Simple ways to teach your child to count. Counting is fun and easy! How easy is it to teach a child to count in his head? Numeracy training 1 3 years

Peculiarities of mathematical perception of a preschooler

In order for our classes to only benefit the baby, it is necessary to represent his real capabilities and needs. We must understand that a small child’s thinking apparatus is still immature, and he does not know how to fully generalize and draw conclusions. So a two-year-old baby can, poking his finger at objects, followIt’s easy to pronounce:
- One, two, three, four.
However, to the question: “How many items are there in total?” - the child cannot answer yet. Only at three and a half is he ready to begin meaningful, rather than mechanical, teaching of mathematics. He is already able to learn to add and subtract numbers within five in his head, but the child is usually not yet able to do the same actions with large numbers until he is four or four and a half years old.
It is completely normal for preschool children to believe that any mathematical operation is true only at the moment and only with these objects. Kids believe that if you move objects apart, there will be more of them, and if you put them closer to each other, then there will be fewer of them. If you move or change the position of objects, their number will also change. The kid, adding 4 and 3, will definitely count all the objects first:
- 1, 2, 3, 4, 5, 6, 7, - and only after that will it give an answer.
A more mature child will begin to count and reason differently:
- There are 4 objects here, so 4 + 1 + 1 + 1 = 7.
The baby also does not quite correctly imagine the volume and weight of objects. The preschooler believes that the flattened candy has become smaller, and the elongated one has become larger, and that cotton wool is always lighter than iron, since he relies on his feelings, and not on the incomprehensible readings of the scales.
The first to notice and describe such features of the development of preschoolers was the French psychologist Jean Piaget. They are called “Piaget’s phenomena” in his honor.
Many of these phenomena in the process of growth and learning of the child weaken by 6-7 years, but some of them persist until 9-10 years. Despite this, all children can learn to count, add, subtract and solve simple problems by school.

Where does mathematics begin?

Any learning goes through three stages: habituation, understanding and meaningful memorization. At the same time, mathematics should not be something abstract, but a natural part of a child’s life, otherwise he will soon forget everything we taught him.
First, while playing and talking with the child, we teach him to compare objects and their properties, to distinguish a large thing from a small one, long from short, heavy from light, round from rectangular, and much more.
Usually, even before a child can understand what simple counting is, we mention numbers and mathematical concepts in conversation with him:
- Once upon a time there were three bears.
- You have a lot of toys. Share with Seryozha!
- Your bucket is smaller than mine.
- Please give Masha one pig, and take the other for yourself.
- Do you want to play alone or will you go with me?
- You have two hands, which means there were two mittens. Where's the second mitten?
- Wait five minutes, please.

Along with the poems of Agnia Barto, children are usually asked to learn a little rhyme about a bunny.
One, two, three, four, five -
The bunny went out for a walk.

As a result, most children after three and a half years old can count, and even add and subtract within four to five. However, they may not know this, and they need help to demonstrate their knowledge, but first the child must learn to count meaningfully, and not mechanically.

Understanding counting in play and movement

“Olenka willingly counts everything and knows how many objects there are, and yet I’m not sure that Olenka counts intelligently enough.
To make the counting more meaningful, Olenka and I slightly transformed the famous rhyme:
We shared an orange
There are many of us, but he is one.
This slice is for the hedgehog.
This slice is two for the siskin.
This slice is for kittens - three.
This slice is for ducklings - four.
This slice is five for the beaver.
And for the wolf - peel!
The wolf is angry - trouble,
Run away in all directions!”

Understanding counting is sometimes a rather difficult process and can take quite a lot of time, so we, without rushing or getting upset, try all new techniques and games.
“Once again I tried to bring Olenka closer to understanding the account.
First, I lined up four toys one after another. Then we counted them and assigned a serial number to each one. Then we discussed which animal comes before and which comes after, for example, the bunny. I tried to ask clear questions:
-Who is standing in front of the bunny? Who comes after the bunny?
Then they remembered a cartoon about a kid who could count to 10, and again they counted everyone:
- Dog - 1, bunny - 2, fox - 3, cat - 4.
And only after that I began to ask:
- What number comes after one? What number comes before 2?
Olenka clearly answered both questions, but since the usual ten minutes of our classes came to an end, we had to take a break.”
Only when a child can clearly say without errors which number is in front of any of the first five numbers and which is behind, we can assume that he understands what he is doing and move on to understanding counting to ten and at the same time mastering addition and subtraction.

