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Mathematics for the smallest (from one and a half to three years)

we Will talk about quantity

Should not be begun with studying of large numbers or on fast and intensive advance forward at once. Master at first the first ten, then you will pass into the second, be late in the first two tens when all is clear, you will go further. Never it is necessary to check the child whether he knows. And how then to understand whether it is possible to go further?

needs to listen very attentively to the child when you enter new numbers, the new relations between numbers. And if you noticed that the kid ceases to be interested, turns away, it means, he began to lose an understanding thread, so and interest. Return back a little, give the chance to feel surely, then you will go further. Only do not think that you detain the child in development, without giving it the chance to see all at once, to work at once red points Domana or “Stochsetom“ of Zaytsev. Better let he perfectly understands the little, than will try to penetrate into all, so nothing up to the end and without having fixed.

Very important prevention - you do not enter

to the child of figure ahead of time when the child begins to understand concept of quantity precisely. When you see that he understands that it one, two and so on, but will repeat not just after you as a senseless word-play. It is very important. And here when it will acquire it when itself begins to use these concepts of the speech and game to destination and intentionally, but not incidentally, then, it is possible, it is ready to communication of figure and number. But as it, most likely, will occur not earlier than two - two and a half - three years, we will not say about it now.

U us the set of occasions to talk to the child about quantity is.

  1. Ya. Yes, it is necessary to begin with the child, and to begin it it is possible not in one and a half years, and much earlier (for example, in 6 - 8 months or even earlier). But if you before it did not do though I doubt it because it is so natural, then begin now.
  2. Count everything that the child has, all from what it consists: two eyes, fish soup, two hands, legs, one nose etc. the Child like to examine and discuss themselves again and again, and you ask: “Where you have legs?“, it will show, and you will tell: “Katya has two legs!“ you can also add:“ Here one and here the second“. So see everything and count. And, you tell every time differently. So you will begin to study the account from one to two.
    the Most universal grant for training in mathematics are fingers. The way of mankind to decimal system in which we and with the kid will consider goes from fingers of the person. Begin with one handle. Recalculate fingers, hide a little and consider how many remained. Hide all and get acquainted with concept of zero. Separate one fingers from others and find out that five it is one and four, two and three. Then begin to add the second handle. One finger of the left hand came on a visit to fingers of right - and there were six fingers. Then to them one more came, and them became seven etc. Or let come on two at once - three fingers, and you find out how many they became.
  3. Recalculate all you play. For this purpose it is not necessary to arrange special occupations with a usazhivaniye for a school desk and pulling from a portfolio of calculating sticks. You, for certain, in something play with the child, here and talk: “There lives a chicken, and here - two elephant calves“. Or “How many animals will go by train?“ And you answer that the child began to understand how such question is answered by “Two cats, three horses, one camel etc.“ . Specially create game situations where the hero something has to count or give to other toy or the person the necessary quantity of mushrooms, flowers, hippopotamuses, anything. Right there, that is in any game it is possible to give elements of mathematical operations, to acquaint with structure of number. That is you as if play a mathematical task in persons and solve it in the face of the child in the ways available to it.
    For example
    “To a camel on a visit by the big ship the elephant, and then two more monkeys came. Also three guests“ etc.
    “Became at a camel the girl baked two jam pies and two pies with cabbage, then put all these four pies in a basket and went to the wood to the familiar woodcutter (you represent all this toys, and it is even better if you do it together, on roles). The woodcutter was just at home moreover on a visit at him two hunters sat. The girl prepared tea and all of them began to drink it with pies. Also it turned out so that all got to about one pie. As also people and pies was on four, that is equally (and distribute to all on pie)“. The game plot, naturally, has to be such as you want, proceeding from those toys what you have. Therein design game space with the child: wood, path and other. Do not focus attention that it is necessary to remember something or at least attentively to listen. Let the child will be keen on game, and all to be remembered by itself.
    At Katya three hares - two white and one gray; in a basket five berries - three cheesecakes and two raspberries lay; and so on are data on structure of number.
be not afraid to give to

in game concepts of multiplication and division: we constructed three lodges on four cubes: only twelve cubes at us left! Let`s divide equally for three animals - six apples (or anything), to everyone on two!

Recalculate all you are anyway connected in life with - you set the table or you put on boots, you clean toys from a floor or you peel potatoes - consider everything, only not really focus attention on it.

of Game and options of occupations on quantity

If the kid likes to put something where - nibud, to push cylinders or coins in a hole in a box, to roll balls from a hill - it can be connected with the account too. Here at you more than ten can turn out or two - gradually we leave farther. The child puts, you consider. He listens and tries to repeat. So the child not only remembers sequence of the account, but also can visually see those twenty or thirty five coins which he put in a jar. Options of such games:


coins (you, for certain, will have a lot of old trifle or new kopeks which already cost nothing) and a plastic can with a narrow opening in a cover (as in a moneybox) lay out a long path how many at you it turned out coins - 12, 17, 25 on a table? Count together with the kid, repeat how many at you coins. Also begin to put coins in bank a hole, calling every time how many coins remained - it will be game in the return account 25, remained 24, 23, 22...

Can spread coins not the long road, but “turrets“ (4,3,2,1), can one, two, three whole turrets or more moreover several coins separately will turn out, and tell the kid - ten, ten more moreover ten moreover four coins - only thirty four! Let`s put in bank: remained 33, 32...

“Cheerful recounting“. The geometrical figures which are cut out from color paper or a cardboard and also any other same objects which differ from each other can be useful to you. For example:

If you have on a table a motley cloth or on a floor a motley carpet, and you are going to play there, then enclose a clean sheet of a cardboard or something monophonic. Put on it one figure and tell “One!“, then following also call “Two!“ and so to five. Then examine that turned out. At you five figures identical can turn out, then you will tell - all red! - or several others, then you can tell - three red and two blue, and only five. And then begin to clean on one, attract in it the child and cheerfully clean and spread five figures, including them again forward - back. On the course of game change quantity of multi-colored figures in yours to “heel“ imperceptibly for the child and pay his attention to it - “Look: one red and four blue, and all the same five!“ .

bring game to structure of number ten After a while, then take at the same time twenty figures that it could turn out the whole ten one colors, whole - another, nine one - one another etc.

Can use at game cardboard pallets for eggs (pallets on ten eggs with a cover are on sale now - from them it is only necessary to cut off a cover, or to take the big pallet on three tens and sharp to knife it so that two rows on five turned out). Displaying in such “ten“ coin, balls or something else, the kid himself will see how many it was necessary to put that the whole ten turned out that when there is no place in one box, the second ten begins, will easily remember structure of numbers of the second ten and further.

Signs and properties we Will begin


with absolutely not mathematical concepts. Signs and properties are available for any objects. About them you constantly talk to the child because his rough vital energy is directed now generally to comprehension of properties of various objects. He is engaged in it in a bathroom and in a sandbox, holding paints or the designer`s details, Zaytsev`s cubes in hand or “Put a pattern“. And you, adults, actively help the child to classify everything in this world, providing the maximum information, explaining different categories - color, a form, the size, an origin, appointment, material of production and other signs by which it is possible to classify objects.

A as we can give to the child the chance to manipulate actively signs of objects? Are most convenient for this purpose - geometrical figures - their signs are brightly expressed and visible even to very small child.


three main figures - a circle, a triangle and a square, three primary colors - red, blue, yellow, three sizes - big average small. At you has to twenty seven figures will turn out, each of which has three signs - a form, color, the size. It is possible to cut out figures from a color cardboard or to draw on cards of identical size. It would be quite good to make two absolutely identical sets that there was an opportunity to find absolutely identical figures on all three signs.

Having such cards in hands it is possible to play indefinitely.

Display them on one sign, for example, look for all red or all squares or all small figures. You can use them as cookies, berries, balls, cubes or anything in yours syuzhetno - role-playing games, adapting to a plot. Complicating game plots, complicate the maintenance of a task. If at first your steamship, going to the North Pole, took tasty berries which it never tasted for polar bears (you chose from all red figures only circles or in general from all figures circles of any color). That it is possible to expand “the area of port“ now and “to load“ at the same time two “ships“ - berries or balls (circles) for polar bears and cookies or juice in packages or interesting books (small squares) for a kangaroo in Australia. Or still something - cubes as a gift to a teddy bear (small squares) and a collection of kites to plush hare (triangles).

you Can put figures in the flowers on the sheet of color paper of the necessary color. Or in a form - on sheets of the white paper which is cut out in the form of the necessary figure. Or - by the size on a lodge or a silhouette of a sack from paper according to big, average and small.


you Can make the cards of this kind uniting two signs.

Simple option - a red square - for red squares, a small triangle for small triangles, a big red lodge - for big red figures.

the Option is more difficult than

- all cards are carried out in the form of identical lodges which from above have on an attic two symbols of signs - a triangle and a red blot - for red triangles, a big bag and a square - for big squares etc.

At more advanced age can expand and modernize variants of tasks for this game.

of the Logician

Aged from one and a half till three years the child cannot and should not solve any logical problems. He is not familiar with logic yet. And we can begin to acquaint it with it on vital examples. Here it is important to follow several rules. That the child believed in existence prichinno - investigative communications: