There are three types of shapes in the designer. Design: cubes and constructors

First, acquaintance of a preschooler with geometric figures, and then with the basics of geometry, opens up new opportunities for organizing effective educational activities. As part of the course for kids, offer your little one a design from geometric shapes, about the benefits, methods and principles of which we will now discuss. Interesting? Then let's figure it out together!

The benefits of geometric design

Compiling a variety of designs (ornaments, abstractions, simple images or even whole story paintings) from flat geometric shapes is an effective key to the comprehensive development of the imagination:

acquaints with geometric figures, expands and consolidates knowledge on this topic;
creates favorable conditions for the assimilation of the concepts of “color”, “form”, “size”;
develops spatial, abstract and figurative thinking;
stimulates the imagination;
helps to reveal creativity;
promotes the development of speech;
trains fine motor skills;
improves hand-eye coordination.

Designing from geometric shapes is a universal activity that can captivate boys and girls of different ages and temperaments. You can suggest to very young designers just to play with the details of the designer, carefully consider them, and try to sort them by one or another attribute (shape, color, size). The level of difficulty of the tasks should grow with the child.

Young creators, owners of a rich imagination, in compiling images from flat geometric figures are attracted by the opportunity to realize interesting images, to give vent to their fantasies. Such kids can easily cope with creative tasks, without presenting a sample, sometimes incredibly interesting schemes are added from existing parts.

Calm, reasonable, logical-inclined preschool children like working with clear forms. They are happy to perform verbal algorithms and rejoice, having received a tangible result, visualization of their work.

By combining different methods of geometric planar design, you develop both hemispheres of the child’s brain, which favorably affects the creative and logical thinking of the child.

DIY geometric designer

In children's stores, geometric designers are represented by a rich assortment. You can buy magnetic designers, in-ear frames, puzzles ... Or you can make a useful educational game yourself. All you need is a ruler, pencil, compass, scissors and, of course, a supply of suitable material:

color cardboard (you can use velvet, foil, design with different textures);
felt;
carpet;
thin linoleum;
polyurethane mat;
plastic folders and folders.

Important! To prevent the child from getting hurt, carefully treat the edges of the figures.

If you have a stock of fabrics of different textures, use it for your DIY designer: prepare a set of figures from thick cardboard, and then paste each of them with jeans, velveteen, velvet, satin, felt ... If you attach a small piece to each figure on one side sewing contact tape (in other words, Velcro), you get an excellent material for geometric design on flannel graph.

What specific figures for a home-made geometric designer to include in the kit is up to you. The younger the child, the less elements he needs. For children 2-3 years, prepare kits containing:

circles
squares;
triangles
rectangles;
ovals.

Each figure should be represented in different colors and sizes.

If you wish, you can supplement your kit with more complex curly objects - various arches, stars, irregular shapes (resembling clouds, puddles or blots - as you wish).

For starters, you can make small sets: 5 options for each basic figure. As necessary, your kit will replenish with new parts. It's not a problem.

Working with geometric shapes: instructions for parents

Classes with the details of the geometric designer can be organized in different ways:

repeat according to the pattern;
perform according to the verbal description;
independent work.

Children 2-3 years old offer ready-made templates, help the kids repeat the image from the available details, discuss which shapes you used.

Children 4–5 years old You can give a set of figures and ask them to put together simple images. For instance:

Make a Christmas tree of three triangles and a rectangle.
Fold a house of three squares, a triangle and a rectangle.
Use any shapes from your set to get a flower.

When the baby solves the task on its own or with your help, discuss the figures of what color and size he used. Ask the little designer to justify his choice.

In older preschool age children are able to create whole plot pictures from geometric figures. Invite your child to make an original greeting card with his own hands, decorating it with an applique of geometric shapes.

On a note! Geometric applications, like geometric mosaics, are varieties of plane construction from geometric shapes. Combine these methods when organizing preschool math classes with children of different ages.

Friends! Remember, the best way to teach your child is to set a good example. If you want your baby to grow up creative, enthusiastic and smart, feel free to fantasize, coming up with interesting tasks for him with a geometric constructor.

We wish you a happy, creative parenthood. See you soon!

Mathematical games for the compilation of plane figures-silhouettes of geometric figures have been used since ancient times. The most popular of these games are “Tangram”, “Magic Circle”, “Columbus Egg”. A square, a circle, an oval are cut into several parts, from which various plot figures can be folded. They arouse interest in children by their unusualness and amusement, require mental and volitional stress, contribute to the development of spatial representations, creative initiative, ingenuity, and quick wit.

