How to easily teach a child to count in his head - methods of teaching counting for preschoolers and schoolchildren

Mental arithmetic is a skill that will be useful to a child not only at school, but also in everyday life. If you still doubt whether you should teach children to count in their heads, here are good reasons:

mental arithmetic develops the ability to think rationally and improves mental abilities (memory, logic, concentration);
useful in everyday life - calculate a discount in a store, account balance;
it is part of development, as necessary a skill as the ability to read and write.

In this article we talk about the nuances of training and the most popular methods.

The benefits of mental counting

A person’s ability to quickly count orally indicates an analytical mind; it can significantly delay the time of dementia and insanity associated with the natural aging process of the human body.
This skill will help you avoid being deceived when making daily purchases.
In the absence of such a skill, it is difficult for a person to quickly make verified, correct decisions, calculate various vectors of development of events and look for rational options for complex professional tasks.
When training the brain using the mental arithmetic method, an increase in a person’s mental abilities is observed, and as a result, his self-esteem increases, which contributes to professional growth.
For children, the ability to count in their head allows them to master speech much faster, their mental reaction speeds up, and the ability to make extraordinary decisions is formed. Mental arithmetic develops memory, and, just like in adults, gives self-confidence.

Teaching mental arithmetic by memorizing tables

At school, the main way to learn how to quickly count in your head is to memorize tables. Moreover, it is understood that the child must do this independently under the supervision of his parents. Usually, during the lesson, the teacher only introduces the children to the principle of constructing a table and performs only a few training exercises with the children on its use.

There are many ways to memorize tables. Children memorize almost half of the examples in addition and multiplication tables automatically after familiarizing themselves with the commutative law.

You can also use rhymes and songs. The most famous example for such a case is the lines of the song “Twice two is four, everyone in the whole world knows this.” Good material can be found by familiarizing yourself with Nikolai Zaitsev’s methodology or the “Pesneznayka” program.

Another interesting technique for familiarizing yourself with tables is the use of eidetic techniques. Based on them, you can come up with fairy tales or pictures using images - numbers.

To consolidate knowledge of tables, you can offer children:

coloring books;
computer mathematical games - simulators;
multimedia presentations;
tests.

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

Preparing for training

First of all, the child must develop the concept of number. For a child, this category is an abstract concept. At first, it is difficult to explain to a child what a number or figure is.

Anything can be chosen as educational material: favorite blocks, balls, soft toys, cars, etc. It is important that the baby understands that you can not only play with them, but also count them.

This should not be in the form of a boring and intrusive lesson; the child simply will not understand it. Everything should look like a game, as if “by the way.”

It is important not to miss the time when the child perceives everything as an exciting game, then learning will become an enjoyable experience for him.

Don’t forget the main thing correctly – classes should be interesting and enjoyable!

Please note that activities with your child should be varied. If you organize everything in the form of a game, then learning to read at 6 years old and working with reading techniques at 9 years old will be enjoyable and will not seem tiresome. As a way to relax during classes, your child can be offered puzzles, other educational games, or logic tasks.

Best age to start learning

We begin teaching counting as soon as the baby shows interest in it. This usually happens around 2 years. At this age he begins to play with numbers. Adults should encourage and support this hobby in every possible way and show their favorite toys, naming their number, and correlating the quantity with the corresponding number.

By older preschool age, the child counts objects and begins to understand the composition of numbers. The main thing is to take your time and conduct training based on his interests, including game techniques.

A child’s mental counting skills usually begin to develop after the age of 4. But by this time the baby should have accumulated the following skills:

Counting to 10 and back;
Understanding simple math operations - adding and calculating;
Understanding the meanings of “many” and “little”, “big” and “small”;
Knowledge of geometric shapes and primary colors.

Mental arithmetic is formed on the basis of these skills. Start counting with a small number of items in different ways. First out loud, then to yourself or very quietly, without resorting to fingers and sticks.

Gradually it is necessary to increase the quantitative series and consolidate the material covered. This happens in a fun and relaxed way during play activities or while walking down the street. You ask your child to count the various objects that he sees around him. Then you complicate the tasks.

For example, count only round objects, only yellow ones, etc. Don't forget to praise your child for his smallest achievements.

How to teach correctly?

Teaching a child the basics of mathematical calculation should only take place in a playful way and if the child wishes.
Learning to count should be done in a fun way and continuously (every day). The baby's visual and tactile memory is involved.
Classes must be structured in a clear algorithm and have a system. Let’s say that first the understanding of “one” and “many” is consolidated, then “more” and “less”.
It is important to explain the difference between the concepts of “more”, “less”, “equal”.
In a playful way, for example, while going down the stairs, teach your child ordinal counting from 1 to 10;
Show your child on objects how the spoken numbers relate to the real quantity;
Try to explain to your child in elementary life situations how the number of objects increases or decreases, for example, another car came to one car, you got two cars, etc.

If you think that it is better to entrust the formation of such an important skill to professionals, then we recommend that you enroll your child in mental arithmetic courses. The results of the classes will pleasantly surprise you!

Where to start

To start teaching your child to count, you don’t need to set aside time and wait for the right opportunity. At the first stages, mathematics (intermediate group) is suitable - counting within 5.

Showing numbers, talking about numbers, the number of objects and why they are needed should be done in a playful way that is easy and accessible to a small child. For example:

It is worth asking to show the dogs on the street and voice this number, and then count together.
You can count the molds that were brought into the sandbox.
It is useful to purchase special cards for kids, which depict animals and a number that indicates their number.

Finger gymnastics classes in kindergarten for children 3-4 years old

Note! You can come up with simple examples yourself and include them in games and activities. This way, the child will quietly learn the simplest mathematical operations and recognize numbers from one to five, and then beyond.

Cut out numbers

Learning to count to 10

It is necessary to introduce an understanding of quantity into the child’s daily life; this requires constant emphasis on objects, mentioning their number.

It is useful to learn counting rhymes with your child, poems in which numbers are mentioned.

To teach a child to count from 1 to 10, it is necessary to use various educational materials. Currently, there are many animated educational videos in which, in a child-friendly form, your favorite cartoon characters play and teach your child to count.

