Amazing snowflake geometric patterns symmetry. Celestial geometry

Symmetry has always been a mark of perfection and beauty in classical Greek illustration and aesthetics. The natural symmetry of nature, in particular, has been the subject of study by philosophers, astronomers, mathematicians, artists, architects and physicists such as Leonardo Da Vinci. We see this perfection every second, although we don’t always notice it. Here are 10 beautiful examples of symmetry, of which we ourselves are a part.

Broccoli Romanesco

This type of cabbage is known for its fractal symmetry. This is a complex pattern where the object is formed in the same geometric figure. In this case, all the broccoli is made up of the same logarithmic spiral. Broccoli Romanesco is not only beautiful, but also very healthy, rich in carotenoids, vitamins C and K, and tastes similar to cauliflower.

Honeycomb

For thousands of years, bees have instinctively produced perfectly shaped hexagons. Many scientists believe that bees produce honeycombs in this form to retain the most honey while using the least amount of wax. Others are not so sure and believe that it is a natural formation, and the wax is formed when bees create their home.


Sunflowers

These children of the sun have two forms of symmetry at once - radial symmetry, and numerical symmetry of the Fibonacci sequence. The Fibonacci sequence appears in the number of spirals from the seeds of a flower.


Nautilus shell

Another natural Fibonacci sequence appears in the shell of the Nautilus. The shell of the Nautilus grows in a “Fibonacci spiral” in a proportional shape, allowing the Nautilus inside to maintain the same shape throughout its lifespan.


Animals

Animals, like people, are symmetrical on both sides. This means that there is a center line where they can be divided into two identical halves.


Spider web

Spiders create perfect circular webs. The web network consists of equally spaced radial levels that spread out from the center in a spiral, intertwining with each other with maximum strength.


Crop Circles.

Crop circles don't occur "naturally" at all, but they are a pretty amazing symmetry that humans can achieve. Many believed that crop circles were the result of a UFO visit, but in the end it turned out that they were the work of man. Crop circles exhibit various forms of symmetry, including Fibonacci spirals and fractals.


Snowflakes

You'll definitely need a microscope to witness the beautiful radial symmetry in these miniature six-sided crystals. This symmetry is formed through the process of crystallization in the water molecules that form the snowflake. When water molecules freeze, they form hydrogen bonds with the hexagonal shapes.


Milky Way Galaxy

The Earth is not the only place that adheres to natural symmetry and mathematics. The Milky Way Galaxy is a striking example of mirror symmetry and is composed of two main arms known as the Perseus and Centauri Shield. Each of these arms has a logarithmic spiral, similar to the shell of a nautilus, with a Fibonacci sequence that begins at the center of the galaxy and expands.


Lunar-solar symmetry

The sun is much larger than the moon, four hundred times larger in fact. However, the phenomenon of a solar eclipse occurs every five years when the lunar disk completely blocks the sunlight. The symmetry occurs because the Sun is four hundred times farther from the Earth than the Moon.


In fact, symmetry is inherent in nature itself. Mathematical and logarithmic perfection creates beauty around and within us.

Title: Poluyanovich N.V.

“Axial symmetry.

Pattern design

based on axial symmetry"

(extracurricular activities,

course "Geometrics" 2nd grade)

The lesson is aimed at:

Application of knowledge about symmetry acquired in the lessons of the surrounding world, computer science and ICT, Origins;

Application of the skills to analyze the shapes of objects, combine objects into groups according to certain characteristics, isolate the “extra” from a group of objects;

Development of spatial imagination and thinking;

Creating conditions for

Increasing motivation to study,

Gaining experience in collective work;

Cultivating interest in traditional Russian folk arts and crafts.

Equipment:

computer, interactive whiteboard, TIKO constructor, exhibition of children's works, DPI circle, window drawings.

  1. Updating the topic

Teacher:

Name the fastest artist (mirror)

The expression “mirror-like surface of water” is also interesting. Why did they start saying that? (slides 3,4)

Student:

In the quiet backwater of a pond

Where the water flows

Sun, sky and moon

It will definitely be reflected.

Student:

Water reflects the space of heaven,
Coastal mountains, birch forest.
There is silence again over the surface of the water,
The breeze has died down and the waves are not splashing.

2. Repetition of types of symmetry.

2.1. Teacher:

Experiments with mirrorsallowed us to touch an amazing mathematical phenomenon - symmetry. We know what symmetry is from the subject of ICT. Remind me what symmetry is?

