Secrets of the magic of mathematics. How to learn to count quickly in your head? Basic number operations without a calculator Solve examples quickly in your head

The ability to count in your head is a useful skill not only at school, but also in everyday life. With its help, you can almost instantly and accurately perform any operations with numbers without the help of a calculator or paper. Today we will talk about developing mental counting skills, look at useful exercises and give advice.

Advantages of mental counting

We are taught counting skills from childhood. These are the elementary operations of addition, subtraction, multiplication and division. In the case of small numbers, even primary schoolchildren can easily cope with them, but the task becomes significantly more complicated when you need to perform an operation with a two- or three-digit number. However, with the help of training, simple exercises and little tricks, it is quite possible to subordinate these operations to rapid mental processing.

You may ask why this is necessary, because there is such a convenient thing as a calculator, and in case of emergency there is always paper at hand to carry out calculations. Quick mental arithmetic has many benefits:

1. Save time. Calculate the cost of purchases in a store or cafe and check the correctness of the change, get ahead of your classmates in solving an example or writing a test - all this is possible if you count well in your head.
2. Opportunity to address other aspects of the task. Often tasks contain at least two sides: purely arithmetic (operations with numbers) and intellectual and creative (choosing an appropriate solution for a specific problem, a non-standard approach for a faster solution, etc.). If a student does not cope well and quickly with the first side, then the second suffers from this: concentrating on completing the arithmetic component, the child does not think about the meaning of the problem, and may not see a catch or a simpler solution. If counting operations are brought to automaticity or simply do not require a lot of time, then a detailed consideration of the meaning of the problem is “turned on”, and it becomes possible to apply a creative approach to it.
3. Intelligence training. Mental arithmetic allows you to keep your intellect in good shape and constantly engage your mental processes. This is especially true for operations with large numbers, when we select a method to simplify the operation as much as possible.

Exercises with tables

The exercises are designed for children of any age who have difficulty performing operations with prime numbers (one- and two-digit). Allows you to train mental calculation skills and bring simple arithmetic operations to automation.

Necessary materials: To complete the exercises you will need a grid of one- and two-digit numbers. Example:

The first column contains the numbers with which you need to perform actions. The second contains responses to these actions. Using a specially cut bookmark, you can check the correctness of the calculation. For example:

Picture from the book: Postalovsky I.Z. “Training tables for automating mental counting”

Exercise options:

1. Consistently add pairs of numbers in a grid in your mind. Say the answer out loud and test yourself using the second column and bookmark. The task can be completed at a free pace or against time.
2. Consistently subtract numbers from the grid in your head.
3. Consistently add pairs of numbers in a grid in your mind. Add the number 5 to each sum and say the answer out loud.
4. Consistently add up triplets of numbers in a grid in your mind.
5. Perform the following actions sequentially with all the numbers in the grid: add the bottom number, subtract the next number in the column from the resulting amount.

Based on such tables, you can create any tasks. Grids are compiled depending on the modification of the exercise.

IMPORTANT! For the exercise to be effective, it must be performed regularly until the skill is fully mastered.

Mastering multiplication

The exercise is intended for children who have mastered the multiplication table from 1 to 10. It trains the skill of multiplying a two-digit number by a single-digit number.

A column is made up of arbitrary two-digit numbers. Task for the child: sequentially multiply these numbers, first by 1, then by 2, by 3, etc. The answer is spoken out loud. This is carried out until the answers are remembered and given automatically.

The main thing is attention

So, you say, we need to decide?

Exercise: add the numbers in sequence: 3000 + 2000+ 30 + 2000 + 10 + 20 + 1000 + 10 + 1000 + 30 =

State the answer. Test yourself with a calculator.

If the answer turns out to be correct, you need to consolidate your success and solve several more similar examples (can be compiled arbitrarily). If there was an error in the answer, you need to go back to the sequence of numbers and correct it.

What's the idea: As a result of adding the numbers, the sum is 9100. But if you do this inattentively, the answer 10000 will automatically appear (the brain tries to round the sum, to make the answer more beautiful). Therefore, it is very important to maintain control over your actions when performing arithmetic problems in several steps.