The child’s visual memory is used here, and information is also perceived by ear.

Simple tasks will help your child not only depict the above numbers and form an idea about them, but also practice fine motor skills, hand-eye coordination and attention.

Learning to count to 20

When the child can easily count to 10, confidently show the numbers and correlate the drawn number with the number of objects corresponding to it, you can begin to study further counting.

In addition to the mechanical method of learning further counting, using the same methods as were used when learning to count from 1 to 10, the child needs to explain the concepts of “ten” and “one”.

This game can be accompanied by a demonstration of cards on which the numbers being studied will be depicted.

It is important to explain to your child that after 10, all numbers will consist of two digits.

The first of which is “ten” (the first box of chocolates), and the second one (the second box of chocolates).

The child must understand the system in which all the numbers follow one another: 11 after 10, 12 after 11, etc.

We need to continue to actively use educational cartoons, counting rhymes, songs, coloring books with tasks, etc. - everything that was used when learning to count from 1 to 10.

When the child’s understanding of “ten” and “one” is formed, then he can master counting further up to 100.

Don't forget to pay attention to others too

Teaching methods at different ages

For children 2-3 years old

It is necessary to instill in the child, in a playful way, an understanding of counting and the initial skills of applying it to objects. For example, we count fingers on one hand, ask you to bring one, two... objects. We instill the concepts: “many”, “little”, “big”, “small”.

For children 4-5 years old

You need to use the baby’s desire to help his parents with household chores.
Putting toys together in a box, you can count them or ask the child to bring one or more plates from the table.

Gradually, the baby should develop the concept of “one” and “many”, “less”, “more”, “wider”, “narrower”.

Also, the baby should be unobtrusively introduced to understanding the shape of objects: a round ball or a square cube, etc.

Contact learning is much more effective; at this moment the baby senses the object, several zones of object perception are activated and learning is easier.

Kids compare “many” and “one”. Different objects need to be compared in order to develop an understanding of their properties, without overloading the baby with the characteristics of the object. Gradually, the child himself must combine different objects according to one characteristic (small - large, long - short).

Gaming techniques and didactic games are widely used in classes (it is proposed to put objects on pictures, sample cards, etc.).

For children 5-6 years old

Children learn to compare adjacent sets element by element, that is, compare sets that differ in the number of elements by one.

The main methods are overlay, application, comparison. As a result of this activity, children should learn to establish equality from inequality by adding one element, i.e. increasing, or removing, i.e. decreasing, the set.

For 1st grade students

First of all, the child masters counting in groups of 2, 3, and 5, and is gradually brought to an understanding of the decimal number system.

At this age, much attention is paid to mental arithmetic, for which teaching methods with a playful bias are used.
For example, the manual “A Thousand Plus” (author N.A. Zaitsev).

The technique allows the operation of addition and subtraction within 100 to be brought to automaticity, and in the mind.

When using Glen Doman's method, children learn to count while playing, using cards with dots, and the child's visual memory develops. There are other methods of teaching children to count.

Are you having trouble teaching your child how to put accents correctly? Or do you have problems telling time using a watch? Then you should check out our materials on these topics.

For 2nd grade students

In the second grade, you can continue to use the techniques that were used in teaching in the first grade. It is important to choose one teaching method to make it easier for the child to learn the material.

The materials used at home should correlate with those used by the teacher at school. In the form of a game, you can quickly solve addition and subtraction examples with two-digit numbers in your head.

If you still have questions about teaching counting to schoolchildren, we advise you to watch the following video:

The most common methods of teaching children to count

To begin with, we note that counting on fingers has been and continues to be considered one of the most common techniques at all times. It is considered a classic, but, of course, is becoming outdated.

Counting sticks also belong to this category. Using special sets with such sticks, mothers and fathers begin to give their children simple tasks, such as, for example, putting one, two or three sticks in front of them, removing four sticks, etc.

However, such methods, according to the authors of more modern developments, may be able to explain in an accessible form what one, two and three are, but are completely unsuitable for memorizing numbers and solutions. In addition, the child will subsequently count very slowly. Alternative and more modern options help replace these “ineffective” methods.

The following deserve special attention (due to their wide distribution and popularity):

Nikolai Zaitsev's method, which uses cubes of various colors, weights and sizes, as well as tables and cells corresponding to these cubes
Glen Doman's method using dot cards
Sergei Polyakov’s method, which uses multi-colored cubes (interestingly, these cubes can be glued together from colored paper and then filled with cereal)

We will talk in detail about the methods of Zaitsev and Doman (as well as some others) and their advantages and disadvantages in the third lesson, and now, taking into account the simplicity and possibility of independently preparing didactic material, we will analyze the Polyakov method in more detail.

Oral counting based on the composition of the number

Knowing the composition of a number, a child can verbally perform addition and subtraction operations. Understanding, for example, that the number 8 is made up of 5 and 3, or 1 and 7, or 6 and 2, or 4 and 4, he can solve addition and subtraction problems with that number without thinking.

For better memorization, it is recommended to solve simple tasks with your child:

Place a certain number of items into 2 boxes (for example, take 8 peas and arrange them in different ways: 5+3, 1+7, etc.). Items need to be constantly changed so that the child does not lose interest.
Invite your child to complete the number to the correct number . For example, hang 5 toys on the tree and ask to add 8 toys to the tree, etc.

Then you need to complicate the problem and solve examples that go beyond ten, for example 8+5. To do this you need:

Add the first term to 10. That is, the child already knows that 10=8+2. That is, he needs to “take away” the number 2 from the second term.
It calculates how much more needs to be added (based on knowing the composition of the number 5 = 2+3);
Calculate 8+2+3=13,

The child will use the same technique (bringing to 10) when subtracting.

Having mastered these methods, the child will subsequently use them when solving examples with numbers between 100 and 1000.

Quick techniques

Methodology of Sergei Polyakov

It takes the integrity of children’s thinking as a basis, while along with visual memory, motor memory is also activated.

A series of exercises is presented with cubes on which numbers are shown. Kids learn the quantitative characteristics of objects without counting them.

Mastery begins with the ability to count to 10. Then there is an addition not by one, but by 3, 5, 6, etc. This is how children develop an understanding of “more” and “less” on an intuitive level.