RULES OF THE GAME

Use for the preparation of each figure all parts of a square, circle, oval.
Connect them only along the edges so that they fit tightly against one another.
Do not allow the imposition of one part on another.

STAGES OF TEACHING CHILDREN OF GAMES

Teaching children the games "Tantram", "Magic Circle",

The Columbus Egg should be carried out sequentially, taking into account the individual abilities of the child.

Stage 1. Familiarizing children with the game: communicating the name, examining the individual parts, clarifying their names, the ratio of the parts in size, learning how to connect them together.

Children should know and be able to practically distinguish the distinguishing features of geometric shapes (triangles, quadrangles, circle, oval), subject to their different location in space. You can exercise the children in creating a variety of new geometric shapes from the figures of this set.

Children should have the necessary practical skills in the transfiguration of geometric shapes (combining several shapes in order to create a new one). After a series of such exercises, you can proceed to the second stage.

2 stage. Drawing up plot figures from the elemental image of the subject.

Drawing up subject figures from the elemental image consists in mechanical selection, copying the way the parts of the game are arranged. It is necessary to carefully consider the sample, name the components, their location and connection. This method does not allow the child to show creativity, independence, therefore, it is undesirable to linger for a long time at this stage. It is enough to offer children 2-8 silhouettes and move on to the next stage.

3 stage. Drawing up plot figures from a partial elemental image. Children are offered samples on which the location of one of the two components is indicated, the rest they must arrange independently. Children can lay parts on the pattern, given the direction of the contour lines, a proportional ratio. The child is independently looking for ways to create a silhouette - Through trial and error, he achieves the desired result.

4th stage. Drawing up plot figures on a contour, or silhouette, sample.

At this stage, the child must learn to visually differentiate the direction of the lines of the silhouette (contour) of the composed figure. In the process of preliminary analysis of the sample, it must visually dissect the complex figure into its constituent elements. Then practically check your assumption. For children, such a process of reconstruction is difficult, causes the active work of thought, imagination

The help of an adult is very important at this stage. If the child is at a loss in drawing up a plot figure, it is necessary to pay attention to the direction and ratio of the lines, the general structure, the shape of the object depicted on the sample, and indicate the location of some parts. As children learn the methods and techniques for compiling various plot figures, they have a desire to create something of their own. The child’s transition to the construction of figures by design is a vivid manifestation of creative abilities, independence, flexibility of mind, ingenuity and quick wit.

Figures made up of parts of the Tangram game

Shapes Composed from Parts of the Magic Circle Game

Figures made up of parts of the game

Columbus Egg

"Tangram" "Magic Circle" "Columbus Egg"

Tangram

This game is a set of seven geometric shapes - parts of a square. A square, equally colored on both sides, is cut, strictly following certain rules, into seven parts. In this case, 5 rectangular triangles of different sizes are obtained: 2 large (in the figure are indicated by the number 1),

1 medium (in the figure indicated by the number 2), 2 small (in the figure indicated by the number 3); 1 square (indicated by 4 in the figure);

1 parallelogram (indicated by 5 in the figure).

COMPOSITION OF SUBJECT FIGURESBY ELEMENTARY IMAGE

Bunny

Cat

WARRIOR Christmas tree

COMPOSITION OF SUBJECT FIGURES

BY PARTIAL ELEMENTARY IMAGE

COMPOSITION OF FIGURES ON THE CONTOUROR SILHOUETTE SAMPLE

Cockerel Ship Cow Plane

Magic circle

A circle equally colored on both sides is cut

into 10 parts. The result is 4 identical triangles (indicated by the number 1 in the figure); the remaining parts, pairwise equal to each other, resemble triangular shapes, but one of the sides is rounded (indicated by 2 in the figure).

JACKET ROCKET WARRIOR

COMPOSITION OF FIGURES

LADY KIT

COMPOSITION OF FIGURES

BY CONTOUR OR SILHOUETTE SAMPLELILY CANCER

Columbus Egg

An oval that is equally colored on both sides is cut as shown. The result is 10 parts. Four - geometric shapes: 2 small and 2 large triangles (indicated by the number 1 in the figure). The remaining 6 have only similarities with geometric figures: 4 - with triangles, but one of the sides is rounded (indicated by 2 in the figure); 2 parts - with quadrangles, but one of the sides is rounded (indicated by the number 3 in the figure).

