Counting is fun and easy! How easy is it to teach a child to count in his head?

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

1. 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.
2. This skill will help you avoid being deceived when making daily purchases.
3. 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.
4. 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.
5. 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.

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.

Drawing conclusions

There is no doubt about the importance of mental calculation skills. To achieve the desired results, every parent should:

• Be patient. Remember, the baby is not a robot. It is impossible to learn all the numbers and actions with them the first time. Do not scold children for mistakes, try to maintain an atmosphere of love, care and mutual understanding.
• Prepare the material. Buy ready-made educational kits or make them by hand. Cards, cubes and toys will provide serious learning assistance.
• Praise your baby. Children, like no one else, need parental approval. Don't forget to praise your child for his successes.

If you don't have enough time or teaching talent, use the BrainApps service. Using effective techniques developed by leading experts will save your nerves and prove that your child is capable of incredible intellectual 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.

Age groups in kindergarten by year according to Federal State Educational Standards

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.

Algorithms

When the child has learned the basic mathematical operations, you can consolidate the material covered using a specific algorithm. Children can be introduced to number formation using comparisons between groups of objects. To do this you need:

1. Present to the child two different groups of objects that he can count.
2. “how many items are in each group?”
3. After he counts the items, let him compare their quantities, where and how much more or less.
4. Ask him how to get a new number.
5. Add a few more items to the items and repeat the count to the new limit.

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

How to help a child?

To help children learn to count in their heads as quickly as possible, invite them to “play” with numbers:

• “Touching” the numbers. Make large blanks of numbers from cardboard, cover them with cloth or thick paper. Then put them in a box or opaque bag. Invite your child to touch the number with his fingers and say what it is called.
• We find a couple. On a large sheet of paper, draw or stick numbers of different sizes and colors. Ask your child to find the same ones without being distracted by extraneous signs.
• Draw on the back. Stand behind your baby and draw a number with your fingers. Let him try to guess it. Then invite him to change places.
• Dice. Take cards with pictures of numbers and a dice. Throw it and ask your baby to count the number of dots and then find the matching card. To make the challenge more difficult, roll two dice at the same time.
• Little house. Draw a house on a large piece of paper and divide it into 3 parts using vertical lines. Place a card with a number in the center. The child needs to find adjacent numbers and place them on the left and right.
• High-rise building. Draw a 9-story house on a piece of paper. Hand your child cards with numbers and ask them to number each floor.
• The missing. Place numbers from 1 to 9 on the surface. Then ask the baby to close his eyes and remove one. He needs to tell which card is lost.

There is another effective way to achieve positive results - games from BrainApps. The service offers parents a unique opportunity to spend time with their child using useful and educational exercise equipment. For example, the following will help in mastering mental arithmetic:

• "Numerical Reach". You need to remember the suggested numbers and reproduce them in the exact sequence.
• "Fruit mathematics." 3 areas will appear on the monitor in which a variety of fruits will be located. The main task is to quickly count them and answer the specified question.
• “Call in the correct order Plus.” A table with numbers arranged randomly will be displayed on the screen. Depending on the proposed task, you must click all the numbers in descending or ascending order.

It is also worth paying attention to the games “Piggy Bank”, “Adding Numbers from Memory”, “Memorize and Call”, “Guess the Operation” and others.

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.

An easy way to teach your child to count

Tatyana Vyacheslavovna Kuzmina

An easy way to teach your child to count

A surprisingly easy way to teach your child mental math

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, this will be just a game, and all that is required from parents is to devote a few minutes a day to this 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.

First, a few introductory words.

The first question that some parents have is: 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.

The 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.

Do not 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, resulting in 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.

At the first stage

In 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

preschoolers learn 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 mental arithmetic? 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 it discourages 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 toys, fish, birds, or ladybugs 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 (see video file 056). 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, since the duration of each is only 10-20 minutes. They can also be combined with reading lessons. 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.

Classes with children in mental counting in a small group can begin from approximately the age of three, if they already know how to count objects with their fingers, at least up to five. And with their own child, parents can easily start elementary lessons using this method from the age of two.

Initial lessons of the first stage.

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. 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 out a drawing on thick paper, 200-250 g/m2, and then cut out cube blanks from it, glue them together in accordance with the instructions, fill them with any filler, for example, some kind of cereal, and cover 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 a pattern 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.

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.

Game “Putting numbers to cubes”

with two cubes.

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 in its place

2. 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.

Game "Dwarves in a 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 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. the 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.

Sergey Polyakov

Article provided by the site “7 steps to a book. How I teach children to read"

https://www.7ya.ru/article/Udivitelno-legkij-sposob-obucheniya-rebenka-ustno

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.

At what age should children be taught to do mental addition?

The easiest time to teach a child to perform arithmetic operations in his head is during the period when his brain is developing most actively. Usually this is the age of 5-7 years. However, children show interest in counting much earlier. You can develop and maintain a thirst for knowledge even in children under 1 year of age. The first games contribute to this:

• "Magpie-Crow";
• “The fingers went out for a walk”;
• “Ladushki” and the like.

At 2-4 years old, children love to play with cubes, pyramids and sorters. They enjoy building towers and attaching rings to the rod. Explain to your child that first you take the largest circle (first), then a little smaller (second), even smaller (third) and so on. Such games stimulate the child’s curiosity and desire to count everything that is around.

At an older age, children calmly memorize numbers and learn to count. A preschooler can easily cope with simple arithmetic problems, distinguish between “a lot and a little” and count mentally up to 10. How to familiarize a child with numbers and the first manipulations with them? You need to understand the basic rules for learning numbers.

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.

Other techniques

In addition to the methods developed by teachers, there are many “folk” methods developed by thousands of parents from their own experience. They may not be as effective as the previous ones, but together with them they give a visible result. Therefore, such techniques can be used as a favorable background for the main teaching method. So how else can you speed up the process of learning numbers and arithmetic operations?

Count surrounding objects

In order to teach your child to count in his head, you can count all the objects that surround you with him. For example, at breakfast you can count cutlery, in the living room - flowers in a vase, while exploring courtyards and streets - cars. Even if you meet a large crowd of people, you can turn this to your advantage and count them. For this technique to have the best result, the resulting numbers can be written down on a separate piece of paper.