The technique is aimed at the fact that the toddler begins to remember the number on the cubes, which is based on the number of similar objects.

The method helps the child recognize the quantitative composition of objects without counting them.

The most important thing is that classes can be held in any place where at least some variety of subjects is presented. The big advantage of the method is that classes are conducted in the form of a game for 15-20 minutes.

Peterson technique

Based on the “layer cake” structure. Its essence is that during the learning process, the material being studied is layered on top of existing material, like in a layer cake.

The age characteristics of the children are taken into account. Classes begin at the age of three in a game format.

The peculiarity of the method is that the child obtains knowledge on his own and learns to solve tasks and problems in his own ways, so the knowledge becomes deeper.

The important thing is that it is possible to conduct classes at home with the help of books and teaching aids for each age.

Training according to Zaitsev

Developmental activities begin at the age of three. It is based on a set of developed schemes, which represent numbers from 0 to 9.

The first scheme makes it possible to quickly do mathematical operations in your head within a hundred.

The following table makes it possible to master three-digit numbers and their composition: hundreds, tens, thousand.

The third is given for the purpose of manipulating multi-digit numbers.

The essence of this technique is to show the relationship between various functions of numbers based on the completion of training tasks.

The author is confident that when they complete tasks, they quickly master arithmetic operations with numbers within a hundred.

Using Computational Techniques

The ability to find the optimal way to calculate the result in your head is the result of numerous and regular training. It is important to master certain techniques that allow you to quickly make calculations.

For example, in primary school they often use the frog game. First, the “frog” (or “bird” - it doesn’t matter) jumps over the number 1, the child automatically subtracts or adds examples from 1, then through 2, etc.

Children are also introduced to other techniques for quick mental arithmetic:

rearrangements of terms (for example, to count 2 + 57, it’s easier to swap numbers and add);
counting in parts (14 + 8 = 14 + 6 + 2);
reduction to a round number (44 – 15 = 44 – 4 – 10 – 1).

General recommendations

Before you start learning, check if your child is ready.

Developing thinking

Mental arithmetic requires developed abstract thinking, which allows a person to understand various concepts and work with abstract images and concepts.

The problem is that in 5-7 year old children it is just beginning to develop. This is a labor-intensive process: teenagers and even young adults continue to develop abstract logical thinking over time.

Therefore, it is necessary to use visual-figurative thinking based on specific visual images - this will make it easier for the child to understand what is required of him:

use counting sticks, magnets and pictures to learn math;
ask to see the numbers you name - let this become a daily exercise;
connect them with concepts already familiar to the baby (3 heroes, 5 fingers, 7 gnomes);
together draw objects by which you can remember the numbers (8 legs for a spider, 4 for a cat);
ask what numbers are near you right now - signs, price tags, numbers;
use them more often in speech: “You are 5 years old now, next year you will be 6. How old is Masha?”

Basics of arithmetic

First of all, make sure that your baby can count to 10 and back freely, otherwise further exercises will be difficult. Then you can master basic arithmetic operations.

Tell and show what the composition of a number is: it turns out that 4 apples are both 3+1 and 2+2. Place them on the table and demonstrate each example in detail.

Gradually you can move on to subtraction and multiplication. Children should know the concepts of “more”, “less”, “equally” and understand why they are needed.

The main rules that will simplify classes:

math is just a game, don’t turn your studies into a long lecture about numbers;
make the explanation as clear as possible;
praise for the slightest successes;
counting in your head should become commonplace - count trees while walking, pencils in your pencil case, cars on the road;
Regularity and repetition of material are the basis of strong knowledge.

Learning in the game

Learning to count with cubes

Before you start, you need to understand how many cubes your baby can identify at the same time, without counting them one by one with his finger. When constantly playing with blocks, the child should be encouraged with kind words and prompted to the correct answer.

Game “Matching the dice to the numbers”

Cards must be made with numbers and cubes written on them. Gradually, the child, starting from 1 and 2, understands how many cubes correspond to a certain card.

Game “Dwarfs in the House”

The game has different options.
The house can be drawn on a board; it is divided into squares - “rooms”. The “gnomes” will come and go to visit each other, sometimes “entering” and sometimes “leaving” the cage in the house. Children must answer how many “gnomes” are in which room.

Game “Silence”

The teacher writes examples on the board in one, two or more steps. The whole class is solving an example in their minds; when called by the teacher, the child silently writes the answer.

If he is faithful, all the other children clap once; if not, the children are silent. This game develops attention and strengthens discipline.

Lotto game

Depending on the material being studied, children solve various tasks placed on the cards. Cards can be made in the form of separate pictures; if the examples are solved correctly, an overall picture must be assembled.

Game “Arithmetic Mazes”

How does your baby feel about classes?

Love does not love

Children are asked to solve problems by mentally making their way through a circular maze with funnels with numbers to the center of the circle.

It shows a certain number that should be obtained if the examples are solved correctly.

Tasks can be of varying degrees of difficulty, depending on the material covered. There are several ways out of the maze.

Game “Catch the pilot”

An airplane is drawn on the board with loops in which examples are written. Children are divided into 2 teams. Team representatives solve tasks by writing down answers to the left and right of the loops. The winning team is the one that solves the task faster and more correctly.

Game “Circle Examples”

Children are given teaching material consisting of cards with examples of different content. They are placed in envelopes. There are 8 of them in each envelope. The solution to each previous example is the “key” to starting the next one.

Sergey Polyakov An amazingly easy way to teach a child mental calculation Experience of teaching preschoolers addition and subtraction using counting cubes
Part 1 Why do I call my method easy and even surprisingly easy?
Yes, simply because I have not yet come across a simpler and more reliable way of teaching kids to count. You will soon see this for yourself if you use it to educate your child. For a child it will be just a game, and all that is required from parents is to devote a few minutes a day to the game, and if you follow my recommendations, sooner or later your child will definitely start counting in a race with you. But is this possible if the child is only three or four years old? It turns out that it is quite possible. In any case, I have been doing this successfully for over ten years. I outline the entire learning process further in great detail, with a detailed description of each educational game, so that any mother can repeat it with her child. And in addition, on the Internet on my website “Seven Steps to a Book” * I posted video recordings of fragments of my classes with children to make these lessons even more accessible for playback.