What's the best way to represent a number?

In order for a child to distinguish different numbers well, images of these numbers must appear in his mind. Of course, a child can create these images without us, but we can help him find more suitable and capacious ones. Colored dots of a large children's domino are best suited for this. However, they can also be replaced with balls, bunnies or daisies. The main thing is that the objects are small enough that they can be represented as domino points if desired. Agree that it is easier to imagine the number five if it is depicted compactly in the form of small objects, so it is impossible to come up with anything more convenient than images on dominoes.

However, a child has a great need to touch everything and see for himself, so the children and I began making an additional aid from quickly hardening plasticine, which we called “mathematical balls.” These are several small quadrangles, each with five recesses for balls. The round holes are arranged in the same order as the dots on the dominoes. You can insert a ball (or other convenient shape) into each recess. You can transfer the balls to another, identical quadrilateral, and notice how the same numbers look, or think about what to do to make these numbers equal.

The clarity of the manual and the fact that a child can transform one number into another with his own hands greatly helps him to more easily understand how different numbers differ. At this stage this is a very important task. This is what distinguishes a child who can count from a child who simply memorized numbers without any understanding and cannot actually count.

Forming images of numbers from 1 to 5

We divide this important topic in teaching children into four stages.

1. Remember what the numbers from one to five look like. We learn to count to five and get used to the correct layout of numbers in squares in the form of domino points.
Educational:
- These are houses. Bunny balls live in them. Let's count how many bunnies live in each house.
After this, the teacher invites the child to populate another house with the same number of characters and in the same order.

2. We transform passive knowledge into active ones. To do this, let's play our favorite game: “Guess what I hid.” It will help your child learn to find out how many balls are placed on one square, without even counting, and remember which numbers correspond to a given number of balls.

It is better to start with two quadrangles, which in the game can be called by different names that are more pleasant for the child’s hearing, for example, houses or cars. We can, of course, decorate our squares with a roof or wheels for this, but kids usually have such a good imagination that it’s enough to say that this square is now a magic carpet and they can already see it. We also need plastic numbers, from 1 to 5 for now.

The flow of the game might be something like this:
- Look, I have two houses. These colored balls live in everyone. How many red balls live in the first house, and how many yellow balls live in the second? That's right, there are 3 balls in the first house, and four in the second house. Now a cloud (a piece of paper) has crawled onto the house. How many balls are hidden under the cloud? That's right, a cloud covered the house with three balls. Now find the numbers 3 and 4 in the box and put the three next to the house in which three balls live, and where should we put the four? Of course, next to the house where 4 balls live.

Gradually we increase the number of hidden “houses” to 3-4, not forgetting to come up with new plots for the game. For example, somehow our squares turned into sea ships, and our balls into sailors. Some of the ships hid behind a rock, and I had to urgently remember how many sailors on each ship needed to be saved.

For greater clarity, we invite the child to close his eyes and tell from memory what a number looks like, and then open his eyes and draw it on paper or type it himself on a square.

3. Fixing the material. At this stage, it is useful to learn how to play the domino game itself. We play openly, turning all the dominoes upside down. Each player places his domino and loudly announces the number of dots, for example: “five - three.” It would be good if plush toys also took part in the game. The child and I can make moves for them. The one who runs out of dominoes or has fewer dominoes wins.
Of course, an adult wins very rarely - otherwise the game will quickly get boring.
Another fun game with an imaginary Baba Yaga. The teacher lays out a number series from one to five, then distracts the child and disrupts the order of the numbers.
Educational:
- Baba Yaga mixed up all the numbers again. Can you fix everything?
The child knows that this is a game, and Baba Yaga is imaginary, but she happily plays along with us:
- Look, Baba Yaga. We put all the numbers back in place!

4. Deepening the understanding of concepts: equally, the same number, the same number and how the numbers differ.

We take three squares and arrange them so that two of them have the same number of balls, for example 3, and the third has a different number, for example 4.
- Look, these are three nests. Sparrows sit in them. Which nest has the same number of sparrows? Is it equal in these two? What needs to be done so that they have the same number of chicks? That's right, remove one!
We invite the child to “guess” the difference between three dots and two, two and four, etc.
The answer, obvious to an adult, is not so obvious to a child. The child should answer something like this:
- Three differs from two by one point.

Using colored dominoes you can make the game more difficult and interesting. Compare domino dots according to three criteria: color, location and number of dots.

Mathematical outdoor games

“Sometimes Olin’s friend Yura joined our classes. They already knew how to add and subtract a little, but in order for the children to better understand the difference between addition and subtraction, we decided to go back a little. I remembered how, on a walk, Olya and Yura excitedly jumped up the stairs, counting the steps, and I suggested that they jump along the musical track with numbers. First they jumped forward, from number to number, from 1 to 10, each time saying:
- Add one more - it will turn out...
Then in the opposite direction from 10 to 1, saying:
- Let's subtract one more - it will work out...
The children loved the game so much that Yura now, no matter how he walks in, asks from the doorway:
- Are we going to jump and count today?
When the guys stopped making mistakes when adding and subtracting one, they began to count backwards and forwards by twos:
“Two, add one and one more - four, add one and one more - six...”

A rug like this can help us too. You can buy it or make it yourself by drawing on fabric or paper 10 cells with the first ten numbers of the digital series from 1 to 10. Below are several games that kids especially like.

1. The game will help your child learn to count meaningfully from one to ten and back. Of course, taking turns jumping with someone is more interesting.
“One, two, three, four, five - five, four, three, two, one,” says the baby, jumping from number to number back and forth. For variety, you can jump on one leg, then on two, or something else. Over time, we increase the number of cells to ten.
When the child remembers the order of counting, you can ask him to count out loud again, but with his eyes closed.

2. This game will help your child get closer to understanding what addition and subtraction are.
Now the baby is jumping from cell to cell saying:
- One, add one or two. Two, add one - three. Three, add one - four. Four, add one - five. Five, subtract one - four. Four, subtract one - three. Three, subtract one - two. “Two, subtract one - one,” the kid carefully pronounces, jumping from number to number back and forth.

3. Another game that is also perceived by children as fun entertainment. Despite this, it extremely clearly shows how numbers change with the addition or subtraction of one.

The child jumps from cell to cell with a “bush” and takes out one berry (or other toy) from it and puts it on each cell, saying:

1 berry, add 1, you get 2 berries; 2 berries, add 1, you get 3 berries; 3 berries, add 1, you get 4 berries; 4 berries, add 1, you get 5 berries.

Then in the opposite direction, collecting one berry with each jump:

5 berries, subtract 1, 4 berries remain; 4 berries, subtract 1, 3 berries remain; 3 berries, subtract 1, 2 berries remain; 2 berries, subtract 1, 1 berry remains; 1 berry, subtract one, nothing remains - zero.

At first, the child does not understand that he is already adding and subtracting one, he is just getting used to these concepts, understanding will come later.

"Grandmother! – Katyusha asks while walking, “let’s play numbers.” I'm a five and you're a four.
“Okay,” I agree, “so who’s first?”
- I, of course, I’m more! - the girl runs forward.
“Then I’m a seven now,” I say and stand in front of Katya.
“And I’m already ten,” says Katya and again stands in front.
“Okay,” I say, “then let’s play who is smaller.” I am a seven!
“And I’m a six,” Katyushka runs ahead again.
The little girl really likes this game, as there is a certain sense of competition in it.”

It’s very good when it’s not us, but the child who initiates the activities. Sometimes it is useful to put aside your own “adult” affairs so that the child can feel the importance of his small affairs.

Lesson 14.

Purpose of the lesson: Teach children to recognize numbers 1, 2 and 3. Solving constructive problems.

Exercise 1.

Purpose of the exercise: teach to recognize numbers.

The game “Find the Number” in this form: numbers are written on geometric figures: 1 2 3.

Editor's Note: one is written on triangles (3 pieces), two on circles (3 pieces), three on squares (3 pieces). The shapes come in three different colors (for example, blue, green and red) and three sizes (large, medium, small).