COMPOSITION OF FIGURES BY ELEMENTARY IMAGE

DEER

WARRIOR

COMPOSITION OF FIGURES

ON PARTIAL ELEMENT IMAGE

What only designers you will not meet now on shelves of shops! Some consist of tubes, others of geometric figures with slots, the components of the third resemble the details of a puzzle-puzzle. Constructors on magnets, Velcro, lego-compatible constructors and "ego". Many designers come with detailed assembly diagrams of a particular model. But still, unfading popularity continues to be enjoyed by ordinary wooden cubes and Stroitel kits, in which besides cubes there are bricks, cylinders, prisms and other details. Our grandfathers and grandmothers, dads and mothers played dice. Our children are happy to play cubes.

Play cubes

Cubes are different. Wooden - with sharp corners, large plastic with smooth corners (especially for the smallest). There are cardboard and foam cubes (covered with a cloth or washable vinyl material).

At different ages, cubes are used in different ways. A one-year-old baby, puffing diligently, builds a tower of two cubes. A three-year-old girl builds a cubic for a baby doll from cubes. A seven-year-old boy is building a huge palace of the snow queen or the crusader fortress.

When to start playing cubes with your child? Does the child need adult help playing with them? Do I need to teach children to build from cubes? Can a set of dice be an educational game?

Let's try to understand these issues.
Age 1.5–3 years
Getting to know the shapes

Show and name the baby all the geometric bodies that are in your building kit. It can be: cubes, bricks, cylinders, triangular prisms, arches, blocks, cones, other figures. Sometimes sets with wooden balls come across, if you don’t have one, add a couple of small rubber balls to games with building material.

Ask the baby to put the figures in piles in shape or to distribute these or those figures to different toys (a bear - cubes, a bunny - bricks, and so on). Fold a few pieces in a small bag and ask the baby without looking to get a figure out of him that you will name or show.

When playing with your baby, be sure to name the colors of the details. You can play a game with laying out figures in your houses (you can cut the silhouettes of houses from colored paper or make them from shoe boxes, painted in the right colors, but this option is more time-consuming). If there are identical geometric bodies of different sizes, consider where large and where small. Make houses of different sizes (paper silhouettes of the same color (neutral) or boxes of two or more sizes, if necessary).

Try to roll different parts of the "Builder" from the gorochka. Any small board placed on a large cube or a stack of books can serve as a small pot. Cubes and bricks, prisms slowly slide off the slide, balls and cylinders (if put on their side) quickly roll. Pay attention to the child how the speed of movement of the figures rolling down the hill, and the distance that they will travel if you change the angle of its inclination in this or that direction. Or if you put the same part on top of the slide, then in the middle, then on the very edge - below.
Building

Show your child how to build turrets. Let him try it. Consider with him which figures can be stacked on top of each other and which are not possible (for example, balls, cylinders sideways, triangular prisms, if you put them on the base).

The baby still cannot build real large structures, but with great pleasure he will make a primitive house for a sweetie or a soldier (two bricks standing at the end, one lying across from above). Girls willingly make cots, armchairs, benches for dolls and nesting dolls. Boys build garages for small cars.

To make the kid want to build large structures, build them yourself before his eyes. Involve the child in joint construction - let him give you the right part in time or put any in the place that he liked. Do not be angry with the baby if he disrupted your plan.

Try not to build the same type of projects, come up with something new and unusual every time. Do not strive for symmetry in your structures, on the contrary, make castles, houses, palaces unlike anything else.

After the game, the cubes must be removed so that they do not lie under your feet. Make the kid a piggy bank with slots corresponding to the details of the set. Suppose that after each game he puts the cubes into a box on his own (at first, of course, you can help him a little). Or put them in an ordinary box.
3-5 years old
Getting to know the shapes

From the age of three, children begin to be taught not only to distinguish, but also to correctly name the main details of building kits.

Tell the baby what the parts of the figures are called - face, corner, edge. Ask to show you these parts from different figures.

Most likely, the child is already familiar with the concepts of big - small. It's time to add concepts to the dictionary: high - low, wide - narrow, long - short, describing individual details or entire buildings. Ask to build a short or long track, low or high fences and turrets, wide or narrow gates, walkways and so on.
"Monkey"

Play “Monkey” with the baby (the game is described in the Nikitins book “Intellectual Games”). First, take two parts (two cubes, a cube or brick, two bricks). Give the baby exactly the same shape, color and size. Agree with him that he is a monkey, and monkeys love to repeat everything after everyone. You will build, and the monkey will repeat after you.

Build the simplest model - a turret, track, fence. Wait until the child copies it, then collect the next one. Too long to play is not worth it, finish as soon as you notice that the child is tired or tired. Then he will play with you next time with pleasure. Do not complete the task for a child if he cannot copy your model on his own. Better suggest another, simpler option.

Gradually move on to copying buildings of three to five or more details. During the game, ask the baby to think about what this or that building looks like.
Redoing

The next most difficult task is to transform the samples. An adult builds a small structure and asks the child to build the same model, changing some parameters. The simplest thing is to change the color. Your tower is completely red, and let the children's tower be made of the same details, but blue. Then - let it resize. Instead of small details, let him take large (or vice versa). Then change the shape: instead of cubes - bricks (but the number of parts, their color and location are preserved) and so on.
We build according to the description

Invite your child to build two houses on their own - for a large and a small doll (or garages for different cars). Let him pick up the details and think over the design so that the characters (objects) fit in the house (garage).
Sequences

Teach your child to continue the series in which certain figures are repeated sequentially. Lay out the beginning of the path (fence), for example a cube - brick - cube - brick or cubes: red - blue - red - blue. Ask the child to guess which part will be next. Gradually complicate tasks, alternating three different details. Or a part of one type, followed by two parts of another type, and so on. Pay attention of the child not only to the sequence of figures, but also to their location: the brick can lie flat, and the baby will put it on the edge, you have an arch with a notch (collars) down, and in it up.
Building a city

Draw a path on a piece of paper, and along it from two sides the contours of the faces of geometric bodies (attach cubes, bricks, cylinders directly on the sheet and circle). This will be a new city project. Let the child arrange the houses according to the project and play in the new city - ride cars, lodge dolls, small animals.
Mirror

Place two or three figures on a table in a row (or one below the other - a turret). Ask the child to arrange the same figures next to them in the reverse order. Over time, increase the number of elements in the game.
Remember

Make a path or tower on the table from several parts (start with three or four elements, when the child is comfortable - increase the number). Ask him to look at the path (tower) and turn away. Change the location of one shape (then two or three). Ask the child to restore the original arrangement of the figures.

Make a path (tower) from the figures, let the child look at it, and then remove it. Invite the baby to restore the structure on their own.

Ask your child what this or that part looks like. Ask to find objects similar to her in the room. Ask to recall that he had seen the same form before.
Age 5–7 years
Build on assignment

Older preschool children like to play cubes for a long time on their own (naturally, if they do not sit out all day with the Dandy in their hands, which caring parents, of course, will not allow).

But sometimes you can give your child an order for the construction of certain structures. For example, build a house in which there will be a certain number of floors and apartments. Or a garage for two small and one large car. Children who love fairy tales can be offered to build a house for seven gnomes (small, but with seven apartments) or a house for Carlson (of course, on the roof of an apartment building).
We build masterpieces of world architecture

If you acquaint your child with the history of world art and architecture (from reproductions and photographs) or the famous buildings of your city, you can suggest that he try to depict this or that architectural monument in cubes. The simplest of all the famous buildings to reproduce using the building kit is, of course, Stonehenge. But I think that children with no less inspiration will respond to the proposal to build a likeness of the Cheops pyramid or the Kremlin wall.
Game "Drawing"

For the game you will need cubes, bricks, as well as a set of geometric shapes. They can be cut from color cardboard of the same color.

Rectangles from cardboard of the same color (six pieces of each size):

2.5 x 5 cm;

2.5 x 10 cm;

Squares from a cardboard of one color (ten pieces):

5 x 5 cm.

Ask the child to give you all the figures (cardboard). Tell us about their parts. What is the angle and side. Offer to show equal sides for one figure, for two different figures.

Show and name the child the parts of these geometric bodies (cubes and bricks) - face, corner, side.

Compare geometric bodies with rectangles and squares. Pay attention to the fact that each face of the cube is a square, and the brick has a pair of different rectangular faces. Let the child compare the rectangles with the faces of the brick and find the display of the front, side and top faces.

Invite your child to build a simple house of three to six elements. Draw on the table the plan of its construction with geometric figures (front view). Then switch roles - you build, the child makes a plan.

Then do the same, depicting the building on the side (left).

Then the same thing, but a top view.

Gradually come to depict all three types of buildings at the same time (as in this drawing).
We play constructors

The very first designer can be presented to a baby in a year and a half. Designer parts should be large, connect with each other easily, without effort.

Show your baby how to connect the parts. Build several houses, cars or other simple models before his eyes so that the kid sees the possibilities of this game.

Try to use constructors as educational games. Name the colors of the figures, compare the sizes of buildings. Encourage your child to complete the tasks described in building dice games.

You should not buy many designers with various details and the principles of their connection. It is enough to buy designers of one or two types. If the details are not enough, it is better to buy another set of the same type.

We are pleased to post your articles and materials indicating authorship.
Send information by mail

"... they are always in a hurry somewhere, not a minute of free time ... no time to either sit down or think, but if there is a slight gap in the continuous stream of their entertainments - there is a catfish here, a wonderful catfish ...", - he wrote famous English writer Aldous Huxley.

The Chinese tangram puzzle, known for several millennia, is a square of some delicate material, cut into seven parts in a certain way (for more information on tangram, see chapter 23). The game consists in the fact that various figures are made up of seven elements. From time to time, attempts have been made to create three-dimensional analogues of tangram, but none of them can be compared with the catfish cubes invented by the Danes Pete Hane, about whose mathematical games hex and tactics we have already talked about.

Pete Heyn invented cubes of catfish during a lecture by Werner Heisenberg on quantum mechanics. While the famous physicist was talking about space cut into cubes, Pete Haine's vivid imagination prompted him to formulate a curious geometric theorem: if you take all the irregular shapes, which are made up of three or four cubes glued together by faces, then you can make one larger cube .

Let us explain what was said. The simplest irregular figure - “irregular” in the sense that there are protrusions and depressions on it — is obtained by gluing three cubes as shown in Fig. 115, 1. This is the only irregular figure that can be built from three cubes (obviously, one or two irregular figures cannot be made from one or two cubes). By taking four dice, we can build six different irregular bodies. They are shown in fig. 115, 2-7. To somehow distinguish the constructed figures, Hein renumbered them. All seven irregular figures are pairwise distinct, although figures 5 and 6 are aligned in mirror image. Hein drew attention to the fact that by gluing together two cubes, we increase the length of the body in only one direction. To increase the length of the body in the other direction, we need another, third cube. Four cubes will increase the length of the body in three directions. Since even taking five cubes does not increase the dimension of the figure to four, it is reasonable to limit the set of catfish cubes to the seven figures shown in Fig. 115. Quite unexpectedly, it turned out that one of the seven elements can be combined into one large cube.

Immediately at a Heisenberg lecture, Pete Heyn figured out on a piece of paper that out of seven elements glued from 27 small cubes, you can make a 3 × 3 × 3 cube. After the lecture, he glued his seven elements from 27 cubes and quickly became convinced of the correctness of his guess. Toy companies have released Heine cubes on sale under the name Soma. Drawing figures from seven irregular elements is very popular in the Scandinavian countries.

To make the cubes for the catfish game yourself - and we strongly recommend this game to our readers, everyone will like it - just take the most ordinary children's cubes and glue all seven elements from them. In fact, the catfish game can be considered as a three-dimensional version of the poliomino, which we already talked about.

As an introduction to the art of playing catfish, try to add the step shape shown in fig. 116. Having coped with this elementary task, try to collect a cube from all seven elements. One of the readers has compiled a list of more than 230 different solutions (not counting those obtained by turning and reflecting the cube), but the exact number of all solutions is still unknown. When compiling a cube, it is advantageous to first take more irregular elements (5, 6, and 7 in Fig. 115), since it is not so difficult to fill the voids formed with the rest of the elements. In particular, element 1 is best taken last.

Having built the cube, test your strengths in folding the more complex figures shown in Fig. 117. By trial and error, you will lose a lot of time. It is more reasonable to analyze the structure and speed up the construction. Your geometric imagination will help you with this. For example, elements 5, 6, and 7 cannot serve as steps leading to a "well." Having made several sets for playing catfish, you can conduct competitions. The winner is the one who folds a given figure faster than others. In order to avoid disputes about how this or that figure should look, it should be said that the back sides of the “pyramid” and “steamboat” look exactly the same as the front sides of these figures; the recess in the "bath" and the shaft of the "well" have a volume equal to three cubes; on the back wall of the “skyscraper” there are no ledges or indentations, and the table forming the back of the head of the “dog” consists of four cubes (the lowermost cube is not visible in the figure).

Having spent several days with unusual cubes, many are so familiar with their shape that when drawing up new figures of the catfish they can perform all the necessary actions in the mind. Tests conducted by European psychologists showed that there is a certain correlation between the ability to solve puzzles with catfish cubes and the general level of development, but strong differences are possible at both ends of the curve characterizing mental development. Some geniuses are completely incapable of playing, and, conversely, in some mentally retarded individuals, the kind of spatial imagination that is required for playing the catfish is highly developed. It is interesting that everyone who undergoes such a test is happy to continue the game even after it is over.

Like two-dimensional poliominoes, the construction of catfish cubes is associated with interesting theorems of combinatorial geometry, in particular, with the proof of the impossibility of one or another construction. Let's consider the left figure in fig. 118. Nobody succeeded in building it, but only recently it has been strictly proved that it is really impossible to compose it from catfish cubes. We will give here this witty evidence of Solomon. V. Golombu.

First of all, we will redraw the top view of the figure depicted in Fig. 118 on the left, and color the columns (when viewed from above, each column "hides" under the edge of its upper cube) in a checkerboard pattern. In each column, with the exception of the central one, two cubes. The central column is built of three cubes. In total, there are 8 white cubes and 19 black. Amazing asymmetry!

The next stage of the proof is that for each of the seven elements of the catfish game, they find an orientation in which this element, if placed under our chess stencil, will have the maximum number of black dice. The maximum number of black cubes for each element is indicated in the table. As you can see from it, there are a total of 18 black and 9 white cubes, that is, for a 19: 8 ratio that characterizes our figure, only one black cube is missing. If the upper black cube is moved to any of the white columns, the ratio of black and white cubes will be equal to 18: 9. Such a figure can be built.

I must admit that one of the figures shown in Fig. 117, it is impossible to make up the elements of the catfish game, however, in order to find it, the reader will have to spend more than one day. Below we will not dwell on the methods of constructing the remaining figures shown in Fig. 117 (mastering the art of drawing up such figures is only a matter of time), but we indicate the one that cannot be built.

The number of funny figures that can be composed of the seven elements of the catfish, apparently, is as unlimited as the number of flat figures laid out of the seven elements of the tangram. It is interesting to note that if you postpone element 1, then from the six remaining elements you can make a figure in exactly the same shape as element 1, but twice as large.

Having written a note about the catfish game, I assumed that only a few readers would take the trouble to make a complete set of its elements, and I was cruelly mistaken. Thousands of readers sent sketches of new figures of the catfish game, and many wrote that their leisure time began to pass much more interesting since they were "bitten by a catfish fly." Teachers made sets of catfish cubes for their classes, psychologists included drawing figures from them in their tests. Fans of catfish cubes made sets of seven elements for their friends who were in the hospital, for acquaintances as a Christmas present. Toy companies became interested in the rights to make catfish cubes. On the shelves of toy stores appeared sets of wooden catfish cubes.

In fig. 119 shows 12 of many hundreds of new figures sent by readers. All 12 figures can really be built.

In my opinion, the popularity of catfish cubes is due to the fact that in this game only seven elements are used and the player is not suppressed by excessive complexity. Involuntarily begs the thought of creating other games that use a larger number of elements. The description of such games is devoted to many of the letters I received.

T. Katsanis proposed a set of eight different elements that can be composed of four cubes. Its set includes six elements of catfish cubes plus a chain of four cubes glued in a row and a 2 × 2 square. Katzanis called his game a quad. Later, other readers proposed tetracubes. It is impossible to build a cube out of eight quadrocubes, but they can be positioned close to each other so that they form a rectangular parallelepiped 2 × 4 × 4 in size, twice the size of a square tetracube. In a similar way, enlarged models of the other seven elements can be compiled.

Katzanis also discovered that the eight elements of the game he invented can be divided into two groups of four elements in each, so that from the elements of each group it will be possible to construct a rectangular parallelepiped 2 × 4 × 4. By combining these parallelepipeds, you can build enlarged models of six of the eight source elements.