* Website address - follow the link with the author’s name and surname under the article.

* * *

First, a few introductory words.

First question

question that some parents have: is it worth starting to teach your child arithmetic before school? I believe that a child should be taught when he shows interest in the subject of study, and not after this interest has faded away. And children show interest in counting and counting early; it only needs to be slightly nourished and the games imperceptibly made more complex day by day. If for some reason your child is indifferent to counting objects, do not say to yourself: “He has no inclination for mathematics, I was also behind in mathematics at school.” Try to awaken this interest in him. Just include in his educational games what you have missed so far: counting toys, buttons on a shirt, steps when walking, etc.

Second question

: What is the best way to teach a child? You will get the answer to this question by reading here a complete description of my method of teaching mental arithmetic. In the meantime, I want to warn you against using some teaching methods that do not benefit the child.

Don't teach your child to add and subtract by one!

“To add 3 to 2, you must first add 1 to 2, you get 3, then add another 1 to 3, you get 4, and finally add another 1 to 4, the result is 5.” ; “To subtract 3 from 5, you must first subtract 1, leaving 4, then subtract 1 more from 4, leaving 3, and finally subtract 1 more from 3, leaving 2.”

This unfortunately common method develops and reinforces the habit of slow counting and does not stimulate the child’s mental development. After all, counting means adding and subtracting in whole numerical groups at once, and not adding and subtracting one by one, and even by counting fingers or sticks. Why is this method, which is not useful for a child, so widespread? I think because it’s easier for the teacher. I hope that some teachers, having become familiar with my methodology, will abandon it.

Don't start teaching your child to count with sticks or fingers and make sure that he doesn't start using them later on the advice of an older sister or brother. It's easy to learn to count on your fingers, but difficult to unlearn. While the child is counting on his fingers, the memory mechanism is not involved; the results of addition and subtraction in whole number groups are not stored in memory.

And finally, under no circumstances use the “ruler” method of counting that has appeared in recent years!

“To add 3 to 2, you need to take a ruler, find the number 2 on it, count from it to the right 3 times in centimeters and read the result 5 on the ruler”; “To subtract 3 from 5, you need to take a ruler, find the number 5 on it, count from it to the left 3 times in centimeters and read the result 2 on the ruler.”

This method of counting, using such a primitive “calculator” as a ruler, seems to have been deliberately invented in order to wean a child from thinking and remembering. Instead of teaching how to count like this, it’s better not to teach at all, but to immediately show how to use a calculator. After all, this method, just like a calculator, eliminates memory training and inhibits the child’s mental development.

* * *

I address my further explanations to both parents and teachers at the same time, because they can be used by both.

At the first stage of learning mental arithmetic, it is necessary to teach the child to count within ten. We need to help him firmly remember the results of all variants of adding and subtracting numbers within ten, just as we adults remember them.

At the second stage of education, preschoolers master the basic methods of adding and subtracting two-digit numbers in their heads. The main thing now is not the automatic retrieval of ready-made solutions from memory, but the understanding and memorization of addition and subtraction methods in subsequent tens.

Both at the first and second stages, learning mental arithmetic occurs using elements of play and competition. With the help of educational games built in a certain sequence, not formal memorization is achieved, but conscious memorization using the child’s visual and tactile memory, followed by consolidation in memory of each learned step.

Why do I teach oral

account? Because only mental arithmetic develops the child’s memory, intelligence and what we call ingenuity. And this is exactly what he will need in his subsequent adult life. And writing “examples” with long thinking and calculating the answer on the fingers of a preschooler does nothing but harm, because discourages you from thinking quickly. He will solve examples later, at school, practicing the accuracy of the design. And intelligence must be developed at an early age, which is facilitated by mental calculation.

Even before starting to teach a child addition and subtraction, parents should teach him to count objects in pictures and in reality, count steps on a ladder, steps while walking. By the beginning of learning mental counting, a child should be able to count at least five of his toys, five fish, birds or ladybugs in drawings, and at the same time master the concepts of “more” and “less.” But all these various objects and creatures should not be used in the future for teaching addition and subtraction. Learning mental arithmetic should begin with addition and subtraction of the same homogeneous objects, forming a certain configuration for each number.

This will allow the child to use the visual and tactile memory when memorizing the results of addition and subtraction in whole number groups. As a tool for teaching mental counting, I used a set of small counting cubes in a counting box (detailed description below). And children will return to fish, birds, dolls, ladybugs and other objects and creatures later, when solving arithmetic problems. But by this time, adding and subtracting any numbers in the mind will no longer be difficult for them.

For ease of presentation, I divided the first stage of training (counting within the first ten) into 40 lessons, and the second stage of training (counting within the next tens) into another 10-15 lessons. Don't be intimidated by the large number of lessons. The breakdown of the entire training course into lessons is approximate; with prepared children, I sometimes go through 2-3 lessons in one lesson, and it is quite possible that your child will not need so many lessons. In addition, these classes can be called lessons only conditionally, because each lasts only 10-20 minutes. It is advisable to study twice a week, and it is enough to spend 5-7 minutes on homework on other days. Not every child needs the very first lesson; it is designed only for children who do not yet know the number 1 and, looking at two objects, cannot say how many there are without first counting with their finger. Their training must begin practically “from scratch.” More prepared children can start immediately from the second, and some - from the third or fourth lesson.

I conduct classes with three children at a time, no more, in order to keep the attention of each of them and not let them get bored. When the level of preparation of children is slightly different, you have to work with them on different tasks one by one, all the time switching from one child to another. At the initial lessons, the presence of parents is desirable so that they understand the essence of the methodology and correctly perform simple and short daily homework with their children. But the parents must be placed so that the children forget about their presence. Parents should not interfere or discipline their children, even if they are naughty or distracted.

