Consultation for teachers on the topic: "Formation of elementary mathematical representations of preschool children (number and count)". Methods of teaching quantitative counting in different age groups: stages, techniques and counting skills

Number and count within ten.

Target : Introduce the number and number ten. To promote logical thinking and development in the classroom in mathematics.

Tasks :

Tutorials:

- fix the ordinal score within 10, introduce the number 10,

To form in children an interest in mathematics, a sense of confidence in their knowledge.

Train mental operations - analysis, comparison, generalization, abstraction.

Developing:

Develop attention, memory, speech, fantasy, imagination, logical thinking, Creative skills, initiative;

Develop fine motor skills hands

Educators:

To cultivate positive motivation for learning, interest in mathematics;

Cultivate a friendly relationship with each other.

Material : handouts, pictures, demonstration material.

Do you know the characters from which cartoon are shown in the picture? Do you love this cartoon? Let's play with the characters of this cartoon today.

Masha came to visit the bear, andbearwas very busy with important work. He played checkers. Masha wanted to eat, and the bear treated her to porridge. She did not like porridge and decided to cook it. She put the pot on the stove. She poured porridge into it.

How many boxes did she put in the pot?

Nine boxes of porridge!

Nine!

How many bottles of milk did you pour?

Nine!

How many pots did Masha fill with porridge?

Nine!

Offended bearto Masha. Decided to make jam. And then Masha ate all the berries and fruits from the bear. He decided not to be friends with her anymore.

Here, go and bring me fruits and berries.

He showed Masha the number 9. But she doesn't know what number it is and she can't count. Can we help Masha?

Collect 9 apples, 9 berries, 9 pears. Thanks guys helped Masha!

Physical minute:

What other characters are in this cartoon?

Zainka prepared a game for you:

The hare began to jump

One, two, three, four, five

jump hare much

He jumped 10 times

I decided bearMasha to teach mathematics. Today he will introduce her to a new number and a new figure.

Do you want to get acquainted? Guess what number? Correctly! With the number ten.

How can you get it?

How much to add to 9? by 8? by 7? by 6? by 5?

And this is the number 10. It stands for the number 10.

Let's put the number 10 out of the counting sticks.

A round zero is so pretty that it does not mean anything at all if, together with it, we can fit one. That is more, it will weigh, because it is ten!

After what number is she on the number line? After 9.

Is the number 10 greater or less than nine? More.

How much? For one.

Let's count to 10.

Masha and the bear have prepared a task for you, let's complete it.

Our lesson has come to an end.

Who did we visit today?

What did you like about the lesson?

What have you learned?

Formation of elementary mathematical representations children preschool age(number and count)

Mathematics in kindergarten starts from the second junior group, where they begin to carry out special work on the formation of elementary mathematical representations. On how successfully the first perception of quantitative relations and spatial forms of real objects will be organized, the further depends. mathematical development of children.
Modern mathematics, in substantiating such important concepts as "number", "geometric figure", etc., relies on set theory.
The performance by children in kindergarten of various mathematical operations with object sets allows them to further develop an understanding of quantitative relations in children and form the concept of a natural number. The ability to single out the qualitative features of objects and combine objects into a group on the basis of one feature common to all of them is an important condition for the transition from qualitative to quantitative observations.
Work with kids begins with tasks for selecting and combining objects into groups according to a common feature (“Select all the blue cubes”, etc.) Using the methods of imposition or application, children establish the presence or absence of a one-to-one correspondence between elements of groups of objects (sets) .
The concept of a one-to-one correspondence for two groups is that each element of the first group corresponds to only one element of the second and, conversely, each element of the second group corresponds to only one element of the first (there are as many cups as there are saucers; there are as many brushes as there are children, etc.). . P.). In modern teaching mathematics in kindergarten, the formation of the concept of a natural number is based on the establishment of a one-to-one correspondence between the elements of compared groups of objects.
Kids are not taught to count, but by organizing a variety of actions with objects, they lead to the assimilation of the account, create opportunities for the formation of the concept of a natural number.

Methods of mathematics in kindergarten

Main methodology for teaching mathematics in kindergarten- teaching children in the classroom. Mathematics classes in kindergarten are held from the beginning of the school year, that is, from September 1. In September, it is advisable to conduct classes with subgroups (6-8 people each), but at the same time cover all children of this age group. Since October, on a certain day of the week, they are engaged immediately with all the children.
In order for classes to give the expected effect, they must be properly organized. New knowledge is given to children gradually, taking into account what they already know and can do. When determining the amount of work, it is important not to underestimate or overestimate the capabilities of children, since both would inevitably lead to their inaction in the classroom.
Strong assimilation of knowledge is ensured by repeated repetition of the same type of exercises, while the visual material changes, the methods of work vary, since the same actions quickly tire the children.
To maintain activity and prevent fatigue of children allows a change in the nature of their activities: children listen to the teacher, following his actions, perform any actions themselves, participate in a common game. They are offered no more than 2 - 3 homogeneous tasks. In one lesson, they give from 2 to 4 different tasks. Each is repeated no more than 2-3 times.
When children get acquainted with new material, the duration of the lesson can be 10-12 minutes, since mastering the new requires considerable stress from the baby; classes devoted to repeated exercises can be extended up to 15 minutes. The teacher monitors the behavior of children in class and, if they show signs of fatigue (frequent distraction, errors in answering questions, increased excitability, etc.), stops the lesson. Monitoring the condition of children during classes is very important, as fatigue can lead to children losing interest in classes.