Possible examples:

3000 – 700 - 60 – 500 - 40 – 300 -20 – 100 =

100:2:2*3*2 + 50 – 100 + 200 – 30 =

If most of the examples are solved with errors (BUT! not related to the ability to count in principle), then it makes sense to increase concentration. To do this you can:

• Minimize external stimuli. For example, if possible, go into another room, turn off the music, close the window, etc. If you need to concentrate on an example during a lesson, when it is not possible to go out and achieve complete silence, you need to close your eyes and imagine the numbers with which the actions are carried out.
• Add an element of competition. Knowing that a correct and quick solution will bring victory over the opponent and/or some kind of encouragement, the student will be more willing to focus on the numbers and make maximum effort in the calculation process.
• Set personal records. You can visualize all the mistakes made by the student during the calculation process. For example, draw a flower with large petals (number of petals = number of solved examples). As many petals will be painted black as the number of examples that were solved with errors. The goal is to reduce the number of black petals as much as possible, setting personal records with each batch of examples.

Small tricks and tips for quick counting

1. Grouping. By sequentially adding/subtracting several numbers, you need to see which of them, when added/subtracted, will give an integer: 13 and 67, 98 and 32, 49 and 11, etc. First perform actions with these numbers, and then move on to the rest. Example: 7+65+43+82+64+28=(7+43)+(82+28)+65+64=50+110+124=289
2. Decomposition into tens and ones. When multiplying two two-digit numbers (for example, 24 and 57), it is advantageous to decompose one of them (ending in a smaller digit) into tens and units: 24 as 20 and 4. The second number is multiplied first by tens (57 by 20), then by units ( 57 by 4). Then both values ​​are added together. Example: 24?57=57?20+57?4=1140+228=1368
3. Multiply by 5. When multiplying any number by 5, it is more profitable to first multiply it by 10 and then divide it by 2. Example: 45?5=45?10/2=450/2=225
4. Multiplying by 4 and 8. When multiplying by 4, it is more profitable to multiply the number twice by 2; by 8 - three times by 2. Example: 63?4=63x2x2=126?2=252
5. Division by 4 and 8. Similar to multiplication: when dividing by 4, divide the number twice by 2, by 8 - three times by 2. Example: 192/8=192/2/2/2=96/2/2=48/2=24
6. Squaring numbers ending in 5. The following algorithm will make this action easier: the number of tens squared is multiplied by the same number plus one and added at the end to 25. Example: 75^2=7x(7+1)=7?8=5625
7. Multiplication by formula. In some cases, to make calculations easier, you can use the difference of squares formula: (a+b)x(a-b)=a^2-b^2. Example: 52?48=(50+2)x(50-2)=50^2-2^2=2500-4=2496

P.S. These rules can significantly simplify mental counting, but regular training is necessary so that you can use the rule correctly at the right time. Therefore, it is recommended to solve as many examples for each of them as will allow you to automate the skill. To begin with, you can write down calculations on paper, gradually reducing the amount of writing and transferring the operations into a mental plan. At first, it is also recommended to check your answers using a calculator or standard column calculations.

Quick counting techniques: magic accessible to everyone

In order to understand what role numbers play in our lives, perform a simple experiment. Try to do without them for a while. Without numbers, without calculations, without measurements... You will find yourself in a strange world where you will feel absolutely helpless, tied hand and foot. How to make it to a meeting on time? Can you tell one bus from another? Make a phone call? Buy bread, sausage, tea? Cook soup or potatoes? Without numbers, and therefore without counting, life is impossible. But how difficult this science is sometimes! Try quickly multiplying 65 by 23? Does not work? The hand itself reaches for a mobile phone with a calculator. Meanwhile, semi-literate Russian peasants 200 years ago calmly did this, using only the first column of the multiplication table - multiplication by two. Don't believe me? But in vain. This is reality.

Stone Age "computer"

Even without knowing the numbers, people were already trying to count. If our ancestors, who lived in caves and wore skins, needed to exchange something with a neighboring tribe, they did it simply: they cleared the area and laid out, for example, an arrowhead. A fish or a handful of nuts lay nearby. And so on until one of the exchanged goods ran out, or the head of the “trade mission” decided that enough was enough. It’s primitive, but very convenient in its own way: you won’t get confused and won’t be deceived.

With the development of cattle breeding, the tasks became more complicated. A large herd had to be counted somehow in order to know whether all the goats or cows were there. The “calculating machine” of the illiterate but smart shepherds was a hollowed-out pumpkin with pebbles. As soon as the animal left the pen, the shepherd placed a pebble in the pumpkin. In the evening the herd returned, and the shepherd took out a pebble with each animal that entered the pen. If the pumpkin was empty, he knew that the herd was all right. If there were stones left, he went to look for the loss.

When the numbers came in, things got better. Although for a long time our ancestors had only three numerals in use: “one”, “pair” and “many”.

Is it possible to count faster than a computer?

Overtake a device performing hundreds of millions of operations per second? Impossible... But the one who says this is cruelly disingenuous, or simply deliberately overlooks something. A computer is just a set of chips in plastic; it does not count on its own.

Let's pose the question differently: can a person, counting in his head, outperform someone who does calculations on a computer? And here the answer is yes. After all, in order to receive a response from the “black suitcase”, the data must first be entered into it. This will be done by a person using his fingers or voice. And all these actions have time limits. Insurmountable restrictions. Nature itself supplied them to the human body. Everything - except one organ. Brain!

The calculator can perform only two operations: addition and subtraction. For him, multiplication is multiple addition, and division is multiple subtraction.

Our brains act differently.

The class where the future king of mathematics, Carl Gauss, studied, once received a task: add all the numbers from 1 to 100. Carl wrote the absolutely correct answer on his board as soon as the teacher finished explaining the task. He did not diligently add the numbers in order, as any self-respecting computer would do. He applied the formula he himself discovered: 101 x 50 = 5050. And this is far from the only technique that speeds up mental calculations.

The simplest techniques for quick counting

They are studied at school. The simplest thing: if you need to add 9 to any number, add 10 and subtract 1 if 8 (+ 10 - 2), 7 (+ 10 - 3), etc.

54 + 9 = 54 + 10 - 1 = 63. Fast and convenient.

Two-digit numbers add just as easily. If the last digit in the second term is greater than five, the number is rounded to the next ten, and then the “extra” is subtracted. 22 + 47 = 22 + 50 - 3 = 69. If the key number is less than five, then you need to add the tens first, then the ones: 27 + 51 = 20 + 50 + 7 + 1 = 78.

With three-digit numbers, no difficulties arise in the same way. We add them up as we read, from left to right: 321 + 543 = 300 + 500 + 20 + 40 + 1 + 3 = 864. Much easier than in a column. And much faster.

What about subtraction? The principle is the same: we round what is subtracted to a whole number and add what is missing: 57 - 8 = 57 - 10 + 2 = 49; 43 - 27 = 43 - 30 + 3 = 16. Faster than using a calculator - and no complaints from the teacher, even during the test!

Do I need to learn the multiplication table?

Children, as a rule, cannot stand this. And they do it right. There's no point in teaching her! But don’t rush to be indignant. No one is saying that you don't need to know the table.

Its invention is attributed to Pythagoras, but, most likely, the great mathematician only gave a complete, laconic form to what was already known. At the excavations of ancient Mesopotamia, archaeologists found clay tablets with the sacramental: “2 x 2”. People have been using this extremely convenient system of calculations for a long time and have discovered many ways that help to comprehend the internal logic and beauty of the table, to understand it - and not to stupidly, mechanically memorize it.

In ancient China, they began to learn the table by multiplying by 9. It’s easier this way, and not least because you can multiply by 9 “on your fingers.”