Lessons with children in mental arithmetic in a small group can begin at about the age of three

age, if they can already count objects with their fingers to at least five.
And with their own child, parents can easily begin elementary lessons using this method from the age of two
.
First stage.
Learning to count within the first ten (lessons No. 1 - No. 40) Initial lessons of the first stage (No. 1 - No. 5), learning to count within five

To conduct initial lessons, you will need five cards with the numbers 1, 2, 3, 4, 5 and five cubes with an edge size of approximately 1.5-2 cm, installed in a box (see Appendix below, Figure 1). For cubes, I use “knowledge cubes” or “learning bricks” sold in educational game stores, 36 cubes per box. For the entire training course you will need three such boxes, i.e. 108 cubes. For initial lessons I take five cubes, the rest will be needed later. If you are unable to find ready-made cubes, it will not be difficult to make them yourself. To do this, you just need to print on thick paper, 200-250 g/m2, Figure 2 of the Appendix, and then cut out cube blanks from it, glue them in accordance with the instructions, fill them with any filler, for example, some kind of cereal, and paste them on the outside with tape. It is also necessary to make a box to place these five cubes in a row. Gluing it together is just as easy from Figure 3 of Appendix printed on thick paper and cut out. At the bottom of the box, five cells are drawn according to the size of the cubes; the cubes should fit in it freely. And the numbers 1, 2, 3, 4, 5 need to be cut out from Table 1 of the Appendix printed on thick paper.

You have already understood that learning to count at the initial stage will be done with the help of five cubes and a box with five cells for them. In this regard, the question arises: why is the method of learning with the help of five counting cubes and a box with five cells better than learning with the help of five fingers? Mainly because the teacher can cover the box with his palm from time to time or remove it, due to which the cubes and empty cells located in it are very quickly imprinted in the child’s memory. But the child’s fingers always remain with him, he can see or feel them, and there is simply no need for memorization; the memory mechanism is not stimulated.

You should also not try to replace the box of cubes with counting sticks, other counting objects, or cubes that are not lined up in the box. Unlike cubes lined up in a box, these objects are arranged randomly, do not form a permanent configuration and therefore are not stored in memory as a memorable picture.

Lesson #1

Before the start of the lesson, find out how many cubes the child can identify at the same time, without counting them one by one with his finger. Usually, by the age of three, children can tell immediately, without counting, how many cubes are in a box, if their number does not exceed two or three, and only a few of them see four at once. But there are children who can only name one object so far. In order to say that they see two objects, they must count them by pointing with their finger. The first lesson is intended for such children. The others will join them later.

To determine how many cubes a child sees at once, alternately place different numbers of cubes in a box and ask: “How many cubes are in the box? Don't count, say it right away. Well done! And now? And now? You are right, well done!" Children can sit or stand at the table. Place the box with cubes on the table next to the child parallel to the edge of the table.

To complete the tasks of the first lesson, leave the children who can only identify one cube so far. Play with them one by one.

1. Game “Putting numbers to dice” with two dice.

Place a card with number 1 and a card with number 2 on the table. Place a box on the table and put one cube into it. Ask your child how many cubes are in the box. After he answers “one,” show and tell him the number 1 and ask him to put it next to the box. Add a second cube to the box and ask him to count how many cubes are in the box now. Let him, if he wants, count the cubes with his finger. After the child says that there are already two cubes in the box, show him and call the number 2 and ask him to remove the number 1 from the box and put the number 2 in its place. Repeat this game several times. Very soon the child will remember what two cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the numbers 1 and 2 and will move the number corresponding to the number of cubes in it towards the box.

2. Game “Dwarfs in the House” with two dice.

Tell your child that you will now play the game “Gnomes in the House” with him. The box is a make-believe house, the cells in it are little rooms, and the cubes are the gnomes who live in them. Place one cube on the first square to the left of the child and say: “One gnome came to the house.” Then ask: “And if another one comes to him, how many gnomes will be in the house?” If the child finds it difficult to answer, place the second cube on the table next to the house. After the child says that now there will be two gnomes in the house, allow him to place the second gnome next to the first on the second square. Then ask: “And if now one gnome leaves, how many gnomes will remain in the house?” This time your question will not cause difficulty and the child will answer: “One will remain.”

Then make the game more difficult. Say: “Now let’s put a roof on the house.” Cover the box with your palm and repeat the game. Every time the child says how many gnomes there are in the house after one came, or how many of them are left in it after one left, remove the palm roof and allow the child to add or remove the cube himself and make sure his answer is correct. . This helps connect not only the child’s visual, but also tactile memory. You always need to remove the last cube, i.e. second from the left.

Play games 1 and 2 alternately with all the children in the group. Tell the parents present at the lesson that they should play these games with their children once a day every day at home, unless the children themselves ask for more.

Lesson #2

In the second lesson, children who, when tested in lesson No. 1, were able to immediately say, without counting, that there are two cubes in the box, can join the games. If there are many such children, it is advisable to divide them into groups of three children. Take turns playing with the children.

1. Game “Putting numbers to dice” with three dice.

Place three cards with the numbers 1, 2 and 3 on the table. Place a box on the table and put two cubes into it. Ask your child how many cubes are in the box. After he answers “two,” ask him to put the number 2 next to the box (he already knows the numbers 1 and 2). Add a third cube to the box and ask him to count how many cubes are in the box now. Let him, if he wants, count the cubes with his finger. After the child says that there are already three cubes in the box, show him and call the number 3 and ask him to remove the number 2 from the box and put the number 3 in its place. Then remove two cubes from the box and ask how many cubes are left. After the child answers “one,” ask him to remove the number 3 from the box and put the number 1 in its place. Repeat this game several times. Very soon the child will remember what three cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the number 3 and will now know the numbers 1, 2, 3 and move the number corresponding to the number of cubes in it to the box.

2. Game “Dwarfs in a House” with three dice.

Play the same way as in lesson No. 1 (see lesson No. 1, p. 2), but this time the gnomes will come to the house and leave it, one and two at a time. Start the game with an open box, and then make a roof by covering the box with your palm. Play through with each child all possible addition and subtraction options within three. You can also ask: “And if three leave, how many will remain?” When the child answers that there are none left, tell him that “not a single one” is another name for zero. Show him the number 0, which can also be cut out from Table 1 of Appendix 2 for this purpose. Each time after the child answers, remove the roof-palm and allow the child to add or remove cubes himself and make sure his answer is correct. You always need to remove the last cubes, counting them from left to right of the child.