Methods for teaching mathematics in kindergarten

Teaching children mathematics in kindergarten in the younger group is visual and effective. The child acquires new knowledge on the basis of direct perception, when he follows the actions of the teacher, listens to his explanations and instructions, and acts with the didactic material himself.
Classes often begin with elements of the game, surprise moments - the unexpected appearance of toys, things, the arrival of "guests", etc. This interests and activates the kids. However, when a property is first highlighted and it is important to focus the attention of children on it, playful moments may not be present. The elucidation of mathematical properties is carried out on the basis of a comparison of objects characterized by either similar or opposite properties (long - short, round - non-round, etc.). Objects are used in which the cognizable property is pronounced, which are familiar to children, without unnecessary details, differ in no more than 1-2 features. Accuracy of perception is facilitated by movements (hand gestures), guiding the model with the hand geometric figure(along the contour) helps children more accurately perceive its shape, and holding a hand along, say, a scarf, ribbon (when compared in length) - to establish the ratio of objects precisely on this basis.
Children are taught to consistently identify and compare the homogeneous properties of things. (“What is it? What color?, What size?”) The comparison is based on practical ways of matching: overlay or application.
Great importance attached to the work of children with didactic material. Toddlers are already able to perform rather complex actions in a certain sequence (impose objects on pictures, sample cards, etc.). However, if the child does not cope with the task, works unproductively, he quickly loses interest in him, gets tired and is distracted from work. Given this, the teacher gives the children a sample of each new mode of action. In an effort to prevent possible errors, he shows all the methods of work and explains in detail the sequence of actions. At the same time, explanations should be extremely clear, clear, specific, given at a pace accessible to the perception of a small child. If the teacher speaks in a hurry, then the children stop understanding him and get distracted. The teacher demonstrates the most complex methods of action 2-3 times, each time drawing the attention of the kids to new details. Only repeated demonstration and naming of the same methods of action in different situations with a change in visual material allow children to learn them. In the course of work, the teacher not only points out mistakes to children, but also finds out their causes. All errors are corrected directly in action with didactic material. Explanations should not be intrusive, wordy. In some cases, children's mistakes are corrected without explanation at all. ("Take it in right hand, here in this one! Put this strip on top, you see, it is longer than this one! etc.) When the children learn the way of action, then showing it becomes unnecessary. Now they can be asked to complete the task only according to verbal instructions. Starting in January, you can give combined tasks that allow children to learn new knowledge, and train them in what they have learned earlier. (“Look at which Christmas tree is lower and put a lot of fungi under it!”)
Young children are much better at absorbing emotionally perceived material. Their memorization is characterized by unintentionality. Therefore, in the classroom, gaming techniques are widely used and didactic games. They are organized in such a way that, if possible, all children participate in the action at the same time, and they do not have to wait for their turn. There are games associated with active movements: walking and running. However, using game techniques, the teacher does not allow them to distract children from the main thing (albeit elementary, but mathematical work).
Spatial and quantitative relations can be reflected at this stage only with the help of words. Each new mode of action learned by children, each newly distinguished property, is fixed in the exact word. The teacher pronounces the new word slowly, highlighting it with intonation. All the children together (in chorus) repeat it.
The most difficult thing for kids is the reflection in speech of mathematical connections and relationships, since it requires the ability to build not only simple, but also complex sentences, using the adversative union -A - and the connective -I-. At first, you have to ask the children auxiliary questions, and then ask them to tell everything at once. For example: “How many pebbles are on the red stripe? How many pebbles are on the blue stripe? Now tell me right away about the pebbles on the blue and red stripes. So the child is led to reflect the connections: “There is one pebble on the red strip, and there are many pebbles on the blue one.”
The teacher gives an example of such an answer. If the child finds it difficult, the teacher can start the answer phrase, and the child will finish it. In order for children to understand the mode of action, they are offered to say in the course of work what and how they are doing, and when the action has already been mastered, before starting work, make an assumption about what and how to do. (“What needs to be done to find out which board is wider? How to find out if the children have enough pencils?”) Connections are established between the properties of things and the actions by which they are revealed. At the same time, the teacher does not allow the use of words whose meaning is not clear to children.

Methodology for the formation of quantitative representations

Very early in the speech of children, the first numerals appear. Of course, this is still a spontaneously used technique. At 2-3 years old, children move on to mastering the sequence of numbers in a limited segment of the natural series. These are the numbers 1,2,3.

As a rule, the account begins with the word "time". The chain of numeral words memorized by the child is broken if suddenly an adult corrects the mistake and suggests starting the count with the word “one”.

Sometimes a child perceives the first 2-3 numerals as a single whole and refers to one subject: two.

Under the influence of learning, children memorize an increasing number of numbers. Having learned the numbers of the first ten, the children easily move on to the second ten, and then they count as follows: “Twenty ten, twenty eleven ...”. But if the child is corrected and named after 29 - thirty, then the stereotype is restored and the child correctly counts until the next stop.

However, the auditory image of the natural series of numbers formed in children does not indicate that they have mastered counting skills.

The formation of ideas about quantity in the second younger group is limited to the pre-numerical period.

Selecting individual items from groups

and grouping items

Children must understand that each group consists of separate items, learn to single out one from the group.

The teacher brings in a tray with ducks, joyfully exclaims: “That's how many ducks! A lot here, here, here. And now all the children will take a duck, both Seryozha and Olya. All the children took a duck, not a single one remained.

Basic conditions:

1. The number of toys should match the number of children.
2. The teacher encourages the use of words - many, one,

alone, none.

Learning to count middle group

"The program of education and training in kindergarten" provides for an account within 5

Quantitative counting is taught in two stages:

1. on the basis of a comparison of the numbers of 2 groups of objects, the goal of counting activity is revealed to children (to find the final number). They are taught to develop groups of subjects into 1, 2, and 3 subjects and name the final number based on the teacher's score.
2. accounting training. Comparing two groups of items that are equal or unequal in number, the teacher shows the formation of each next number

Accounting operations

1. Naming numerals in order;
2. Matching each numeral with a hand gesture;
3. Calling the final number in combination with a circular gesture;
4. "Naming" the final number (total 3 matryoshkas).

Counting direction from left to right.

Children's mistakes in the counting process:

Counting from the word "one", not "one";

Naming numerals together with a noun in the process of counting;

The numeral "one" does not agree with the noun;

The final number is not named (1,2,3 - only 3);

The final number is not called (1,2,3 - total fungi together) 4

The direction of the account is not respected.

The sequence of complicating counting actions in preschool age:

Counting out loud, touching the object with your hand;

Counting out loud with a pointer

Counting aloud at a distance;

Account in a whisper;

Account "to myself", mentally.

Learning to count objects

The countdown involves the selection of a specified number of items from a larger one.

Counting algorithm.

Remember the number of items to be counted;

Take objects silently and only when the objects are placed, call the number;

Children's mistakes when counting:

They do not count objects, but their actions (took a toy - one, put - two),

Works with both right and left hand.

Task options

Sample count. The teacher offers to count the toys on the table and set aside the same number of circles;

Countdown by the named number: find two ducks, put aside three fungi;

Counting items in combination with tasks for spatial orientation: set aside 4 circles and put them on the bottom strip, 4 ducks on the table.

The following games are used:

"Treat the bears with tea"

Bear cubs come to visit children, treats, cups, saucers are prepared in advance. After the guests sit down at the table, the children are invited to bring as many cups as there are guests, count the same number of saucers, etc.

"Let's dress the doll for a walk"

The same learning task is involved in another plot: the children are getting ready for a walk, they are going to take their dolls with them. But they must be dressed according to the season: from more coats, hats, scarves, mittens must be taken according to the number of dolls.

Showing the independence of a number from the features of objects

It is important to draw the attention of children to the fact that the number of objects does not depend on their size, shape of location, occupied area.

Children are taught to use various methods of practical comparison, overlay, application, pairing, use of equivalents (substitutes for objects). Equivalents apply when other known ways it is impossible to use. For example, to make sure that the same number of objects is drawn on both cards, you need to take circles and superimpose them on the drawings of another card.

Account including analyzers.

Interesting tasks help to activate counting skills

Account by ear

Task options:

Behind the screen, the teacher makes sounds, the children count with their eyes open;

Counting sounds with closed eyes;

Movements to extract sounds are performed under the table, behind the back - this sharpens the activity of the auditory analyzer.