If we take three-dimensional pentamino, composed not of squares, but of single cubes, then from twelve elements we can construct a rectangular parallelepiped 3 × 4 × 5. From three-dimensional pentamino can be combined rectangular parallelepipeds 2X5X6 and 2 × 3 × 10.

The next most difficult game is the folding of figures of 29 elements built of five dice. It was also invented by Katsanis. He suggested calling this game pentacubic. Six pairs of pentacubes pass into each other during reflections. Taking one element from each pair, we will reduce the number of elements in the complete set to 23. Both 29 and 23 are prime numbers, so no matter how many or no sets of pentacubes we take, we will still fail to build a rectangular box. Katzanis formulated the problem of tripling: having chosen one of the 29 elements, to build from the other 28 three times his large model.

An elegant set of pentacubes sent D. Clarner. Having shaken them out of the box into which they were packed, I still could not (until now) put them back. Clarner spent a lot of time designing unusual shapes from pentacubics, I had to spend a lot of time to reproduce some of them. He also informed me that there are 166 hexacubes (figures obtained by gluing six cubes), but was so kind that he did not send me their set.

The answers

The only figure in fig. 117, which cannot be built from the seven elements of the catfish cubes, is a skyscraper.

there are three main types of construction: according to the model, the conditions and the design.

Designing according to the model - when there is a ready-made model of what you need to build (for example, an image or a house diagram).

When constructing according to the conditions of the sample, there is no one - only the conditions are set that the building must comply with (for example, the house for the dog should be small, and for the horse - large).

Design by design suggests that the child himself, without any external restrictions, will create the image of the future structure and embody it in the material that is at his disposal. This type of design is better than the rest develops the creative abilities of the baby.

Classes from here, there are 1-2 years of age and 2-3, I take different, which are interesting

Lesson number 23

Subject: "Truck".
goal : Exercise children in simultaneous action with two kinds of parts: cubes and bricks. Continue to learn how to attach parts. Continue to teach children to build a building within the meaning of the plot.
Material : nesting doll, 2 cubes of yellow color, 2 bricks of blue color.
Game Activity: Build a truck model: take the bricks and apply them to each other. Then we take cubes and put on bricks. The truck turned out. What is it, Masha? (Truck) And now we put a nesting doll on the truck and go. “BBC! Go!" Suggest a model for the children to build a truck. If the children coped with the task, the teacher does not explain the methods of construction, but only helps with questions, advice, reference to the sample, action (if necessary).

Lesson number 66

Theme: "Garage."
Goal: continue to learn to correlate the size of buildings with the size of toys, analyze the sample and follow it. Develop imagination, constructive creativity. To consolidate the ability to distinguish and correctly name the details of the building set (brick, plate), develop the ability to beat the situation.
Material: on each table - a set of building material, toy cars of different sizes.
The course of the game - classes:The teacher has a garage built on the table, next to it is a toy - a car. He addresses the children: “Look, I built a garage. This is a car house. Garage. Look at what the garage has: walls, roof, doors. Do you have windows at the garage? No. What parts is the roof made of? (made of bricks). What are the walls made of? (also made of bricks). What is the name of this part? (plate). What can be built from it? That's right, the path to the garage along which the car will go. Now we will put the car in the garage. She rides on the track, but can not stop at the garage. Why? Who guessed? Yes, the doors are very narrow. Maybe this car will go in there? (shows a small one). Sasha, try putting this car in the garage. This garage turns out to be for a small car. And for the big one we’ll build now. What will we build first? (walls), yes, I will put the bricks wider so that a large car can enter the garage - the walls are ready. What else needs to be built? (roof). Now we will lay bricks like this, it will be a roof. Build a garage for your car so that it fits there. Think of what else can be done at the garage (doors, fence). The teacher encourages children to play. Construction can be done individually and as a subgroup.

Our photos

Model building, the bridge was built

Timur likes to build a race track only, the rest is all without much enthusiasm))), this is the construction we planned

And on assignments they built a small large garage, one garage for two cars and a truck for the track (construction on the terms)

I will also share books that I liked

1 - primer for learning to read, it is without pictures. Apparently Timur, like me, doesn’t like textbooks with pictures))))) we are learning letters from him, I really like him (I printed it on a4 and packed it in a folder)

2 - to teach the child to draw, also printed, tasks there just by age