The concept of the volumetric form of objects. Shape as a mathematical concept

1st grade Goryachev ___________________

Lesson #2

Topic: "FORM OF OBJECTS"

Goals: teach to determine the shape of objects, group objects by shape, identify patterns in grouping objects by shape.

Equipment: bring any items that are easily described by signs, for example: a sugar cube, a chocolate bar, a wooden or plastic ruler, a plain student notebook, etc.; any items for comparison in pairs, for example: a coin and a button, the same size, two colored pencils, 2 balls, etc.; task for the game "Rebus" .

During the classes

    Checking homework 8 in a notebook.

The students list the items “collected” in the first bag and highlight their common feature. Similarly, the items collected in the second bag are listed.

The teacher finds out which objects were difficult to color in (most likely it is a car) and how the students coped with them (the car should be either gray or green). (Grey items, green items.)

II. Repetition.

III. Learning new material.

Signs of objects. The form

The teacher offers to consider the shape of objects. The teacher explains that the objects around us have a complex shape, so we will study only simple shapes, that is, the shapes of geometric shapes.

Students should name and draw on the board the main geometric shapes: circle, oval, triangle, rectangle, square, rhombus etc.

    The game "Name the shape!" (with a ball).

The teacher names the object by throwing the ball to the student. The student returns the ball to the teacher with the answer, what shape is the named object.

Examples: a wheel is round, a door is rectangular, the roof of a house is triangular, a book is rectangular, the sun is round, a lemon is oval, etc.

    Task 9 in the notebook.

Students have to dream up, come up with what each figure looks like, and finish it in such a way that a picture is obtained. It is necessary to give the opportunity to present the result of their work to as many students as possible. Some of them can be drawn on the board.

    Task 10 in the notebook. Key:

a) round wheel - round watch,

b) rectangular the envelope - rectangular notebook,

in) oval painting - oval mirror.

Students must connect objects of the same shape with lines of different colors. The called student pronounces the name of each object and its shape, after which pairs are formed.

    The game "What is this shape?".

The teacher names any form and invites the children to name as many objects of this form as possible. Examples:

    A circle - plate, watch, compass, wheel, etc.

    Square- cube, box, sandbox, etc.

    Oval- mirror, egg, lemon, pear, etc.

    Rectangle- an envelope, a picture, a pencil case, a notebook, a book, etc.
    The winner is the student who last named the subject of this

    Task 11 in the notebook.

Students should color the shapes that make up the drawing with a certain color. When completing this task, the called student comments: “The sun is round, we color it in yellow. Clouds are oval, color blue. You can summarize the performance of this task with the questions: “What parts of the Picture are square in shape? (Window.) Rectangular? (Door, pipe, house.)".

    Task 12 * in a notebook.

Students have to compare three cakes, fill in the missing figures and color them so that the cakes are the same.

    Task 13 * in a notebook. Key:

a) triangles

c) squares.

Students must identify a common feature of the figures in each group. To do this, you need to enumerate these figures. The figures in the first group can be said aloud: “The first group shows a blue triangle, a white triangle, a gray triangle, a black triangle. All triangles in the first group. Most likely, the second and third groups will not cause difficulties, it is enough to say the conclusion.

    Task 14 in a notebook.

Students must cross out the extra item in each group.

a) Pupils need to list the objects in the group, naming their shape (wheel - round, watch - round, coin - round, compass - round, button - round, book - rectangular). Almost all items in the group are round. The book makes it difficult to name the general form of all objects, it must be crossed out.

b*) The students should pay attention to the shape and color of each shape.* One solution is to cross out the red box, since all the other shapes are blue. The second option is an extra circle, the rest of the figures with corners. If the second solution did not sound, the teacher should bring the children to him, asking leading questions (“Maybe it’s superfluous ...”).

    Task 15 in a notebook.

Key: red round ball.

The students have to draw a ball for the Eeyore donkey and color it in the appropriate color.

To do this, you need to determine the color of the ball and its shape. All the balls of the heroes are red, which means that the Eeyore ball should be red. The shape of the balls alternates, so you need to say: “Winnie has a round ball, the Owl has an oval ball, the Rabbit has a round ball, Piglet has an oval ball, Eeyore ... round.

IV. Lesson results.

Name the shape of objects.

    Rebus game.

The teacher shows the children a sequence of figures with letters and asks them to read the names of the children. One name is written in triangles, the second in circles, and the third in squares.

You can prepare figures on the board for writing names.

    Riddles, joke tasks (see Annex 1, pp. 139-140).

Homework.

    Task 16 in the notebook.

Students should color all the triangles in brown and the rest of the shapes in blue. The result is a picture.

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The original content of the concept of form are real items surrounding reality.

The form- this is the main visual and tactile property of an object which helps to distinguish one object from another.

Mankind created a system of standards for designating the shapes of specific objects. it system of geometric shapes.

The grouping of geometric shapes can be represented as follows:

flat and bulky,

Having corners and not having them, that is, rounded,

Differing in appearance.

In this way, geometric figures act samples, standards of the form of real objects or their parts.

With geometric shapes held analysis of the surrounding world, satisfies the need to understand the variety of forms, in "what looks like what". As a result, one object is likened to another in shape (it looks like a cucumber, like a window), etc.

Classification of geometric shapes under construction both emotionally and logically. The child's perception of the surrounding objects at first, as shown by special studies, does not mean the selection of a form. First, the object itself appears, and only then - its form.