Requirements for the implementation and organization of exercises.

1. Children should not see movements, but count sounds.
2. Sounds and movements should be rhythmic, varied: hitting a tambourine, a drum, knocking on a door, pronouncing the same word.

Touch count.

Task options:

Get the indicated number of items from the "wonderful bag";

Counting small items under a napkin.

Movement count.

Interestingly, such tasks are carried out in the form of a physical minute.

The poetic form sets the rhythm of the movements, the entertaining plot captivates children, enlivens their interest.

Ordinal account.

To teach ordinal counting, objects that are qualitatively different from each other are used, arranged in a row. It can be a set of nesting dolls, different sizes, familiar geometric figures, illustrative material for the fairy tales "3 Bears", "Turnip".

A certain situation is created for learning: nesting dolls go for a walk, children go to the forest, etc. their serial number is determined.

Children often confuse the questions "which?" and which?" The latter requires the selection of qualitative properties: color, size, and others. How many interleaved questions? which the? what's the score? Allows you to reveal their meaning. Children encounter ordinal counting in everyday life (Lena, get up first), in physical education classes, when the teacher makes different rebuildings (first link, second link) in music classes.

The methodology of work on the section "quantity and count" in senior group.

Count within 10

To obtain the numbers of the second heel and learn to count up to 10, they use techniques similar to those used in the middle group. The formation of numbers is demonstrated on the basis of a comparison of two sets of objects. In one lesson, you need to get two new numbers at once, so that the children learn the principle of obtaining the previous and subsequent numbers. Didactic games are used to consolidate counting skills. GAMES "What has changed?", "Fix the mistake." Several groups of objects are placed on a flannelograph, a board, and numerical figures are placed nearby (cards with a certain number of circles). The player closes his eyes, the leader swaps numerical figures or removes one object from any group, making up numerical cards without change. Children must find the error. GAME "How much?" On the board are fixed cards with a different number of objects. The facilitator makes a riddle. The one who guesses must count the items on the card and show a numerical figure. For example: a girl is sitting in the dark, and the braid is on the street. The players, who guessed that it was a carrot, count how many carrots are drawn on the card and show the number 4. For the first time in the older group, they learn to count in different directions. Children are explained that to answer the question how much? It doesn't matter which direction the score is taken from: right to left, top to bottom, or bottom to top. Later, we give the children an idea that it is possible to count objects located not only in a row, but also in a variety of ways (in a circle, diagonally, in an indefinite group). Conclusion: you can start counting from any object and lead in any direction, but it is important not to miss a single object and not to count one twice.

Ordinal count up to 10

Continuing to teach counting in the older group, the teacher clarifies the difference between the quantitative and ordinal values ​​of the number. When they want to find out how many objects, they count one, two, three ... But when you need to find the order, the place of objects among others, they count differently: first, second ...

As a counting material, first use homogeneous objects that differ in color or size (flags different color), and later - sets of objects of the same type (dishes, animals), as well as plotless materials (strips, figures). A new direction of work is to show the dependence of the ordinal place of an object on the direction of the account. For example: does the teacher put 3 different cars on the table in a row (truck, car, tractor)? It suggests answering the question: how many are there? Then the game begins: the cars went to the gas station: the truck goes first, the second - the car? the third is a tractor. The teacher asks questions: which is the passenger car? tractor? But here is a car sign on the way, showing that you can’t go further, you have to go back. The cars turn in the other direction: now the one that was last is the first. Cars drive, and the teacher finds out which each of the cars is in a row. The ability to distinguish between quantitative and ordinal counting can be consolidated in didactic games.

The game "Which toy is gone?".

Arrange the toys in a certain order. Children close their eyes, and the leader removes one of the toys.

The game "Who will call first?".

Children are shown a picture in which objects are arranged in a row (left to right or top to bottom). The facilitator agrees where to start counting items: from left to right, top to bottom. Hits with a hammer several times. Children must count the number of sounds and find the toy that stands in the indicated place. Whoever names the toy first wins.

Number Comparison

Children learn to make connections and relationships between adjacent numbers. Connections between numbers - definition: which number is greater, which is less. Relations between numbers - definition: how much one number is greater (less) than another. All numbers within 10 are compared. It is advisable to start with the numbers 2 and 3, and not o1 and 2. A visual basis for comparing numbers is a comparison of two sets of objects. For example, by comparing 2 nesting dolls with 3 dice, they find out that there are fewer nesting dolls than dice, and more dice than nesting dolls. This means that 2 is less than 3, and 3 is greater than 2. The use of the words “extra” and “not enough” helps to understand the reciprocal relationship between numbers. Comparing 4 chickens and 5 chickens, the teacher draws the attention of the children to the fact that 1 chicken is superfluous, there are 5 of them, which means that the number 5 is more than 4. However, there is not enough duckling, and there are 4 of them, which means 4 is less than 5.

Task options:

1. Comparison of groups of subjects presented conventional signs, models of geometric shapes.

For example, children guess who is more in the tram: boys or girls, if boys are represented on the board by circles, and girls by squares.

1. Inclusion of various analyzers. For example, raise your hand 1 time more than the buttons on the card; count down 1 square less than you hear sounds.
2. Using the number ladder. Blue and red mugs painted on both sides are laid out in rows of 5 (10) pieces. The number of circles in a row is successively increased by 1, and the “additional” circle is turned to the other side. The numerical ladder allows you to visualize the sequence of numbers in the natural series.

The quantitative composition of the number of units

Children are introduced to the composition of the number of units within 5.

Equipment:

A) items of the same type that differ in color, shape, size (sets of dolls, flags of different colors);

B) objects united by a generic concept (dishes, furniture, clothes, shoes, animals);

C) plotless material (geometric figures, stripes of different widths).

Algorithm for solving this problem

1. How is the group made up?
2. How many different things are in it?
3. How many items in total?
4. Name the objects and their quantity.

Task options:

1. Game "Name 3 (4.5) items
2. With elements of the competition "Who can name 3 (4.5) hats faster
3. Ball game "I know 5 names of girls"

Formation of quantitative representations in the preparatory group

Counting groups of objects

When consolidating the skills of counting and counting, it is important to exercise not only in counting individual objects, but also in groups consisting of homogeneous objects. Children are shown a group of objects (matryoshka). Questions "How many groups?" How many dolls are in each group? How many matryoshkas are there? Each time, a relationship is established between the number of groups and the number of items in the group. Children see: increase the number of objects in the group - the number of groups decreases and vice versa. Children are being prepared for the assimilation of the decimal number system, counting in tens.

The teacher has 10 circles on the board. Questions how many circles? About ten items can be said in another way: one dozen. Places 10 more circles on the next strip. Questions how many circles are there? We can say: another dozen. How many tens are there? Two dozen. What is more than 2 tens or 1? What is less? Conclusion: 2 tens is more than 1, a dozen is less than 2. You can introduce children to the use of counting in groups in everyday life: it is convenient to buy small items in dozens (buttons, hair clips, pins, eggs).