Place both hands on the table, palms down. The first finger on the left is 1, the second is 2, etc. Let's say you need to solve the example 6 x 9. Raise your sixth finger. The fingers on the left will show tens, on the right - ones. Answer 54.

Example: 8 x 7. Left hand is the first multiplier, right hand is the second. There are five fingers on the hand, but we need 8 and 7. We bend three fingers on the left hand (5 + 3 = 8), on the right hand 2 (5 + 2 = 7). We have five bent fingers, which means five dozen. Now let's multiply the remaining ones: 2 x 3 = 6. These are units. Total 56.

This is just one of the simplest “finger” multiplication techniques. There are many of them. You can operate with numbers up to 10,000 on your fingers!

The “finger” system has a bonus: the child perceives it as a fun game. He studies willingly, experiences a lot of positive emotions and, as a result, very soon begins to perform all operations in his mind, without the help of his fingers.

You can also divide using your fingers, but it is a little more difficult. Programmers still use their hands to convert numbers from decimal to binary - it is more convenient and much faster than on a computer. But within the framework of the school curriculum, you can learn to quickly divide even without fingers, in your mind.

Let's say we need to solve example 91: 13. Column? There is no need to dirty the paper. The dividend ends in one. And the divisor is by three. What is the very first thing in the multiplication table that involves a three and ends with a one? 3 x 7 = 21. Seven! That's it, we caught her. You need 84: 14. Remember the table: 6 x 4 = 24. The answer is 6. Simple? Still would!

The magic of numbers

Most fast counting techniques are similar to magic tricks. Take the well-known example of multiplying by 11. To, for example, 32 x 11, you need to write 3 and 2 at the edges, and put their sum in the middle: 352.

To multiply a two-digit number by 101, you simply write the number twice. 34 x 101 = 3434.

To multiply a number by 4, you need to multiply it by 2 twice. To divide, divide it by 2 twice.

Many witty and, most importantly, quick techniques help raise a number to a power and extract the square root. The famous “30 techniques of Perelman” for mathematically minded people will be cooler than the Copperfield show, because they also UNDERSTAND what is happening and how it is happening. Well, the rest can just enjoy the beautiful focus. For example, you need to multiply 45 by 37. Write the numbers on a sheet of paper and divide them with a vertical line. Divide the left number by 2, discarding the remainder until we get one. Right - multiply until the number of lines in the column is equal. Then we cross out from the RIGHT column all those numbers opposite which in the LEFT column we got an even result. We add up the remaining numbers from the right column. The result is 1665. Multiply the numbers in the usual way. The answer will fit.

"Charge" for the mind

Quick counting techniques can greatly make life easier for a child at school, for a mother in a store or in the kitchen, and for a father at work or in the office. But we prefer a calculator. Why? We don't like to strain ourselves. It's hard for us to keep numbers, even two-digit ones, in our heads. For some reason they don't hold up.

Try going to the middle of the room and doing the splits. For some reason it doesn’t “plant”, right? And the gymnast does it completely calmly, without straining. Need to train!

The easiest way to train and, at the same time, warm up the brain: mentally count out loud (required!) through numbers to one hundred and back. In the morning, while standing in the shower, or while preparing breakfast, count: 2.. 4.. 6.. 100... 98.. 96. You can count in three, in eight - the main thing is to do it out loud. After just a couple of weeks of regular practice, you will be surprised how much EASIER it will become to handle numbers.

The principle of operation is based on generating examples in mathematics of a suitable level of complexity for all classes, the solution of which contributes to the development of mental calculation skills.

The application has a beneficial effect on the mental activity of both children and adults.

Variety of modes

On the mode settings page, you can set the necessary parameters for generating examples in mathematics for any class.

The mental arithmetic simulator allows you to practice 4 well-known arithmetic operations at six difficulty levels.

At this stage of development, modes were thought out and implemented that allow you to work with two sets of numbers: Positive And Negative. In each of them you can practice different types of tasks: Example, Equation, Comparison.

This mode includes regular arithmetic examples in mathematics consisting of two or three numbers.

A mode in which the desired number can be in any position.

