Ogoltsova Julia

The purpose of this work is to study the properties of simple geometric shapes in Everyday life man, since geometric figures surround us everywhere, and knowledge of their properties makes our life easier.

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Scientific and practical conference

« Science step by step»

Research - project work mathematics

Unusual Properties simple geometric shapes

Completed by: 5th grade students

MBOU "Secondary School No. 11"

Ogoltsova Julia

Supervisor:

Lenshina Yu. A.

Donskoy

year 2014

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

Basic geometric shapes…………………………….………………...4

Why in the world around us there are many simple geometric shapes.……….6

What simple geometric shapes are most useful in our world....... 9

How geometric shapes were used at all times ..……………….13

This is interesting.……………… .……………….……………….………………..16

Practical experiments.……………….……………….…………… .……………18

Conclusion………………………………………………………………………….20

References………………………………………………………………21

INTRODUCTION

One of the most interesting subjects for me is mathematics. Studying the history of the development of this subject, I, referring to many sources, found that the influence of mathematics on other subjects such as geography, history, physics is very great.

Geometric figures surround us everywhere: in construction, in everyday life, in architecture, in fine arts etc.,and the knowledge of their properties facilitates man's existence. Since the first grade, everyone has known such geometric shapes as a triangle, a circle, a square. It is worth looking closely, and you can see many items similar to them. The walls, the ceiling, the floor, the chalkboard, the door—they all look like rectangles. An ordinary glass and a water pipe have a cylindrical shape. The cabinet is a parallelepiped, and its doors, walls, shelves are rectangles.

And since I wanted to carefully study the properties of geometric shapes, I chose the topic "Unusual properties of simple geometric shapes."

Before starting this research work I have set the following target: explore how the properties of simple geometric shapes help us in everyday life.

I have put the following tasks:

1. Study the literature on the topic
2. Familiarize yourself with the history of the use of geometric shapes at all times
3. Learn the properties of simple geometric shapes
4. Set the most useful properties of geometric shapes.

BASIC GEOMETRIC FIGURES

The main geometric figures on the plane are the point and the straight line. A segment, a ray, a broken line are the simplest geometric figures on a plane.

Dot - is the smallestgeometric figure, which is the basis of all other constructions (figures) in any image or drawing.

Any more complex geometric figure is a set points , which have a certain property that is characteristic only for this figure.

An example of such geometric shapes are the circle and the circle:

straight line , or a straight line, can be thought of as an infinite set points , which are located on the same line, which has neither beginning nor end. On a sheet of paper, you can see only part of a straight line, since it is infinite.

The straight line is shown like this:

Line segment - part of a straight line bounded on both sides dots , The segment is depicted as follows:

Ray is a directed half-line that has point beginning and has no end. The beam is shown like this:

If you put a point on a straight line , then this point divides the line into two beam , oppositely directed. Such rays are called complementary.

A broken line is several segments connected to each other so that the end of the first segment is the beginning of the second segment, and the end of the second segment is the beginning of the third segment, etc., while adjacent (having one common point ) the segments are not on the same straight line.

If the end of the last segment does not coincide with the beginning of the first, then such a broken line is called open.

If the end of the last segment of the polyline coincides with the beginning of the first segment, then such a polyline is called closed. An example of a closed polygon is any polygon:

WHY THE AROUND WORLD IS MANY SIMPLE GEOMETRIC FIGURES

I decided to explore such geometric shapes that are most often found around us. Having become interested in the problem, I made a work plan. I decided to find out why there are a lot of simple geometric shapes in the world around us.

During my research, I came to the conclusion that only round objects can roll and therefore are easier to move. Therefore, wherever we go, we return, i.e. we go in a circle.

The circle has no corners, and therefore it is convenient to use, for example, round coins cannot tear a pocket, you won’t prick or cut yourself on them.

The ball cannot be square, it will not bounce.

The dishes were made of clay, and it was easier to give a rounded shape than a square one. Round dishes are easier to wash, no need to scrape out of the corners, it is more convenient to stir in it.

It is easier to make round than angular. Many technical processes are easier for bodies of revolution. There is less material for a round shape than for a square one. A round manhole cover will never fail, unlike a square one.

All jars and lids are round in shape. each point of the circle is a point of concentration of stress, and it is easy to open it, in a rectangular shape, only the corners are such points.

Why are there actually so many round bodies? This question can be answered by considering a soap bubble, because it is perfectly round. The forces of surface tension do not allow the soap bubble to burst and tend to give the soap bubble the most compact shape. The most compact shape in nature is a sphere. With a spherical shape, the air inside the bubble evenly presses on all parts of its inner wall.

In addition, the circle and circle in the form of a sphere and a ball are the most common shape in the universe.

A circle and a circle are also the trajectory of the Earth around the Sun, this is the movement of stars in the sky, this is the cyclicality of all processes occurring in the world. If it were necessary to choose a form that most accurately conveys the structure of the world, then these would be circles and circles.

Thus, the circle in human life has a very important role, and in life it is impossible to do without round objects.

The triangle is a rigid figure. But what does this mean? Let's imagine two slats, in which two ends are fastened with a nail. This design is not rigid: by shifting or pushing the free ends of the rails, we can change the angle between them. Now take another rail and fasten its ends to the free ends of the first two rails. The resulting construction - a triangle - will already be rigid. No two sides can be moved or moved apart in it, that is, not a single corner can be changed. Thus, if three sides of a triangle are given, then the shape of the triangle can no longer change. As a result of the study, we can conclude that the triangle is the only geometric figure that has the property of rigidity. The rigidity property of a triangle is widely used in practice.