Student:

Translated, the word “symmetry” means “proportionality in the arrangement of parts of something or strict correctness.” If a symmetrical figure is folded in half along the axis of symmetry, then the halves of the figure will coincide.

Teacher:

Let's make sure of this. Fold the flower (cut from construction paper) in half. Did the halves match? This means the figure is symmetrical. How many axes of symmetry does this figure have?

Students:

Some.

2.2. Working with an interactive whiteboard

Teacher:

What two groups can objects be divided into? (Symmetrical and asymmetrical). Distribute.

2.3. Teacher:

Symmetry in nature always fascinates, enchants with its beauty...

Student:

All four petals of the flower moved

I wanted to pick it, it fluttered and flew away (butterfly).

(slide 5 – butterfly – vertical symmetry)

2.4. Practical activities.

Teacher:

Vertical symmetry is the exact reflection of the left half of the pattern in the right. Now we will learn how to make such a pattern with paints.

(move to the table with paints. Each student folds the sheet in half, unfolds it, applies paint of several colors to the fold line, folds the sheet along the fold line, sliding the palm along the sheet from the fold line to the edges, stretches the paint. Unfolds the sheet and observes the symmetry of the pattern relative to the vertical axis of symmetry. Leave the sheet to dry.)

(Children return to their seats)

2.5. Observing nature, people have often encountered amazing examples of symmetry.

Student:

The star spun

There's a little in the air

Sat down and melted

On my palm

(snowflake - slide 6 - axial symmetry)

7-9 - central symmetry.

2.6. Human use of symmetry

Teacher:

4. Man has long used symmetry in architecture. Symmetry gives harmony and completeness to ancient temples, towers of medieval castles, and modern buildings.

(Slides 10, 12)

2.7. The exhibition of children's works from the DPI group presents works with symmetrical designs. Children learn to cut out parts with a jigsaw, which are held together with glue. Finished products: cassette holder, carved chair, box, photo frame, blanks for a coffee table.

Teacher:

People use symmetry when creating ornaments.

Student: - An ornament is a decoration made from a combination of periodically repeating geometric, plant or animal elements. In Rus', people decorated towers and churches with ornaments.

Student:

This is a house carving (slide 14 - 16). The origins of house carving go back to ancient times. In Ancient Rus', it was used, first of all, to attract powerful forces of light in order to protect a person’s home, his family, and his household from the invasion of evil and dark principles. Then there was a whole system of both symbols and signs protecting the space of a peasant house. The most striking part of the home has always been the cornices, trim, and porch.

Student:

The porch was decorated with house carvings,platbands , cornices , pricheliny. Simple geometric motifs - repeating rows of triangles, semicircles, piers with framing tasselsgables gable roofs of houses. These are the most ancient Slavic symbols of rain, heavenly moisture, on which fertility, and therefore the life of the farmer, depended. The celestial sphere is associated with ideas about the Sun, which gives heat and light.

Teacher:

- The signs of the Sun are solar symbols, indicating the daily path of the luminary. The figurative world was especially important and interestingplatbands windows The windows themselves in the idea of ​​a house are a border zone between the world inside the home and the other, natural, often unknown, surrounding the house on all sides. The upper part of the casing signified the heavenly world; symbols of the Sun were depicted on it.

(Slides 16 -18 - symmetry in patterns on window shutters)

  1. Practical application of skills

Teacher:

Today we will create symmetrical patterns for window frames or shutters. The amount of work is very large. What did they do in the old days in Rus' when they built a house? How can we manage to decorate a window in a short time? What should I do?

Students:

Previously, they worked as an artel. And we will work in tandem with the distribution of work into parts.

Teacher:

Let's remember the rules of working in pairs and groups (slide No. 19).

We outline the stages of work:

  1. We select the axis of symmetry – vertical.
  2. The pattern above the window is horizontal, but with a vertical axis of symmetry relative to the center.
  3. The pattern on the side sashes and window frames is symmetrical
  4. Independent creative work of students in pairs.
  5. The teacher helps and corrects.
  1. Result of the work

Exhibition of children's works.

We did a great job today!

We tried our best!

We made it!

Vocabulary work

Platband - design of a window or doorway in the form of overhead figured strips. Made of wood and richly decorated with carvings - carved platband.

Lush window casings with carved pediments crowning them on the outside and exquisite carvings depicting herbs and animals.

Prichelina - from the word to repair, do, attach, in Russian wooden architecture - a board covering the ends of the logs on the facade of a hut, cage

Solar sign . Circle - common solar sign, symbol Sun; wave - a sign of water; zigzag - lightning, thunderstorms and life-giving rain;


Municipal state educational institution

"Secondary school No. 1"

Research

"Symmetry and Snowflakes"

Completed by: Anna Davtyan

student of 8th grade "A"

Head: Volkova S.V.

Mathematic teacher

Shchuchye, 2016

Content

Introduction ……………………………………………………………………..……3

1. Theoretical part ……………………………………………….…….....4-5

1.1. Symmetry in nature................................................................... .......................................4

1.2. How is a snowflake born?……………………………………………..…..4

1.3. Shapes of snowflakes................................................... ...........................................4-5

1.4 Snowflake researchers...................................................…………… ……...…5

2. Practical part …………………………………………………...……6-7

2.1. Experiment 1. Are all snowflakes the same?.................…………………...…….6

2.2. Experiment 2. Let’s take a photo of a snowflake and make sure that it has six points…………………………………………………………………………………...…..6

2.3. Questioning classmates and analyzing questionnaires…………………………6-7

Conclusion ……………………………………………………………………….8

Literature ………………………………………………………………………..9

Applications .........................................................................................................10

Introduction

“...to be beautiful means to be symmetrical and proportionate”

Symmetry (ancient Greek συμμετρία - “proportionality”), in a broad sense - immutability under any transformations. The principles of symmetry play an important role in physics and mathematics, chemistry and biology, technology and architecture, painting and sculpture. “Is it possible to create order, beauty and perfection with the help of symmetry?”, “Should there be symmetry in everything in life?” - I asked myself these questions a long time ago, and I will try to answer them in this work.The subject of this study is symmetry as one of the mathematical foundations behindbeauty laws using snowflakes as an example. Relevance The problem lies in showing that beauty is an external sign of symmetry and, above all, has a mathematical basis.Goal of the work - use examples to consider and study the formation and shape of snowflakes.Job objectives: 1. collect information on the topic under consideration; 2.highlight symmetry as the mathematical basis of the laws of beauty of snowflakes.3.conduct a survey among classmates “What do you know about snowflakes?”4.competition for the most beautiful hand-made snowflake.To solve the problems, the following were usedmethods: searching for the necessary information on the Internet, scientific literature, questioning classmates and analyzing questionnaires, observation, comparison,. generalization. Practical significance research consists

    in drawing up a presentation that can be used in mathematics lessons, the natural world, fine arts and technology, and extracurricular activities;

    in enriching vocabulary.

1. Theoretical part. 1.1. Symmetry of snowflakes. Unlike art or technology, beauty in nature is not created, but only recorded and expressed. Among the infinite variety of forms of living and inanimate nature, such perfect images are found in abundance, whose appearance invariably attracts our attention. Such images include some crystals and many plants.Each snowflake is a small crystal of frozen water. The shape of snowflakes can be very diverse, but they all have symmetry - rotational symmetry of the 6th order and, in addition, mirror symmetry. 1.2. How a snowflake is born. People living in northern latitudes have long been interested in why in winter when snow falls it is not round, like rain. Where do they come from?
Snowflakes also fall from clouds, just like rain, but they are not formed quite like rain. Previously, they thought that snow was frozen droplets of water and that it came from the same clouds as rain. And not so long ago, the mystery of the birth of snowflakes was solved. And then they learned that snow will never be born from droplets of water. Snow crystals form in cold clouds high above the ground when an ice crystal forms around a small speck of dust or bacteria. Ice crystals are hexagon shaped. It is because of this that most snowflakes are shaped like a six-pointed star. Then this crystal begins to grow. Its rays may begin to grow, these rays may have shoots, or, conversely, the snowflake begins to grow in thickness. Regular snowflakes have a diameter of about 5 mm and a weight of 0.004 grams. The world's largest snowflake was discovered in the USA in January 1887. The diameter of the snow beauty was as much as 38 cm! And in Moscow on April 30, 1944, the strangest snow in the history of mankind fell. Snowflakes the size of a palm circled over the capital, and their shape resembled ostrich feathers.

1.3. Snowflake shapes.

The shape and growth of snowflakes depend on air temperature and humidity.As the snowflake grows, it becomes heavier and falls to the ground, changing its shape. If a snowflake spins like a top when it falls, then its shape is perfectly symmetrical. If it falls sideways or otherwise, then its shape will be asymmetrical. The greater the distance a snowflake flies from the cloud to the ground, the larger it will be. Falling crystals stick together to form snow flakes. Most often, their size does not exceed 1-2 cm. Sometimes these flakes are of record sizes. In Serbia in the winter of 1971, snow fell with flakes up to 30 cm in diameter! Snowflakes are 95% air. This is why snowflakes fall to the ground so slowly.

Scientists studying snowflakes have identified nine main forms of snow crystals. They were given interesting names: plate, star, column, needle, fluff, hedgehog, cufflink, icy snowflake, croup-shaped snowflake. (Appendix 1)

1.4. Snezhinka researchers.

Hexagonal openwork snowflakes became the subject of study back in 1550. Archbishop Olaf Magnus of Sweden was the first to observe snowflakes with the naked eye and sketch them.His drawings suggest that he did not notice their six-pointed symmetry.

AstronomerJohannes Keplerpublished a scientific treatise “On Hexagonal Snowflakes”. He “disassembled the snowflake” from the point of view of strict geometry.
In 1635, a French philosopher, mathematician and natural scientist became interested in the shape of snowflakes.
Rene Descartes. He classified the geometric shape of snowflakes.

The first photograph of a snowflake under a microscope was taken by an American farmer in 1885.Wilson Bentley. Wilson has been photographing all types of snow for nearly fifty years and has taken over 5,000 unique photographs over the years. Based on his work, it was proven that there is not a single pair of absolutely identical snowflakes.

In 1939Ukihiro Nakaya, a professor at Hokkaido University, also began to seriously study and classify snowflakes. And over time, he even created the “Ice Crystal Museum” in the city of Kaga (500 km west of Tokyo).

Since 2001, snowflakes have been grown artificially in the laboratory of Professor Kenneth Libbrecht.

Thanks to the photographerDonKomarechkafrom Canadawe havethere was an opportunity to admire the beauty and diversitysnowflakes. He takes macro photographs of snowflakes. (Appendix 2).

2. Practical part.

1.1. Experiment 1. Are all snowflakes the same?

When snowflakes began to fall from the sky to the ground, I took a magnifying glass, a notebook with a pencil and sketched the snowflakes. I managed to make drawings of several snowflakes. This means that snowflakes have different shapes.

1.2. Experiment 2. Let's take a photo of a snowflake and make sure that it has six points.

For this experiment I needed a digital camera and black velvet paper.

When the snowflakes began to fall to the ground, I took the black paper and waited for the snowflakes to fall on it. I photographed several snowflakes with a digital camera. Output the images via computer. When the pictures were enlarged, it was clearly visible that the snowflakes had 6 rays. It is impossible to get beautiful snowflakes at home. But you can “grow” your own snowflakes by cutting them out of paper. Or bake from dough. You can also draw entire snow dances. After all, everyone can do this! (Appendix 3.4).

1.3. Questioning classmates and analyzing questionnaires.

At the first stage of the study, a survey was conducted among children in grade 8A: “What do you know about snowflakes?” 24 people took part in the survey. Here's what I found out.

    What is a snowflake made of?

a) I know - 17 people.

b) I don’t know - 7 people.

    Are all snowflakes the same?

a) yes – 0 people.

b) no – 20 people.

c) I don’t know – 4 people.

    Why is a snowflake hexagonal?

a) I know – 6 people.

b) don’t know – 18 people

    Is it possible to photograph a snowflake?

a) yes – 24 people.

b) no – 0 people.

c) I don’t know – 0 people.

5. Is it possible to get a snowflake at home:

a) possible – 3 people.

b) impossible – 21 people.

Conclusion: knowledge about snowflakes is not 100%.

At the second stage, a competition was held for the most beautiful snowflake cut out of paper.

Based on the results of the survey, diagrams were constructed (Appendix 5).

Conclusion

Symmetry, manifesting itself in a wide variety of objects of the material world, undoubtedly reflects its most general, most fundamental properties.
Therefore, the study of the symmetry of various natural objects and the comparison of its results is a convenient and reliable tool for understanding the basic laws of the existence of matter. You can see that this apparent simplicity will take us far into the world of science and technology and will allow us to test the abilities of our brain from time to time (since it is the brain that is programmed for symmetry). “The principle of symmetry covers all new areas. From the field of crystallography, solid state physics, he entered the field of chemistry, the field of molecular processes and atomic physics. There is no doubt that we will find its manifestations in the world of the electron, even more distant from the complexes surrounding us, and the phenomena of quanta will be subordinate to it,” these are the words of Academician V.I. Vernadsky, who studied the principles of symmetry in inanimate nature.

Literature:

    Great schoolchild encyclopedia. " Planet Earth". – Publishing house “Rosman-Press”, 2001 - 660 p. / A.Yu.Biryukova.

    Everything about everything. Popular encyclopedia for children. – Publishing house

“Klyuch-S, Philological Society “Slovo”, 1994 - 488 pp. / Slavkin V.

    Colors of nature: A book for elementary school students - M: Prosveshchenie, 1989 - 160 pp. / Korabelnikov V.A.

Internet resources:

    http://vorotila.ru/Otdyh-turizm-oteli-kurorty/Snezhnye-tayny-i174550

    Electronic children's encyclopedia "Pochemuchki".

Presentation on the topic "Celestial Geometry" on geometry in powerpoint format. The presentation for schoolchildren tells how the “birth” of a snowflake occurs, how the shape of a snowflake depends on external conditions. The presentation also contains information about who and when studied snow crystals. Authors of the presentation: Evgenia Ustinova, Polina Likhacheva, Ekaterina Lapshina.

Fragments from the presentation

Goals and objectives

Target: give a physical and mathematical justification for the diversity of snowflake shapes.

Tasks:
  • study the history of the appearance of photographs with images of snowflakes;
  • study the process of formation and growth of snowflakes;
  • determine the dependence of the shapes of snowflakes on external conditions (temperature, air humidity);
  • explain the variety of shapes of snowflakes in terms of symmetry.

From the history of the study of snowflakes

  • Wilson Bentley (USA) took the first photograph of a snow crystal under a microscope on January 15, 1885. Over 47 years, Bentley compiled a collection of photographs of snowflakes (more than 5000) taken under a microscope.
  • Sigson (Rybinsk) found a not the worst way to photograph snowflakes: snowflakes should be placed on the finest, almost gossamer, mesh of silkworms - then they can be photographed in all details, and the mesh can then be retouched.
  • In 1933, an observer at a polar station on Franz Josef Land Kasatkin received more than 300 photographs of snowflakes of various shapes.
  • In 1955, A. Zamorsky divided snowflakes into 9 classes and 48 species. These are plates, stars, hedgehogs, columns, fluffs, cufflinks, prisms, group ones.
  • Kenneth Liebrecht (California) has compiled a complete guide to snowflakes.
Johannes Kepler
  • noted that all snowflakes have 6 faces and one axis of symmetry;
  • analyzed the symmetry of snowflakes.

Birth of a crystal

A ball of dust and water molecules grows, taking the shape of a hexagonal prism.

Conclusion

  • There are 48 types of snow crystals, divided into 9 classes.
  • The size, shape and pattern of snowflakes depend on temperature and humidity.
  • The internal structure of a snow crystal determines its appearance.
  • All snowflakes have 6 faces and one axis of symmetry.
  • The cross section of the crystal, perpendicular to the axis of symmetry, has a hexagonal shape.

And yet, the mystery remains a mystery to us: why are hexagonal shapes so common in nature?





















Back forward

Attention! Slide previews are for informational purposes only and may not represent all the features of the presentation. If you are interested in this work, please download the full version.

The lesson is aimed at:

  • application of knowledge about symmetry acquired in the lessons of the surrounding world, computer science and ICT, Origins;
  • application of the skills to analyze the shapes of objects, combine objects into groups according to certain characteristics, isolate the “extra” from a group of objects;
  • development of spatial imagination and thinking;
  • creating conditions for
  • increasing motivation to learn,
  • gaining experience in collective work;
  • nurturing interest in traditional Russian folk arts and crafts.

Equipment:

  • computer,
  • interactive board,
  • designer TIKO,
  • exhibition of children's works of the DPI circle,
  • window drawings.

1. Updating the topic

Teacher:

Name the fastest artist (mirror)

The expression “mirror-like surface of water” is also interesting. Why did they start saying that? (slides 3,4)

Student:

In the quiet backwater of a pond
Where the water flows
Sun, sky and moon
It will definitely be reflected.

Student:

Water reflects the space of heaven,
Coastal mountains, birch forest.
There is silence again over the surface of the water,
The breeze has died down and the waves are not splashing.

2. Repetition of types of symmetry.

2.1. Teacher:

Experiments with mirrors made it possible to touch upon an amazing mathematical phenomenon - symmetry. We know what symmetry is from the subject of ICT. Remind me what symmetry is?

Student:

Translated, the word “symmetry” means “proportionality in the arrangement of parts of something or strict correctness.” If a symmetrical figure is folded in half along the axis of symmetry, then the halves of the figure will coincide.

