How to master verbal counting for schoolchildren and adults

Keep your brain in good shape. To work effectively, the intellect, like the muscles, needs constant training. Counting in the mind develops memory, logical thinking and concentration, increases the ability to learn, helps to quickly navigate the situation and make the right decisions.
Take care of your mental health. Research shows Could mental math boost emotional health? / EurekAlert! / American Association for the Advancement of Science that verbal counting involves areas of the brain responsible for depression and anxiety. The more actively these zones work, the less the risk of neuroses and black melancholy.
Insure yourself against punctures in everyday situations. The ability to quickly calculate change, tip, calories or interest on a loan protects you from unplanned spending, excess weight and fraud.

You can learn quick counting techniques at any age. It doesn't matter if you slow down a little at first. Practice basic arithmetic operations daily for 10-15 minutes and in a couple of months you will achieve noticeable results.

How to learn to add in your mind

Summing single-digit numbers

Start your workout at an elementary level - adding single numbers with the transition through ten. This technique is mastered in the first grade, but for some reason it is often forgotten with age.

Let's say you need to add 7 and 8.
Count how many seven are missing to ten: 10 - 7 = 3.
Expand the number eight into the sum of three and the second part: 8 = 3 + 5.
Add the second part to ten: 10 + 5 = 15.

Use the same technique of "support for ten" when summing single-digit numbers with two-digit, three-digit, and so on. Hone the simplest addition until you can do one operation in a couple of seconds.

Summing up multivalued numbers

The basic principle is to break down the terms of a number into digits (thousands, hundreds, tens, ones) and add up the same ones, starting with the largest ones.

Let's say you add 1,574 to 689.

1,574 is decomposed into four categories: 1,000, 500, 70 and 4.689 - into three: 600, 80 and 9.
Now let's summarize: thousands with thousands (1,000 + 0 = 1,000), hundreds with hundreds (500 + 600 = 1 100), tens with tens (70 + 80 = 150), units with ones (4 + 9 = 13).
We group the numbers in the way that suits us, and add up what we get: (1,000 + 1,100) + (150 + 13) = 2,100 + 163 = 2,263.

The main difficulty is to keep in mind all the intermediate results. By doing this, you train your memory at the same time.

How to learn to read in your mind

Subtract single digits

We return to first grade again and hone the skill of subtracting a single-digit number with the transition through ten.

Let's say you want to subtract 8 from 35.

Imagine 35 as 30 + 5.
You can't subtract 8 from 5, so we split 8 into 5 + 3.
Subtract 5 from 35 and get 30. Then subtract the remaining three from 30: 30 - 3 = 27.

Subtract multi-digit numbers

Unlike addition, when subtracting multi-digit numbers into digits, you only need to split the one that you subtract.

For example, you are asked to subtract 347 from 932.

The number 347 consists of three digit parts: 300 + 40 + 7.
First, subtract hundreds: 932 - 300 = 632.
Let's move on to tens: 632 - 40. For convenience, 40 can be represented as a sum of 30 + 10. First, subtract 30 and get 632 - 30 = 602. Now, subtract the remaining 10 from 602 and get 592.
It remains to deal with the units, using the same "support for ten". First, subtract two from 592: 592 - 2 = 590. And then what remains of the seven: 7 - 2 = 5. We get: 590 - 5 = 585.

How to learn to multiply in your mind

The life hacker has already written about how to quickly master the multiplication table.

We add that the greatest difficulty for both children and adults is the multiplication of 7 by 8. There is a simple rule that will help you never to be mistaken in this matter. Just remember, "five, six, seven, eight" - 56 = 7 × 8.

Now let's move on to more complex cases.

Multiply single-digit numbers by multi-digit numbers

In fact, everything is elementary here. We split the multi-digit number into digits, multiply each by a single-digit number and sum the results.

Let's look at a specific example: 759 × 8.

We break 759 into bit parts: 700, 50 and 9.
We multiply each digit separately: 700 × 8 = 5600, 50 × 8 = 400, 9 × 8 = 72.
We add the results, dividing them into categories: 5,600 + 400 + 72 = 5,000 + (600 + 400) + 72 = 5,000 + 1,000 + 72 = 6,000 + 72 = 6,072.

Multiplying two-digit numbers

Here the hand itself reaches for a calculator, or at least for paper and a pen, in order to use the good old multiplication in the column. Although there is nothing super complicated in this operation. You just need to do some short-term memory training.

Let's try to multiply 47 by 32, breaking down the process into several steps.

47x32 is the same as 47x (30 + 2) or 47x30 + 47x2.
First, multiply 47 by 30. It couldn't be easier: 47 × 3 = 40 × 3 + 7 × 3 = 120 + 21 = 141. We add a zero to the right and get: 1 410.
Let's go further: 47 × 2 = 40 × 2 + 7 × 2 = 80 + 14 = 94.
It remains to add the results: 1 410 + 94 = 1 500 + 4 = 1 504.

This principle can be applied to numbers with a large number of digits, but not everyone can keep in mind so many operations.

Simplifying multiplication

In addition to the general rules, there are several life hacks that facilitate multiplication by certain single-digit numbers.

