of the Rings trilogy.
J.K. Rowling is a British author best known for writing the Harry Potter fantasy series. She was born in Yate, Gloucestershire, England in 1965 and had a difficult childhood as her mother suffered from multiple sclerosis. Rowling went from living on welfare to becoming the first billionaire author due to the immense success of the Harry Potter books, which she later expanded into films. She has since written other works but is still best known as the creator of the beloved boy wizard Harry Potter.
Hans Zimmer is a renowned German film score composer born in 1957. He is known for critically-acclaimed and commercially successful scores for films like The Lion King, Gladiator, and Inception. Zimmer has received four Grammys, three Classical BRIT Awards, two Golden Globes, and an Academy Award. He began his career in the 1970s and had a breakthrough with the 1988 film Rain Man, receiving his first Oscar nomination. Zimmer is now head of the film music division at DreamWorks studios.
The document discusses creative ideas for Christmas in 2017. It suggests decorating your home in unique colors like blush pink or mint green instead of traditional reds and greens. DIY crafts are also recommended such as making ornaments from pinecones, berries and ribbons or homemade gifts like baked goods, candles or knitted items. Overall the document promotes coming up with new and imaginative ways to celebrate the holidays this year.
The educational system in Poland is dominated by public schools and includes external examinations at the end of primary and secondary school. Education is compulsory until age 18 and free in public schools. The system is centrally managed by the Ministry of National Education and Ministry of Science and Higher Education. Primary school lasts 8 years and concludes with an examination. Secondary education includes basic vocational, technical, general lyceum, and vocational programs lasting 2-5 years. Higher education takes place at universities and institutes, with bachelor's, master's and doctorate programs available.
Arts Talk To Us - Czech educational system Holasová Alena
This document outlines the schedule and curriculum for a primary school in Ostrava, Czech Republic across 6 grades. It shows the weekly schedule for each grade, which includes core subjects like Czech, Math, Science, and elective classes like Art, Music, and Crafts. The schedule allocates time for each subject and notes are included about the constructivist teaching methodology used, with a focus on approaches for teaching reading in Czech. Additional documents provide more details on the Czech education system, including the structure of primary vs secondary education, typical school days and years, compulsory attendance ages, and qualifications for teachers.
This document summarizes an open house event hosted by Class 4.B to showcase their eTwinning project funded by the European Union. The class prepared displays of toys, books, cubes and visual aids used in their English lessons. They also created a noticeboard to promote their project and inform visitors about upcoming meetings in Marbella, Spain and Desio, Italy where they would visit exhibitions. The event was used to engage children and parents in the classroom's project and its goals of fostering international collaboration.
Czech national folk costumes vary between men and women as well as between villages and towns. Women's costumes typically include a long decorated skirt, shirt, and headpiece, with wealthier women decorating their costumes with precious stones. Men's costumes consist of a shirt, trousers, hat, and vest, with decorated hats and vests indicating higher social status. Folk songs were traditionally sung communally with small variations, but younger generations now favor new Czech songs, though older folk songs remain widely known. Typical folk instruments include bagpipes, flutes, violins, bass, and accordions.
The document describes a project where a Czech student team worked with other international teams to create a trivial game. The Czech team wrote questions about the Czech Republic and biology to put in templates provided by the Belgium team. They involved other students to help write questions. They then played the trivial game in mixed international groups. To further use the questions, they incorporated them into their physical education class by having students answer questions in a relay race and hunt for question cards. They also made the questions into puzzles for students to solve.
The document contains 5 multiple choice questions asking what part of a house is seen in an unseen picture, with answer options being common house parts like doors, windows, walls, roofs, and chimneys. The questions are intended as a quiz, with the correct answers provided at the end being: chimney, window, roof, door, and chimney. The quiz was developed by Monika Vernerová.
History of lemon, variaties, taste and aroma Holasová Alena
The origin of lemons is unknown, but they are thought to have first grown in regions of northeast India, northern Burma or China. Lemons entered Europe around the 2nd century AD in southern Italy. The first substantial cultivation of lemons in Europe began in Genoa in the 15th century, and lemons were introduced to the Americas by Christopher Columbus in 1493. Spanish conquest helped spread lemons throughout the New World, where they were mainly used ornamentally and for medicine. Major lemon producing countries today include the US, Italy, Greece and Spain.
