Mental counting games. Mental arithmetic

Verbal counting has existed as long as humanity has existed. Skills at different times quick count played a big role in the development of not only people, but all of humanity. Now science has advanced so far that powerful computers are used for calculations, and a person is simply not able to do as many calculations as is necessary to just run the Large Hadron Collider or an ordinary smartphone.

But even now, when computer systems keep accounting records for millions of companies, automate all complex and routine operations at enterprises, factories, airports and even in stores - quick count has not lost and will not lose its relevance.

Examples of exercises for mental counting

Fruit mathematics

1. Develops attention span.
2. Improves logic.

The Fruit Math game will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.

Numerical coverage

1. Develops memory capacity.
2. Improves semantic memory.

You need to remember the numbers and reproduce them in the correct order. You can use the keyboard.

Mental numeracy skills

Mental numeracy skills are different and before going further, please answer a few questions:

1. Do you want to learn count quickly in your mind?
2. For what purpose do you want learn to count quickly?
3. How often do you use a calculator?
4. Do you always feel comfortable using a calculator?
5. How much time do you spend finding it or running it on your phone/computer?
6. Would you learn to count quickly for your intellectual development?
7. You want quickly count change in a store?
8. Do you often need to perform complex mathematical operations?
9. Don't you want to strain every time to count something in your head?
10. Are you interested in comprehensive or highly specialized development of intelligence?
11. Do you want to become a genius or just expand your horizons? :)

These were questions to think about. They help not only to involve you in the process, but also to show alternative options when quick counting skills are very necessary. Think, perhaps you will find other advantages, what other benefits this mathematical skill can bring.

If you answered “Yes” to at least one of the questions, then I hope that you will learn to do better mental math.

Mental arithmetic lessons

To learn count quickly mentally, you will need to train your brain every day. Do mental counting exercises for 15-30 minutes a day. Already in the first days you will notice the result; most achieve success already in the first lesson.

I remember it was the same for me, when I had not considered anything for a long time and decided to see what was left of my former abilities. At first I counted very slowly, but then I got faster and faster.. At the first lesson, I began to quickly add almost all three-digit numbers. Memory development plays a very important role in the counting process. The better the memory is developed, the faster the most frequent combinations are remembered.

As a result, the brain remembers different options and produces results faster. Therefore, the counting then proceeds more from memory than from calculations. To calculate complex actions, the results of simpler ones can be taken from memory.

Mental arithmetic lessons online

Use mental counting techniques 15-20 minutes a day, you will feel the result already in the first lessons. Interesting ones will appear there soon mental counting simulators who teach this art in a playful way.

Games for developing mental arithmetic

Have you ever thought: " How can you practice counting easily and interestingly?". Most likely yes, because it is very difficult to train mental calculation in the traditional way, as is customary at school.

Our brain loves to play, it loves interesting tasks where progress is visible in graphs or points. This is why many scientists have been studying the functioning of the brain over the last century. They found that skills are best developed through play. Play 3-5 games a day, for 2 minutes and you will see the result. The speed of your answers and the points you earn will gradually increase.

Game "Guess the operation"

This is one of the best exercises to practice counting, because you will need to insert the correct math symbols to get the correct result. This exercise will help you develop verbal counting, logic and speed of thought. With each correct answer the difficulty increases.

Game "Mathematical matrices"

"Mathematical matrices" is a great exercise for development. oral counting which will help develop the mental functioning of the brain, verbal counting, quick search for the necessary components, attentiveness. The essence of the game is that the player has to find a pair from the proposed 16 numbers that will add up to a given number, for example, the picture shows the number “29”, and the desired pair is “5” and “24”.

Game "Piggy Bank"

I can’t resist recommending to you the game “Piggy Bank” from the same site where you need to register, specify only your E-mail and password. This game will give you fitness for your brain and relaxation for your body. The essence of the game is to indicate 1 of 4 windows in which the amount of coins is the largest. Will you be able to show excellent results? We are waiting for you.