So, to fix the column in a vertical position, a backup is placed on it. Telegraph poles with support are called anchor poles. When making a garden gate, be sure to nail the bar to get a triangle. This gives the gate strength, otherwise it will warp. The rafters of the buildings look like triangles. This gives them strength and stability. During the construction of any bridges, triangles are also present in their structures. Triangles make high-voltage power line designs reliable. The rigidity of triangles is used in the construction of cranes.

A square in nature is presented in the form of pyrite (Greek, literally - a stone that strikes fire), sulfur pyrites, iron pyrites - a mineral, iron disulfide.Pyrite is a raw material for obtainingsulfuric acid , sulfur And iron sulphate , But Lately rarely used for these purposes. Recently, it has been increasingly used as a corrective additive in the production of cements.

One example of a regular polygon in nature is the honeycomb, which is a polygon covered with regular hexagons. Of course, they did not study geometry, but nature endowed them with the talent to build houses in the form of geometric shapes.On these hexagons, bees grow cells from wax. In them, bees lay honey, and then again cover it with a solid rectangle of wax.

WHICH SIMPLE GEOMETRIC FIGURES ARE THE MOST USEFUL IN OUR WORLD

In order to answer the question of which simple geometric shapes are most useful in a person’s daily life, it is necessary to look around and understand which geometric shapes constantly surround us.

We cannot imagine our life without cars: a bus, a tractor, a bicycle, a sewing machine, a washing machine, a typewriter, an airplane, an all-terrain vehicle, a lunar rover, various machine tools, a crane ... They do not look alike, but let's take a closer look at them. They all have similar parts - details, and one of them is a wheel. At first the wheels were round and smooth, so that they rolled easily on the ground, and then a man came up with many different wheels. Gears are hidden inside many machines, one wheel makes another rotate, grooved wheels are blocks that help lift heavy loads. Machines have been improved and improved from century to century, but the use of the wheel in them as the main part remains unchanged.

Circle and circumference are widely used in architecture and art: round arches, vaults, domes. The circle is a form of nomadic tents and settlements, which among many peoples symbolizes dynamism and endless movement, as opposed to the squares of houses, plots of land and cities of settled and grain-sowing peoples. Even the ancient Greeks discovered that with the help of a compass and ruler, you can build many shapes, including hexagons, squares and other regular polygons, and create magical patterns.

Pictures with magic circles people use in medical purposes when you look at them, it seems that they are moving. If you look at them for a few minutes, then the headache goes away.

The roofs of old wooden houses and modern high-rise buildings are triangular in shape. This is due to the fact that melted snow does not linger on such roofs and rainwater easily drains.

The triangle has always been widely used in practical life. So, in the art of building, from time immemorial, the property of the rigidity of a triangle has been used to strengthen various buildings and their details. The triangle is also used: in architecture, in everyday life, in the construction of a drawing, in navigation.

Starting a game of billiards, you need to arrange the balls in the form of a triangle. To do this, use a special device.

The arrangement of pins in the bowling game is also in the form of an equilateral triangle.

The rule of the "golden triangle" is based on the psychology of the buyer - having found the product he needs, the buyer rushes to the cashier. The task of the sellers is to make him stay longer in the store by placing the goods the buyer needs at the vertices of an imaginary triangle, that is, to “anchor” the buyer. How more area triangle, the more successful the layout of the store can be called.

There is an amazing art of making bouquets and compositions from flowers, objects and plants - floristry, where the color scheme of a bouquet or composition, its shape, is selected using the triangle method. There are also geographical objects in the name of which there is a triangle. Thus, the world of triangles is diverse. They are widely used by man and decorate his life.

Regular polygons from ancient times were considered a symbol of beauty and perfection. Over time, a person learned to use the properties of figures in practical life. Geometry in everyday life. Walls, floor and ceiling are rectangles. Many things resemble a square, a rhombus, a trapezoid.

Parquet flooring has always been considered a symbol of prestige and good taste. The use of valuable wood species for the production of elite parquet and the use of various geometric patterns give the room sophistication and respectability.

A regular partition of the plane, called a "mosaic" is a set of closed figures that can be used to tile the plane without intersections of the figures and gaps between them. Usually, simple polygons, such as squares, triangles, hexagons, octagons, or combinations of these shapes, are used as a tiling shape.

Beautiful parquets made of regular polygons: triangles, squares, pentagons, hexagons, octagons. For example, circles cannot form parquet.

Patchwork from polygons.If stripes, squares and triangles can be dealt with without special training and without skills with a sewing machine, then polygons will require a lot of patience and skill from us. Many patchwork craftswomen prefer to assemble polygons by hand. The life of every person is a kind of patchwork, where bright and magical moments alternate with gray and black days. Quilts, pillows, napkins, handbags were obtained from patchwork.

Ornament is one of ancient species pictorial activity of a person, which in the distant past carried a symbolic magical meaning, a certain symbolism. The ornament was almost exclusively geometric, consisting of the strict forms of the circle, semicircle, spiral, square, rhombus, triangle, and various combinations thereof. ancient man endowed with certain signs his ideas about the structure of the world. For all that, the ornamentist has wide scope for choosing motifs for his composition. They are delivered to him in abundance by two sources - geometry and nature.

For example, a circle is the sun, a square is the earth.

Geometric carving is one of the most ancient types of woodcarving, in which the depicted figures have a geometric shape in various combinations. Geometric carving consists of a number of elements that form various ornamental compositions. Squares, triangles, trapezoids, rhombuses and rectangles are an arsenal of geometric elements that make it possible to create original compositions with a rich play of chiaroscuro.

With the help of an ax, a knife and some other auxiliary tools, a person provided himself with everything necessary for: life: he built dwellings and outbuildings, bridges and windmills, fortress walls and towers, churches, made machine tools and tools, ships and boats, sledges and carts , furniture, dishes, children's toys and much more.

HOW GEOMETRIC FIGURES HAVE BEEN USED AT ALL TIMES

A person encountered specific geometric figures in his labor activity in the manufacture of tools and vessels, in the processing of fields and the construction of buildings. Already in ancient times, scrapers and knives in the form of discs, triangles, rhombuses and segments, round vessels were made; fields usually had the shape of a rectangle, and buildings - the shape of a cone, cylinder and parallelepiped.

For primitive people, the shape of the objects around them played an important role. By shape and color, they distinguished edible mushrooms from inedible ones, tree species suitable for buildings from those that are suitable only for firewood, tasty nuts from bitter ones, etc. Coconut palm nuts, which looked like a ball, seemed especially tasty to them. Of course, there were no special names for geometric shapes. They said: “same as a coconut” or “same as salt”, etc. So, mastering the world around them, people got acquainted with the simplest geometric shapes.

Round bodies have been of interest to man since ancient times. In ancient Egypt for the construction of the famous Egyptian pyramids there were no technical facilities yet. Even huge blocks of stone had to be polished by hand, and they were moved using round logs. We noticed that rolling is easier if you take a piece of wood with almost the same thickness at the beginning and at the end. So people got to know one of the major bodies- cylinder. Rolling pins of a cylindrical shape were also used by women, rolling out linen after washing. It was quite difficult to transport goods on skating rinks, because the tree trunks themselves weighed a lot. To facilitate the work, they began to cut thin round plates from the trunks, which rolled more easily and with their help they dragged loads. This is how the first wheel appeared. Unfortunately, the direct inventor of the wheel is unknown.

Not only in the process of work, people got acquainted with various figures. Since ancient times, they loved to decorate themselves, their clothes, their homes. And many of the decorations created a long time ago had one form or another. The beads were spherical, bracelets and rings had the shape of a circle. Ancient craftsmen learned how to give a beautiful shape to bronze, gold, silver, and precious stones. The artists who painted the palaces also used the circle. Since the invention of the potter's wheel, people have learned to make round dishes - pots, vases, amphorae. The columns supporting the buildings were also round.

The triangle is one of the first geometric figures that began to be used in the ornaments of ancient peoples.

With the help of stretched ropes 3, 4 and 5 units long, Egyptian priests received right angles when erecting temples, etc.

Various dwellings of people: wigwam, yurt, tent. All of them have a conical shape, a triangle is obtained in cross section. Such structures are easily blown by the winds, water quickly drains from them.

Sailing ships use triangular sails.

Man's clothing. Various hats: cocked hats, caps, caps, scarves - have a triangular shape. Women's scarves, before being thrown over the head, are folded in half. When sewing skirts, wedges are often sewn in, which also have the shape of a triangle, which gives the skirt splendor. To prevent the clothes from wrinkling, they are stored on a hanger that has a triangular shape.

Ancient people made ornaments of triangles, rhombuses, circles on the walls of caves. Of all polygons with a given number of sides, the most pleasing to the eye is a regular polygon, in which all sides are equal and all angles are equal. One of these polygons is a square, or in other words, a square is a regular quadrilateral.

There are several ways to define a square: a square is a rectangle with all sides equal and a square is a rhombus with all right angles.

The square has a number of interesting properties. So, for example, if it is necessary to enclose a quadrangular section of the largest area with a fence of a given length, then this section should be selected in the form of a square.

The square has a symmetry that gives it simplicity and a certain perfection of form: the square serves as a standard for measuring the areas of all figures.

These examples show that geometric standards first appeared in geometry: a ball for spherical objects, a pine cone for pointed objects, etc., and later the names of these standards became the names of abstract geometric shapes.

THIS IS INTERESTING

In order to determine the character of a person, his abilities and manner of communication, there are a large number of different methods and systems, including all kinds of horoscopes. But even in such a situation, mathematics, or rather geometric shapes, will help.

Psychogeometry is a relatively young personality analysis system that allows predicting and evaluating somecharacter traits , a model of behavior and a person's lifestyle with the help of simple geometric shapes. It was developed in the USA by Susan Dellinger, PhD, who worked with staff for many years and summarized her experience in psychogeometry.

Look carefully at the geometric shapes, feel your own, about which you can say: "It's me!".

Circle. This figure is a mythological symbol of harmony. The Circle Man is sincerely interested in good interpersonal relationships. For him, the most important thing is the well-being of people. The circle is the most benevolent of all shapes. It is he who holds the team, family, loved ones together. The circle is able to show enviable firmness when it comes to issues of morality or violations of justice.

Triangle. This figure symbolizes leadership. So the Triangle is strong personality. He is decisive, energetic, unstoppable, sets clear goals and, as a rule, achieves them. The triangle is a very confident person who constantly tries to prove his case in everything, admits his mistakes with great difficulty, He is programmed to win, win, succeed.