In the system of geometric figures concentrated generalized experience of human sensory activity.

The form is perceived by the visual-tactile-motor way. Acquaintance of children with the form of objects has always been the focus of attention of psychologists, teachers and methodologists of the past and present.

FEATURES AND METHODS OF MASTERING THE FORM OF OBJECTS AND GEOMETRIC FIGURES BY CHILDREN OF PRESCHOOL AGE

In the knowledge of the surrounding world, orientation in the variety of shapes of objects (objects) and geometric figures is especially significant.

Form has a special place among the variety of properties learned in preschool age..

Perceiving form, child distinguishes an object from others, recognizes and calls him, groups(sorts) and relates it to other things.

Parallel or after child learn geometric shapes, highlighting before their form, and then the structure.

In the knowledge of geometric shapes preschool children it is customary to distinguish three stages:

At 3-4 years old, geometric figures are perceived as whole and differ by children mainly in shape;

At the age of 4-5, geometric figures are perceived analytically, children establish their properties and structure empirically (experimentally);

At the age of 5-6, children perceive geometric figures in a certain relationship in terms of structure, properties, and realize their commonality.

As a result of psychological research, it became known that the process of cognition by children of form as a property is long and complex.

FOR CHILDREN 2-3 YEARS main identification figure signsurface, plane. They are take the figure in hand, manipulate; run your hand across the plane, as if trying to discover the subject basis.

In this age children allocate among the others and call separate geometric shapes using the words " circle», « cube», « ball».

Or compare the shape of a real object with geometric and use the expressions “This is like a cube”, “This is like a handkerchief”.

Usually, they " objectify» geometric figures calling them " roof», « handkerchief», « cucumber" etc.

Mastering the shape of objects and geometric shapes passes at this age in active work. Children put one cube on another, building a tower, put objects in cars; roll figures, shift; make up the rows.

CHILDREN 3—4 YEARS start distinguish geometric shapes from objects, highlighting their shape. Naming the figures, they say: "The triangle is like a roof", "The handkerchief is like a square."

Children examine the figures tactile-motor way trying hold your hand along the contour. At the same time, they willingly pronounce the words and expressions they like. Begin to perceive structural elements geometric shapes: corners, sides. When perceiving figures abstracted from color, size, highlighting their shape.

However child's visual perception remains fluent, his the gaze does not focus on the contour or plane. Because of this, children often confuse similar shapes: an oval and a circle, a rectangle and a square.

CHILDREN 4-5 YEARS successfully examine geometric shapes, swiping index finger along the contour. However, they usually called structural components: vertices, sides, corners. traced with a wave of the hand lines forming angles; detect line intersection points. Survey becomes accurate and effective.

Typically, at this age, children shapes are formedreference ideas about them. They begin to successfully identify the similarities and differences in the shapes of objects with geometric figures; use the standards they have developed in order to determine any unknown form; display forms in productive activities.

At 5-6 YEARS children in general visualize geometric shapes. Tactile-motor examination becomes unnecessary. In the process of visual perception they fix the contour and on this basis, include a figure in a specific group, allocate types of figures, classify, sort and organize objects according to form.

At senior preschool age prevails visual recognition of shapes and their distinctive signs, verbal description of the shape of objects and geometric shapes.

So, perception of form by a preschool child carried out based simultaneous examination of it in a visual and tactile-motor way, accompanied by naming the main features of a particular form.

For example, round - no corners; quadrilateral - it has sides, angles and vertices.

Geometric figures become standards for determining the shape of surrounding objects and their parts.

Form is a sign of an object, accessible to visual and muscular-tactile perception.

In the form of an object, more or less typical features are distinguished: roundness or elongation, stability or dissection, symmetry of parts or asymmetry.

The specific tasks of mental education when getting acquainted with the form are:

Formation of ideas and knowledge about form as a sign of an object and beauty;

Development of the ability to see, distinguish, compare, group objects according to their shape;

· Development of the ability to see the form in combination with other signs in life, in objects of art;

Development of vocabulary and coherent speech and teaching children to use the exact names of forms and their features, figurative, expressive words, generalized words-concepts;

Teaching children how to apply knowledge about the form in a variety of activities;

· Education of cognitive interests.

The ability of a child to perceive, to see the form in an object is not innate, but is formed in the process of education and training.

Familiarization of children with the form as a sign of an object and a generalizing concept has a certain sequence, repetition and complication from one age group to another.

Junior group.

The teacher teaches children to see and distinguish objects by their shape, introduces the basic geometric shapes - a ball and a cube - and names them himself. The teacher organizes visual and tactile-muscular perception, cognitive actions with objects, teaches how to examine objects, test them in games, in classes with building materials, with toys.

In classes with an individual child or with a small subgroup, the teacher shows the ball and says: “This is a ball” - and performs actions with it, emphasizing its shape.

Cognitive practical actions should be performed repeatedly. The period of practical testing should not be shortened. In repeated classes, in games, the teacher again calls the figure and its features.

In subsequent lessons, in games, the teacher asks the children to show, bring. Put the balls in the basket. According to the action performed, he checks whether the children have learned the name and whether they correlate the word with the object. In the future, he exercises the children in the name of the form of the object.

By organizing games with balls and other toys, the teacher exercises the children in distinguishing them by shape and at the same time includes a new one - color - into the familiar and teaches them to distinguish balls by color. In the next lessons, the teacher offers balls of different sizes - large and small, then calls the words "big - small" and uses the word to reinforce the difference.