Game "Mathematical Comparisons"

I present a wonderful game “Mathematical Comparisons”, with which you can relax your body and tense your brain. The screenshot shows an example of this game, in which there will be a question related to the picture, and you will need to answer. Time is limited. How much time will you have to answer?

Game "2 back"

For development of mental arithmetic We recommend the “2 back” exercise. This game helps in the development of mental arithmetic, memory and attention. The screen will show a sequence of numbers that you need to remember, and then compare the number of the last card with the previous one. This exercise trains not only mental arithmetic, but also the brain as a whole. The exercise is available after registration, are you ready? Grow with us.

Game "Visual Geometry"

“Visual Geometry” - an exercise that will help speed up your train of thought and increase memorability and memory. With each successfully completed level the game becomes more difficult. The game helps develop mental arithmetic. How many levels can you complete?

In addition to these exercises, there are more than 30 free educational game-simulators that are available immediately after registration.

To gain access to free games, you only need to register and enter your Email and password (or log in using social networks).

Oral calculation for the Unified State Exam and State Examination

Verbal counting It can also be useful in mathematics exams, including the unified state exam, which is written by all eleventh grade students. This skill will help you worry less about complex calculations. Break them down into smaller mathematical operations that are easier to calculate in your head.

Mental arithmetic improves not only your computational abilities, but also other mental strategic operations, such as memory, which will allow you to remember any information even faster and better and apply your new abilities not only in exams, but also in your everyday life.

To learn how to count faster and better prepare for the Unified State Exam or State Examination, sign up for the course “Accelerating mental arithmetic, NOT mental arithmetic.” From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

Mental arithmetic in mathematics

Training and mental arithmetic lessons are perfect for adults and school-age children. Children especially need them because they are just learning to count, but schoolchildren in grades 1, 2 and 3 need simpler lessons in mental arithmetic in mathematics.

For elementary school students, simple arithmetic exercises are quite enough. But how can they be trained, especially if you do it in a playful way.

Game "Number Reach: Revolution"

An interesting and useful game “Numeric Span: Revolution”, which will help you improve your memory. The essence of the game is that the monitor will display numbers in order, one at a time, which you should remember and then reproduce. Such chains will consist of 4, 5 and even 6 digits. Time is limited. Beat the daily record among all players.

Courses for mental arithmetic and brain development

We speed up mental arithmetic, NOT mental arithmetic

Secret and popular techniques and life hacks, suitable even for a child. From the course you will not only learn dozens of techniques for simplified and quick subtraction, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games. Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

Development of memory and attention in a child 5-10 years old

The purpose of the course: to develop the child’s memory and attention so that it is easier for him to study at school, so that he can remember better.

After completing the course, the child will be able to:

1. 2-5 times better to remember texts, faces, numbers, words
2. Learn to remember for a longer period of time
3. The speed of recalling the necessary information will increase

Super memory in 30 days

As soon as you sign up for this course, you will begin a powerful 30-day training in the development of super-memory and brain pumping.

Within 30 days after subscribing, you will receive interesting exercises and educational games in your email that you can apply in your life.

We will learn to remember everything that may be needed in work or personal life: learn to remember texts, sequences of words, numbers, images, events that happened during the day, week, month, and even road maps.

Secrets of brain fitness, training memory, attention, thinking, counting

If you want to speed up your brain, improve its functioning, improve your memory, attention, concentration, develop more creativity, perform exciting exercises, train in a playful way and solve interesting problems, then sign up! 30 days of powerful brain fitness are guaranteed to you:)

Money and the Millionaire Mindset

Why are there problems with money? In this course we will answer this question in detail, look deep into the problem, and consider our relationship with money from psychological, economic and emotional points of view. From the course you will learn what you need to do to solve all your financial problems, save money and invest it in the future.

Speed ​​reading in 30 days

Sign up for the Speed ​​Reading course in 30 days to learn to read 3-4 times faster. Since 2015, 1,507 people from Moscow, St. Petersburg, Yekaterinburg, Novosibirsk, Kazan, Chelyabinsk, Ufa, Orenburg, Nizhny Novgorod, Kyiv, Minsk and other cities have studied under our program.