A mode in which it is necessary to correctly place a comparison sign between the results of two examples.

All settings changes are immediately applied and you can immediately see what the new example will look like in the graph "For example". And when the selection of the desired characteristics is completed, click on the button GO.

A bonus is the ability to download and subsequently print “independent work” in PDF format, consisting of 26 examples of the corresponding mode, click on the icon Printer.

Counting process

At the top there are 4 quick access buttons: to the main page of the site, user profile. It is also possible to enable/disable sound notifications or go to the Error and Hint Log.

You solve the given example, enter the answer using the on-screen keyboard, and click on the CHECK button. If you find it difficult to answer, use the hint. After checking the result, you will see a message either about the correct answer entered or about an error.

If for any reason you want to reset your results, click on the “Reset Result” icon.

Game form

The application also provides game animation “Fencer Battle”.

Depending on the correctness of the entered answer, one or another fencer strikes, pushing back his opponent. However, it is worth considering that every second of inactivity the enemy crowds your player, and if you wait for a long time, he will pop up loss message.

This interface makes the process of solving mathematical examples more interesting, while also being a simple motivation for children.

If the animation mode bothers you, you can disable it on the settings page using the icon

Error log

At any time while working with the simulator, you can go to the “Error Log” section of the application by clicking on the corresponding icon at the top, or by scrolling down the page.

Here you can see your statistics (number of examples by category) for the last day and for the last mode.

And also see a list of errors and hints (maximum 6 pieces), or go to detailed statistics.

Additional Information

site domain + application section + encoding of this mode

For example: website/app/#12301

Thus, you can easily invite anyone to compete in solving arithmetic examples in mathematics, simply by passing them a link to the current mode.

Verbal counting- an activity that fewer and fewer people bother with these days. It’s much easier to take out a calculator on your phone and calculate any example.

But is this really so? In this article, we will present math hacks that will help you learn how to quickly add, subtract, multiply and divide numbers in your head. Moreover, operating not with units and tens, but with at least two-digit and three-digit numbers.

After mastering the methods in this article, the idea of ​​reaching into your phone for a calculator will no longer seem so good. After all, you can not waste time and calculate everything in your head much faster, and at the same time stretch your brains and impress others (of the opposite sex).

We warn you! If you are an ordinary person and not a child prodigy, then developing mental arithmetic skills will require training and practice, concentration and patience. At first everything may be slow, but then things will get better and you will be able to quickly count any numbers in your head.

Gauss and mental arithmetic

One of the mathematicians with phenomenal mental arithmetic speed was the famous Carl Friedrich Gauss (1777-1855). Yes, yes, the same Gauss who invented the normal distribution.

In his own words, he learned to count before he spoke. When Gauss was 3 years old, the boy looked at his father's payroll and declared, "The calculations are wrong." After the adults double-checked everything, it turned out that little Gauss was right.

Subsequently, this mathematician reached considerable heights, and his works are still actively used in theoretical and applied sciences. Until his death, Gauss performed most of his calculations in his head.

Here we will not engage in complex calculations, but will start with the simplest.

Adding numbers in your head

To learn how to add large numbers in your head, you need to be able to accurately add numbers up to 10 . Ultimately, any complex task comes down to performing a few trivial actions.

Most often, problems and errors arise when adding numbers with “passing through 10 " When adding (and even when subtracting), it is convenient to use the “support by ten” technique. What is this? First, we mentally ask ourselves how much one of the terms is missing to 10 , and then add to 10 the difference remaining until the second term.

For example, let's add the numbers 8 And 6 . To from 8 get 10 , lacks 2 . Then to 10 all that remains is to add 4=6-2 . As a result we get: 8+6=(8+2)+4=10+4=14

The main trick to adding large numbers is to break them down into place value parts, and then add those parts together.

Suppose we need to add two numbers: 356 And 728 . Number 356 can be represented as 300+50+6 . Likewise, 728 will look like 700+20+8 . Now we add:

356+728=(300+700)+(50+20)+(8+6)=1000+70+14=1084

Subtracting numbers in your head

Subtracting numbers will also be easy. But unlike addition, where each number is broken down into place value parts, when subtracting we only need to “break down” the number we are subtracting.