Square. If you have chosen a square as your main shape, then you are a tireless worker! You are diligent, feel the need to bring the work you have started to the end and always finish it. Such a person is able to collect, systematize, instantly issue and apply information. He is considered a polymath, at least in his field.

Rectangle. It symbolizes the state of transition and change. This is, as it were, a temporary form of personality that the other four figures can have at some time in their lives. The rectangle is often in a state of confusion, uncertainty about itself. He has low self-esteem, strives to become better at something, looks for new methods of work, tries to change his lifestyle.

Broken line. This form - a symbol of creativity - is the only open figure of the five. If you have firmly chosen a broken line as the main form, then you are characterized by figurativeness, intuitiveness, mosaicism. Strictness and consistency is not your style. That is why it is difficult for representatives of other forms to understand you. You are a creative person. You will achieve success in various fields of art.

I used this test to determine the personality types of my classmates and found out that in the fifth grade, five of my classmates chose the shape of a circle, four each of a triangle and a broken line, two chose a rectangle, and no one chose a square.

PRACTICAL EXPERIENCES

Having finished studying the theoretical part of my project work, I decided to move on to the practical one and find out on my own whether round dishes are easier to wash, whether a triangle really has the property of rigidity, and why a square is a standard of symmetry.

In order to find out why it is easier to wash round dishes, I did the following work: I took a round plate, rectangular with rounded corners, a square-shaped salad bowl and a small vase with a triangular side. All types of dishes were equally soiled and stood in this condition for some time.

Then I washed the dishes, turning Special attention ease and convenience of removing contaminants. And I came to the conclusion that it is really faster and more convenient to wash round-shaped dishes, since they have no corners where pollution could remain, and less time was spent cleaning them.

To identify the rigidity property of a triangle, I made several blanks from cardboard and sequentially assembled two parts first, then attached another one to make a triangle, and then added the last one to form a square shape.

As a result of my research, I determined that when two parts of my blanks are fastened, the resulting figure will be mobile, and when four parts are fastened, the resulting square will not have rigidity, and only when three parts are fastened, the resulting triangle will be the only rigid figure.

Any square can be broken down into smaller squares.
The diagonals of a square are equal and mutually perpendicular. At the point of intersection, they are divided in half and, in turn, divide the corners of the square in half.

A square is the most symmetrical figure because all its sides are equal, all angles are always straight and equal to each other, opposite sides are parallel, and diagonals are equal and perpendicular.

CONCLUSION

The simplest geometric shapes, such as a circle, a triangle, a rectangle, are exactly those figures that a person met in ancient times. The properties of these figures were the first to come to the aid of man, since these figures have always been widely used in practical life.

So, after doing research work, I can draw conclusions about the most useful properties of geometric shapes:

The circle and the circle are surprisingly harmonious figures. The circle is the only curve that can "slide on its own", rotating around the center.

The circle is the wheel. The wheel is progress - moving forward. If the wheel stops, then the wheel of History stops. Everything moves in a circle.

The triangle is the only geometric figure that has the rigidity property. The triangle has always been widely used in practical life. So, in the art of building, from time immemorial, the property of the rigidity of a triangle has been used to strengthen various buildings and their details.

The square serves as a standard for measuring the areas of all figures. Knowing about polygons and their types, you can create very beautiful decorations, build diverse and unique buildings.

Human ideas about beauty are formed under the influence of what a person sees in wildlife. In her various creations, very far from each other, she can use the same principles. https://accounts.google.com

Slides captions:

Research and design work in mathematics on the topic: “Unusual properties of simple geometric shapes” Scientific and practical conference “Into science step by step”, Donskoy, 2014 Prepared by: 5th grade student of MBOU “Secondary School No. 11” Yulia Ogoltsova Head: Mathematics teacher MBOU "Secondary School No. 11" Lenshina Yu. A.

Purpose To study how the properties of simple geometric shapes help us in everyday life.

OBJECTIVES To study the literature on this topic To get acquainted with the history of the use of geometric shapes at all times To study the properties of simple geometric shapes To establish the most useful properties of geometric shapes.

Basic geometric shapes Point - is the basis of all other shapes

Why there are many simple geometric shapes in the world around us Circle Round objects are easier to move Coins Manhole cover

Why are there many simple geometric figures in the surrounding world? The Truss Triangle is a rod system in structural mechanics that remains geometrically unchanged after replacing its rigid nodes with hinged ones.

Why are there many simple geometric figures in the world around us? in 1915, one of the most discussed and most famous paintings in Russian art.

What simple geometric figures are most useful in our world? Circle An ancient temple complex in Beijing, one of the best examples of Chinese architecture. The circle is a wheel. The wheel is progress - moving forward The world's first circle-shaped skyscraper has been erected on Al Raha Beach in Abu Dhabi, UAE. Round baking dish

What simple geometric shapes are most useful in our world Triangle Triangle in billiards Roof of the house Triangle in bowling Tepee red yellow blue orange green purple Triangle method in floristry

What simple geometric shapes are most useful in our world Square Triangle in billiards Chessboard Square windows Square house facades Square furniture Patchwork

How geometric figures were used at all times Pottery The first tools of labor The first decorations The tricorne A bunch of logs was used to move loads The rigidity property of the triangle was used in the construction of the pyramids

This is interesting - psychogeometry Circle Triangle Square Rectangle Broken line Look carefully at the geometric shapes, feel your own, about which you can say: "It's me!".