A lot of game activities are organized by the educator with objects of a cubic shape - he encourages to inspect the cubes, rearrange, move. Visually-motor perceiving the cube, the child feels the edges and planes and practically learns the features of this figure.

The definition of shape and size can already be included in one lesson, since the previous mastery of the shape of the ball contributed to the development of children's attention, the ability to look and see. Both in subsequent lessons and in games, the teacher exercises the ability of children to choose large and small cubes from building material.

Then the teacher organizes a comparison of the ball and the cube as two different figures.

In the future, he reinforces the idea of ​​​​a ball and a cube in various classes, in games ..

Thus, educator ml. gr. in accordance with the program, teaches children to distinguish between a ball and a cube in shape and call them the exact word, teaches them to apply the acquired ideas in various activities.

Middle group.

The teacher consolidates ideas about the ball and the cube and improves the methods of sensorimotor examination of objects based on visual and tactile-muscular perception. Introduces children to new shapes: rectangle, square, triangle, cylinder - and teaches to distinguish between straight, naked, square, triangular objects. With the expansion and complication of the content, the requirements for the mental activity of children expand and become more complicated, and new qualities of cognitive activity are formed. The educator teaches to see the same form in objects of different content.

And in the middle group, the educator first introduces objects in which various forms are expressed, and especially those with which children need to be introduced in accordance with the requirements of the program.

The teacher introduces children to new figures in the usual and already familiar way for children.

The new quality of form as a common feature of many surrounding objects should be revealed on the basis of content familiar to the child.

Mastering ideas about the basic forms of objects, the ability to group objects according to their forms does not occur only in the classroom, in didactic games, it requires “practice” in life.


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You already know that the main task of drawing is to learn to see objects in three-dimensional forms, so that in practical work you can convey volume by certain expressive means - a line, a stroke, a tone. If you have correctly and expressively drawn an object, this means that its internal basis - the structure - is correctly built in the pencil image and the material properties (surface texture) are expressively conveyed. All this, it would seem, looks simple, but you have to work long and hard to learn how to perform such drawings. One should never rely only on certain abilities for the fine arts. A lot of painstaking work is needed, because knowledge, skills and abilities do not come by themselves, but are the result of huge and strenuous efforts.

There are no formless bodies in nature. If one could imagine such a thing, then apart from some kind of abstract (abstract) emptiness, nothing else turned out to be in consciousness. Therefore, one should believe in the form as an organization of certain parts, built expediently and in strict accordance. An object in the usual sense of the word is a product created by a person that is necessary for people and performs a specific function. When studying a drawing, you must be guided by the form in your work. The well-known artist-teacher Dmitry Nikolaevich Kardovsky, in his book “Drawing Handbook” published in Moscow in 1938, wrote: “What is a form? This is a mass that has one or another character, like geometric bodies: a cube, a ball, a cylinder, etc. The living form of living nature, of course, is not a regular geometric form, but in the scheme it also approaches these geometric forms and thus repeats the same laws of the arrangement of light along perspectively receding planes that exist for geometric bodies.

The student's task is precisely to combine and coordinate the understanding of form with the techniques for depicting (constructing) on ​​a plane with light ... surfaces that limit the form in space. When drawing a ball, they know what techniques should be used to depict the transitions of its surfaces in shadow and in the light, just as techniques are known when depicting a cube, pyramid, cylinder, or some more complex figure, etc. ... What characterizes, for example, the shape of a human body? This is a cylindrical shape. If the torso were a regular cylinder, then its image would be very simple, but there are bulges, depressions and other deviations in it that violate the simplicity of the cylinder. At the same time, these bulges and recesses are located in a large cylinder shape either on the side receiving direct light rays, or on the side not receiving them, or in transitional places. When drawing, these deviations must be maintained in tone, respectively: 1) light, 2) shadow and 3) penumbra. A sense of form, the ability to see and convey it must be developed by the student so that it, as they say, “transfers to the ends of the fingers” from consciousness, i.e. when depicting a form on a plane, the painter should feel it in the same way as a sculptor who sculpts a form from clay or cuts it out of stone ”(Kardovsky D.N. Drawing Handbook. M., 1938. P. 9).


People use the word "form" very often. Everyone correctly understands the meaning attached to this concept. Yes, indeed, the term "form" (from lat. forma) is translated as a concept that allows a person to comprehend the external outline, appearance, contours of an object. In any image, they always show, first of all, the shape of the object being drawn, i.e. true outline of it. When the artists say that the three-dimensional form is well conveyed in this drawing, they emphasize the veracity of the image. In fact, the concept of "volumetric form" essentially points to two words that are close in meaning, because the volume of an object also contains mass, configuration, inherent in the form. The volume itself should be regarded primarily as one of the quantitative characteristics of geometric bodies - capacity, which is expressed in the number of cubic units. Figures of fine arts and architecture understand this word as the appearance of a space bounded by planes.

Thus, under the volumetric form of objects, one should consider the regularities of the structure, i.e. features of their design.

To depict a three-dimensional form, you need: the ability of the painter to see and understand the design features (structure) of objects and the transfer of three-dimensionality - length (or width), height and depth - the shape of these same objects on the two-dimensional plane of a sheet of paper.