Bottom line

In this article I have given a general idea about oral counting, ways to develop mental counting, simulators, spoke about the course “Accelerating mental counting, NOT mental arithmetic,” which will help you learn to count at supersonic speed.

From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

Why do we need mental arithmetic if this is the 21st century, and all sorts of gadgets are capable of performing any arithmetic operations almost at lightning speed? You don’t even have to point your finger at your smartphone, but give a voice command and immediately receive the correct answer. Now this is successfully done even by elementary school students who are too lazy to divide, multiply, add and subtract on their own.

But this coin also has a flip side: scientists warn that if you don’t train, don’t overload with work and make tasks easier for him, he begins to be lazy and declines. In the same way, without physical training, our muscles weaken.

Mikhail Vasilyevich Lomonosov also spoke about the benefits of mathematics, calling it the most beautiful of sciences: “You have to love mathematics because it puts your mind in order.”

Oral arithmetic develops attention and reaction speed. It is not for nothing that more and more new methods of rapid mental calculation are appearing, intended for both children and adults. One of them is the Japanese mental counting system, which uses the ancient Japanese soroban abacus. The methodology itself was developed in Japan 25 years ago, and now it is successfully used in some of our mental counting schools. It uses visual images, each of which corresponds to a specific number. Such training develops the right hemisphere of the brain, which is responsible for spatial thinking, constructing analogies, etc.

It is curious that in just two years, students of such schools (they accept children aged 4–11 years) learn to perform arithmetic operations with 2-digit and even 3-digit numbers. Kids who don't know multiplication tables can multiply here. They add and subtract large numbers without writing them down. But, of course, the goal of training is the balanced development of the right and left.

You can also master mental arithmetic with the help of the problem book “1001 problems for mental arithmetic at school,” compiled back in the 19th century by a rural teacher and famous educator Sergei Aleksandrovich Rachinsky. This problem book is supported by the fact that it went through several editions. This book can be found and downloaded on the Internet.

People who practice quick counting recommend Yakov Trachtenberg’s book “The Quick Counting System.” The history of the creation of this system is very unusual. To survive the concentration camp where he was sent by the Nazis in 1941, and not lose his mental clarity, a Zurich mathematics professor began developing algorithms for mathematical operations that allow him to quickly count in his head. And after the war, he wrote a book in which the quick counting system is presented so clearly and accessiblely that it is still in demand.

There are also good reviews about Yakov Perelman’s book “Quick Counting. Thirty simple examples of mental counting." The chapters of this book are devoted to multiplying by single-digit and two-digit numbers, in particular multiplying by 4 and 8, 5 and 25, by 11/2, 11/4, *, dividing by 15, squaring, and formula calculations.

The simplest methods of mental counting

People who have certain abilities will master this skill faster, namely: the ability to think logically, the ability to concentrate and store several images in short-term memory at the same time.

No less important is knowledge of special action algorithms and some mathematical laws that allow, as well as the ability to choose the most effective one for a given situation.

And, of course, you can’t do without regular training!

Some of the most common quick counting techniques are:

1. Multiplying a two-digit number by a one-digit number

The easiest way to multiply a two-digit number by a single-digit number is to split it into two components. For example, 45 - by 40 and 5. Next, we multiply each component by the required number, for example, by 7, separately. We get: 40 × 7 = 280; 5 × 7 = 35. Then we add the resulting results: 280 + 35 = 315.

2. Multiplying a three-digit number

Multiplying a three-digit number in your head is also much easier if you break it down into its components, but present the multiplicand in such a way that it is easier to perform mathematical operations with it. For example, we need to multiply 137 by 5.

We represent 137 as 140 − 3. That is, it turns out that we now have to multiply by 5 not 137, but 140 − 3. Or (140 − 3) x 5.

Knowing the multiplication table within 19 x 9, you can count even faster. We decompose the number 137 into 130 and 7. Next, we multiply by 5, first 130, and then 7, and add the results. That is, 137 × 5 = 130 × 5 + 7 × 5 = 650 + 35 = 685.

You can expand not only the multiplicand, but also the multiplier. For example, we need to multiply 235 by 6. We get six by multiplying 2 by 3. Thus, we first multiply 235 by 2 and get 470, and then multiply 470 by 3. Total 1410.

The same action can be done differently by representing 235 as 200 and 35. It turns out 235 × 6 = (200 + 35) × 6 = 200 × 6 + 35 × 6 = 1200 + 210 = 1410.

In the same way, by breaking down numbers into their components, you can perform addition, subtraction and division.

3. Multiplying by 10

Everyone knows how to multiply by 10: simply add zero to the multiplicand. For example, 15 × 10 = 150. Based on this, it is no less simple to multiply by 9. First, we add 0 to the multiplicand, that is, multiply it by 10, and then subtract the multiplicand from the resulting number: 150 × 9 = 150 × 10 = 1500 − 150 = 1,350.

4. Multiplication by 5

It is easy to multiply by 5. You just need to multiply the number by 10, and divide the resulting result by 2.

5. Multiplying by 11

It’s interesting to multiply two-digit numbers by 11. Let’s take 18, for example. Let’s mentally expand 1 and 8, and between them write the sum of these numbers: 1 + 8. We get 1 (1 + 8) 8. Or 198.

6. Multiply by 1.5

If you need to multiply a number by 1.5, divide it by two and add the resulting half to the whole: 24 × 1.5 = 24 / 2 + 24 = 36.

These are just the simplest ways of mental counting with which we can train our brains in everyday life. For example, counting the cost of purchases while standing in line at the checkout. Or perform mathematical operations with numbers on the license plates of passing cars. Those who like to “play” with numbers and want to develop their thinking abilities can turn to the books of the above-mentioned authors.

“You should love mathematics because it puts your mind in order,” said Mikhail Lomonosov. The ability to count in your head remains a useful skill for modern man, despite the fact that he owns all kinds of devices that can count for him. The ability to do without special devices and quickly solve an arithmetic problem at the right time is not the only use of this skill. In addition to its utilitarian purpose, mental calculation techniques will allow you to learn how to organize yourself in various life situations. In addition, the ability to count in your head will undoubtedly have a positive impact on the image of your intellectual abilities and will distinguish you from the surrounding “humanists.”

Mental counting training

There are people who can perform simple arithmetic operations in their heads. Multiply a two-digit number by a single-digit number, multiply within 20, multiply two small two-digit numbers, etc. - they can perform all these actions in their minds and quickly enough, faster than the average person. Often this skill is justified by the need for constant practical use. Typically, people who are good at mental arithmetic have a background in mathematics or at least experience solving numerous arithmetic problems.

Undoubtedly, experience and training play a vital role in the development of any ability. But the skill of mental calculation does not rely on experience alone. This is proven by people who, unlike those described above, are able to count much more complex examples in their minds. For example, such people can multiply and divide three-digit numbers, perform complex arithmetic operations that not every person can count in a column.

What does an ordinary person need to know and be able to do in order to master such a phenomenal ability? Today, there are various techniques that help you learn to count quickly in your head. Having studied many approaches to teaching the skill of counting orally, we can highlight 3 main components of this skill:

1. Abilities. The ability to concentrate and the ability to hold several things in short-term memory at the same time. Predisposition to mathematics and logical thinking.

2. Algorithms. Knowledge of special algorithms and the ability to quickly select the necessary, most effective algorithm in each specific situation.

3. Training and experience, the importance of which for any skill has not been canceled. Constant training and gradual complication of solved problems and exercises will allow you to improve the speed and quality of mental calculation.

It should be noted that the third factor is of key importance. Without the necessary experience, you will not be able to surprise others with a quick score, even if you know the most convenient algorithm. However, do not underestimate the importance of the first two components, since having in your arsenal the abilities and a set of necessary algorithms, you can “outdo” even the most experienced “accountant”, provided that you have trained for the same amount of time.