3. Playing "Cards" with numbers 1, 2 and 3.

Throw cards randomly to your child with the numbers 1, 2, 3. If you name it correctly, you win; if you make a mistake, you name the number correctly, take it for yourself, and after one turn give it to the child again. When everyone wins, ask him to add the numbers in a column in order.

Play games 1, 2 and 3 alternately with all the children in the group. Tell the parents present at the lesson that they should play these games with their children once a day every day at home, unless the children themselves ask for more.

Note.

Do not move on to the next lesson if, after lesson No. 2, the child does not want to immediately say, without counting, that there are three cubes in the box. To help such a child overcome the habit of counting with his finger, repeat the games of lesson No. 2 with him for some time.

Lesson #3

In the third lesson, children who, when tested in lesson No. 1, were able to immediately say, without counting, that there are three cubes in the box, can join the games. If there are many such children, it is advisable to divide them into groups of three children. Take turns playing with the children.

1. Game “Putting numbers to dice” with four dice.

Place four cards with the numbers 1, 2, 3 and 4 on the table. Place a box on the table and put three cubes in it. Ask your child how many cubes are in the box. After he answers “three,” ask him to put the number 3 next to the box (he already knows the numbers 1, 2 and 3). Add a fourth cube to the box and ask him to count how many cubes are in the box now. Let him, if he wants, count the cubes with his finger. After the child says that there are already four cubes in the box, show him and call the number 4 and ask him to remove the number 3 from the box and put the number 4 in its place. Then remove two cubes from the box and ask how many cubes are left. After the child answers “two,” ask him to remove the number 4 from the box and put the number 2 in its place. Then remove another cube and ask how many cubes are left. The child has already understood the meaning of this game. He will say that there is one cube left in the box, move away the number 2 and move the number 1 towards the box. Repeat this game several times. Very soon the child will remember what four cubes look like and will begin to name this number immediately, without counting. At the same time, he will remember the number 4 and will now know the numbers 1, 2, 3, 4 and move the number corresponding to the number of cubes set in it to the box.

2. Game "Divide in half" with four dice.

Place four cubes in a box and ask your child to divide them equally between you and him so that everyone has the same number of cubes. When the child takes two cubes and gives you the same number, ask him to say how many cubes he has and how many you have.

3. Game “Dwarfs in the House” with four dice.

Play the same way as in previous lessons, but this time the gnomes will come to the house and leave it one, two, and three at a time. Start the game with an open box, and then make a roof by covering the box with your palm. If, with the box covered, it is still difficult for the child to guess how many gnomes there will be in the house after two or three more are added to the ones already there, place these two or three cubes next to the covered box. This will make it easier for the child to mentally add some cubes to others. And if, with the box covered, it is difficult for him to guess how many gnomes will remain in the house after two or three leave, take these two or three cubes out of the box so that it is not visible how many cubes are still left in the box, and place them next to in a box. For example, there were four gnomes in the box, but three left. The child has not yet forgotten what those four looked like, and, looking at the three cubes that you took out from under your palm and placed next to them, without any explanation, he will guess that there is only one left under the roof in the house. Play through all possible addition and subtraction variations within four with each child. You can also remind that there are zero cubes in an empty box. Start the game by placing all four dice, cover the box and ask: “How many gnomes are in the house now? That's right, four. And if two leave, how many will remain?” If the child cannot answer immediately, remind him how he just divided four in half: he took two cubes for himself and gave two to you.

When adding, first add the smaller number to the larger number, and immediately after that, on the contrary, add the larger number to the smaller number. Do this first with the box open and clearly show the child that if, for example, one comes to three gnomes, then there will be four of them, and if three come to one, then there will also be four. Do not demand that the child understand and assimilate this explanation the first time. It will come to him gradually.

Each time after the child answers, remove the roof-palm and allow the child to add or remove cubes himself and make sure that his answer is correct (you always need to remove the last cubes, counting them from left to right of the child).

4. Hide and seek game with four dice.

Take the cubes out of the box, place them on the table in a row as they were in it, and turn the box over so that the cells are not visible. Tell your child that the gnomes went for a walk, the house was closed, and now they will play hide and seek with him. Remind your child that there are four gnomes on the table, then cover them with your palms, take one cube in your right hand, and three in your left. Then the game goes like this. You, placing a cube from your right hand on the table: - How many cubes are in this hand? Child: - Alone. You: - How much was hidden in this one? Child: - Three. You, placing three cubes on the table from your left hand: - That's right, three! Well done! Then you line up the four cubes again, remind them that there are four of them, and repeat the game, this time hiding two cubes in each palm. On the third repetition of the game, there are three cubes in the right hand, and one is hidden in the left. At the last repetition, you can take all the cubes in your right hand, but there will be none in your left. Remind your child that “none” is another name for zero. After each repetition, do not forget to re-arrange the cubes in a row and name their total number.

5. Playing "Cards" with numbers 1, 2, 3 and 4.

Throw cards randomly to your child with the numbers 1, 2, 3, 4. If you name it correctly, you win; if you make a mistake, you name the number correctly, take it for yourself, and after one turn give it to the child again. When everyone wins, ask him to add the numbers in a column in order.

Play games 1, 2, 3, 4, 5 alternately with all the children in the group. Tell the parents present at the lesson that they should play these games with their children once a day every day at home, unless the children themselves ask for more.

Lesson #4

In the fourth lesson, children who, when tested in lesson No. 1, were able to immediately say, without counting, that there are four cubes in the box, can join the games. If there are many such children, it is advisable to divide them into groups of three children. Take turns playing with the children.

1. Game “Putting numbers to dice” with five dice.

Place five cards with the numbers 1, 2, 3, 4, 5 on the table. Place a box on the table and put four cubes in it. Ask your child how many cubes are in the box. After he answers “four,” ask him to put the number 4 next to the box (he already knows the numbers 1, 2, 3 and 4). Add a fifth cube to the box and ask him to count how many cubes are in the box now. Let him, if he wants, count the cubes with his finger. After the child says that there are already five cubes in the box, show him and tell him the number 5 and ask him to remove the number 4 from the box and put the number 5 in its place. Then put a different number of cubes in the box within five, each time asking , how many cubes are in the box and asking them to attach the corresponding number to the box. Repeat this game several times. The child will easily remember what five cubes look like, because five cubes is a full box, and will soon begin to name this number immediately, without counting. At the same time, he will remember the number 5 and will now know the numbers 1, 2, 3, 4, 5 and move the number corresponding to the number of cubes set in it to the box.