Consequently, the representation of a form in any drawing from nature should be based on its construction, and not on drawing the external appearance of the object. Such a construction presupposes that the draftsman has a clear constructive approach to surrounding objects. Since you have a two-dimensional plane in front of you, and you need to draw three-dimensional volumes, imagine a sheet of paper as a certain (conditional) space and try, based on your knowledge of perspective drawing methods, to place the depicted shape in it. Remember what examples from the world of geometric bodies can be used to solve the problem of placing a form in sheet space using their combinations, visible in nature.

tone pattern

Drawing any object from life, you simultaneously solve several problems, one of which is the transfer of light and shade in the image.

To see the object being drawn, it must be lit either naturally (daylight) or artificially (electric light). The physical phenomenon of the distribution of light, due to which our vision distinguishes the surrounding reality, is called chiaroscuro in visual practice.

The perception of various forms becomes possible because reflected light rays enter the eye. Such emitted light allows you to visually perceive any object.

Illuminated objects located in space are distinguished by us as three-dimensional. The volumetric shape of an object, in accordance with its constructive structure, is determined by the play of light and shadow. The peculiarity here is that the shape of the object is made up of variously located surfaces located at different angles to the rays of light, due to which the illumination of this object turns out to be uneven: the light hits the areas that are perpendicular to the rays completely, and the others are distributed Weaker depending on from their position at a certain angle - as if “sliding”, but does not fall on others at all.

For the draftsman, the degree of illumination of the surface of the object is also important, which depends on the strength of the source and on the distance to it. The perception of the illumination of the drawn object is also affected by the distance between it and the person drawing. This is due to the light-air environment, which forms a “haze” (from the smallest particles of dust, droplets of moisture and other substances in suspension), which dissolves the sharp outlines of the boundaries of light and shadow, darkens the illuminated areas and brightens deep shadows.

So, the emission of light will give a luminous flux that propagates in one direction, reaches the object and reveals the lightness of its surface. Depending on the brightness of the light rays, the lightness of the object becomes contrasting. The word "lightness" should be understood as the reflective ability of the surface of an object. You know; that everything that we see and distinguish is connected with the physical nature of light, which, due to the reflectivity of material bodies, is capable of giving certain signals to our eye, which reacts to them with a remarkable property - color perception. It goes without saying that lightness is determined primarily by the feature of the surface of an object in the reflection of light. White, yellow, blue colors reflect more light than black, blue and brown.

Therefore, it is necessary to talk in more detail about chiaroscuro. Best of all, perhaps, a detailed description of all gradations of chiaroscuro is possible using the example of a spherical surface.

The shape of the ball is remarkable in that it is uniform on all sides, not distorted due to the peculiarities of perspective changes in the subject, and gives a complete understanding of the laws of chiaroscuro. Being in space, the ball in any position is equally illuminated by one light source and shaded from the opposite side. This means that the rays of light fall on this geometric body, illuminating exactly half of its spherical surface in different ways. Why is it different? you might ask. After all, if half is illuminated, then the illumination is the same everywhere here. That's the thing, it's not the same. Only an inept draftsman can imagine an illuminated surface of the same tone, and even if he sees that this is not the case, he will nevertheless retain his conviction. Is it because in the drawings of the ball for people unfamiliar with the concept of chiaroscuro, half of the image is left untouched with a pencil, and the second is shaded evenly.

Let's look at the patterns of light distribution on the surface of the ball. Let the gypsum model of the ball be on a light gray plane at a distance of one of its magnitude from a white matte wall and illuminated by artificial light pouring from the left side from above at an angle of 45°. It will not be difficult to think correctly that the model is illuminated at this angle and that the brightest light on the surface of the geometric body will concentrate on the area that is perpendicular to the direction of the rays from the source. As you can see, we are talking about a direct hit of light rays on the surface and, therefore, about the right angle of the surface and the beam that fell on it. Part of the light rays hit the surface of the ball due to its structure at ever sharper angles, and the sharper the angle, the less light hits the sphere. It turns out that the curved surface should gradually fade into shadow with decreasing light.

Finally, in the distribution of rays over the sphere, there comes a moment when the curved surface goes beyond the reach of light and plunges into shadow.

The most brightly illuminated spot on the surface of the ball is called a glare, which is very clearly visible on any shiny surface, such as glass. A light penumbra is visible around the glare, proving the rules for the distribution of light over a spherical surface. Artists call it a semitone. The semitone of the first stripe around the glare passes imperceptibly along its outer edge into the next one, which also imperceptibly merges with the now third one, and so on. All these transitions imperceptible to the eye merge with each other due to the spherical surface of the body, until the last of them just as smoothly leaves its edge into the shadow. Each new semitone is slightly darker than the previous one.

A shadow is a part of an object that got its name due to the absence of light, being outside its distribution. But everything that is in the shade also obeys its own laws, being exposed to the environment. You remember that the condition was set according to which the ball must be separated from the white wall at a distance of one of its magnitude. The word "white" is used in relation to the wall, and this is no accident. You begin to guess that the wall is illuminated by the same source, and therefore, by reflecting the light, it must now make its own amendment to the light-and-shadow relations within the spatial environment. The light reflected from the wall at an angle of 45 °, but now from the right side, hits the shadow, and although it is much weaker than the direct one, nevertheless, its effect significantly affects the smooth highlighting of the shadow. On the surface of the ball, which is in the shade, due to the light reflected from the wall, a phenomenon called a reflex is formed. In that part of the ball that is connected with the surface of the table, a reflection from this surface is visible.

The shadow on the ball is called its own shadow. On the table from the ball in strict accordance with the direction of the light flux from the source lay another shadow, which is called a falling shadow.

The regularities of the distribution of light on the surface and around the visible object should be well known to every painter.

A person perceives the surrounding reality with all its phenomena, forms and volumes visually. In visual perception, the main role is played by his ability to see the world in color. If our primitive ancestor did not have this innate ability, who knows, humanity would exist as such. Distinguishing shades of color helped people of those distant centuries literally survive in the struggle against the harsh and merciless forces of nature. Could they survive if the world around them was absolutely colorless, what is called gray or black and white?

But why then, - you can rightfully ask, - black and white literate drawings are so truthful and attractive? We will wait a little while answering this question, but here we will come close to the concept with which we will have to associate the execution of images, taking into account the requirements of truthfulness, tone.

Before defining this concept, let us turn to the surrounding reality and name some examples related to visual activity.

The remarkable Russian landscape painters Alexei Kondratievich Savrasov, Ivan Ivanovich Shishkin and Fyodor Alexandrovich Vasiliev performed many completed pencil drawings of nature in their work. Each drawing not only impresses with its excellent craftsmanship, but also has a number of other advantages, which include correctly taken light and shade ratios. Indeed, how can one achieve differences in the tone of the crown of a tree and grass, foreground and background, shrubs and weeds? Masters achieved such a difference with brilliance, and a black-and-white pencil in their hands gave such tonal effects that it is just right to compare with picturesque ones.

With a simple graphite pencil, you can convey the brilliance of water and glass, velvet and satin fabric, tree bark and the most delicate form of a rose petal. And the point here is in the tone, and only in it.

The word "tone" (from the Greek tonos - tension) means the general chiaroscuro structure of the image (in painting, this concept corresponds to the color structure of the work).

So, the tone is called the chiaroscuro system of the image. Consequently, the artist who performs a long-term creative drawing of a landscape or everyday scene is faced with the task of conveying in his work the tonal relationships between all elements of the image, so that the drawing impresses the viewer not only with deep life content, but also with the expressiveness of form.

You already know that the whitest paper is much darker than the true highlight on a glossy surface, and the softest drawing material, not to mention the graphite pencil, which gives the blackest spot on paper, is still many times lighter than natural black space. Therefore, one must always remember that truthfulness in a light-tone (tone) pattern can be achieved only when the light-and-shadow ratios are proportional to nature.

For a preliminary acquaintance with the solution of the problems of tone drawing, let us turn to the analysis of a still life, composed in our imagination of three objects. Let it be a glass jar with cherry jam, a light yellow apple and a white tablecloth. All these objects pop up in your memory both at once and one by one. A shiny jar filled with dark jam with an abundance of berries looks wet black, and the apple is darker than the tablecloth, despite its light hue.

The still life is illuminated by daylight, and all its contrasting features are visible as well as possible. All reflexes are clearly visible on the jar, and the apple in front of the vessel with jam contrasts sharply with a part of the dark silhouette even in the shadow. The snow-white tablecloth beautifully emphasizes the voluminous forms of the fruit and the jar. Of course, such a still life rightfully claims to be a picturesque solution, since its color merits are obvious.

Is it possible to draw this still life, preserving in the image the first impression of this freshness and being able to subordinate the sharp contrasts between all objects to the general tone state of nature. Of course, you can draw such a still life if you have the necessary knowledge and skills of visual activity based on a holistic vision of nature.

In the process of graphic representation, it is completely pointless to try to convey the absolute ratios of the lightness of nature. You already know why this is not possible. It is only necessary to adhere to proportional ratios of brightness.

All the various tonal relationships can be conveyed by modest means of drawing.

Where to start? Since the establishment of the so-called tonal scale - the relationship between just white paper and the thickest layer of graphite substance deposited on its surface. Between these two extremes are in the appropriate relationship from light to dark all other gradations of tone.

So, in the presented still life, all the illuminated and shadowy places of objects are distinguished by a wide variety of different tonalities, which are revealed with a simple graphite pencil. Therefore, when working on any educational task, be sure to set the tonal scale. It can be depicted as a strip of several (according to the number of main spots of light and shadow observed in nature) rectangles shaded to convey the entire gamut of shades in the correct subordination. This will help a lot in your work, give you a great opportunity to “feel” the gradations and give you confidence.

It is very important to practice in developing the ability to subtly distinguish the gradations of lightness in natural productions. After a while, you will begin to catch even small tonal differences in nature.

But back to the imaginary still life. You set the tonal scale and it turned out that nine main spots of light and shadow are visible in nature. These are highlights on a glass jar and an apple, common spots of the tablecloth and background, as well as apples, two shadow spots of shadows from the jar and an apple, a common spot of the jar with its contents in the light and a common spot in the vessel's own shadow.

When modeling an image in tone, you would need to observe a proportional relationship between the luminosity of some spots in nature and their corresponding places in the picture. At the same time, in no case should you be carried away by the study of any particular part of the image, but only work with relationships all the time, constantly comparing the drawing with nature. The study of a separate place in a drawing without connection with others is fraught with complications associated with a violation of the integrity of the image. By doing such a study, you begin to compare a separate piece with the same in nature and, naturally, move away from a conscious decrease in the brightness or density of the shadow in the drawing.