Verbal counting

To clarify knowledge about the sequence of the natural series of numbers, we use special exercises to the account in direct and reverse order. The teacher, starting with 1 item, sequentially adds items one at a time, each time asking the children about the number. Similarly, exercises are carried out for sequential reduction of numbers (there were 9 objects, one was removed, how much is left? Children “step” up and down the steps of the ladder, counting either the number of steps that have already passed, or the number of steps that they still have to go. (Let's count how many steps to the tumbler. We will count how many steps we have left to go to the tumbler: 10,9,8 ...)

Exercises with numbers.

Numerical figures from 1 to 10 are arranged in a row along the board, two figures are placed out of place. Children determine which figure is "lost". A number of figures can be arranged in reverse order.

Game "Conversation of numbers"

Summoned children receive numerical figures in their hands. Children are numbers, and which ones, numerical cards will tell them. Team playing: "Numbers, stand in order, starting from the smallest!" After that, the teacher invites you to tell about yourself. For example: “Number 4 said to number 5: I am one less than you! What will the number 5 answer him? And what will the number 6 say? To consolidate counting skills in forward and reverse order, games are used: “Name the missing number”, “Count further”, “Who knows, let him count further”.

The teacher explains the rules of the game "I will put toys on the table, and you count how many there are." So, there are 3 cubes on the table. The teacher puts another 1 - the child says "four", etc. Interest in such games increases if they are held in a circle, the teacher throws the ball to the children, passes the handkerchief. The rules of the game do not repeat the already named number, do not keep score from the beginning, from the number 1.

Establishment of mutually inverse relationships between adjacent numbers.

From exercises in comparing the numbers of sets of objects expressed by adjacent numbers, children move on to comparing numbers without relying on visual material.

2. Name a number greater than 5 (6.7) by 1.

1. Name the "neighbors of the number"

To perform such tasks, it is necessary to explain the meaning of the words “before” and “after”, “previous and “next” number. The expression "before" indicates that the numbers are less, and "after" are greater than the named. Worth up to 5? What after 5?

1. Name the numbers /3,4 numbers/ that come after 4,
2. Guess what number is missing between 7 and 5, 8 and 6?
3. Say 2 numbers, skipping 1 number between them.

Composition of a number from two smaller numbers

All ways of composition of numbers within the heel are shown.

The number 2 is 1 and 1, 3 is 2 and 1, 1 and 2, 4 is 3 and 1, 2 and 2, 1 and 3, 5 is 4 and 1, 2 and 3, 1 and 4.

There are 3 mugs of the same color on the typesetting canvas. turning reverse side the last circle, we ask “How much? How is the group made up? From 2 red and 1 blue circle. Then we turn over another one, find out how the group is now composed. Conclusion: the number 3 can be composed in different ways; from 2 and 1, from 1 and 2. To consolidate knowledge, we use the exercises:

1. Stories - tasks “3 swallows sat on the upper wire, 1 swallow moved to the lower wire. How many swallows are there? How are they sitting now? How else can they sit?
2. Assignments: for one child to take 3 acorns / pebbles / in both hands, the rest to guess how many are in each hand.
3. Game Guess the number. There are 3 to 5 circles on the card, the other card is turned over with the back side. You need to guess the number on the flipped card, if together they form the number 3 / 4.5 /.

Assimilation of the composition of the number of 2 numbers provides a transition to teaching children to calculate.

Introduction to numbers.

In the process of learning to count, the teacher shows different ways of designating a quantity. To do this, to the right of a group of objects / after counting them / they lay out the same number of sticks, hang out a counting card, a numerical figure. Then they show the way graphic symbol numbers - digit. Research by A.M. Leushina showed the effectiveness of acquaintance with numbers in parallel with the formation of two numbers at once. At the first lesson, the formation of numbers 1 and 2 is shown, the numbers 1 and 2 are shown. The number 1 is indicated by the number 1, poems are read "Here is one or one, very thin, like a knitting needle." Various survey actions are widely used: tracing a figure with a finger, drawing in the air, shading contour figures, as well as using figurative comparisons during the survey (a unit is like a soldier, 8 is like a snowman). The number 10 deserves special attention, since it is written as two digits 0 and 1. Therefore, it is first necessary to introduce children to zero. Children get the concept of zero by completing the task of counting objects one at a time. For example, there are 9 cubes and the number 9 on the table. Sequentially removing one cube at a time, the teacher asks to recount and show the corresponding number. When 1 cube remains on the table, the teacher offers to remove it. How many cubes now? None or zero dice. Zero cubes is indicated by the number 0. There are 0 cubes on the table, and Kolya has 1 cube. Where are more cubes? This means that 1 is greater than 0, 0 is less than 1. When all the numbers have been studied, didactic games are used to consolidate them.

The game "The figure got lost", "Confusion". The numbers are laid out on the table in order, one or more numbers are swapped. Children must find these changes. The game "What number is missing?" The game also removes 1-2 numbers. The players not only notice the changes, but also say where which number is and why. The game "Find the neighbors of the figure." Each child is offered a card with a picture of a number, and he must name the previous and subsequent numbers. The game "Remove the numbers." You can end the lesson with a game if the numbers are not needed in the future. Numbers are laid out in front of everyone on the tables. Children take turns guessing riddles about numbers. Each child, guessing what number is being discussed, removes it from the number row. Riddles can be very different. For example, remove the number that comes after the number 6 before the number 4; remove the number, remove the number that shows how many times I will clap my hands: a number that occurs in the fairy tale about Snow White.

The division of the whole into parts.

With the help of this task, preparation for the assimilation of fractions is carried out.

Work sequence:

1. Dividing an object into parts by folding (bending) (Fold the square in half, into 4 parts)
2. Dividing an object into parts by cutting. (Cut a strip of paper into 2 parts, a square into 2 parts to make 2 triangles).
3. Dividing into parts of "delicious" things: cookies, apple, candy, etc. These tasks stimulate the activity of children in the assimilation of the material. / What to do if you need to buy only half a loaf of bread in the store, share cookies, an apple between girlfriends /.

Equalizing the whole object and parts, the children come to the conclusion: the whole is more than half, half is more than a quarter, the whole is more than a quarter. It is important to show children the need for precise actions when folding and cutting. Items can be divided into equal or unequal parts. Parts are called halves only when the parts are equal. Vocabulary work: divide into parts, whole, half, in half, one of two parts, one of 4 parts, one second, one fourth part. In subsequent classes, exercises are carried out in dividing geometric shapes into 2, 4, 8 parts and composing whole figures from parts. For example: how to fold and cut a square to get 2 equal rectangles? After the children master the measurement techniques, it is proposed to divide the stick, rail, plank into 2, 4, 8 equal parts. The guys see that these items do not add up, the learned methods of division are not suitable. How to be? The teacher lays out objects in front of the children that can be used as measurements. As a result, with the teacher, the children come to the conclusion that it is necessary to choose a suitable measure, measure a piece equal to the length of the object, divide the measure / fold / into the appropriate number of parts and then measure these parts on the object, make marks with a pencil. It is useful to exercise in the division of geometric shapes, drawn on paper in a cage. Children draw figures of a given size, and then, at the direction of the teacher, divide them into 2, 4 equal parts, measuring by cells.