The figures are placed in a box. The child must sort them “by numbers”.

Find all the ones!

The game can be designed with a plot: Monkey, Baby Elephant and Parrot share the figures. The monkey gets a one, the Parrot gets a two, the Elephant gets a three. (If you introduced your child only to the number 1 or only to the numbers 1 and 2, play with these numbers. Then introduce a new number and play the game, including recognizing it.)

The tasks proceed sequentially: first you need to select all 1, then among the remaining figures we invite the child to find all 2, then 3. At this stage, the child may notice that threes are written on all the remaining figures, so there is no need to specifically select them.

When the grouping is completed, we ask the child the question: “Here you have all the ones, but what else interesting can you say about this bunch of figures?” (These are all triangles.)

If the child notices this, we consider the next two groups, making a generalization: “These are all circles. These are all squares.”

We suggest that another child, if he was nearby, do the same exercise (having mixed everything first), but choose triplets first, etc.

It would be interesting if the second child took into account the results of the previous work and immediately selected all the squares, knowing that only they had threes, etc.

Exercise 2.

Purpose of the exercise: training in solving constructive problems.

Editor's Note: to carry out exercises No. 2 and No. 3 you will need two sets of geometric shapes (one for you, the other for the child). Each set contains 2 circles, 10 squares and 11 triangles. All figures must be the same color, for example gray, and the same size. The triangle in this task is half of a square, i.e. it is rectangular and isosceles.

From these figures we lay out the “Machine”. (We lay it out in front of the child, accompanying this work with the words: square, square, circle...)

Exercise 3.

Purpose of the exercise: development of constructive activity. Training in quantitative design analysis.

Accompanying the plot with toys or drawings “Hedgehog” and “Bunny”, we complement the design of the “drawing”, pausing after each figure so that the child repeats our actions:

The hedgehog went to the store for groceries, and the bunny remained waiting for him in the house. Show me which direction the car is going. (The child shows the direction of movement with his finger.)

A Hedgehog rides through the forest past the fir trees:

Show me the tallest tree, the shortest one.
Arrived at the store:

I bought bread, milk, carrots, cabbage, apples and went back:
- Show me where he’s going now? Which way?

Show me the big house, the little house. Let's count the trees: first, second, third.

If the child cannot name the ordinal numbers himself, take the child by the hand and, pointing his finger at the Christmas trees, name the ordinal numbers, encouraging the child to repeat their names (we count in the direction from the big house, since the car is moving in that direction).

Exercise 4.

We end the lesson with a nursery rhyme about pancakes. We distribute "pancakes" to the hare and the hedgehog.

Deep learning in mathematics is somewhat different from the usual: “One, two, three.” If you want your child to come to school thoroughly prepared, read the review of methods on the topic of how to teach your child to count. Who are the authors of these systems? How do benefits work? Are they effective, and which one should you choose? You will find out all this right now.

A little preface: early mathematics yes or no?

Perhaps someone will be surprised to see familiar names in the subheadings - Montessori, Doman, Zaitsev and the Nikitin family. Of course, they appear as innovative authors who offered the world fundamentally different reading methods or teaching methods, like Maria Montessori.

However, each of these people invented something that deserves close attention - non-standard techniques for teaching mathematics. Please note - no counting, no addition and subtraction, namely mathematics. Each method is valuable. They have no contraindications or special limiting recommendations. They have a lot in common. They can be used in a way that your child likes or seems rational to you: all together, one at a time, part of the technique, or the whole technique at once.

Nikitin family: teaching counting by dots

Teaching children to count “according to Nikitin” can be done in different ways. This technique is a verification test transformed into a game. The manual consists of small squares on which numerical figures from large dots are built in a certain symmetry. They come with digital cards of the same size.

It is necessary for the child to learn to organize the cards: first by color, then by quantity and numbers. The following is a standard set of mathematical tasks, selected specifically to teach a child to count:

how much - in different versions;
pick a number;
find quickly;
compare;
count;
what is superfluous and others.

Thus, in the game, children develop an idea of number and its connection with numbers.

Nikitin table “Hundreds” - a way to overtake peers

You might be interested to know why many authors of developmental techniques prefer simple geometric shapes - circles, squares, etc.? As you know, children are distractible people. So why risk losing useful and short minutes once again by posting bright pictures?