All details in nature should never be conveyed in a drawing. This is impossible. In nature, all the details are connected with the general, obey it, but in the drawing it is hardly possible to link all this with the general. Thus, a tone pattern requires a developed sense of form, construction, skillful study of form with chiaroscuro and final generalization so that the image looks collected and solid, and, most importantly, proportions in tone proportional to nature must be conveyed in it.

cube drawing

One of the outstanding artists of France, Ingres, once said well about drawing: “Drawing does not mean just making contours; A drawing is not just lines. Drawing is also expressiveness, inner form, plan, modeling” (Ingres on Art. Collection. M., 1962, p. 56).

When drawing from life plaster models of geometric bodies, you need to depict each body, modeling it by transferring light and shade ratios. You learned about the tone pattern in the previous paragraph.

Essentially, this is your first rather lengthy drawing, in which you will have to do difficult work related to the technique of pencil drawing. You are faced with the choice of technique - to draw in tone with shading or shading. Hatching is recommended, as it largely disciplines, teaches you to treat the drawing carefully and with concentration. The peculiarity of this technique is that the strokes must be placed according to the shape of the model, and if this requirement is not followed, very soon you can see that the strokes that covered the surface of the paper, applied at random, i.e. thoughtlessly, destroy the drawing, do not reveal the three-dimensional form.

The cube model should be illuminated with artificial light, the source of which should be placed from the top left. In this case, both the entire volume of the body and the chiaroscuro gradations are clearly visible from the point of view you have chosen. The cube is placed at an angle to the painter, slightly below eye level, so that the upper face is visible. The background should be light, and the model should be placed on a gray drapery, spread without folds on a stand for nature.

To get started, you need to remember the previous exercises on drawing from nature the wireframes of geometric bodies. Similar tasks you have to solve now. True, now the cube appears before you in the form in which it is truly perceived as voluminous. The frame made it possible to see through the cube, with all the faces and edges. Now some of them are not visible, but the eye must be able to "see" them, so that when building, taking into account perspective abbreviations, it will certainly be shown. Only then do they speak of the constructive structure of the form of a geometric body.

However, it is not possible to draw on paper without first placing the image. Only a few virtuosos of academic drawing could begin the image of this or that statue from any one point and, without lifting the pencil from the paper, draw a very precise contour of the antique sculpture on the sheet. You need to act much more simply and take the pencil off the paper many times in order to look at the natural setting and at your sheet and draw on it the general shape of the cube, thus placing the drawing, and then refine it by comparing it with nature. The general shape of the cube on paper is applied so that the outline is not very large, but not small either. It is most expedient to represent a sheet of paper as a conditional space in which the cube model takes its rightful place. Of course, at first such an idea is given with difficulty, but in each new exercise it is necessary to include this kind of “mechanism” in order to eventually bring it to automatism.

The planned outline of the cube has taken its place on the paper, and you can step back a little to see the layout of the picture from a distance and once again check whether the location of the image in the format is correct or incorrect in this case. Of course, further work largely depends on how you first placed the drawing.

Start refining values ​​by visual comparison. Having chosen a certain height of the front vertical edge of the cube, subordinate the rest to it, but already taking into account the perspective changes in nature. First determine the location of this edge closest to you in the outlined image silhouette. Then mark the height of this edge, draw a vertical segment, and draw a strictly horizontal line at its lowest point, which will become auxiliary during construction. It will be necessary a little later to imagine a horizontal line perpendicular to the base of the edge in kind, in order to show, together with the one drawn on paper, the angle formed by the horizontal edge of the right side. For comparison, put a pencil or ruler at the base of the plaster model of the cube to see the angle in kind.

Further work on drawing a plaster model of the cube is carried out as a gradual revelation of the constructive basis of the object. Using the landmarks, build the lower face, trying to "see" its outlines from all sides, i.e. show the invisible edges, as was done when building the cube frame. At the same time, mark all the other vertical edges, constantly comparing their size with the edge closest to you.

Knowing the rules of perspective, associate visible changes in the shape of the cube with the construction. The two vanishing points of the conditional continuations of the edges, which are at an angle to you, remain guidelines for constructing all the remaining four upper ones.

After you have built the "skeleton" of the cube, compare the drawing with nature and think about what catches your eye first of all - the whole cube or the details of the shape. In this case, the inaccuracies will become visible. So far, it is easy to eliminate them, because when constructing the shape of a geometric body, we hope that you did not overdo it in drawing pencil marks on paper. Remember, when building the shape of the depicted object, all lines should be drawn easily and confidently.

Why did you see inaccuracies in the drawing? Our vision, as it became known thanks to the experimental data of psychologists, first grasps the general shape of the object, for a short time, as it were, fixes it.

Having eliminated construction errors, check the image with nature again and make sure that the construction of the drawn cube corresponds to the visible model. Since the image of a cube on paper is carried out relatively quickly, with the correct construction, you should not outline the three-dimensional shape of a geometric body with light hatching, thereby showing the shadow side of the object, because it suggests itself - it is known that we draw a semblance of an object, and what our eye sees in kind, he "wants" to see in the drawing.

Cut-off ratios in the drawing must also be built. We use different words in relation to visual activity, for example, “building scale”, “tonal scale”. In the first expression, one must keep in mind the definition in the drawing of the dimensions and ratios of the parts of the object in comparison with nature.

When drawing from life, you are rightfully trying to convey the image the way you perceive the subject. By shading or shading, you simulate the volume of an object, showing in the image the illuminated, transitional from light to shadow and shaded areas peeped in nature. You finish this work only after making sure that the light-and-shadow ratios are correctly conveyed in the drawing. By doing this, you have maintained the tone scale in the image, i.e. managed to find proportional ratios of the darkest and lightest tones.