A person is a Circle A circle is a non-linear form, and those who confidently identify themselves with a circle are more likely to be “right hemisphere” thinkers, this is a more imaginative, intuitive, emotionally colored thinking. Therefore, the processing of information by the Circles is carried out not in a sequential format, but rather in a mosaic, with breakthroughs with omissions of individual links. The main features in their thinking are an orientation towards the subjective factors of the problem (values, assessments, feelings, etc.) and the desire to find common ground even in opposing points of view. Circle

Triangle Person Triangle Triangle Triangle is a very confident person who wants to be right about everything! Triangles have a hard time admitting their mistakes! We can say that they see what they want to see, do not like to change their decisions, are often categorical, do not recognize objections. Fortunately, triangles quickly and successfully learn (absorb useful information like a sponge), however, only that which contributes to the achievement of the main goal.

Man - Square Square If you have chosen a square for yourself - a linear figure, then most likely you belong to the “left hemisphere” thinkers, that is, those who process data in a sequential format: a-b-c-d .. The square "computes the result" rather than guessing about it. You are extremely attentive to details, details, love the routine once and for all. Your ideal is a planned, predictable life, and the square does not like changing the usual course of events.

The Rectangle Man The main mental state of the Rectangles is a more or less conscious state of confusion, confusion in problems and uncertainty about oneself at a given moment in time. The most characteristic features are the inconsistency and unpredictability of actions during the transition period. They strive to become better in something, they are looking for new methods of work, lifestyles. Rectangle

Man - Broken Line If you have firmly chosen the Broken Line as the main form, then you are most likely a true "right-brained" thinker. You, like your closest relative Krug, only to an even greater extent, are characterized by figurativeness, intuitiveness. Your thoughts make desperate jumps from "a" to "z", so you have a developed aesthetic sense. broken line

Practical experiences

Conclusions After doing research work, I can draw conclusions about the most useful properties of geometric shapes: A circle is a wheel. The wheel is progress - moving forward. If the wheel stops, then the wheel of history stops, because everything moves in a circle. The triangle is the only geometric figure that has the rigidity property. The square has symmetry and serves as a standard for measuring the areas of all figures.

Thank you for your attention!

four year old child knows and distinguishes such geometric figures as a circle, a square and a triangle. Difficulties arise in distinguishing between a circle and an oval, a square and a rectangle. When comparing objects, the child already takes into account several properties: length, width, height. The above games and tasks will help you teach your baby to distinguish between geometric shapes and compare objects according to different criteria. Older children are offered tasks with three-dimensional figures.

geometric lotto

1 . Take a sheet of paper and divide it into 6 squares or rectangles. Make as many of the same cards. Draw geometric shapes on them. If your child can read, instead of drawing a figure on paper, write the name of this figure. Let the cards be with a picture. The task of the child is to read the name of the figure and put a card with the image of this figure.

2 . Another version of the geometric lotto - you name the cell in which the child should place a specific figure.
For example: "Put a circle in the top left corner, or put a triangle in the bottom right corner." If your geometric shapes are multi-colored, then indicate the color of the shape that you want to see in the cell. This way you reinforce the concepts of right/left, top/bottom and color names. Complete your card with your child. When all the cells are filled, compare your cards.

Item Comparison

The essence of the task is that the child is invited to compare the picture with geometric shapes.
To do this, you need to find (or draw yourself) pictures of objects that will resemble a geometric figure. For example: circle - button, ball, watermelon. Oval - melon, cucumber. Rectangle - door, table, etc.

Find an item

Geometric shapes are drawn on paper. The task of the child is to draw objects similar to the figures depicted on paper or to find objects of a similar shape in the room.

"Magic Pouch"

Figures are put into the bag, and at your request, the child pulls out the object you need by touch. The baby can feel objects both through the fabric and by lowering his hands into the bag. The main condition is not to look into the bag with the figures.

Shape and size

1. Prepare paper geometric shapes of different sizes. Now ask the child to line up all the circles in ascending order (from a small circle to a large one), then all the triangles - in descending order (from big triangle to small). Each row should not contain more than 5 items.

2. Take boxes of different sizes, but the same shape. Invite the child to put toys in the boxes and close them with a suitable lid. First help the baby, show how to close the box.
When he learns to distinguish the sizes of one form, complicate the task: along with the boxes, give the child jars of different sizes with lids. Now the baby needs not only to distinguish between "big / small", but also - "round / square".

Size and color

You can work out with the child the concepts of “size”, “shape” and “color” of an object as follows: take a sheet of drawing paper and with colored tape mark (“circle”) the contours of your geometric shapes (these can be designer parts or home-made models). Now the child, taking one figure at a time, fills in all the fields on the drawing paper, taking into account the shape of the object, as well as its size and color.
To complicate the task, use one-color tape. In this case, the color will not act as a hint.

Exercise machine

Before you start playing, review the table with your child. Please note that the table has rows and columns (columns). List shapes and colors. Make sure your child recognizes shapes by size. Now start exercising:

1. Count!
- How many small circles are shown in the table?
- How many small red circles?
How many big green squares?
How many blue pieces are there? etc.

2. Who lives where?
The child needs to name the location of the indicated figure. For example, you are pointing to a large oval. The child should answer that the large oval is in the first column, in the second row.
You can play the other way around: you name the "address" of the figure (for example, the fifth row, fifth column), and the child finds the figure you have guessed and names it (large blue square).

3. Right/left, top/bottom
On this simulator you can learn (repeat) the directions of the sides. For example, what shape is to the left of the big red rectangle? (big blue circle) What's on top of the big blue circle? (large blue square), etc.

Fold the figure

Invite the child to fold a circle (square, etc.) from pre-prepared parts. First, offer to fold the figure from two parts (two identical semicircles for a circle), then from 3, etc. At first, keep the details for each figure in separate envelopes. Later, details from different geometric shapes can be mixed. To facilitate the task, paint each shape in a separate color (circle - red, square - blue, etc.).

Classification of objects by shape

The child needs to arrange the pictures in envelopes or piles in accordance with the shape of the image, thus creating several groups. First, offer to sort the pictures into two groups: round objects in one envelope, square ones in another. At this stage, it is important that the child distinguishes round objects from objects with corners - quadrangular, so the second group will include both square objects (for example, a wall clock) and rectangular objects (for example, a book). Then add a group with triangular items.

Later, you can complicate the task by adding images that are similar in shape, for example, round and oval, square and rectangular, triangular and trapezoidal. Most complex view tasks - sort all the pictures at once.

figurine house

Show the child images of dwellings (hut, igloo, multi-storey building). Ask what geometric shapes they remind the baby. Now he needs to find a suitable house for geometric shapes (triangle, circle, square).

Draw and Guess

An adult and a child take turns drawing in the air and guessing various geometric shapes. You can draw figures with your finger on the back.

Count geometric shapes

Ask the child to look at the picture. Name the geometric shapes yourself. Then ask him to count, name and indicate with numbers the number of squares, rectangles, triangles, rhombuses, trapezoids, circles and ovals depicted.

figure outline

Cut out geometric shapes from thick cardboard (circle, square, rectangle, triangle, rhombus, trapezoid, oval). Ask your child to trace the outline of the shape. Let the child, circling the figure, consider its sides.

Basic elements in a figure

Offer your child:

• show the sides of a square (rectangle, triangle, trapezoid, circle, oval). Show how to move your finger along the side of the figure;
• count the vertices of a square (rectangle, triangle, trapezoid) or mark the vertices with dots on the image with a colored pencil;
• show the corners of a square (rectangle, triangle, trapezoid). Teach your child to show the angle with two fingers: thumb and forefinger;
• circle the border of the depicted figure with a colored pencil;
• shade the inner area of ​​the depicted figure with a colored pencil;
• find the similarities of geometric shapes (for example, a rectangle, a square and a trapezoid have 4 sides, 4 vertices and 4 corners);
• name similar geometric shapes in one word (square, rectangle, trapezoid, rhombus - quadrangles; triangle, quadrilateral, five-hexagon - polygons).

Volumetric figures

1. Talking about volumetric figures, try to get the child to understand the difference between flat and three-dimensional geometric shapes (square - cube, circle - sphere (ball), etc.). Compare them, try to make them out of cardboard or plasticine.

2. Consider sides voluminous figures. Please note that they can be different even for one figure. For example, a cone has 2 sides: one is a circle at the base, and the other is the whole side surface cone.

3. Ask your child to compare cone And pyramid.
Explain that the base of a pyramid can be a triangle, a quadrilateral, or a polygon. And the side faces of the pyramid will be triangles converging at one vertex. If there is a circle at the base, then a cone will be obtained.

4. Ask your child name or draw objects resembling three-dimensional geometric shapes.

Lesson Objectives:

• Cognitive: create conditions for familiarization with the concepts flat And voluminous geometric shapes, to expand the idea of ​​​​the types of three-dimensional figures, to teach how to determine the type of figure, to compare figures.
• Communicative: create conditions for the formation of the ability to work in pairs, groups; fostering a friendly attitude towards each other; to educate students in mutual assistance, mutual assistance.
• Regulatory: create conditions for the formation of plan learning task, build a sequence of necessary operations, adjust their activities.
• Personal: create conditions for the development of computing skills, logical thinking, interest in mathematics, the formation of cognitive interests, intellectual abilities of students, independence in acquiring new knowledge and practical skills.

Planned results:

personal:

• formation of cognitive interests, intellectual abilities of students; formation of valuable relations to each other;
  independence in acquiring new knowledge and practical skills;
• the formation of skills to perceive, process the information received, highlight the main content.

metasubject:

• mastering the skills of independent acquisition of new knowledge;
• organization learning activities, planning;
• development of theoretical thinking based on the formation of the ability to establish facts.

subject:

• to master the concepts of flat and three-dimensional figures, to learn how to compare figures, to find flat and three-dimensional figures in the surrounding reality, to learn how to work with a sweep.

UUD general scientific:

• search and selection of the necessary information;
• application of information retrieval methods, conscious and arbitrary construction speech utterance in oral form.

UUD personal:

• evaluate their own and others' actions;
• manifestation of trust, attentiveness, goodwill;
• ability to work in pairs;
• express a positive attitude towards the process of cognition.

Equipment: textbook, interactive whiteboard, emoticons, models of figures, sweeps of figures, individual traffic lights, rectangles - feedback tools, Explanatory dictionary.

Lesson type: learning new material.

Methods: verbal, research, visual, practical.

Forms of work: frontal, group, steam room, individual.