Lessons on the site

The mental arithmetic lessons presented on the site are aimed specifically at developing these three components. The first lesson tells you how to develop a predisposition for mathematics and arithmetic, and also describes the basics of counting and logic. Then a series of lessons is given on special algorithms for performing various arithmetic operations in the mind. Finally, this training provides additional materials to help train and develop the ability to count orally, in order to be able to apply your talent and knowledge in life.

Under the game there is a description, instructions and rules, as well as thematic links to similar materials - we recommend that you read it.

There is definitely something sporty about this game. The emotional tide increases with the speed at which examples are presented. The process looks simpler than steamed turnips. You see an example on the screen, say “8 - 5 =”, enter the answer “3” on the keyboard and move on to the next one. However, the faster you manage to solve these simple problems, the faster the next examples begin to appear, and as the speed increases, the complexity also increases, and operations with multiplication and division begin to appear. A great game for those who want to test their mental arithmetic skills and also practice basic math.

Can download the game ORAL COUNTING FOR SPEED on your computer, it will not take up much space, but think about whether it makes sense to do this, because it is always available here, you just need to open this page.

Take a break and play Online Games, which develop logic and imagination, allow you to relax pleasantly. Relax and take your mind off things!

Full screen

A game in the categories Logic, Sports available for free, around the clock and without registering with a description in Russian on Min2Win. If the capabilities of the electronic desktop allow, you can expand the plot of ORAL COUNTING AT SPEED in full screen and enhance the effect of completing the scenarios. Many things really make sense to consider in more detail.

Why count in your head when you can solve any arithmetic problem on a calculator. Modern medicine and psychology prove that mental arithmetic is an exercise for gray cells. Performing such gymnastics is necessary for the development of memory and mathematical abilities.

There are many techniques for simplifying mental calculations. Everyone who has seen Bogdanov-Belsky’s famous painting “Oral Abacus” is always surprised - how do peasant children solve such a difficult problem as dividing the sum of five numbers that must first be squared?

It turns out that these children are students of the famous mathematics teacher Sergei Aleksandrovich Rachitsky (he is also depicted in the picture). These are not child prodigies - primary school students from a 19th-century village school. But they all already know how to simplify arithmetic calculations and have learned the multiplication table! Therefore, these kids are quite capable of solving such a problem!

Secrets of mental counting

There are mental counting techniques - simple algorithms that it is desirable to bring to automation. After mastering simple techniques, you can move on to mastering more complex ones.

Add numbers 7,8,9

To simplify calculations, the numbers 7,8,9 must first be rounded to 10 and then subtracted. For example, to add 9 to a two-digit number, you must first add 10 and then subtract 1, etc.

Examples :

Add two-digit numbers quickly

If the last digit of a two-digit number is greater than five, round it up. We perform the addition and subtract the “addition” from the resulting amount.

Examples :

54+39=54+40-1=93

26+38=26+40-2=64

If the last digit of a two-digit number is less than five, then add by digits: first add tens, then add ones.

Example :

57+32=57+30+2=89

If you swap the terms, you can first round the number 57 to 60, and then subtract 3 from the total:

32+57=32+60-3=89

Adding three-digit numbers in your head

Fast counting and addition of three-digit numbers - is it possible? Yes. To do this, you need to parse three-digit numbers into hundreds, tens, units and add them one by one.

Example :

249+533=(200+500)+(40+30)+(9+3)=782

Features of subtraction: reduction to round numbers

We round the subtracted ones to 10, to 100. If you need to subtract a two-digit number, you need to round it to 100, subtract it, and then add the correction to the remainder. This is true if the correction is small.

Examples :

576-88=576-100+12=488

Subtract three-digit numbers in your head

If at one time the composition of numbers from 1 to 10 was well mastered, then subtraction can be done in parts and in the indicated order: hundreds, tens, units.

Example :

843-596=843-500-90-6=343-90-6=253-6=247

Multiply and divide

Instantly multiply and divide in your head? This is possible, but you can’t do it without knowing the multiplication tables. - this is the golden key to quick mental arithmetic! It is used in both multiplication and division. Let us remember that in the primary grades of a village school in the pre-revolutionary Smolensk province (the painting “Oral Calculation”), children knew the continuation of the multiplication table - from 11 to 19!