For example, how much will 528-321 ? Breaking down the number 321 into bit parts and we get: 321=300+20+1 .

Now we count: 528-300-20-1=228-20-1=208-1=207

Try to visualize the processes of addition and subtraction. At school everyone was taught to count in a column, that is, from top to bottom. One way to restructure your thinking and speed up counting is to count not from top to bottom, but from left to right, breaking numbers into place parts.

Multiplying numbers in your head

Multiplication is the repetition of a number over and over again. If you need to multiply 8 on 4 , this means that the number 8 need to repeat 4 times.

8*4=8+8+8+8=32

Since all complex problems are reduced to simpler ones, you need to be able to multiply all single-digit numbers. There is a great tool for this - multiplication table . If you do not know this table by heart, then we strongly recommend that you learn it first and only then start practicing mental counting. Besides, there is essentially nothing to learn there.

Multiplying multi-digit numbers by single-digit numbers

First, practice multiplying multi-digit numbers by single-digit numbers. Let it be necessary to multiply 528 on 6 . Breaking down the number 528 into ranks and go from senior to junior. First we multiply and then add the results.

528=500+20+8

528*6=500*6+20*6+8*6=3000+120+48=3168

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Multiplying two-digit numbers

There is nothing complicated here either, only the load on short-term memory is a little greater.

Let's multiply 28 And 32 . To do this, we reduce the entire operation to multiplication by single-digit numbers. Let's imagine 32 How 30+2

28*32=28*30+28*2=20*30+8*30+20*2+8*2=600+240+40+16=896

One more example. Let's multiply 79 on 57 . This means that you need to take the number " 79 » 57 once. Let's break the whole operation into stages. Let's multiply first 79 on 50 , and then - 79 on 7 .

• 79*50=(70+9)*50=3500+450=3950
• 79*7=(70+9)*7=490+63=553
• 3950+553=4503

Multiplying by 11

Here's a quick mental math trick to multiply any two-digit number by 11 at phenomenal speed.

To multiply a two-digit number by 11 , we add the two digits of the number to each other, and enter the resulting amount between the digits of the original number. The resulting three-digit number is the result of multiplying the original number by 11 .

Let's check and multiply 54 on 11 .

• 5+4=9
• 54*11=594

Take any two-digit number and multiply it by 11 and see for yourself - this trick works!

Squaring

Using another interesting mental counting technique, you can quickly and easily square two-digit numbers. This is especially easy to do with numbers that end in 5 .

The result begins with the product of the first digit of a number by the next one in the hierarchy. That is, if this figure is denoted by n , then the next number in the hierarchy will be n+1 . The result ends with the square of the last digit, that is, the square 5 .

Let's check! Let's square the number 75 .

• 7*8=56
• 5*5=25
• 75*75=5625

Dividing numbers in your head

It remains to deal with division. Essentially, this is the inverse operation of multiplication. With division of numbers up to 100 There shouldn’t be any problems at all - after all, there is a multiplication table that you know by heart.

Division by a single digit number

When dividing multi-digit numbers by single-digit numbers, it is necessary to select the largest possible part that can be divided using the multiplication table.

For example, there is a number 6144 , which must be divided by 8 . We recall the multiplication table and understand that 8 the number will be divided 5600 . Let's present an example in the form:

6144:8=(5600+544):8=700+544:8

544:8=(480+64):8=60+64:8

It remains to divide 64 on 8 and get the result by adding all the division results

64:8=8

6144:8=700+60+8=768

Division by two digits

When dividing by a two-digit number, you must use the rule of the last digit of the result when multiplying two numbers.

When multiplying two multi-digit numbers, the last digit of the multiplication result is always the same as the last digit of the result of multiplying the last digits of those numbers.

For example, let's multiply 1325 on 656 . According to the rule, the last digit in the resulting number will be 0 , because 5*6=30 . Really, 1325*656=869200 .