Do-it-yourself didactic mathematical manual for preschoolers

Master class on making a didactic manual "Fun Account" for individual work with preschoolers

Counting is an activity with finite sets. The account includes structural components:

Purpose (to express the number of items as a number),

Means of achievement (counting process, consisting of a series of actions reflecting the degree of development of the activity),

Result (final number): the difficulty is presented for children in achieving the result of the count, that is, the result, generalization. Developing the ability to answer the question "how much?" in words a lot, a little, one two, the same, equally, more than ... speeds up the process of children's understanding of the knowledge of the final number when counting.

At the age of three to six years, children master the account. During this period they the main mathematical activity is counting. At the beginning of the formation of counting activity (the fourth year of life), children learn to compare sets element by element, by overlapping and applying, that is, they master the so-called "pre-numerical stage" of counting (A. M. Leushina). Later (fifth-seventh year of life) learning to count also occurs only on the basis of practical and logical operations with sets

A. M. Leushina determined six stages of development of counting activities in children. In this case, the first two stages are preparatory. During this period, children operate with sets without using numbers. Quantity is estimated using the words "many", "one", "none", "more - less - equally". These stages are characterized as sub-numerical.

The first stage can be correlated with the second and third years of life. The main goal of this stage is to get acquainted with the structure of the set. The main methods are the selection of individual elements in the set and the compilation of the set from individual elements. Children compare contrasting sets: many and one.

The second stage is also pre-numeric, however, during this period, children master the account in special classes in mathematics.

The goal is to teach how to compare adjacent sets element by element, i.e. compare sets that differ in the number of elements by one.

The main methods are superposition, application, comparison. As a result of this activity, children must learn to establish equality from inequality by adding one element, that is, increasing, or removing, that is, reducing, the set.

The third stage is conditionally correlated with the education of children of the fifth year of life.

The main goal is to familiarize children with the formation of numbers.

Typical methods of activity are comparing adjacent sets, establishing equality from inequality (they added one more object, and they became equal - two, four, etc.).

The result is the total of the score, indicated by a number. Thus, the child first masters the account, and then realizes the result - the number.

The fourth stage of mastering counting activity is carried out in the sixth year of life. At this stage, children are introduced to the relationship between adjacent numbers of the natural series.

The result is an understanding of the basic principle of the natural series: each number has its place, each subsequent number is one more than the previous one, and vice versa, each previous one is one less than the next.

The fifth stage of learning to count corresponds to the seventh year of life. At this stage, children understand the account in groups of 2, 3, 5.

The result is bringing children to an understanding of the decimal number system. This is where the education of preschool children usually ends.

The sixth stage in the development of counting activity is associated with the mastery of the decimal number system by children. In the seventh year of life, children get acquainted with the formation of numbers of the second ten, begin to realize the analogy formed by any number based on the addition of one (increase: і numbers per unit). Understand that ten units make one ten. If you add ten more units to it, you get two tens, etc. A conscious understanding of the decimal system by children occurs during the period of schooling.

All work on the development of counting activities preschoolers pass strictly in accordance with the requirements of the program content. In each age group of the kindergarten, tasks are indicated for the development of elementary mathematical representations in children, in particular, for the development of counting activities, in accordance with the "Program of Education and Training in Kindergarten".

IN THE SECOND JUNIOR GROUP begin to carry out special work on the formation of elementary mathematical representations. The further mathematical development of children depends on how successfully the first perception of quantitative relations and spatial forms of real objects is organized. Toddlers don't learn to count, but organizing a variety of actions with objects, lead to the assimilation of the account, create opportunities for the formation of the concept of a natural number.

Program material of the second junior group limited pre-numeric learning period.

In children ideas about singularity and plurality are formed objects and objects. In the process of exercises, combining objects in the aggregate and breaking up the whole into separate parts, children master the ability to perceive in unity each individual object and the group as a whole. In the future, when getting acquainted with numbers and their properties, this helps them to master the quantitative composition of numbers.

Children are learning group items one at a time, a then on two or three signs- color, shape, size, purpose, etc., pick up pairs of objects. At the same time, children perceive a set of objects formed in a certain way as a single whole, presented visually and consisting of single objects. They make sure that each of the objects has common quality features (color and shape, size and color).

Grouping items on the grounds develops in children the ability to compare, to carry out logical operations of classification. From the understanding of the selected features as properties of objects in the older preschool age, children move on to mastering the community in terms of quantity. They develop a more complete understanding of the numbers.

In children an idea is formed about subject diverse sets: one, many, few (meaning several). They gradually master the ability to distinguish between them, to compare, to single out independently in the environment.

METHODS AND TECHNIQUES OF TRAINING

Children's education junior group wears visual-effective nature. The child acquires new knowledge on the basis of direct perception when he follows the action of the teacher, listens to his explanations and instructions, and acts with the didactic material himself.

Lessons often start with elements of the game, surprise moments- the unexpected appearance of toys, things, the arrival of guests, etc. This interests and activates the kids. However, when highlighting a property for the first time and important focus on it children, game moments may be absent.

Elucidation of mathematical properties carry out based on item comparison, characterized by either similar or opposite properties(long - short, round - non-round, etc.). Are used items, whose knowable property is pronounced. that are familiar to children, without unnecessary details, differ no more than 1-2 signs.

Perceptual Accuracy contribute movements (hand gestures), circling a model of a geometric figure (along the contour) with a hand helps children to more accurately perceive its shape, and holding a hand along, say, a scarf, ribbon (when compared in length) - to establish the ratio of objects precisely on this basis.

Children teach to consistently identify and compare homogeneous properties of things. (What is it? What color? What size?) Comparison is based on practical comparison methods: overlay or application.

Great importance is attached work of children with didactic material. Toddlers are already able to perform rather complex actions in a certain sequence (impose objects on pictures, sample cards, etc.). However, if the child fails to complete the task, works unproductively, it loses interest quickly tired and distracted from work. Considering this, the teacher gives the children a sample of each new way of doing things.

In an effort to prevent possible errors, he shows all the methods of work and explains in detail the sequence of actions. At the same time, explanations should be extremely clear, clear, specific, given at a pace accessible to the perception of a small child. If the teacher speaks in a hurry, then the children stop understanding him and get distracted. The teacher demonstrates the most complex methods of action 2-3 times, each time drawing the attention of the kids to new details. Only repeated demonstration and naming of the same methods of action in different situations with a change in visual material allow children to learn them.