Although, in my opinion, it is enough to know the table from 1 to 10 to be able to multiply larger numbers. For example:

15*16=15*10+(10*6+5*6)=150+60+30=240

Multiply and divide by 4, 6, 8, 9

Having mastered the multiplication table by 2 and 3 to the point of automaticity, making other calculations will be as easy as shelling pears.

To multiply and divide two- and three-digit numbers we use simple techniques:

multiply by 4 is multiplied by 2 twice;

multiply by 6 - this means multiply by 2, and then by 3;

multiply by 8 is multiplied by 2 three times;

Multiplying by 9 is multiplying by 3 twice.

For example :

37*4=(37*2)*2=74*2=148;

412*6=(412*2) 3=824 3=2472

Likewise:

divided by 4 is divided by 2 twice;

to divide by 6 is to first divide by 2 and then by 3;

divided by 8 is divided by 2 three times;

dividing by 9 is dividing by 3 twice.

For example :

412:4=(412:2):2=206:2=103

312:6=(312:2):3=156:3=52

How to multiply and divide by 5

The number 5 is half of 10 (10:2). Therefore, we first multiply by 10, then divide the result in half.

Example :

326*5=(326*10):2=3260:2=1630

The rule for dividing by 5 is even simpler. First, multiply by 2, and then divide the result by 10.

326:5=(326·2):10=652:10=65.2.

Multiply by 9

To multiply a number by 9, it is not necessary to multiply it twice by 3. It is enough to multiply it by 10 and subtract the multiplied number from the resulting number. Let's compare which is faster:

37*9=(37*3)*3=111*3=333

37*9=37*10 - 37=370-37=333

Also, particular patterns have long been noticed that significantly simplify the multiplication of two-digit numbers by 11 or 101. Thus, when multiplied by 11, the two-digit number seems to move apart. The numbers that make it up remain at the edges, and their sum is in the center. For example: 24*11=264. When multiplying by 101, it is enough to add the same to the two-digit number. 24*101= 2424. The simplicity and logic of such examples is admirable. Such problems occur very rarely - these are entertaining examples, so-called little tricks.

Counting on fingers

Today you can still find many advocates of “finger gymnastics” and the method of mental counting on fingers. We are convinced that learning to add and subtract by bending and unbending our fingers is very visual and convenient. The range of such calculations is very limited. As soon as the calculations go beyond the scope of one operation, difficulties arise: you need to master the next technique. And it’s somehow undignified to bend your fingers in the era of iPhones.

For example, in defense of the “finger” method, the technique of multiplying by 9 is cited. The trick of the technique is as follows:

• To multiply any number within the first ten by 9, you need to turn your palms towards you.
• Counting from left to right, bend the finger corresponding to the number being multiplied. For example, to multiply 5 by 9, you need to bend the little finger on your left hand.
• The remaining number of fingers on the left will correspond to tens, on the right - to units. In our example - 4 fingers on the left and 5 on the right. Answer: 45.

Yes, indeed, the solution is quick and clear! But this is from the realm of tricks. The rule only applies when multiplying by 9. Isn’t it easier to learn the multiplication table to multiply 5 by 9? This trick will be forgotten, but a well-learned multiplication table will remain forever.

There are also many similar techniques using fingers for some single mathematical operations, but this is relevant while you are using it and is immediately forgotten when you stop using it. Therefore, it is better to learn standard algorithms that will remain for life.

Oral counting on a machine

First, you need to have a good knowledge of the composition of numbers and the multiplication table.

Secondly, you need to remember the techniques for simplifying calculations. As it turned out, there are not so many such mathematical algorithms.

Thirdly, in order for the technique to turn into a convenient skill, you must constantly conduct short “brainstorming” sessions - practice mental calculations using one or another algorithm.

Training should be short: solve 3-4 examples in your head using the same technique, then move on to the next one. We must strive to use every free minute - both usefully and not boringly. Thanks to simple training, all calculations will eventually be performed at lightning speed and without errors. This will be very useful in life and will help out in difficult situations.