Now, armed with this valuable information, let's look at division by a two-digit number.

How much will 4424:56 ?

Initially, we will use the “fitting” method and find the limits within which the result lies. We need to find a number that, when multiplied by 56 will give 4424 . Intuitively let's try the number 80.

56*80=4480

This means that the required number is less 80 and obviously more 70 . Let's determine its last digit. Her work on 6 must end with a number 4 . According to the multiplication table, the results suit us 4 And 9 . It is logical to assume that the result of division can be either a number 74 , or 79 . We check:

79*56=4424

Done, solution found! If the number didn't fit 79 , the second option would definitely be correct.

In conclusion, here are some useful tips that will help you quickly learn mental arithmetic:

• Don't forget to exercise every day;
• do not quit training if the results do not come as quickly as you would like;
• download a mobile application for mental calculation: this way you don’t have to come up with examples for yourself;
• Read books on fast mental counting techniques. There are different mental counting techniques, and you can master the one that best suits you.

The benefits of mental counting are undeniable. Practice and every day you will count faster and faster. And if you need help in solving more complex and multi-level problems, contact student service specialists for quick and qualified help!

Mental arithmetic trainer— easily and significantly increases a person’s intellectual potential.

The result of acquiring skills and achieving normative qualifications will be the assignment of a sports category (I category, II category, III category, candidate master of sports, master of sports and grandmaster).

1. People from the group are distinguished both by their ability to speak beautifully and correctly, and by their ability to quickly count in their heads, and they are usually classified as smart. For a student, the ability to quickly count in his head allows him to study more successfully, and for an engineer and scientist, he can reduce the time it takes to obtain the result of his work.
2. CS is needed not only by schoolchildren, but also by engineers, teachers, medical workers, scientists and managers at various levels. Those who count quickly find it easier to study and work. The US is not a toy, although it is entertaining. It allows the student to return to those “rails” from which he once fell; increases the speed and quality of information perception; disciplines and produces precision in everything; teaches you to notice details and little things; teaches you to save; creates images of objects and phenomena; allows you to foresee the future and develops human intelligence.
3. “European-quality renovation” in your head needs to start with simple arithmetic operations that allow you to structure your brain.
4. The ability to quickly count in your head gives the student self-confidence. As a rule, those who do well at school or university do the fastest math in their heads. If a lagging student is taught to quickly count in his head, this will certainly have a beneficial effect on his performance, and not only in natural sciences, but also in all other subjects. This has been proven by practice.
5. Voluntary attention and interest during oral counting changes the wandering gaze of a lagging student to a fixed one, and the concentration of attention reaches several levels of depth in the subject or process that is being studied.
6. “The study of mathematics disciplines thinking, accustoms one to the correct verbal expression of thoughts, accuracy, conciseness and clarity of speech, fosters perseverance, the ability to achieve the intended goal, develops efficiency, and promotes correct self-esteem of mastery of the subject being studied.” (Kudryavtsev L.D. – Corresponding Member of the RAS. 2006.).
7. A student who has learned to quickly count in his head, as a rule, begins to think faster.
8. The one who by nature counts well will naturally discover intelligence in any other science, and the one who counts slowly, learning this art and mastering it, will be able to improve his mind, make it sharper (Plato).
9. The acquired mental arithmetic skills will last for some people 5-10 years, and for others for a lifetime.
10. It will be easier for our descendants to learn and gain knowledge. However, the culture of mental calculation will always be an integral part of universal human culture.
11. Those who count quickly in their heads tend to think clearly, perceive quickly, and see more deeply.
12. Mastering CS develops figurative, diagrammatic and systemic thinking, expands working memory, range of perception, accustoms one to thinking several moves ahead, improves the quality of thinking in terms of the quantitative characteristics of objects.
13. CS increases clarity of thinking, self-confidence, as well as strong-willed qualities (patience, perseverance, endurance, hard work). Teaches deep and sustained concentration of attention, conjecture and finishing of begun phrases (especially in preschoolers and primary school students).