5 most beautiful or interesting places in EuropeHolasová Alena
This document lists and describes 5 of the most beautiful or interesting places in Europe: Chernobyl in Ukraine, known for its high radiation following a nuclear accident; Mount Olympus in Greece, said to be the home of the Greek gods; Pravčická Brána, a mountain gate in the Czech Republic that was featured in the Narnia films; the Eiffel Tower in Paris, France, a wrought iron tower designed by Gustave Eiffel; and the Leaning Tower of Pisa in Italy, known for its unintended tilt.
This document describes typical foods in the Czech Republic, including svíčková omáčka s houskovým knedlíkem which is a cream sauce with vegetables, bread dumplings and beef. Other foods mentioned are potato salad served with schnitzel or fish, bramborák which is a potato sauce or pancake, vepřo knedlo zelo consisting of duck with sour cabbage and dumplings, and hovězí guláš, a beef stew served with bread dumplings and onions. Sweets include Honza's cakes, a fluffy bun filled with poppy seed, cottage cheese or jam.
This document lists and briefly describes 10 places to visit in the Czech Republic, including several UNESCO World Heritage sites. Some of the highlights mentioned are Karlštejn Castle, a 14th century Gothic castle; Lednice, an 18th century designed landscape; Prague, the capital and largest city; and Červená Lhota, a Renaissance castle on an island in a lake. The document provides short descriptions of the historical and natural features that make each location notable.
The document provides recipes for several dishes that feature bananas as a main ingredient. This includes banana bread, banana oatmeal chocolate chip cookies, banana pancakes with caramel, Thai banana soup, a banana cocktail, banana cranberry muffins, Kentucky banana pudding, a banana blast smoothie, cocoa cake with bananas, and tiramisu with banana spread. The recipes provide lists of ingredients and instructions for making each of the banana-centered dishes.
Piedmont is a region in northwest Italy that borders France and Switzerland. It has a varied landscape including mountains, hills, and plains. The capital and largest city is Turin. Piedmont has a strong industrial sector led by automaker Fiat and also has important agricultural industries such as winemaking and rice production. The region has a rich cultural heritage including royal palaces in Turin and the Sacred Mountains, which are UNESCO World Heritage Sites.
The legend describes knights sleeping underground in Blaník Hill who will come to the aid of the Czech people during their greatest time of need. The hill is located south of Vlašim and contains ruins of an old castle and stones on top. According to the legend, the knights and their horses sleep below and only emerge at night, leaving behind hoofprints. Two people who entered the hill experienced time passing differently outside. The knights will awake when a dry oak on the hill turns green and a spring begins to flow, signaling an important battle for Czech independence is near. Saint Wenceslas will lead the knights to victory.
Stephenie Meyer is an American author best known for her Twilight series. She was born in 1973 in Connecticut and grew up in Phoenix, Arizona with five siblings. Her first published book was Twilight in 2005, which was inspired by a dream she had about a human girl and vampire. Some of her other popular books include New Moon, Eclipse, and The Host. Meyer is married with three sons and lives in Arizona. In addition to writing, she works as a film producer and has produced adaptations of her books.
John Ronald Reuel Tolkien was an English writer, poet, and professor born in 1892 in South Africa who is best known for his classic fantasy works The Hobbit, The Lord of the Rings, and The Silmarillion. He did not immediately volunteer for the British Army when World War 1 began in 1914. Tolkien had four children with his wife - John, Michael, Priscilla, and Christopher. He is remembered as one of the most popular fantasy authors of all time known for The Lord of the Rings trilogy.
J.K. Rowling is a British author best known for writing the Harry Potter fantasy series. She was born in Yate, Gloucestershire, England in 1965 and had a difficult childhood as her mother suffered from multiple sclerosis. Rowling went from living on welfare to becoming the first billionaire author due to the immense success of the Harry Potter books, which she later expanded into films. She has since written other works but is still best known as the creator of the beloved boy wizard Harry Potter.