Tone patterns are created by the skillful distribution of light, penumbra and shadow using line techniques.

Modeling the shape of a cube with a tone, in no case do not rush to immediately lay the shadow face of the geometric body. Firstly, this will not succeed, and secondly, as they do not draw, they do not apply the tone in parts. The point here is the difference between natural light and the whiteness of paper, the materiality of a natural object and the surface of a sheet of paper shaded with a pencil, etc.

To achieve the right (and not exactly the same) tone allows you to reasonably built proportionate relationships in the figure.

Therefore, we recommend you this approach to the transfer of light and shade relationships: choose the darkest hatching tone that you use in a certain place in the picture and do not repeat it anywhere else, and all other gradations will vary from this dark to the tone of the paper itself.

Watch the general illumination of nature and convey this in the drawing.

Diversify the technique of working with a pencil, do not cover the drawing area with thoughtless, monotonous hatching that is “comfortable” for the hand. The texture of gypsum itself suggests to the thoughtful draftsman how to cover the paper with a layer of pencil.

At the end of the work, generalize the image, i.e. achieve the elimination of contrasts that hurt the eyes or a mechanical set of individual tones, and bring the drawing into a general subordination of all tones (Fig. 18). Learn to convey the correct tonal relationships that express form and material in a drawing.

Rice. eighteen

Cylinder drawing

The principle of lighting the next model for drawing from life remains the same. This time you will perform a tone drawing of a cylinder - a geometric body formed by the rotation of a rectangular plane around a single axis.

The shape of the cylinder is peculiar. Unlike a cube, light is distributed over a cylindrical surface in many ways more complicated. The bases of the cylinder are round planes, and if they are at any angle (in perspective), they already look like ellipses.

You drew a wire model of this body and practically studied its constructive basis.

To build a vertical cylinder, start by laying out the overall shape of the body. In order not to make a mistake in placing the general shape (white silhouette) of the cylinder in the vertical format of a sheet of paper, draw a light vertical in the middle and visually determine the height of the depicted body, and then its width.

Further, the construction of the shape of a cylinder turns out to be an effective means of developing knowledge and practical skills in drawing, as it helps to master the rules of perspective and the constructive structure of objects well. In doing this work, you must act confidently, freely hold the pencil.

Having built the frame of the cylinder, in which both bases are correctly depicted in perspective (the lower one is slightly wider, as it looked in nature), compare the image with nature and proceed to modeling the shape in tone. If in the tonal pattern of the cube there was a certain complexity caused by the transfer of proportional natures of light and shade relations, then in the tonal characteristic of the cylinder, additional efforts are needed to understand the degree of distribution of gradations of light and shadow over its specific surface.

Be sure to understand the gradations, because instead of conveying a three-dimensional form, the drawn image may look like it is wrinkled or flattened. To prevent this from happening, be extremely careful in modeling the surface of a cylinder built on paper.

The cut-off solution for the shape of the cylinder is subject to the knowledge of the painter. Everyone sees how the light propagating along the rounded surface of the cylinder clearly builds the shape of a geometric body. A small area looks most brightly on a cylindrical surface. This is a glare, and its phenomenon is caused by the fact that light rays fall strictly perpendicular to this part of the volume. Further, the light begins, as it were, to slide along the rounded surface and, of course, weakens the illumination of the object, until its effect is interrupted by an area that goes beyond the border between it and the shadow, which becomes the darkest spot. Consequently, the cylindrical surface gives a clear visual representation of the sequential distribution of light and shade gradations in approximately the following alternation: semitone, light, glare, light, semitone, shadow, reflex. Of course, the transitions between them are completely indistinguishable, and this is one of the difficulties of rendering a three-dimensional cylinder shape in a drawing. This means that you do not need to achieve an absolute similarity of the drawn cylinder with nature, but to monitor the correct transmission of the ratios of tone gradations proportional to it (Fig. 19).

The background in the tone pattern is an integral part of the spatial image. In addition, it affects the general state of illumination, being either neutral or actively influencing the perception of an object.

Rice. 19

ball drawing

The construction of such a geometric body as a ball is not particularly difficult, if we exclude the curved line, which is impeccable in terms of accuracy. However, it is needed only during construction, and in the completed tone pattern it will disappear, as if it did not exist at all. It has already been said that lines are not the boundaries of the form.

Rice. twenty

A plaster model of a ball intended for drawing from life is placed in front of the painter at a distance that does not necessarily correspond to the triple value of the height of nature. Well-lit from the left and from above, nature is visible from a slightly greater distance.

You can build a circle with a vertical line that intersects it with a horizontal one and two inclined ones at an angle of 45 °. Having set aside identical radii everywhere from the center, easily draw a closed curve, which will become the boundary of the mass of the ball.

After the circle is outlined, refine its boundaries, remove auxiliary constructions and proceed to identify the spherical shape of the ball.

The sculptural term "modeling" is quite suitable here. Indeed, it is possible to achieve the impression of a spherical shape (spherical volume) in a drawing only if the tonal relationships are correctly determined - as if by “sculpting” the shape.

The gradual change in the illumination of the ball is also expressed in the same gradations as in the cylinder, differing only in the characters of the surface. In the cylinder, all the imperceptible, brightening towards the highlight and gradually fading away when approaching the shadow, are distributed along a straight vertical line. The ball has its own, spherical, character of the surface, and chiaroscuro goes along it as in a circle.