The Hundreds table itself looks like a grid. In its central part there are numbers, and along the perimeter there are dots in corresponding quantities. She easily solves another problem for parents - how to teach a child to count to 100. Actions with numbers containing tens and hundreds are added to the tasks listed above.

Actually, these two simple but comprehensive techniques cover the elementary school curriculum regarding counting with the signs “+” and “-.” The Nikitins themselves give an example of how their six-year-old daughter surprised her parents and composed a difficult logic problem using numbers from 50 to 500. And this is aerobatics even for a fourth-grader. In addition to these games, teachers have developed other equally useful techniques, which we will talk about in future articles.

Zaitsev’s “No!”: teaching mathematics not up to ten, but up to a thousand...at least

How to teach a child to count to 10 is a puzzling question that makes more than one diligent mother cry. If only it were easy enough to count, otherwise you still need to learn the composition, understand the plus and minus, learn to compare and even solve equations!

Nikolai Alexandrovich thought and invented a technique as innovative as cubes, but under the name “Hundred Counting”. The author himself warned that one hundred is a minuscule amount that the brain of a five-year-old child is capable of. Having swapped the types of activities, Zaitsev determined that mental arithmetic is more important and primary, and only then come written calculations.

“Stoschet” is a set of manuals in which, again, the theme of numbers and geometric shapes is played out. Figures are necessary to quantitatively illustrate a figure.

The tape "Hundred Counting" introduces children to all types of mathematical operations with numbers. Children who have mastered the tape algorithm easily go beyond hundreds, reach thousands, and even step beyond this threshold. The child learns mental calculation as if unnoticed. Plus, he's passionate, and that's worth a lot.

The chips that make up the tape look like a double didactic set: the required number of circles, squares and the corresponding number. The figures are arranged symmetrically and clearly show the structure of the number in two versions.

The “Hundred Count” table consists of the same chips, but they are placed in a rectangle. The tasks created by the author for children are structured in such a way that children do not solve, but search. During the game, they master the composition of numbers, learn to count and compare, and all this without poring over a notebook until 23.00.

The genius of Glenn Doman: teaching math

The most famous and useful method for the rehabilitation of seriously ill children with brain damage... We cannot help but say a few words in defense of Glenn Doman. Being a doctor who restored children after injuries, the author invented his system as one of the methods of treatment and adaptation. The technique gave excellent results with this very difficult audience.

In Doman's cards, created for children with disabilities, a new method of teaching children to count was “seen”.

What do Doman counting cards represent? These are sets of squares on which dots are located either systematically or chaotically. By showing the cards for a few minutes a day, parents can teach children to recognize numbers and count. Considering that Doman operated with large numbers, the effectiveness of solving examples without special point counting raises doubts.

How to teach a child to count using Doman? Is learning using the author's math cards suitable for ordinary children? How to form the perception of numbers at the level of intuition (without counting units) - yes. But as a separate method, it leaves many blind spots in a person’s mathematical thinking.

Maria Motessori - a rich set of techniques for teaching mathematics

The most capacious and universal method that helps parents figure out how to teach counting to a preschool child. It is no secret that most innovative systems are based on the developments of Maria Montessori. This attractive Italian was not a teacher either. But she came up with all the best that exists in the world of pedagogy even today, almost a hundred years after the founding of the system.

Based on the various everyday experiences of children (sensory, memory, imprinted images), Montessori based her method, which includes exercises for the development of abilities of all types. The author's manuals are made taking into account many parameters: weight, tactile sensations, sound, size, color. This approach allows you to use all types of human memory and makes it possible to assimilate the material comprehensively, through sensations.

Montessori Math Aids to Ten

Aids in the form of wooden blocks from 10 cm to 1 m long - Montessori bars - will help you cope with the first ten. Children will be able to compare the values in practice, because the rods have different lengths and are divided into units - segments of 10 cm. How to teach children to count even faster? Use Montessori cards. These are chips that depict circles and numbers up to 10.

In addition to the mentioned bars, the Montessori system includes spindles, wooden chips, various digital cards, skittles and much more.

