How can a child learn to count quickly in their head?

Parents of modern children enviously observe the prodigies - participants in the television shows "Best of All" and "Amazing People" - and worry that their children are not distinguished by outstanding intelligence and super-quick wit: they do not master the elementary school curriculum, do not like to strain their brains and are afraid of lessons mathematics.

From the first grade, they count on fingers and sticks, do not know the techniques of oral counting, therefore they experience big problems in all subjects of the school course.

The techniques of rapid verbal counting are simple and easy to learn, but one must remember that their successful mastery presupposes not mechanical, but quite conscious use of techniques and, in addition, more or less lengthy training.

Having mastered the elementary techniques of oral counting, the users of them will be able to correctly and quickly perform instant calculations in their minds with the same accuracy as in written calculations.

Features:

There are so many techniques to help you learn quick mental math. With all the visible differences, they have an important similarity - they are based on three "whales":

Training and gaining experience. Regular practice, solving tasks from simple to complex, qualitatively and quantitatively change the skill of oral calculations.
Algorithm. Knowledge and application of "secret" techniques and laws greatly simplifies the counting process.
Abilities and natural endowments. Developed short-term memory and its considerable volume, as well as a high concentration of attention, are of great help in practicing quick mental arithmetic. A definite plus is the presence of a mathematical mindset and a predisposition to logical thinking.

The benefits of oral counting

Humans are not iron robots, but the fact that they create smart machines speaks volumes about their intellectual superiority. A person needs to constantly keep his brain in good shape, which is actively promoted by training the skill of counting in the mind.

For everyday life:

successful oral counting is an indicator of an analytical mindset;
regular mental counting will save you from early dementia and senile marasmus;
your ability to add and subtract well will not allow you to be fooled in the store.

For successful studies:

mental activity is activated;
memory, speech, attention, the ability to perceive what is said by ear, speed of reaction, ingenuity, the ability to find the most rational ways to solve the task are developing;
confidence in their capabilities is strengthened.

When should you start learning?

According to learned minds (psychologists and teachers), a child by the age of 4 is already able to add and subtract. And by the age of 5, the baby can freely solve examples and simple problems. But these are statistics, and children do not always adjust to it. therefore everything here is purely individual.

In any case, it is better to teach children to count quickly in their head already before entering school - there will be fewer problems, and a stock of useful skills and abilities will help them master modern school programs more successfully.

Rules

The queen of sciences - mathematics - took care of the students and compiled a set of laws, algorithms and rules, having learned and skillfully using them, children will love mathematics and mental work:

The displacement property of addition: by swapping the components of an action, we get the same result.
Combination property of addition: when adding three or more numbers, any two (or more) numerical values can be replaced with their sum.
Ten-step addition and subtraction: complement a larger component
Up to round tens, and then add the remainder of the other component.

First, subtract individual units from the number up to the action sign, and then subtract the remainder of the subtracted from the round tens.
Representing the reduced as a sum of tens and units, we remove the smaller from the tens of larger ones and add the unit of the reduced to the answer.
When adding and subtracting round tens (they are also called "round" numbers), tens can be counted in the same way as units.
Addition and subtraction of tens and units. It is more convenient to add tens to tens, and units to units.

Add a number to a sum

The methods are as follows:

We calculate its value, and then add this value to it.
We add it to the first term, and then we add the second term to the result.
We add the number to the second term, and then add the first term to the answer.

Add sum to number

The methods are as follows:

Let's calculate its reading, and then add it to the number.
Add the first term to the number, and then add the second term to the result.
Add the second term to the number, and then add the first term to the result.

Adding two sums. By adding the two sums, we choose the most convenient calculation method.

Using the main properties of multiplication

The techniques are as follows:

The travel property of multiplication. If you swap the factors, their product will not change.
Combination property of multiplication. When multiplying three or more numbers, any two (or more) numbers can be replaced by their product.
Distribution property of multiplication. To multiply the sum by a number, you must multiply each of its components by this number and add the resulting products.

Multiplying and dividing numbers by 10 and 100

Methods:

To increase any number 10 times, you must assign one zero to it on the right.
To do this 100 times, you need to assign two zeros to it on the right.
To reduce the number 10 times, you need to drop one zero on the right, and to divide by 100 - two zeros.

Multiplying a sum by a number

Methods:

1st method. Let's calculate the amount and multiply it by this value.
2nd way. Let's multiply the number with each of the terms, and add the received answers.

Multiplying a number by a sum

Methods:

1st method. Find the sum and multiply the number by what we get.
2nd way. We multiply the number by each of the terms, and add the resulting products.

Dividing an amount by a number

Methods:

1st method. Let's calculate the sum and divide it by a number.
2nd way. We divide each of the terms by a number and add the resulting quotients.

Dividing a number by a product

Options:

1st method. Divide the number by the first factor, and then divide the result by the second factor.
2nd way. Divide the number by the second factor, and then divide the result by the first factor.

Kinds

In the classroom, scanty time is allocated for oral counting, but this does not diminish its importance for the development of the mental activity of the children. Oral computing skills are developed in mathematics lessons in elementary school by performing a variety of types of tasks and exercises.

Find the value of a mathematical expression

These can be regular numeric expressions or variable expressions (literal), and numeric values are suggested for letters. Substituting numbers instead of letters, find the numerical value of the resulting expression.

Compare math expressions

Such tasks are varied:

determine the equality or inequality of two given expressions (having previously found and compared their values);
to the relation given to the sign and one of the expressions, compose a second expression or add an unfinished proposal;
such exercises can use single, two-digit, three-digit numbers and quantities in expressions, and all four arithmetic operations. The main purpose of such tasks is the solid assimilation of theoretical material and the development of computational skills.

Solve equations. They help you learn the connections between components and arithmetic results.
To solve a problem. These can be both simple and complex tasks. With their help, theoretical knowledge is strengthened, computational skills are developed, and the mental activity of children is activated.

Oral counting techniques

Divisibility of numbers:

by 2: everything that exceeds it, and in the number row go through one;
by 3 and 9: if the sum of the digits is a multiple of these indicators without a remainder;
by 4: if the last two digits in the record sequentially form a number that is divided by 4;
by 5: round tens and those with 5 at the end;
by 6: numbers that are multiples of two and three are divided;
by 10: numeric values with 0 at the end;
by 12: divides numbers that can be divided into three and four at the same time;
by 15: numbers that are divisible simultaneously by whole single-digit components of this number of factors.

Primary school account forms

It is well known that the main activity of preschoolers and younger students is play, which is useful to include in all stages of the lesson. Some forms of oral counting are given below.

Game "Silent"

Promotes the education of attention and discipline. Silence can consist of examples in one action, two or more. It is played in all grades of elementary school with both abstract integers and named numbers.

Students count in their heads and silently, when called by the teacher, write answers to the examples given to them on the board. Correct answers are met with light claps, and incorrect answers are met with silence.

Lotto game

There may be several types, corresponding to those sections of mathematics that have been studied and need to be consolidated. For example, a lotto with examples of multiplication and division within the "hundreds".

To add more interest to the game, answer tires can be made from a cut picture. If all examples are solved correctly, a picture is obtained from the tires.

Game "Arithmetic labyrinths"

They look like concentric circles with gates with numbers. To get to the center, you need to dial the number in the center. Solving mazes may require either one action (addition) or several. It should be noted that these tasks have several solutions.

Game "Catch the Pilot" (a kind of "Ladders")

On the board is a drawing: an airplane with loops, in which there are examples. The two called students write the answers to the left and right of the loops. Whoever decides correctly and faster will catch up with the pilot.

The game "Circular examples"

Didactic material is a set of cards laid out in envelopes; each has 8 cards, each with one example written on it.

The numerical examples in each envelope are different in their content and are selected according to the principle of self-control: when solving them, the result of one example will be the beginning of the next.

Circular examples can be provided as ladders.

Development methods and techniques

Considering the ways to teach children of 6 years old rapid mental counting, it is impossible not to note the uniqueness and simplicity of the Japanese method of counting "Soroban". The Soroban methodology allows you to teach children from 4 to 11 years old, developing their mental abilities and expanding the range of intellectual capabilities of children. It is easy to teach any student to count examples in mathematics in their head, using the Japanese method of counting on soroban. When we practice mental counting, we use the whole brain., thereby unloading the left hemisphere, which is responsible for solving mathematical problems.

Mental arithmetic makes it possible to interest even the "figurative" hemisphere in computational operations, which increases the efficiency of the brain.

Large numbers require written computational techniques, although there are individuals who hone their skills in working with and with them.

Counting math examples in your mind is a vital necessity, since exams at school are now held without the use of calculators, and the ability to count in the head is included in the list of mandatory skills for graduates of grades 9 and 11.

A basic rule of thumb for mental addition:

If the first term is a two-digit number (not a round ten), then add 9 to it like this: add 10, remove 1.
Add 8: add 10, subtract 2.

Quickly add two-digit numbers:

If the last digit of the second term is more than 5, round it up. We carry out the addition, we remove the "addition" from the resulting sum.
If the last digit of the second term is less than 5, then we add up by digits: first we add tens, then units.
You can swap the terms, but add the numbers using the same algorithm.

Features of Subtraction: Casting to Round Numbers

Single-digit deductible ones are rounded to 10, two-digit ones - to 100. Subtract 10 or 100 and add the correction. Reception is relevant for small amendments.

Mental subtraction of three-digit numbers

Based on a good knowledge of the composition of the first ten numbers, you can subtract parts by part in this order: hundreds, tens, ones.

You can multiply and divide without any problems, knowing the multiplication table - a "magic wand" to quickly master the number in the mind. It is noteworthy that the village children of pre-revolutionary Russia knew the continuation of the so-called Pythagorean table - from 11 to 19, and modern schoolchildren would be nice to know the table up to 19 * 9 by heart.

The most interesting tricks

To captivate children with mathematics and make difficult moments in the school curriculum closer and more accessible, there are ways and methodological techniques, turning difficulties into fun and interesting:

To multiply any single number by 9, show everyone our empty palms. Bend the finger corresponding in order (counting from the left thumb) to the number of the first factor. We look how many fingers to the left of the bent one - these will be tens of the desired product, and to the right - its units.
Multiplication by 11 of any two-digit number, the sum of the digits of which does not reach 10, is carried out in a funny and simple way: we mentally expand the digits of this number and put their sum between them - the answer is ready.
In the event that the sum of the digits of the number multiplied by 11 turns out to be 10 or more than 10, then between the mentally pushed apart digits of this number, you should put their sum and add the first two digits to the left, leaving the other two unchanged - you got the product.