2. Game “Dwarfs in a House” with five dice.

Play the same way as in the previous lessons, but this time the gnomes will come to the house and leave it one at a time, and two at a time, and three at a time, and four at a time. Start the game with an open box, and then make a roof by covering the box with your palm.

If, with the box covered, it is still difficult for the child to guess how many gnomes there will be in the house after adding a few more, place these added cubes next to the covered box. This will make it easier for him to understand. And if, with the box covered, it is difficult for him to guess how many gnomes will remain in the house after several leave, take these few cubes out of the box so that it is not visible how many cubes are still left in the box, and place them next to the box. For example, you said that there were five gnomes in the box, but three left. The child remembers well what five cubes look like, and, looking at the three cubes that you took out from under your palm and placed next to them, without any explanation, he will guess that there are two left under the roof in the house. Play through all the possible addition and subtraction variations within five with each child. Alternate questions about adding a larger number with a smaller number with questions about adding a smaller number with a larger one; This will help the child gradually realize that the order of the terms does not change the sum. Each time after the child answers, remove the roof-palm and allow the child to add or remove cubes himself and make sure that his answer is correct (you always need to remove the last cubes, counting them from left to right of the child).

3. Game “How many empty cells?” with five cubes.

Place different numbers of cubes in the box alternately and ask the child how many cubes are in the box. And after answering, quickly close the box with your palm and ask: “How many empty cells are left?” When showing the cubes, cover the empty cells with your finger.

Games 2 and 3 can be combined. For example, after a child answers the question “How many empty cells are left?” will answer: “Three,” you can ask him: “And if three more gnomes come to two gnomes, how many gnomes will be in the house?” And immediately after answering this question, you can subtract: “And if there are five gnomes in the house, and three leave, how many will remain?”

4. Hide and seek game with five dice.

5. Playing "Cards" with numbers 1, 2, 3, 4 and 5.

Throw cards randomly to your child with the numbers 1, 2, 3, 4, 5. If you name it correctly, you win, if you make a mistake, you name the number correctly, take it for yourself, and after one turn give it to the child again. When everyone wins, ask him to add the numbers in a column in order.

6. Game “Knock-knock-knock” within four.

Tell the children that now you will play “Knock Knock Knock” with them. Tap the table twice with your fingernail or the end of a pen so that children cannot see how you do it (you can knock on the tabletop from below). Ask one of the children how many times you knocked. The answer will most likely be correct. For the next child, slowly knock four times. If he can't count the taps correctly, ask someone to help him. For the third child, knock three times. Repeat this game within four twice more with all the children, each time asking each child a different number of taps.

Play games 1, 2, 3, 4, 5, 6 alternately with all the children in the group. Remind parents in the class that they should play these games with their children once a day at home, unless the children request more.

Lesson #5

1. Repeat the six games of lesson No. 4 with all the children in turn.

2. Game "Ball without a ball" within five.

Over the past four lessons, children have learned to add and subtract numbers within five, imagining a box of cubes in their minds. And now the game “Ball Without a Ball” will help your kids gradually consolidate in their memory the results of all variants of addition and subtraction of numbers within five and begin to count faster, gradually forgetting the box.

Tell your child that you will play pretend ball with him: there will be no ball, you will simply make a movement with your hands, as if throwing a ball, and at the same time ask a question, and he will seem to catch it and throw it back to you, while answering the question. question. For example, you seem to throw a ball and ask: “There were five gnomes, three left. Left?" The child seems to throw the ball back to you and answer: “Two!”

Do not move the box with the cubes far away; it is under your hands, but covered with a sheet of paper. If your child makes a mistake or thinks too long, show him the solution to this example using blocks.

As the child memorizes the results of addition and subtraction in whole number groups within five, the game becomes faster. And even if someone once taught him to count on his fingers, now he doesn’t remember them. And his fingers are visible to you in this game.

Usually I continue to play this game within five for at least two more lessons, and if some child in the group still plays it unsure, I leave this game only for him for a few more lessons, alternating it with games 3, 4 lesson No. 4. Gradually move from the “gnomes” that “came” and “went” to the accepted terms “add” and “subtract.” If necessary, explain: “To add means to add, to subtract means to take away.” “Dwarves” will remain in the future only in the game “Hide and Seek”. Take turns playing with all the children in the group. Ask five questions to one child at a time and then move on to the next.

Remind parents present at the lesson that at home they should play game 2 of this lesson, as well as games 3, 4, 5 of lesson No. 4, with their children once a day, unless the children themselves ask for more.

3. Game "Ball with a real ball" within five.

This is the same game as the previous one, but using a ball. I play it with my children only occasionally when a warm-up is needed. This game takes up more time in the lesson than “Ball without a ball”, because It can be difficult for a child to concentrate on two tasks at once: to comprehend the question and to cope with the ball.

But for some children this game is necessary in every lesson. These are the children who answer the teacher’s questions at random, without thinking, especially when they start counting without the help of cubes in the game “Ball Without a Ball.” You ask him or her: “Take one from five. How much will be left? Answers: “Eight.” Although, if you ask him to think, he will say: “Four.” This usually happens if the child previously studied at some preparatory school, or in kindergarten in a large group and, falling behind the older children, simply memorized the answers without delving into their meaning.

In order to maintain such children's interest in mental counting without the help of cubes, it is advisable to come up with some kind of incentives for them when conducting lessons. For example, those who answered five questions in the game “Ball without a ball” and never made a mistake can be allowed to play “Ball with a real ball” three or four more times, but on the condition that the one who made a mistake is eliminated from the game.

And to do homework with a child who does not yet want to comprehend the questions and answers randomly, we can recommend two other ways for parents to stimulate his attentiveness.