Teacher:

Let's make sure of this. Fold the flower (cut from construction paper) in half. Did the halves match? This means the figure is symmetrical. How many axes of symmetry does this figure have?

Students:

Some.

2.2. Working with an interactive whiteboard

What two groups can objects be divided into? (Symmetrical and asymmetrical). Distribute.

2.3. Teacher:

Symmetry in nature always fascinates, enchants with its beauty...

Student:

All four petals of the flower moved
I wanted to pick it, it fluttered and flew away (butterfly).

(slide 5 – butterfly – vertical symmetry)

2.4. Practical activities.

Teacher:

Vertical symmetry is the exact reflection of the left half of the pattern in the right. Now we will learn how to make such a pattern with paints.

(move to the table with paints. Each student folds the sheet in half, unfolds it, applies paint of several colors to the fold line, folds the sheet along the fold line, sliding the palm along the sheet from the fold line to the edges, stretches the paint. Unfolds the sheet and observes the symmetry of the pattern relative to the vertical axis of symmetry. Leave the sheet to dry.)

(Children return to their seats)

2.5. Observing nature, people have often encountered amazing examples of symmetry.

Student:

The star spun
There's a little in the air
Sat down and melted
On my palm

(snowflake - slide 6 - axial symmetry)

7-9 - central symmetry.

2.6. Human use of symmetry

Teacher:

4. Man has long used symmetry in architecture. Symmetry gives harmony and completeness to ancient temples, towers of medieval castles, and modern buildings.

(Slides 10, 12)

2.7. The exhibition of children's works from the DPI group presents works with symmetrical designs. Children learn to cut out parts with a jigsaw, which are held together with glue. Finished products: cassette holder, carved chair, box, photo frame, blanks for a coffee table.

Teacher:

People use symmetry when creating ornaments.

Student: - An ornament is a decoration made from a combination of periodically repeating geometric, plant or animal elements. In Rus', people decorated towers and churches with ornaments.

Student:

This is a house carving (slide 14 - 16). The origins of house carving go back to ancient times. In Ancient Rus', it was used, first of all, to attract powerful forces of light in order to protect a person’s home, his family, and his household from the invasion of evil and dark principles. Then there was a whole system of both symbols and signs protecting the space of a peasant house. The most striking part of the home has always been the cornices, trim, and porch.

Student:

The porch was decorated with house carvings, platbands , cornices, pricheliny. Simple geometric motifs - repeating rows of triangles, semicircles, piers with framing tassels gables gable roofs of houses . These are the most ancient Slavic symbols of rain, heavenly moisture, on which fertility, and therefore the life of the farmer, depended. The celestial sphere is associated with ideas about the Sun, which gives heat and light.

Teacher:

The signs of the Sun are solar symbols, indicating the daily path of the luminary. The figurative world was especially important and interesting platbands windows The windows themselves in the idea of ​​a house are a border zone between the world inside the home and the other, natural, often unknown, surrounding the house on all sides. The upper part of the casing signified the heavenly world; symbols of the Sun were depicted on it.

(Slides 16 -18 - symmetry in patterns on window shutters)

3. Practical application of skills

Teacher:

Today we will create symmetrical patterns for window frames or shutters. The amount of work is very large. What did they do in the old days in Rus' when they built a house? How can we manage to decorate a window in a short time? What should I do?

Students:

Previously, they worked as an artel. And we will work in tandem with the distribution of work into parts.

Teacher:

Let's remember the rules of working in pairs and groups (slide No. 19).

We outline the stages of work:

  • We select the axis of symmetry – vertical.
  • The pattern above the window is horizontal, but with a vertical axis of symmetry relative to the center.
  • The pattern on the side sashes and window frames is symmetrical
  • Independent creative work of students in pairs.
  • The teacher helps and corrects.
  • 4. Result of the work

    Exhibition of children's works.

    We did a great job today!

    We tried our best!

    We made it!

    Vocabulary work

    • Platband- design of a window or doorway in the form of overhead figured strips. Made of wood and richly decorated with carvings - carved platband.
      Lush window frames with carved pediments crowning them on the outside and delicate carvings depicting herbs and animals.
    • Prichelina- from the word to repair, do, attach, in Russian wooden architecture - a board covering the ends of the logs on the facade of a hut, cage
    • Solar sign. The circle is a common solar sign, a symbol of the Sun; wave - a sign of water; zigzag - lightning, thunderstorms and life-giving rain.