In the course of work, the teacher not only points out mistakes to children, but also finds out their causes. All errors are corrected directly in action with didactic material. Explanations should not be intrusive, wordy. In some cases, children's mistakes are corrected without explanation at all. (“Take it in your right hand, in this one! Put this strip on top, you see, it is longer than this one!” Etc.) When the children learn the method of action, then showing it becomes unnecessary.

Small children are much better assimilate emotionally perceived material. Their memorization is characterized by unintentionality. Therefore, in the classroom are widely used game techniques and didactic games. They are organized in such a way that, if possible, all children participate in the action at the same time and they do not have to wait for their turn. There are games associated with active movements: walking and running. However, using playing tricks, teacher does not allow them to distract children from the main(albeit elementary, but mathematical work).

Spatial and quantitative relations can be reflected at this stage only with words. Each new mode of action, assimilated by children, each the newly highlighted property is fixed in the exact word. The teacher pronounces the new word slowly, highlighting it with intonation. All the children together (in chorus) repeat it.

The most difficult for toddlers is reflection in speech of mathematical connections and relationships, since it requires the ability to build not only simple, but also complex sentences, using the adversative conjunction A and the connective I. First, you have to ask the children auxiliary questions, and then ask them to tell you everything at once. For example: How many pebbles are on the red stripe? How many pebbles are on the blue stripe? Now tell me right away about the pebbles on the blue and red stripes. So baby lead to the reflection of connections: There is one pebble on the red stripe, and many pebbles on the blue one. The teacher gives an example of such an answer. If the child finds it difficult, the teacher can start the answer phrase, and the child will finish it.

For children to understand the way of action they are offered to say in the course of work what and how they are doing, and when the action has already been mastered, before starting work, make an assumption about what and how to do. (What needs to be done to find out which board is wider? How to find out if the children have enough pencils?) Connections are established between the properties of things and the actions by which they are revealed. At the same time, the teacher does not allow the use of words whose meaning is not clear to children.

In the process of various practical actions with aggregates, children learn and use in their speech simple words and expressions, denoting the level of quantitative representations: many, one, one at a time, not one, not at all (nothing), few, the same, the same (in color, shape), the same, equally; as much as; more than; less than; each of all.

So , at preschool age, in the pre-numeric period of training, children master practical methods of comparison (overlay, application, pairing), as a result of which mathematical relationships are comprehended: “more”, “less”, “equally”. On this basis, the ability to identify the qualitative and quantitative characteristics of sets of objects, to see the commonality and differences in objects according to the selected characteristics is formed.

MIDDLE GROUP PROGRAM directed for further development mathematical concepts in children.

One of the main program tasks education of children of the fifth year of life consists in the formation of their ability to count, the development of appropriate skills and on this basis development of the concept of number.

Formed at primary preschool age (2-4 years) the ability to analyze sets of objects in terms of their number, to see the sequence and differences in terms of qualitative and quantitative characteristics, the idea of ​​equality and inequality of subject groups, the ability to properly answer the question "how much?" (the same, more here than there) is the basis for mastering the account.

Middle preschool age(fifth year of life) in the process of comparing two groups of objects, highlighting their properties, as well as counting in children representations are formed:

1. about the number, allowing them to give an accurate quantitative assessment of the totality, they master the techniques and rules for counting objects, sounds, movements (within 5);

2. about the natural series of numbers (sequence, place of a number) they are introduced to the formation of a number (within 5) in the process of comparing two sets of objects and increasing or decreasing one of them by one;

3. Attention is paid to comparing sets of objects by the number of their constituent elements (both without counting and in combination with counting), equalizing sets that differ in one element, establishing the relationship of “more - less” relationships (if there are fewer bears, then there are more hares);

4.children, having mastered the ability to count objects, sounds, movements, answer the question “how much?”, Learn to determine the order of objects (first, last, fifth), answer the question “which?”, i.e. practically use a quantitative and ordinal account;

5. children develop the ability to reproduce sets, counting objects according to a pattern, according to a given number from a larger number, memorize numbers, an idea of ​​a number as a common feature of various sets (objects, sounds), they are convinced that the number is independent of non-essential features (for example, colors occupied area, sizes of objects, etc.), use various methods of obtaining groups equal and unequal in number and learn to see identity (identity), generalize the number of objects of sets (the same number, four, five, the same number, i.e. . number).

6. ideas are formed about the first five numbers of the natural series (their order, the relationship between adjacent numbers: more, less), skills are developed to use them in various everyday and game situations.

Learning to count within 5. Teaching counting should help children understand the purpose of this activity (only by counting the objects can you accurately answer the question how much?) And master its means: naming numerals in order and correlating them to each element of the group. It is difficult for four-year-olds to learn both sides of this activity at the same time. Therefore, in the middle group Learning to count is recommended to be carried out in two stages.

AT THE FIRST STAGE based comparison of the sizes of two groups items for children reveal the purpose this activity ( find the final number). They are taught to distinguish between groups of objects in 1 and 2, 2 and 3 elements and name the final number based on the teacher's score. Such "collaboration" is carried out in the first two lessons.

Comparing 2 groups of items, located in 2 parallel rows, one under the other, the children see which group has more (less) objects or they are equally divided in both. They designate these differences with numeral words and make sure: in groups there are equal numbers of objects, their number is indicated by the same word (2 red circles and 2 blue circles), they added (removed) 1 object, they became more (less), and the group became denoted by a new word.

Children begin to understand that each number represents a certain amount items, gradually make connections between numbers (2 > 1, 1 < 2 и т. д.).

Organizing comparison of 2 populations subjects, in one of which there is 1 more subject than in the other, the teacher counts objects and draws attention children on the total. He first finds out which items are larger (less), and then which number is larger, which is smaller. The basis for comparing numbers serves distinction children set sizes(groups of) objects and their names are numerals.

Important for the children to see not only how you can get the next number (n+1), but also how to get previous number: 1 out of 2, 2 out of 3, etc. (n - 1). The teacher either increases the group by adding 1 item, then reduces it by removing 1 item from it. Every time finding out which items are more, which are less, goes to comparing numbers. He teaches children to indicate not only which number is greater, but also which is smaller (2> 1, 1<2, 3>2, 2<3 и т. д.). Отношения "more", "less" always considered in connection with each other. In the course of work, the teacher constantly emphasizes: in order to find out how many objects in total, you need to count them.

Focusing the attention of children on the total, the teacher accompanies naming it generalizing gesture(circling a group of objects with a hand) and names(i.e. pronounces the name of the item itself). In the process of counting, the numbers are not named (1, 2, 3 - only 3 mushrooms).

Children are encouraged name and show,where 1, where 2, where 3 items, which serves to establish associative links between groups, containing 1, 2, 3 items, and corresponding numeral words.

great attention give reflection in the speech of children of the results of comparison of aggregates objects and numbers. ("There are more matryoshkas than roosters. There are fewer roosters than nesting dolls. 2 is more, and 1 is less, 2 is more than 1, 1 is less than 2.")

AT THE SECOND STAGE children master counting operations. After the children learn to distinguish between sets (groups) containing 1 and 2, 2 and 3 objects, and understand what exactly to answer the question how much? it is possible, only by counting the objects, they are taught keep count of objects within 3, then 4 and 5.

From the first lesson numeracy should be structured in such a way that for the children to understand, how each subsequent (previous) number is formed, i.e. general principle of constructing natural series. Therefore, the display of the formation of each next number is preceded by a repetition of how the previous number was obtained.

Sequential comparison of 2-3 numbers to show children that any natural number greater than one and less than another, "neighbor" (3 < 4 < 5), разумеется, except for one, less than which there is no no natural number. In the future, on this basis, children will understand the relativity of the concepts "more", "less".

They must learn independently transform sets items. For example, decide how to make the items equal, what needs to be done to make (remain) 3 items instead of 2 (instead of 4), etc.

In the middle group develop numeracy skills. The teacher repeatedly shows and explains counting techniques, teaches children to count objects with their right hand from left to right; in the process of counting, point to objects in order, touching them with your hand; having named the last numeral, make a generalizing gesture, circle a group of objects with your hand.

Children usually find it difficult to agree numerals with nouns(the numeral one is replaced by the word times). The teacher selects masculine, feminine and neuter items for counting (for example, color images of apples, plums, pears) and shows how words one, two change depending on which items are counted. The child counts: "One, two, three." The teacher stops him, picks up one bear and asks: "How many bears do I have?" - "One bear", - the child answers. "That's right, one bear. You can't say "once a bear." And you need to count like this: one, two ..."

To consolidate counting skills used a large number of exercises. Exercises in the account should be in almost every lesson until the end of the school year. In order to create the prerequisites for independent counting, they change the counting material, the classroom environment, alternate teamwork with independent work of children with benefits, and diversify techniques. A variety of game exercises are used, including those that allow not only to consolidate the ability to count objects, but also to form ideas about the shape, size, and contribute to the development of orientation in space. Counting is associated with comparing the sizes of objects, with distinguishing geometric shapes and highlighting their features; with the definition of spatial directions (left, right, front, rear).

Children are offered to find a certain number of objects in the environment. First, the child is given a sample (card). He is looking for as many toys or things as there are circles on the card. Later, children learn to act only on the word. ("Find 4 toys.") When working with handouts, it must be taken into account that children still do not know how to count objects. Tasks are initially given such that require them to be able to count, but not to count.

Application of the account in different types children's activities.

Teaching counting should not be limited to conducting formal exercises in the classroom. The teacher should strive to ensure that the account is used by children everywhere, and the number, along with the quantitative and spatial characteristics of objects, would help children better navigate the surrounding reality.

The teacher constantly uses and creates various life and game situations that require children to use counting skills. In games with dolls, for example, children find out if there are enough dishes for receiving guests, clothes to collect dolls for a walk, etc. In the game of "shop" they use receipt cards on which a certain number of objects or circles are drawn. The teacher promptly introduces the appropriate attributes and prompts game actions, including counting and counting objects.

In everyday life, situations often arise that require counting: on the instructions of the teacher, children find out whether certain benefits or things are enough for children sitting at the same table (boxes with pencils, coasters, plates, etc.). Children count the toys they took for a walk. Going home, check if all the toys are collected. The guys love to simply count the items that they meet along the way.

Learning to count accompanied by conversations with children about the appointment, application of the account in various activities. In an effort to deepen the children's ideas about the meaning of counting, the teacher explains to them why people think they want to know when they count objects. He advises children to see what their mothers, fathers, grandmothers think.

So, in the middle group under the influence of training, counting activity is formed, the ability to count various sets of objects in different conditions and relationships.

IN THE SENIOR GROUP program is aimed at expanding, deepening and generalizing elementary mathematical concepts in children, further developing the activity of counting.

- continues Work on the formation of ideas about the number(quantitative characteristics) of sets, ways of forming numbers, quantification of quantities by measurement;

Children master the techniques of counting objects, sounds, movements by touch within 10, determine the number of conditional measures when measuring extended objects, volumes of liquids, masses of bulk substances;

Children learn to form numbers by increasing or decreasing a given number by one, equalize sets according to the number of items subject to quantitative differences between them in 1, 2 and 3 elements, as in the middle group, children count the number of objects according to the named number or pattern(numerical figure, card) or more (less) per unit, exercise in generalizing the number of objects of a number of specific sets that differ in spatial and qualitative features (shape, location, direction of counting, etc.) based on perception by various analyzers;

In order to prepare children for counting groups of their teaches the ability to split aggregates in 4, 6, 8, 9, 10 items in groups of 2, 3, 4, 5 items, determine the number of groups and the number of individual items;

Children get acquainted with the quantitative composition of numbers from units within 5 on specific objects and in the process of measurement, which clarifies and concretizes the idea of ​​a number, unit, place of a number in the natural series of numbers;

- continues children's education distinction between quantitative and ordinal value of a number, skills are developed to apply quantitative and ordinal counting in practical activities;

During the comparison of sets and numbers, children learn numbers from 0 to 9, they learn to relate them to numbers, to distinguish, to use in games.

METHODS AND TECHNIQUES OF TEACHING ACCOUNT

Repetition of the past. In the middle group, children were taught to count objects within 5. Consolidation of the relevant ideas and methods of action serves as the basis for the further development of counting activities.

Comparison of two sets containing an equal and unequal (more or less by 1) number of objects within 5 allows you to remind children how the numbers of the first heel are formed. In order to bring to the consciousness of children the meaning of counting and methods of piece-by-piece comparison of objects of two groups one to one to clarify the relationship "equal", "not equal", "more", "less", tasks are given to equalize the aggregates. ("Bring so many cups so that all the dolls have enough and there are no extra ones", etc.)

Much attention is paid to strengthening counting skills; children are taught to count objects from left to right, pointing to objects in order, agree on numerals with nouns in gender and number, name the result of the count. If one of the children does not understand the final value of the last number called when counting, then he is invited to circle the counted objects with his hand. A circular generalizing gesture helps the child to correlate the last numeral with the entire set of objects. But in working with children of 5 years old, as a rule, it is no longer needed. Children can now be offered to count objects at a distance, silently, that is, to themselves.

Children are reminded of the methods of counting sounds and objects by touch. They reproduce a certain number of movements in a pattern and a specified number.

Count within 10. To obtain the numbers of the second heel and learn to count up to 10, methods are used similar to those used in the middle group to obtain the numbers of the first heel.

The formation of numbers is demonstrated on the basis of a comparison of two sets of objects. Children must understand the principle of obtaining each subsequent number from the previous one and the previous one from the next (n + 1). In this regard, in one lesson it is advisable to consistently receive 2 new numbers, for example, 6 and 7. As in the middle group, the demonstration of the formation of each next number is preceded by a repetition of how the previous number was obtained. Thus, at least 3 consecutive numbers are always compared. Children sometimes confuse the numbers 7 and 8. Therefore, it is advisable to conduct more exercises in comparing sets consisting of 7 and 8 elements.

Healthy compare not only collections of objects of different types(for example, Christmas trees, mushrooms, etc.), but also groups of objects of the same type are divided into parts and compared with each other(apples are large and small), finally, a collection of objects can be compared with its part. ("Who is more: gray bunnies or gray and white bunnies together?") Such exercises enrich the experience of children with multiple objects.

When assessing the numbers of sets of objects, five-year-old children are still disoriented by the pronounced spatial properties of objects. However, now it is not necessary to devote special classes to showing the independence of the number of objects from their size, shape, location, and the area they occupy. It is possible to simultaneously teach children to see the independence of the number of objects from their spatial properties and to receive new numbers.

The ability to compare collections of objects of different sizes or occupying different areas creates prerequisites for understanding the meaning of the account and piece matching techniques elements of two compared sets (one to one) in revealing the relations "equal", "greater", "less". For example, to find out which apples are more - small or large, which flowers are more - marigolds or daisies, if the latter are located at greater intervals than the former, you must either count the objects and compare their number, or compare the objects of 2 groups (subgroups) one to alone. Different methods of comparison are used: overlay, application, use of equivalents. Children see: in one of the groups there was an extra object, which means there are more of them, and in the other - one object was not enough, which means there are fewer of them. Based on a visual basis, they compare numbers (so 8 > 7, and 7< 8).

Equalizing groups by adding one item to a smaller number or removing one item from a larger number, children learn how to get each of the compared numbers. Considering the relationship of the relationship "greater", "less" will help them further understand the reciprocal nature of the relationship between numbers (7\u003e 6, 6< 7).

Children should tell how each number was received, that is, to what number of objects and how much was added or from what number of objects and how much was taken away (removed). For example, 1 apple was added to 8 apples, it became 9 apples. They took 1 out of 9 apples, 8 apples remained, etc. If the guys find it difficult to give a clear answer, you can ask leading questions: "How much was it? How much was added (removed)? How much was it?"

Change of didactic material, varying tasks help children better understand how to get each number. Receiving a new number, they first act as directed by the teacher (“Add 1 apple to 7 apples”), and then independently transform the aggregates. Achieving conscious actions and answers, the teacher varies the questions. He asks, for example: "What needs to be done to make 8 cylinders? If 1 is added to 7 cylinders, how many will there be?"

To strengthen knowledge, it is necessary to alternate team work with independent work. children with handouts. The child matches 2 sets by laying out items on a card with 2 free strips. Demonstration of methods for obtaining a new number (comparison of 3 neighboring members of the natural series) usually takes at least 8-12 minutes, so that the performance of monotonous tasks does not tire the children, similar work with handouts is carried out more often in the next lesson.

To consolidate counting skills within 10 use a variety of exercises, such as "Show the same." Children find a card on which the same number of objects are drawn as the teacher showed. ("Find as many toys as there are circles on the card", "Who will quickly find which toys we have 6 (7, 8, 9, 10)?".) To complete the last 2 tasks, the teacher makes groups of toys in advance.

When children are introduced to all numbers up to 10, they are shown that to answer the question how many? no matter which direction the score is taken. They themselves are convinced of this by counting the same objects in different directions: from left to right and from right to left; top down and bottom up. Later, children are given an idea of ​​what You can count objects located not only in a row, but also in a variety of ways. They count toys (things) arranged in the form of different figures (in a circle, in pairs, in an indefinite group), images of objects on a lotto card, and finally, circles of numerical figures.

Children are shown different ways of counting the same objects and learn to find more convenient (rational), allowing calculate quickly and correctly items. Recounting the same objects in different ways (3-4 ways) convinces children that you can start counting from any object and lead it in any direction, but at the same time you must not skip a single object and not count one twice. Specially complicate the shape of the arrangement of objects.

If the child is mistaken, then they find out what mistake was made (missed an object, one object counted twice). The teacher, counting the items, may intentionally make a mistake. Children follow the actions of the teacher and indicate what his mistake was. They conclude that it is necessary to remember well the object from which the account was started, so as not to miss any of them and not to count the same object twice.

So quantitative representations in children 5-6 years old, formed under the influence of training, are more generalized than in the middle group. Preschoolers count objects regardless of their external features, generalize by number. They accumulate experience in counting individual objects, groups, using conditional measures.

The skills learned by children to compare numbers on a visual basis, to equalize groups of objects by number indicate the formation of their ideas about the relationship between the numbers of the natural series.

Counting, comparison, measurement, elementary operations on numbers (reduction, increase by one) become available to children in various types of their educational and independent activities.

In the program PREPARATORY FOR SCHOOL GROUP the following areas can be distinguished:

1. Development of counting, measuring activities: accuracy and speed of counting, reproduction of the number of objects in more and less by one of their given number; preparation for the assimilation of numbers based on measurement, the use of numbers in various types of gaming and household activities.

2. Improving the ability to compare numbers, understanding the relativity of the number: when comparing the numbers 4 and 5, it turns out that the number 5 is greater than 4, and when comparing the numbers 5 and 6 - 5 is less than 6. Refine

math score is an action that allows you to determine the amount of something. The score can be quantitative or ordinal.

Quantitative

quantitative account is the determination of the number of objects. A quantitative account allows you to answer the question how much? .

For example, to find out the number of desks in a class or how many trees grow in a garden, you need to count them. The quantitative account lies in the fact that, each time separating one object after another (actually or only mentally), we name the number of separated objects. For example, counting desks in a class, we mentally separate one desk after another and say: one, two, three, four, five, etc. If, when separating the last desk, we said, for example, eight, then there are only eight desks in the class . The number eight in this case is the result of counting.

Score result is the number of items resulting from their count.

The result of the count does not depend on the order in which the items are counted.

So, counting the desks in the class, we get the same number, regardless of whether we count from the front desks to the back or vice versa - from the back to the front. It is only important that when counting the desks, not a single desk is skipped and not a single one is counted twice.

The number at which there is a name of those units from the account of which it was obtained is called named. In our case, since we counted the desks, the number eight is named (eight desks). A number that does not have a unit name is called abstract.

Ordinal

ordinal count- this is the definition of the number of objects and the place of each object relative to others. The ordinal account allows you to answer the question what? (for example, which one in a row? or which one in order?).

For example, to determine the number of pencils, you can use a quantitative account and count the pencils in any order:

But if you need to find out what the green pencil is in the account, then you should use the ordinal account. In this case, each pencil receives a number indicating which account it goes to:

Since the pencils are stacked next to each other, the green pencil will be third if counted from left to right, and fourth if counted from right to left.

With ordinal counting, if all items are counted, then the result of the count will be a number indicating the order of the last item counted. In our case, since the last pencil counted is the sixth, the total number of items is six.

Number is the ordinal number of an object in a series of other objects.