First way

– play “Dog House” with your child. For correct answers, the mother gives the child some sticks (for example, matches with broken heads), which the child places one after another on the lines of a pre-drawn house until he has built the entire house, and for each wrong answer, the mother takes one stick from his house and takes away is building his own house nearby. If mom builds her house earlier, the game starts over. A house with a roof is made up of six sticks (a square of four sticks and a roof of two). As soon as the child builds his house, the game ends; he is free and can do what he wants. Wanting to build his own house before his mother’s, the child begins to listen more carefully to questions and think about the answers. If he becomes interested in this game, you can try to build a large house with him from seventeen sticks with a square of eight sticks, with a window and a door (use halves of matches for the window and the top of the door).

Second way

- play “Dots and Sticks”. Place five dots in a row on the paper. After each correct answer, draw a stick over one dot, and after an incorrect answer, cross out all the sticks and say: “All the sticks are burned.” All sticks burn out, even if a mistake was made in the last answer, after which you need to put new points on the paper and the game starts all over again. The game continues until the child answers correctly five times in a row. Sometimes, if the child himself quickly corrected his incorrect answer, you can draw him half a stick and ask an additional question to complete the drawing. As the game progresses, ask: “How many times have you answered correctly?” And then, covering the stick dots with his hand: “How many times do you still have to answer?” This will be a practical application of the ability to count. If a child is very upset because all his sticks burn out at once, it is better to play “Dog House” with him, where if he answers incorrectly, he loses only one stick, and not all at once.

In the intervals between classes, parents should continue to teach the child to count objects in pictures and in reality, count steps on a staircase, steps while walking, etc. It is desirable that by the beginning of the next lesson he can count at least ten objects, showing them one by one with his finger.

As a result of five initial lessons, children mastered addition and subtraction of numbers within five whole number groups, memorized the numbers 1, 2, 3, 4, 5 and understood their correspondence to the number of objects. After this, you can move on to the main lessons of the first stage.

APPLICATION

Fig. 1 Game “Putting numbers to dice” with five dice

Fig.2 1-5 – blanks for making five cubes Enlarge >>>

Fig.3 Box for five cubes Enlarge >>>

Table 1 Enlarge >>>

Article continues >>>

Author of the article: Sergey Polyakov Published on the website “Sun” on October 19, 2011

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Board games for skill development

The following board games allow you to teach your child counting in a fun, non-memorizing way, and then improve this skill. Your children won't even notice that learning is going on! The effectiveness of these games has already been confirmed by many parents - pay attention to the number of positive reviews.

“Fructo 10”

Suitable for children from 7 years old. Two difficulty levels.

“Fruit 10” forces you to perform many operations with numbers every minute!

Next you can watch the video instructions for the game:

“Turbo account”

Another bestseller, “Turbo Account,” instantly captivates both younger and older schoolchildren.

See video instructions for it below:

“Etazhiki”

In the game “Etazhiki” you will have to travel in a hot air balloon and practice your mental counting skills, and children will clearly understand the principle of moving through tens.

“Kotosovs”

In the game “Kotosovy” your children will learn to instantly determine the quantity without counting.

You can watch the rules and methods of the game in the following video:

You can also purchase several games at once to develop this skill and save money, in this case, turn your attention to the Game Library.

The most interesting techniques

To multiply any single-digit number by 9, you need to look at your empty palms.
Let's bend the finger corresponding in order (counting from the thumb of the left hand) to the number of the first factor.
We look at how many fingers are to the left of the curved one - these will be tens of the desired product, and to the right - its own units.
Multiplying by 11 any two-digit number, the sum of the digits of which does not reach 10, is carried out in a fun and simple way : mentally move the digits of this number apart and put their sum between them, the result is obtained. Example:24 (2+4=6<10)*11=264.
If the sum of the digits of the number multiplied by 11 turns out to be equal to 10 or more than 10, then between the mentally expanded digits of this number you should put their sum and add the first two digits on the left, leaving the other two unchanged - you get the product.
Example: 59 (5+9=14>10)*11= (5+1)49=649.

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

Learn to focus on details and mentally pronounce them.
You should solve basic mathematical problems without resorting to a calculator, for example, in a store. Mathematical operations have their own characteristics, but they are not complex. You need to figure it out once, and then practice. This should happen systematically 5-10 times a day.
Master simple mental arithmetic techniques and set yourself daily brain training goals. There are many mobile applications on the Internet with brain training tasks.

In the next video, a mathematician will tell you how you can learn to count in your head.

Learning to count in your head

Are you sure it's time to get started, but don't know where to start? We offer the most effective training methods - choose what suits you.

Games

At an early age, a person learns about the world in a playful way. Combine business with pleasure.

Organize a small “shop” in the nursery: let the child arrange the goods on his own, stick on price tags and try to sell you something. During the process, he will calculate the total cost of all items and offer the buyer a discount. This game develops mental calculation skills and resourcefulness: children learn to plan actions, negotiate, and quickly respond to circumstances.
Arrange a little competition between your child and his friends. Prepare several problems and offer to solve them. The one who does it faster wins. But do not forget to encourage the efforts of each player, even if someone is slower than others.
The popular game “House” is an introduction to the concept of “number composition”. Print, draw or buy a multi-story house with a roof (a ready-made set of pictures or cubes). On each floor, 2-3 numbers are placed, which add up to the number on the roof. Participants in the game get used to mental arithmetic and enjoy building a house.

Learning rules and tables

There are tables for adding and subtracting numbers. There is no point in memorizing them, like the multiplication tables, but you need to explain to the child how they work. Solve a couple of examples together, and then see if he can cope with the tasks without outside help.

To enhance the memorization effect, hang colorful tables with large numbers on the wall. Visual memory will work, and when counting verbally, the child will imagine exactly them. Using tables speeds up memorization.

Talk about simple rules that help you do mental arithmetic. Adults also use them.

When adding 7, 8, 9, we first add 10, and then subtract the “extra”: 9+9=9+10-1=18.
Adding by parts to get a convenient whole number: 14+8=14+6+2=22.
We subtract gradually, dividing the number into parts: 46-8=46-(6+2)=46-6-2=38.