1. Organization of the beginning of the lesson.

In the morning the sun rose.
A new day has brought us.
Strong and kind
We meet a new day.
Here are my hands, I open
them towards the sun.
Here are my legs, they are firmly
Stand on the ground and lead
me on the right path.
Here is my soul, I reveal
her towards the people.
Come, new day!
Hello new day!

2. Actualization of knowledge.

Let's create good mood. Smile at me and at each other, sit down!

To reach the goal, you must first of all go.

There is a statement in front of you, read it. What does this saying mean?

(To achieve something, you need to do something)

And indeed, guys, only one who sets himself up for composure and organization of his actions can become a target. And so I hope that we will achieve our goal in the lesson.

Let's start our journey to achieve the goal of today's lesson.

3. Preparatory work.

Look at the screen. What do you see? (Geometric figures)

Name these figures.

What task can you offer your classmates? (separate the figures into groups)

You have cards with these figures on your desks. Do this task in pairs.

On what basis did you separate these figures?

• Flat and three-dimensional figures
• Based on three-dimensional figures

What figures have we already worked with? What did they learn to find from them? What figures do we meet in geometry for the first time?

What is the topic of our lesson? (The teacher adds the words on the board: voluminous, the topic of the lesson appears on the board: Volumetric geometric shapes.)

What should we learn in class?

4. "Discovery" of new knowledge in practical research work.

(The teacher shows a cube and a square.)

How are they similar?

Can we say that they are one and the same?

What is the difference between a cube and a square?

Let's do an experiment. (Students receive individual figures - a cube and a square.)

Let's try to attach a square to the flat surface of the port. What do we see? Did he lie all (entirely) on the surface of the desk? Close?

! What is the name of a figure that can be placed entirely on one flat surface? (Flat figure.)

Is it possible to press the cube completely (all) to the desk? Let's check.

Can a cube be called a flat figure? Why? Is there space between the hand and the desk?

! So what can we say about the cube? (It occupies a certain space, is a three-dimensional figure.)

CONCLUSIONS: What is the difference between flat and volumetric figures? (The teacher writes the conclusions on the blackboard.)

• Can be placed entirely on one flat surface.

VOLUMETRIC

• occupy a certain space
• rise above a flat surface.

Volume figures: pyramid, cube, cylinder, cone, sphere, parallelepiped.

4. Discovery of new knowledge.

1. Name the figures shown in the figure.

What shape are the bases of these figures?

What other shapes can be seen on the surface of a cube and a prism?

2. Figures and lines on the surface of three-dimensional figures have their own names.

Suggest your names.

The sides that form a flat figure are called faces. And the side lines are ribs. The corners of polygons are vertices. These are elements of three-dimensional figures.

Guys, what do you think, what are the names of such voluminous figures that have many faces? Polyhedra.

Working with notebooks: reading new material

Correlation of real objects and three-dimensional bodies.

Now select for each object the three-dimensional figure that it looks like.

The box is a parallelepiped.

• An apple is a ball.
• A pyramid is a pyramid.
• Bank - cylinder.
• The flower pot is a cone.
• The cap is a cone.
• Vase - cylinder.
• The ball is a ball.

5. Physical minutes.

1. Imagine a big ball, stroke it from all sides. It's big and smooth.

(Pupils wrap their hands around and stroke an imaginary ball.)

Now imagine a cone, touch its top. The cone grows upward, now it is already above you. Jump to its top.

Imagine that you are inside the cylinder, pat on its upper base, stomp on the bottom, and now with your hands on the side surface.

The cylinder became a small gift box. Imagine that you are the surprise that is in this box. I press the button and... a surprise pops out of the box!

6. Group work:

(Each group receives one of the figures: a cube, a pyramid, a parallelepiped. The children study the resulting figure, write down the conclusions in a card prepared by the teacher.)
Group 1.(To study the parallelepiped)

Group 2(To study the pyramid)

Group 3.(To study the cube)

7. Crossword solution

8. The result of the lesson. Reflection of activity.

Solving a crossword in a presentation

What new did you discover today?

All geometric shapes can be divided into three-dimensional and flat.

And I learned the names of three-dimensional figures

Little kids are ready to learn anywhere and anytime. Their young brain is able to capture, analyze and remember as much information as it is difficult even for an adult. What parents should teach their kids has generally accepted age limits.

Children should learn the basic geometric shapes and their names at the age of 3 to 5 years.

Since all children are multi-educational, these boundaries are only conditionally accepted in our country.

Geometry is the science of shapes, sizes, and arrangement of figures in space. It may seem that this is difficult for babies. However, the subjects of this science are all around us. That is why having basic knowledge in this area is important for both children and adults.

To captivate children in the study of geometry, you can resort to funny pictures. In addition, it would be nice to have aids that the child can touch, feel, circle, color, recognize with his eyes closed. The main principle of any activity with children is to keep their attention and develop a craving for the subject using game techniques and a relaxed, fun environment.

The combination of several means of perception will do the job very quickly. Use our mini-manual to teach your child to distinguish geometric shapes, to know their names.

The circle is the very first of all shapes. In nature around us, much is round: our planet, the sun, the moon, the core of a flower, many fruits and vegetables, the pupils of the eyes. A volumetric circle is a ball (ball, ball)

It is better to start studying the shape of a circle with a child by looking at drawings, and then reinforce the theory with practice by letting the child hold something round in his hands.

A square is a figure in which all sides have the same height and width. Square objects - cubes, boxes, a house, a window, a pillow, a stool, etc.

It is very simple to build all sorts of houses from square cubes. Drawing a square is easier to do on a piece of paper in a cage.

A rectangle is a relative of a square, which differs in that it has the same opposite sides. Just like a square, a rectangle is all equal to 90 degrees.

You can find many items that have the shape of a rectangle: cabinets, appliances, doors, furniture.

In nature, mountains and some trees have the shape of a triangle. From the immediate environment of the kids, one can cite as an example the triangular roof of the house, various road signs.

Some ancient structures, such as temples and pyramids, were built in the shape of a triangle.

An oval is a circle that is elongated on both sides. For example, an oval shape is possessed by: an egg, nuts, many vegetables and fruits, a human face, galaxies, etc.

An oval in volume is called an ellipse. Even the Earth is flattened from the poles - ellipsoidal.

Rhombus

Rhombus - the same square, only elongated, that is, it has two obtuse angles and a pair of sharp ones.

You can study a rhombus with the help of visual aids - a drawn picture or a three-dimensional object.

Memorization techniques

Geometric shapes are easy to remember by name. Learning them for children can be turned into a game by applying the following ideas:

• Buy a children's picture book that contains fun and colorful drawings of figures and their analogies from the outside world.

• Cut out more different figures from multi-colored cardboard, laminate them with adhesive tape and use them as a constructor - you can lay out a lot of interesting combinations by combining different figures.

• Buy a ruler with holes in the shape of a circle, square, triangle and others - for children who are already friends with pencils, drawing with such a ruler is an interesting activity.

You can come up with many opportunities to teach kids to know the names of geometric shapes. All methods are good: drawings, toys, observation of surrounding objects. Start small, gradually complicating the information and tasks. You will not feel how time flies, and the baby will surely please you with success in the near future.

Large selection of sweeps of simple geometric shapes.

Children's first exposure to paper modeling always starts with simple geometric shapes such as the cube and pyramid. Not many succeed in gluing a cube the first time, sometimes it takes several days to make a truly even and flawless cube. More complex cylinder and cone shapes require several times more effort than a simple cube. If you don’t know how to carefully glue geometric shapes, then it’s too early for you to take on complex models. Take care of yourself and teach your children to crate these “elements” of modeling from ready-made scans.

To begin with, I, of course, suggest learning how to glue an ordinary cube. Reamers are made for two cubes, large and small. A more complex figure is a small cube because it is more difficult to glue it than a large one.

So, let's begin! Download the development of all the figures on five sheets and print on thick paper. Before you print and glue geometric shapes, be sure to read the article on how to choose paper and how to cut, bend and glue paper in general.

For better printing, I advise you to use the AutoCAD program, and I give you a sweep for this program, and also read how to print from AutoCAD. Cut out the development of the cubes from the first sheet, along the fold lines, be sure to draw a compass needle under the iron ruler so that the paper folds well. Now you can start gluing the cubes.

To save paper and for every firefighter, I made several scans of a small cube, you never know if you want to glue more than one cube or something will not work the first time. Another simple figure is a pyramid, you will find its sweeps on the second sheet. Similar pyramids cost the ancient Egyptians, though not made of paper and not so small :)

And this is also a pyramid, only unlike the previous one, it has not four, but three faces.

Development of a trihedral pyramid on the first sheet for printing.

And another funny pyramid of five faces, its development on the 4th sheet in the form of an asterisk in two copies.

A more complex figure is the pentahedron, although the pentahedron is more difficult to draw than to glue.

Reamers of the pentahedron on the second sheet.

So we got to the complex figures. Now you have to tighten up, gluing such figures is not easy! To begin with, a regular cylinder, its development on the second sheet.

And this is a more complex figure compared to a cylinder, because at its base is not a circle, but an oval.

The development of this figure is on the second sheet, two spare parts were made for the oval base.

To accurately assemble the cylinder, its parts must be glued end-to-end. On the one hand, the bottom can be glued without problems, just put a pre-glued tube on the table, put a circle on the bottom and fill it with glue from the inside. Make sure that the diameter of the pipe and the round bottom fit snugly together, without gaps, otherwise the glue will leak and everything will stick to the table. The second circle will be more difficult to glue, so glue auxiliary rectangles inside at a paper thickness distance from the edge of the pipe. These rectangles will not let the base fall inward, now you can glue the circle on top without any problems.

A cylinder with an oval base can be glued in the same way as a regular cylinder, but it has a lower height, so it’s easier to insert a paper accordion inside, and put the second base on top and glue it along the edge.

Now a very complex figure - a cone. Its details are on the third sheet, a spare circle for the bottom on the 4th sheet. The whole difficulty of gluing the cone is in its sharp top, and then it will be very difficult to glue the bottom.

A complex and at the same time simple figure is a ball. The ball consists of 12 pentahedrons, the development of the ball is on the 4th sheet. First, the two halves of the ball are glued, and then both are glued together.

A rather interesting figure is a rhombus, its details are on the third sheet.

And now two very similar, but completely different figures, their difference is only in the base.

When you glue these two figures, you will not immediately understand what it is at all, they turned out to be some kind of completely unreceptive.

Another interesting figurine is the torus, only we have it very simplified, its details are on the 5th sheet.

And finally, the last figure from equilateral triangles, I don’t even know what to call it, but the figure looks like a star. Development of this figure on the fifth sheet.

That's all for today! I wish you success in this difficult work!