Multiplication on 4

You can multiply a multi-digit number by 2, and then again by 2.

Example: 146 × 4 = (146 × 2) × 2 = (200 + 80 + 12) × 2 = 292 × 2 = 400 + 180 + 4 = 584.

Multiplication on 5

Multiply the original number by 10, then divide by 2.

Example: 489 × 5 = 4,890 / 2 = 2,445.

Multiplication at 9

Multiply by 10 and then subtract the original number from the result.

Example: 573 × 9 = 5 730 - 573 = 5 730 - (500 + 70 + 3) = 5 230 - (30 + 40) - 3 = 5 200 - 40 - 3 = 5 160 - 3 = 5 157.

Multiplication by 11

The technique boils down to the following: in front and behind, we substitute the first and last digits of the original number. And between them we sequentially sum up all the numbers.

When multiplied by a two-digit number, everything looks extremely simple.

Example: 36 × 11 = 3 (3 + 6) 6 = 396.

If the sum goes over ten, the place of ones remains in the center, and we add one to the first digit.

Example: 37 × 11 = 3 (3 + 7) 7 = 3 (10) 7 = 407.

It's a little harder to multiply by larger numbers.

Example: 543 × 11 = 5 (5 + 4) (4 + 3) 3 = 5 973.

How to learn to divide in your mind

This is the inverse operation of multiplication, therefore, success largely depends on knowledge of the same school table. The rest is a matter of practice.

Divide by a single digit

To do this, we divide the original multi-digit number into convenient parts, which will definitely be divided by our single-digit number.

Let's try to divide 2,436 by 7.

Let's select from 2 436 the largest part, which is completely divided by 7. In our case it is 2 100. We get (2 100 + 336) / 7.
We continue in the same spirit, only now with the number 336. Obviously, 280 will be divided by 7. And the remainder will be 56.
Now we divide each part by 7: (2 100 + 280 + 56) / 7 = 300 + 40 + 8 = 348.

Divide by a two-digit number

This is aerobatics, but we will try anyway.

Let's say you want to divide 1 128 by 24.

Let's estimate how many times 24 can fit into 1 128. Obviously, 1 128 is about half the size of 24 × 100 (2,400). Therefore, for "sighting" we take a multiplier of 50: 24 × 50 = 1 200.
Up to 1 200 our dividend 1 128 is not enough 72. How many times does 24 fit in 72? That's right, 3. So, 1 128 = 24 × 50 - 24 × 3 = 24 × (50 - 3) = 24 × 47. Therefore, 1128/24 = 47.

We took a not the most difficult example, but using the "shooting" method and splitting into convenient parts, you will learn how to perform more complex operations.

What will help you master oral counting

For the exercises, you will have to come up with new and new examples every day, only if you yourself want to. Otherwise, use other available methods.

Board games

Playing those where it is necessary to constantly calculate in your mind, you are not just learning to count quickly. And you combine useful with pleasant pastime with your family or friends.

Card games like "Uno" and all kinds of math dominoes allow schoolchildren to playfully master simple addition, subtraction, multiplication and division. More sophisticated economic strategies a la Monopoly develop financial sense and hone sophisticated numeracy skills.

What to buy

"Uno";
"7 by 9";
"7 by 9 multi";
Traffic Jam;
"Hekmek";
"Mathematical Dominoes";
"Multiplier";
Pharaoh's Code;
Super Farmer;
"Monopoly".

Mobile applications

With them you will be able to bring the verbal counting to automatism. Most of them offer to solve examples of addition, subtraction, multiplication and division according to the elementary school curriculum. But you will be surprised how difficult it is. Especially if tasks need to be clicked at a time, without pen and paper.

Mathematics: counting, multiplication table

Covers verbal counting tasks that correspond to grades 1-6 of the school curriculum, including interest tasks. Allows you to train the speed and quality of the score, as well as adjust the difficulty. For example, you can go from a simple multiplication table to multiplying and dividing two-digit and three-digit numbers.

Math in the mind

Another simple and straightforward verbal counting trainer with detailed statistics and customizable difficulty.

1 001 tasks for mental arithmetic

The appendix uses examples from the mathematics textbook "1,001 Problems for Mental Counting", which was compiled by the scientist and teacher Sergei Rachinsky in the 19th century.

Application not found

Math tricks

The application allows you to easily and unobtrusively master the basic mathematical techniques that facilitate and speed up oral counting. Each technique can be worked out in training mode. And then play on the speed of calculations with yourself or an opponent.

Quick Brain

The goal of the game is to correctly solve as many mathematical examples as possible in a certain period of time. Trains knowledge of the multiplication table, addition and subtraction. It also contains the popular math puzzle "2048".

Web services

You can regularly engage in intelligent exercises with numbers on online math simulators. Choose the type of action you need and the level of difficulty - and forward to new intellectual heights. Here are just a few options.

Mathematics. Club - a trainer of oral counting.
Aristov's school - an oral counting simulator (covers two-digit and three-digit numbers).
"Developing" - training of oral counting within a hundred.
7gy.ru is a math simulator (calculations within a hundred).
Chisloboy is an online counting speed game.
kid-mama - math simulators for grades 0-6.