Golden beads Montessori - learning to count from 10 to... infinity

An effective and efficient means of learning mathematics is Montessori's golden asset. With it, parents do not have a headache, which is called how to teach a child to count correctly. By playing with beads, 4-5 year old children learn numbers on an intuitive level. The manuals, specially constructed from “golden” beads, reveal the concept of number.

The same beads, but in different configurations, tables, boards of a special design, three-dimensional chips with examples of addition, “Fractions” materials, an abacus of an original design - this is a small list of Maria Montessori’s materials for comprehensive teaching of mathematics.

Montessori materials convincingly illustrate mathematical formulas. With gold beads supported by digital cards, you won't have a problem teaching your child how to count with a column. By sorting sets by rank and matching numbers to them, children will understand the relationship between mathematical concepts and actions in a playful way.

Interesting facts about columnar calculations

Having prepared the child for school, later we invariably ask the question: where do the two come from? Why can’t a schoolchild who solves problems well at home be able to tell the answer to the teacher?
As banal as it may be, this only means that in his “mathematical building,” where every brick must be in its place, there is a defect. Most often these are problems such as: ignorance of the composition of a number, the multiplication table, the principle of dividing a number into digits.

Despite the effectiveness of the described methods, they should all lead to a theory. That is, a student, having mastered numbers figuratively, should be able to answer all program questions. Definitely, you will have to cram. However, this is only for the good. The Russian program provides the most clear algorithm for teaching a child to count in a column. Parents whose children studied in foreign schools told us about this.

It turns out that traditional notation with transferring or borrowing bit units gives an excellent result, provided that it is supported by theoretical knowledge.

Early methods - excellent mathematics

Separately, I would like to comment on the negative point of view regarding methods of early teaching of mathematics. If a child wants to know, then this knowledge must be given to him. Moreover, the authors do not suggest seating children at a desk. All classes are conducted “in passing” in a manner that is friendly to children’s health. And this is an excellent alternative, given the pre-school fever, when the child is urgently seated at the desk, given a textbook and counting sticks and told to get ready for school.

In essence, early mathematics teaching methods are several solutions to one problem. A kind of Rubik's cube, in which the only possible and very real result is the child's mathematical knowledge. As always, we advise you to combine the useful and the necessary: non-standard methods, which are certainly useful, and a school curriculum compiled and tested by the most experienced experts in their field.

In children, visual-figurative thinking predominates. The problem is that most mathematical concepts are abstract and difficult for younger students to grasp or remember. Therefore, any mathematical operations must be based on practical actions with objects.

Teachers use three main ways to teach a child to count in his head:

based on knowledge of the composition of numbers;
learning tables of mathematical operations by heart;
using special techniques for performing mathematical operations.

Let's look at each of them.

Preparing to teach mental arithmetic

Preparation for mental arithmetic should begin with the first steps in studying mathematics. When introducing a child to numbers, it is imperative to teach him that each number represents a group with a certain number of objects. It is not enough to count, for example, to three and show the child the number 3. Be sure to invite him to show three fingers, put three candies in front of him, or draw three circles. If possible, associate the number with fairy-tale characters or other concepts known to the child:

3 - three little pigs;
4 - ninja turtles;
5 — fingers on the hand;
6 — heroes of the fairy tale “Turnip”;
7 - gnomes, etc.

The child should form clear images associated with each number. At this stage, it is very useful to play mathematical dominoes with children. Gradually, pictures with dots that correspond to the corresponding numbers will be imprinted in their memory.

You can also practice learning numbers using a box of blocks. Such a box should be divided into 10 cells, which are arranged in two rows. Getting acquainted with each number, the child will fill in the required number of cells and remember the corresponding combinations. The benefit of these games with cubes is that the child will subconsciously notice and remember how many more cubes are needed to complete the number to 10. This is a very important skill for mental counting!

Alternatively, you can use Lego parts for such an exercise or apply the principle of pyramids from Zaitsev’s method. The main result of all the described methods of getting to know numbers should be their recognition. It is necessary to ensure that the child, when looking at a combination of objects, can immediately (without counting) name their quantity and the corresponding number.

Oral counting based on the composition of the number

Based on knowledge of the composition of a number, the child can perform addition and subtraction. For example, to say how much “five plus two” is, he must remember that 5 and 2 are 7. And “nine minus three” is six, because 9 is 3 and 6.