Hans Zimmer is a renowned German film score composer born in 1957. He is known for critically-acclaimed and commercially successful scores for films like The Lion King, Gladiator, and Inception. Zimmer has received four Grammys, three Classical BRIT Awards, two Golden Globes, and an Academy Award. He began his career in the 1970s and had a breakthrough with the 1988 film Rain Man, receiving his first Oscar nomination. Zimmer is now head of the film music division at DreamWorks studios.
The document discusses creative ideas for Christmas in 2017. It suggests decorating your home in unique colors like blush pink or mint green instead of traditional reds and greens. DIY crafts are also recommended such as making ornaments from pinecones, berries and ribbons or homemade gifts like baked goods, candles or knitted items. Overall the document promotes coming up with new and imaginative ways to celebrate the holidays this year.
The educational system in Poland is dominated by public schools and includes external examinations at the end of primary and secondary school. Education is compulsory until age 18 and free in public schools. The system is centrally managed by the Ministry of National Education and Ministry of Science and Higher Education. Primary school lasts 8 years and concludes with an examination. Secondary education includes basic vocational, technical, general lyceum, and vocational programs lasting 2-5 years. Higher education takes place at universities and institutes, with bachelor's, master's and doctorate programs available.
Arts Talk To Us - Czech educational system Holasová Alena
This document outlines the schedule and curriculum for a primary school in Ostrava, Czech Republic across 6 grades. It shows the weekly schedule for each grade, which includes core subjects like Czech, Math, Science, and elective classes like Art, Music, and Crafts. The schedule allocates time for each subject and notes are included about the constructivist teaching methodology used, with a focus on approaches for teaching reading in Czech. Additional documents provide more details on the Czech education system, including the structure of primary vs secondary education, typical school days and years, compulsory attendance ages, and qualifications for teachers.
This document summarizes an open house event hosted by Class 4.B to showcase their eTwinning project funded by the European Union. The class prepared displays of toys, books, cubes and visual aids used in their English lessons. They also created a noticeboard to promote their project and inform visitors about upcoming meetings in Marbella, Spain and Desio, Italy where they would visit exhibitions. The event was used to engage children and parents in the classroom's project and its goals of fostering international collaboration.
Czech national folk costumes vary between men and women as well as between villages and towns. Women's costumes typically include a long decorated skirt, shirt, and headpiece, with wealthier women decorating their costumes with precious stones. Men's costumes consist of a shirt, trousers, hat, and vest, with decorated hats and vests indicating higher social status. Folk songs were traditionally sung communally with small variations, but younger generations now favor new Czech songs, though older folk songs remain widely known. Typical folk instruments include bagpipes, flutes, violins, bass, and accordions.
The document describes a project where a Czech student team worked with other international teams to create a trivial game. The Czech team wrote questions about the Czech Republic and biology to put in templates provided by the Belgium team. They involved other students to help write questions. They then played the trivial game in mixed international groups. To further use the questions, they incorporated them into their physical education class by having students answer questions in a relay race and hunt for question cards. They also made the questions into puzzles for students to solve.
The document contains 5 multiple choice questions asking what part of a house is seen in an unseen picture, with answer options being common house parts like doors, windows, walls, roofs, and chimneys. The questions are intended as a quiz, with the correct answers provided at the end being: chimney, window, roof, door, and chimney. The quiz was developed by Monika Vernerová.
History of lemon, variaties, taste and aroma Holasová Alena
The origin of lemons is unknown, but they are thought to have first grown in regions of northeast India, northern Burma or China. Lemons entered Europe around the 2nd century AD in southern Italy. The first substantial cultivation of lemons in Europe began in Genoa in the 15th century, and lemons were introduced to the Americas by Christopher Columbus in 1493. Spanish conquest helped spread lemons throughout the New World, where they were mainly used ornamentally and for medicine. Major lemon producing countries today include the US, Italy, Greece and Spain.
5 most beautiful or interesting places in EuropeHolasová Alena
This document lists and describes 5 of the most beautiful or interesting places in Europe: Chernobyl in Ukraine, known for its high radiation following a nuclear accident; Mount Olympus in Greece, said to be the home of the Greek gods; Pravčická Brána, a mountain gate in the Czech Republic that was featured in the Narnia films; the Eiffel Tower in Paris, France, a wrought iron tower designed by Gustave Eiffel; and the Leaning Tower of Pisa in Italy, known for its unintended tilt.
This document describes typical foods in the Czech Republic, including svíčková omáčka s houskovým knedlíkem which is a cream sauce with vegetables, bread dumplings and beef. Other foods mentioned are potato salad served with schnitzel or fish, bramborák which is a potato sauce or pancake, vepřo knedlo zelo consisting of duck with sour cabbage and dumplings, and hovězí guláš, a beef stew served with bread dumplings and onions. Sweets include Honza's cakes, a fluffy bun filled with poppy seed, cottage cheese or jam.
This document lists and briefly describes 10 places to visit in the Czech Republic, including several UNESCO World Heritage sites. Some of the highlights mentioned are Karlštejn Castle, a 14th century Gothic castle; Lednice, an 18th century designed landscape; Prague, the capital and largest city; and Červená Lhota, a Renaissance castle on an island in a lake. The document provides short descriptions of the historical and natural features that make each location notable.
The document provides recipes for several dishes that feature bananas as a main ingredient. This includes banana bread, banana oatmeal chocolate chip cookies, banana pancakes with caramel, Thai banana soup, a banana cocktail, banana cranberry muffins, Kentucky banana pudding, a banana blast smoothie, cocoa cake with bananas, and tiramisu with banana spread. The recipes provide lists of ingredients and instructions for making each of the banana-centered dishes.
1. Téma Středová souměrnost
AUTOR MATERIÁLU MGR. ALENA B URO Ň OVÁ
Projekt Šablony K15, registrační číslo projektu CZ.1.07/1.4.00/21.3843
2. Název školy:
ZŠ a MŠ Kosmonautů 15, přísp. org., Kosmonautů 2217/15, 700 30 Ostrava-
Zábřeh
Zařazení materiálu: Šablona: III/2 – Inovace a zkvalitnění výuky prostřednictvím ICT
Název materiálu: VY_32_INOVACE_07_3_12_7_MA_STREDOVA_SOUMERNOST
Téma: Středová souměrnost
Autor materiálu: Mgr. Alena Buroňová
Období vytvoření: 7. + pro účely opakování i vyšší
Vzdělávací oblast: Matematika a její aplikace
Vzdělávací obor: Matematika
Ročník: 7. + pro účely opakování i vyšší
Anotace: Prezentace vysvětluje sestrojování obrazu ve středové souměrnosti
Klíčová slova: středová souměrnost, střed souměrnosti, samodružný bod
Seznam literatury
a pramenů:
ODVÁRKO, Oldřich a Jiří KADLEČEK. Matematika pro 7. ročník základní školy.
1. vyd. Praha: Prometheus, 1999, 87 s. Učebnice pro základní školy
(Prometheus). ISBN 80-719-6129-9.
4. Pojmy
Souměrně sdružené body podle středu S jsou vzor
a obraz (například body A, A´).
Vzor a obraz úsečky jsou souměrně sdružené podle
středu S – jsou shodné a rovnoběžné.
Středová souměrnost je příklad shodného
zobrazení, každý vzor a jeho obraz jsou shodné.
Jediným samodružným bodem je její střed.
5. Postup
Narýsuj zadání a střed souměrnosti.
Narýsuj přímku, která prochází zadaným bodem a středem
souměrnosti.
Zabodni kružítko do bodu S a sestroj obraz zvoleného bodu. S je
uprostřed. AS = SA´
x
S
A
A´
6. Sestroj obraz úsečky ve středové souměrnosti
Úsečka AB měří 6 cm
Narýsuj přímku ↔ AS
Zabodni kružítko do bodu S a sestroj obraz bodu A. AS = SA´
Narýsuj přímku ↔ BS
Zabodni kružítko do bodu S a sestroj obraz bodu B. BS = SB´
Sestroj úsečku A´B´
x
S
A
A´
B
B´
7. Sestroj obraz úsečky ve středové souměrnosti
Úsečka AB měří 6 cm
Narýsuj přímku ↔ AS
Zabodni kružítko do bodu S a sestroj obraz bodu A. AS = SA´
Zabodni kružítko do bodu S a sestroj obraz bodu B. BS = SB´
Sestroj úsečku A´B´
x
S
A
A´
B
B´