Light rays falling perpendicularly on a spherical surface form a glare on the ball, around which an imperceptible darkening begins, spreading more and more along gradually increasing arcs, until, finally, it passes into a moon-shaped shadow in invisible outlines that does not reach the rounded edge of the body, because it hinders the reflex, itself gradually brightening when approaching the falling shadow.

It is very difficult for an inexperienced draftsman to convey such a distribution of light and shade transitions. This requires diligence and culture of drawing, understanding of the task, thoughtfulness of each stage of work.

Please note that compliance with the rules of modeling the shape with a tone with a reasonable variety of hatching techniques inevitably gives positive results.

Correctly taken in the image, the light and shade transitions convey the illusion of the materiality of gypsum (Fig. 20).

Test questions. Practical tasks

1. Define the concept of chiaroscuro.

2. Explain the patterns of distribution of light in shape.

3. What is tone?

4. How to explain tonal relationships?

5. What are the main patterns of tonal relationships?

6. Perform several exercises aimed at mastering a variety of pencil techniques.

7. Do an exercise to gradually increase the tone.

8. Draw from nature any spherical object in tone.

It is in this age group that fairly certain knowledge is formed about the shape of objects and geometric figures as form standards. Children learn to distinguish between a ball, a cube, a square, a circle, a triangle, using the methods of examining these figures using tactile-motor and visual analyzers. in design classes, they get acquainted with some elements of building material: cubes, bricks, plates, prisms, bars.

They look at and compare the ball and the cube, find common and different things in these objects (figures). When addressing a question to the children, the teacher draws their attention to the features of the figures: “What is this? What color are the balls? Which one is smaller?

On the instructions of the teacher, one child picks up a small ball, and the other a large one. Children pass the balls in a circle: the small ball catches up with the big ball. Then the direction of movement changes. In the process of such games, the features of the ball are clarified - it is round, it has no corners, it can be rolled. Children compare balls of different colors and sizes. Thus, the teacher leads them to the conclusion that the shape does not depend on color and item size.

Similarly, knowledge about the cube is clarified and generalized. The kids take the cube in their hands, trying to roll it. It does not roll. The cube has corners and faces, it stands steadily on the table, floor. From cubes you can build houses, columns, putting one cube on another.

The most important points when getting acquainted with the form are visual and tactile-motor perception of the form,

various practical activities that develop the sensory abilities of children. Examination by children of the shape of an object includes the following actions: showing (demonstration) of a geometric figure, examination with the help of specific practical (outlined) actions; comparison of figures, different in color and size; comparison of geometric shapes with objects similar in shape; fixing the features of a geometric figure during drawing, modeling, appliqué.

In the organization of work on familiarization with the form of an object, a significant place is occupied by the display (demonstration) of the figure itself, as well as methods for examining it. The teacher teaches children, when examining an object, to hold it in their left hand, with the index finger of their right hand to circle it along the contour. In order for the guys to better highlight the features of geometric shapes, the models should be compared in pairs: a ball and a cube, a circle and a square, a cube and a square. Figures must be taken different in size and color, so that it is easier to perceive them by touch, find them according to the model, and in conclusion, correctly name their distinguishing features (Fig. 18).

in a bag similar to the one on the table, and shows it. If the child cannot complete the task, the teacher once again recalls the methods of examining the figure: with his right hand he slowly circles around the edge (contour). You can also help with your left hand. When the game is repeated, the number of geometric shapes increases.

In the games “Find an object of the same shape”, “What is in the bag?”, “Geometric loto”, children practice drawing up the shape of objects according to geometric patterns. Such tasks are difficult, but generally accessible to them. They develop in children the ability to analyze the environment, to abstract when designating the shape of objects. The child, perceiving the print that hangs on the wall in front of him, is distracted from the plot of the picture, and highlights only the shape of the frame (square).

Such geometric shapes as a circle and a square are used in mathematics classes as handouts.

Children of this age, when carrying out appropriate purposeful work with them, can analyze complex forms. So, they create an ornament of colored geometric shapes. At the same time, the drawing is analyzed, separate geometric figures are distinguished in it, they are examined along the contour, they are named, and then this drawing is displayed.

In their free time, children of this age group are very fond of games with split pictures, mosaics, and building materials.

Self Test Exercises

Various didactic games and exercises are organized to develop preschoolers' skills in examining the shape of an object and accumulating relevant ideas. So, in order to assimilate the name and clarify the main features of individual geometric shapes, the teacher organizes games: “Name the geometric figure”, “Magic bag”, “Domino figures”, etc.

In the game "Magic Bag", the teacher teaches children to choose figures by touch, to find according to the model. Geometric figures familiar to them are placed on the table, and the same ones are put into the bag. First, attention is drawn to the geometric shapes placed on the table. The children name them. Then, at the direction of the teacher, the child finds

Children of the fourth year of life form certain knowledge about the shape of objects and ... figures as ... forms. Children learn to distinguish between a ball and a cube, ..., a square and

The main thing in learning is the reception ... of these figures ... and in a visual way. A significant place in this process is occupied by ... (demonstration) of ... itself, as well as showing ... its examination.

In order to develop children's skills in examining ... objects and accumulating relevant ... various games and exercises are organized.

geometric references circle triangle survey tactile-motor demonstration of figure ways

presentation forms