Without knowledge of the appropriate tables, a child is unlikely to be able to learn to divide numbers in his head. Constant practice in using tables significantly improves the speed of obtaining results when performing mental calculations.

Using computational techniques for mental counting

The highest degree of mastery of mental counting skills is the ability to find the fastest and most convenient way to calculate the result. Such techniques should begin to be explained to children immediately after familiarizing them with the operations of addition and subtraction.

So, for example, one of the first ways to teach a child to count mentally in the 1st grade is the method of counting and “jumping.” Children quickly understand that adding 1 results in the next number, and subtracting 1 results in the previous number. Then you need to offer to meet number 2’s best friend - a frog who can jump over a number and immediately name the result of adding or subtracting 2.

The principle of performing these mathematical operations with the number 3 is explained in a similar way. The example of a bunny who can jump further away - after two numbers at once - will help with this.

Children also need to demonstrate the following techniques:

rearrangements of terms (for example, to count 3 + 68, it’s easier to swap numbers and add);
counting in parts (28 + 16 = 28 + 2 + 14);
reduction to a round number (74 - 15 = 74 - 4 - 10 - 1).

The counting process is facilitated by the ability to apply combinational and distributive laws. For example, 11 + 53 + 39 = (11 + 39) + 53. At the same time, children should be able to see the simplest way to count.

How to learn to count quickly in your head as an adult

An adult can use more complex algorithms for mental counting. The most convenient way to quickly count in your head is to round numbers and then add them. For example, the example 456 + 297 can be calculated like this:

456 + 300 = 756
756 - 3 = 753

Subtraction is done in the same way.

To perform multiplication and division, special rules have been developed for operating with individual numbers. For example, these:

to multiply a number by 5, it is easier to multiply it by 10 and then divide it in half;
multiplying by 6 involves performing the previous steps and then adding the first factor to the result;
To multiply a two-digit number by 11, you need to write the first digit in the hundreds place, and the second in the units place. In the tens place, the sum of these two digits is written;
You can divide by 5 by multiplying the dividend by 2, and then divide by 10.

There are rules for calculations with decimals, percentages, and exponentiation.

You can learn these techniques at school or find material on the Internet, but in order to learn how to quickly count in your head based on them, you need to practice and practice again! During the training process, many results will be remembered by heart, and the child will name them automatically. He will also learn to operate with large numbers, breaking them down into simpler and more convenient terms.

Greetings, dear readers! In this material we will talk about how to teach a child to count to 10 quickly and easily, using game techniques. After reading this article, you will be able to master basic math skills with your baby in a short time. Want to try it? Then read on!

Preparing inventory

Children begin to learn counting at 2–3 years of age. By the age of 4, many children can already count to 10. When starting to master basic knowledge of mathematics, there is no need to give a three-year-old child real school lessons. Conduct classes in a playful way, for which you will definitely need visual aids. What can you use to interest your baby?

Cubes with numbers (soft or wooden);
plastic numbers with magnets and a tablet for fastening;
number lotto, puzzles;
abacus;
cards with objects and numbers drawn on them;
counting sticks (they can be replaced with matches or popsicle sticks);
educational cartoons, videos.

If you can’t buy bright toys, you can make manuals yourself. Do you have potatoes at home? Cut a thick circle of potato and cut out the number that your baby is currently learning. Fry the preparation and offer it to your baby for breakfast.

You can make numbers from any available materials:

cardboard;
colored paper;
plasticine;
cereals;
shells;
pebbles;
twigs;
beads, etc.

Count any objects and phenomena that you see while walking or on the street:

steps;
cars;
trees;
toys;
people, etc.

Anything that surrounds you can be used as counting material.

Where to start?

The sooner you introduce your baby to counting, the better. If a preschooler at 2 years old already speaks and thinks well, you can start. First, limit your knowledge to the first two numbers. Place one stick in front of the child and say: “One.” Then put the second one down and say, “Two.”

Once these concepts are understood, count to two everything you find in your environment. If the skill is fixed, move on to three, four, etc. Do not rush to introduce your child to writing numbers. Count orally. The baby must understand the practical application of counting skills.

On the way to mastering numbers up to 5, little rhymes and little rhymes can be of great help. By memorizing them, the child will quickly remember the order of the numbers. Play hide and seek, saying the well-known rhyme “I count to five...” The game will be both useful and interesting.

When the direct counting is mastered, we proceed to the reverse counting. Hang a picture of a rocket on the wall. Now imagine that it needs to be launched into space. Try counting back from five. Practice shows that the skill of counting backwards is learned rather slowly and requires maximum patience and attention from parents and children.

at home during everyday activities;
visiting;
on a walk;
in transport;
on the way to kindergarten, etc.

Count forward and backward. Arrange game situations for your child in which simple mathematical skills are simply necessary:

Draw a winding path. Divide it into cells. Throw the dice one at a time and use your chips to go through as many cells as there are dots on the dice. You can buy a ready-made game in a children's store. She is great at training counting skills within 6.
Game "Shop". Place the toys on an imaginary counter, assign a price to each of them within 10. Cut out small rectangles from colored paper - this is money. If you have disused 1-kopeck coins stored, they are perfect for playing. Let the baby be the buyer. His task is to correctly count the number of coins or paper bills.
Introducing to household duties. Invite your baby to wash or dry 3 cups and give the rest to mom. The child’s task is to count the required number of cups.
Game "Messenger". Place cubes, construction sets, magnets and other toys in one room. Go to the next room. The kid plays the role of a messenger: he must bring from the next room as many items as he was asked.

Encourage any achievements and praise the baby. But do not turn praise into training when, after the correct answer, the child receives candy or permission to watch a cartoon. This way the child will get the idea that studying and gifts are directly related.

Learning numbers on paper

Only after the baby has learned to count to 10 verbally and mentally without errors can you introduce him to the graphic design of numbers.

When introducing your child to writing a number, show the corresponding card, play a video of a cartoon or children's TV show that talks about this number. Model a number out of plasticine, draw and color it, cut it out of colored paper, lay it out of matches, etc. The more visuals you use, the sooner you will get the result.

Offer your child the game “Guess!” For this you will need cubes or cards with numbers written on them. Show your baby the number and ask him to name it.

If your baby loves active games and doesn’t want to play with cubes or magnets, do something different. Hang a piece of paper on the door or wall with numbers written randomly. And now the most interesting part: invite your child to do a somersault (jump, throw a ball, etc.), and then name the number you show. So alternate physical and mental exercises. Changing actions perfectly trains not only memory, but also reaction.

Older children can be taught to write numbers. Use printed copybooks for these purposes. Invite your child to first write a large number, then gradually reduce the outline to the size of a cell in a school notebook.

Solving examples

After mastering counting, it’s time to learn how to solve examples. Let's start with something simple: introduce the baby to the plus sign and add: 1 + 1 = 2. For clarity, use counting sticks, matches, or any identical objects.

When this simplest example is mastered, we add one to two and get three. We continue this way until we reach 10. To reinforce addition, repeat the studied examples regularly, orally and in writing. When your child answers your question, how much is, for example, 5 + 1, and begins to answer correctly without hesitation, proceed to the next stage.

Add first 2, then 3, etc. to all numbers up to 10. When addition within 10 is completely mastered, give your child examples randomly, without being tied to a specific addend.

Important! Do not let your baby count on his fingers, use a ruler or other improvised means. Solving examples of addition and subtraction within 10 is the basis of all mathematical operations. The parents’ task is to ensure that the child knows the answers to the examples by heart.

Learn subtraction in the same way as addition. After successfully consolidating the acquired knowledge, you can vary the complexity of the examples: give them in the form of an equation with one unknown (instead of X or Y, used in high school, draw a square, a house or any other image in place of the missing number).

What do you need to remember?

When studying numbers with your child, follow the rules of learning:

One lesson should last no more than 10 minutes, so as not to bore the baby or tire him. Do 3 of these “lessons” throughout the day.
Revisit the material you've studied periodically, but don't do it every day.
Don't scold your child if he doesn't succeed. Calculate the difficulty of tasks correctly.
Reinforce the material in everyday life so that the child sees its practical application.

And most importantly: psychologists believe that in the learning process the baby goes through three stages: