How to explain to a child the subtraction and addition of two-digit numbers. Score is fun and easy! How easy it is to teach a child to count in his mind

Get to know the numbers right

Introduction to mathematics begins with counting. The child learns to count and memorize numbers. This usually happens at the age of 5 - 6 years. At this stage, it is important to form in the child the idea that the number denotes a group of objects with a certain number of elements.

To do this, you need not just teach him to call in order of number, so he will simply memorize the number series. It is recommended to use the method of studying the number, which is used in grade 1. She's next.

Stage number 1. Motivation

Any activity with a child should take place in a fun and relaxed atmosphere. If possible, turn your classes into a game, give preference to practical actions with objects. Start the activity with a bright event - give the child 2 candies, inflate 3 balloons, draw some objects with chalk, etc. Your task is to interest the baby.

Stage number 2. Item Count

After the child's attention is focused on a specific object, invite him to count the objects. It is necessary to ensure that at the same time the baby does not miss objects and does not confuse numbers. Usually children are in a hurry and make inaccuracies. It is important that the child follows the correct algorithm “pointed to an object - named a number - moved to the next object - named the next number, etc.” At first, perform these actions together with the baby - show yourself how to count, and let him repeat, point to objects, and he must count them and vice versa.

Stage number 3. Number Games

When the child recounts the elements and names the final number, you need to fix it. Suggest:

count the objects again, but in a different direction;
put as many circles in front of you as there are objects - count them too;
draw the same number of sticks on a leaf;
look around (or at the picture) and say what items are the appropriate number;
finish (report) objects so that they become the right amount.

Stage number 4. Introduction to numbers

Only after that should the child be shown the number and explain what it means. Many experts recommend coming up with associations "What does the number look like." This will help the baby remember the number and will be useful for applying eidetic techniques.

Stage number 5. Consolidation of a stable chain of the relationship "number of objects - number - number"

There are many didactic games for this stage. Let's describe some of them.

Dominoes

Make “knuckles” - dots on one half, numbers on the other. During the game, the child needs to count the points and select the desired number.

Aquarium

There is a number written on the aquarium. The child needs to put fish in the aquarium, on which the required number of scales (dots, dashes, sticks, etc.) is drawn.

Matchbox

Numbers are written on the matchboxes, and the child must put the right number of beads in each. Egg cartons can be used in the same way.

Mathematical Lego

It is necessary to make a playing field on which circles with written numbers are located. The child must build a turret with the required number of details on each circle.

apples

Make a tree layout with a pocket at the bottom. A card with a number is inserted into it. The child must mold the required number of apples from plasticine and stick it on a tree.

As a result of such training, the child will not perceive the number as an abstract concept, but will associate with a specific number of elements. This is the main foundation for developing computational skills.

Getting to know relationships and mathematical operations

It is equally important to form in the child the concept of the relationship "more", "less", "the same". This should be done only on the basis of practical actions with objects. A child aged 5-7 years has almost no abstract and logical thinking, so he will understand only what you explain with a good example.

To compare groups of objects, it is recommended to teach the child to make pairs - one object from the first group corresponds to one object from the second, etc. He must understand that he needs to compare by the number of elements, and not by their size. You can specifically select such tasks in which there will be a smaller number of large items than those that are smaller. In the future, it will already be possible to explain to the child that a larger number in the number series is further than a smaller one.

Be sure to invite the child to perform certain actions with objects and look at the result, draw conclusions. For example, ask to put 5 circles in front of you. Then put in a few more. Ask your child what has changed and why? You must lead him to the conclusion that there are more circles because you have added circles. Similarly, explain that when objects are removed, there are fewer of them.

Similar exercises should be carried out at almost every lesson, changing actions (something was eaten, someone flew in, brought it, etc.). The child must learn to understand the mathematical essence of ordinary actions.

After a while, you will need to change your approach. Now you must offer the child tasks in which he himself will need to make sure that the objects become more or less. Ask what other actions will increase or decrease the number of items.

This work is a preparation for familiarization with the operations of addition and subtraction. When you see that the child has mastered the essence of actions well, it's time to introduce him to the plus and minus signs. Usually this is done on the basis of a fairy tale. Think of any story that has a big, fat Plus character who likes to be given gifts (or visits, etc.). Be sure to think of his image and draw.

Your task is to ensure that the child learns that the "+" sign denotes the action of addition, when objects are added and there are more of them. Similarly, familiarization with the “-” sign and the subtraction action is carried out. It seems to adults that it is easy and simple to learn, but some children confuse the signs "+" and "-" for quite a long time and do not know what actions they need to perform, so they make a mistake. In this case, you need to practice using the image of a large bold “+” sign and a small “-” sign directly in the examples.

Learning to solve examples within 10

Now it's time to move on to how to teach a child to count examples. The main rule is practical actions and repeated training. Ideally, the child should memorize the results of all examples within 20. However, it is very difficult to achieve this through rote memorization. It is better to do this on the basis of performing various interesting exercises. Working on their solution, the child will gradually remember all the answers in the examples. We give a description of such games.

Table up to 10

Very effective use of cards - tables. It is divided into two rows of five cells each. Also included with this card are 10 tokens. The child puts the required number of chips in the cells, then adds or removes a few and counts the result.

With the help of such a table, you can not only solve examples. The visual image of each number is gradually deposited in the child’s memory, and in the future it will greatly help to make calculations in the mind.

Counting on fingers

Traditionally, the child is often asked to count examples using the fingers. This is very convenient, since this method can be applied in any situation. Therefore, some experts are categorically against teaching children to count on their fingers. They argue that after this it will be difficult to teach the child to count examples in his mind, because he will continue to count "in the old way." Practice shows that this is not so. Children easily switch to oral calculations as soon as they can do it faster than "manually".

abacus

Also popular is learning to solve examples on accounts. With the help of this technique, the child also forms a visual image of the number, which will help to make calculations in the mind.

Hand Calculator

You can make a homemade calculator with your child. To do this, you need a cardboard box and two disposable glasses. The bottom of the glasses must be cut off and attached to the side wall of the box so that they do not reach the bottom of the box. Between the glasses on the wall, write the sign "+", and below the sign "=".

To count an example, a child throws as many beads (pasta, buttons, etc.) into the first glass as the first number shows, and into the second glass as the second number. After that, he counts the total number of beads in the box.

Clothespins

Clothespins can be used to form computational skills. As a basis, you can make any cardboard templates (sun, flower, smiley, face, etc.). The child will solve examples by attaching and removing clothespins. This activity is more interesting for him than the simple use of counting material.

Ruler

To develop the child's ability to do calculations, many teachers use a ruler. First, on the ruler, you need to find the first number from the example, and then move to the required number of divisions to the right (if "+") or to the left ("-"). The number at which they stopped is the answer in the example.

This method is based on the knowledge of the number series. It is shown in many 1st grade math textbooks. With it, you can easily explain how to add and subtract the numbers 1, 2, 3 and 4 by jumping or jumping over the numbers.

Interactive games and simulators

As well as other presentations and materials on the topic:

, and many other materials on the site.

How to count within 20

cards - tables;
counting sticks;
abacus;
knowledge of the composition of the number.

The child needs to be explained the principle of obtaining a result in such examples, in which the first number is first rounded up to 10, and then the final calculations are performed. At first, this also needs to be done on the basis of practical actions, and only later proceed to solving examples based on knowledge of the composition of the number. As a rule, children do not master this topic very well, so do not rush to move on to oral calculations.

At the end of the work on developing the ability to solve examples within 20, children are invited to memorize addition and subtraction tables for each number. This helps to streamline the knowledge that they receive during the training exercises. At this point, the child remembers the results of many examples well, can easily reproduce them, and it will not be difficult for him to cope with such a task.

To teach a child to count examples, it is necessary to alternately offer him different ways to obtain a result. Subsequently, he will choose the most understandable and accessible method for him and will be based only on it. There is no need to impose any solution options on the baby, give him the opportunity to do the calculations himself in a way that is easier for him. The main thing is that the answer is correct, but how the child received it does not matter much.

Some parents, hardly their baby turns at least a year old, want to teach their child to count correctly and quickly. Others are not sure whether this should be done with a preschooler if the school will teach anyway.

Many experts say that this should be done only when the kids show interest in the account, and not try to impose it. Usually, kids show interest in counting early, but parents need to feed it and motivate it to develop in this regard in the form of games and exciting examples.

From time to time interest may fade, but you can warm it up, suggesting together to count the steps while walking, toys or buttons on clothes.

Today you will learn how to teach a child to count, in some cases it can be done quickly, in other cases it will take time.

What parents need to understand

Some parents just don't know how to get started.

Now there are many specialized books on how to teach a child to count. Psychologists say that if you decide to start learning then the following recommendations should be followed:

Educational materials for counting

Teaching at the age of 3-5 years is quite difficult. For early learning different visual materials can be used, in particular:

Pictures;
numbers on the magnet;
cubes and more.

When Learning Moves to Addition and Subtraction, then as visual materials are used:

fingers - invite the kids to count the number of fingers on the hand, then bend and ask how many are left;
sticks - by analogy with fingers;
ruler - show the numbers on the ruler and divisions, count them if you want to teach your baby addition.

However, many psychologists do not encourage the use of such devices in order to teach kids to count, and they believe that this provokes laziness, and thinking and memory are not trained. A number of experts suggest teaching children to count exclusively orally.

Examples for the little ones

Learning to count can begin as early as six months of age.. Naturally, we are not talking about counting objects for a baby who cannot walk and talk, but this will allow parents to create a basis for future learning. A good example in this case is light rhymes where there is an account, for example, such as "1, 2,3, 4, 5, the bunny went out for a walk."

Already at the age of one, the examples will be more difficult. You can take the cubes and tell the baby where there is one cube and where there are many, it will be too early to teach counting to 5 or 10. And from this age, you need to teach the baby on the fingers to show how old he is.

How to teach a child to count to 10

From about three years of age when children are already interested in numbers (moreover, for some, interest may appear at the age of three, for others closer to five), training is based on the following principle:

go through the numbers from 0 to 10 with the baby;
teach your baby to memorize them with cubes or other toys;
tell the difference between larger and smaller numbers, explain such a concept as "half", use simple examples;
count household items at home or items on a walk, offer to count together.

Below we will look at methods for teaching children to count to 10 in more detail. To start say the numbers from one to 10 in front of the child, count improvised items. Good examples are simple addition of objects: for example, "here was one doll, now we will put a second one next to it, and there will be two." Over time, the number of counted items needs to be increased.

As often as possible, ask your child how many plates are on the table, how many birds are sitting on a branch, or how many dogs are walking in the yard.

It is not recommended to ignore the number zero. First you need to learn the numbers from zero to two inclusive, and then all the rest - from three to 10. Zero in terms of learning is difficult in the sense that it is difficult for children to explain that emptiness can be designated as a separate number.

Something like this: draw two squares, put three dots in one, and not one in the second. Explain to the kid that in digital terms, this will mean "3" in the first case and "0" in the second.

Games, examples and rhymes for learning to count up to 10

The easiest and fastest way to teach a child to count is counting on fingers which we have already discussed earlier. But fingers are good only at first, when you teach your baby to understand numbers, then he should be weaned from the skill of counting on them. It is not uncommon for students to start solving examples on their fingers and cannot do it in any other way. The ruler, which was previously used to memorize numbers, is also not particularly welcome in our time, which we also talked about.

Other examples and games include:

we see 10 paws of cats (dogs). Answer how many animals there are. You need to count in pairs: two, four, six, and so on up to ten;
in the same way, he counts how many pairs of shoes a cat or dog needs;
Look at your watch and count in fives to 10.

How to teach kids to add and subtract numbers within ten

When your child has already learned the order of numbers, start solving with him examples on their addition and subtraction. Examples might be:

There are four apples on one plate and two on the other. How many of them are in total?
There are six apples on the table, and three children. How to properly divide them between them?

Other tasks may be something like this, subtraction will look the same. You should also teach in a playful way the baby the rule that changing the terms does not change the sum.

To do this, put a plate with two apples on the table or ask the baby to imagine it. Place another one with four apples next to it. Count how many apples there are, and then rearrange the plates and ask how many there will be now. The correct answer is the same.

In elementary grades students are explained what dozens are with the help of special sticks. Then they are taught to add and subtract numbers with the transition through a dozen.

In the first grade, a student learns to count in full tens with the help of bunches of sticks. And only after that he gets acquainted with the table of addition and subtraction with the transition through a dozen. If the kids give success, then you can teach this even before school.

In the first grade, teaching mathematics is based on three tables:

addition and subtraction up to 10;
examples with a transition through a dozen;
multiplication table.

When a student masters these tables, then in the future he will not have problems with mathematics, even in high school when studying more complex calculations.

And so that the child does not have problems at school, and mathematics is only a joy, it is very important that parents instilled a love of counting at an early age. Therefore, the first steps to the study of mathematics should be in the form of a game and be interesting to serve. And the more exciting this process is for the child, the faster he will master counting skills.

Modern children learn computers and calculators very quickly, but often do not know how to count in their minds at all. But mental counting is a training for the brain, which, like muscles, needs constant training.

Many parents are faced with such a problem: their baby perfectly counts up to 100 and counts directly and backwards, but he won’t learn how to add and subtract. What to do?

Numbers

The child can count - this is wonderful, now is the time to move on to the study of numbers. It is important that the child understands that a number is a designation for a specific number. Three balls, three kittens, three candies - this is the same number, which is indicated by one number. Number magnets are very convenient during this period, with which the child can play, clinging them to various objects. So they will always be in front of your child's eyes.

The child learned the numbers - you can introduce the concept of "zero". Count what is not. There were apples, we ate them, how many apples? Zero. What is not there is zero.

Greater than less and equal

Explain to your child the concepts of more, less. Will there be enough for all the birds on a branch? The branches were left without birds, which means there are more of them, and fewer birds. Did each bird get a branch? So they are equal. Birds and twigs equal number - "equal".

If it works out, then it's time to move on to simple mathematical operations: plus, minus, equal.

How to explain addition to a child

There are many ways to help a child understand the principle of addition, but the easiest is on the fingers.

Now there are a lot of theories that claim that counting on the fingers interferes with the development of mental counting. We won't argue. The choice is always with the parents. Explore other methods, try them with your child.

A good way to teach kids addition is with a ladder with numbers on each step. We go up - we fold.

How to explain subtraction to a child

How to explain subtraction? Subtraction must be taught along with addition. The child must remember the most important thing: when adding, it becomes more, when subtracting, it becomes less. The same ladder can help: go down - subtract.

Try to avoid words like "guess" or "guess" when counting. Mathematics is an exact science. The child should not guess, but count.

Explaining addition and subtraction is simple, the main thing is to understand these actions.

Learning by playing

It should be noted in advance that training should take place exclusively in the form of a game, so you should always monitor the reaction of the child and immediately stop the game if it becomes boring or uninteresting to him.

It is better to start with the simplest, i.e. how to explain addition to a child. But in any case, subtraction will also have to be included in this process, so it will be possible to “kill 2 birds with one stone”:

You need to start with voluminous objects that will certainly attract attention. Those. the first week there is only preparation, where the child hears phrases like "you had one apple, I gave you another one, and you have two of them."

In the second week, it is already possible to give the child the opportunity to independently sum up the results of the calculations. At 2 years old, almost any person is able to perform such operations up to 9. With the right choice of time for such a game, its assimilation occurs from 1 week to 1 month.

As soon as the first successes in addition appear, subtraction can begin.

This step is the most responsible, so the child should get the most out of the game. Memorization should occur unconsciously, but in exceptional cases the child himself becomes interested in the process, which makes further work much easier. If you try to force, then this can only cause antipathy for further education.

Video tutorials

Addition examples:

Educational cartoons in mathematics:

Parents often ask how to teach a child to count within 20. Sometimes a small student successfully performs calculations up to 10, but does not fully understand how to add / subtract large numbers.

The material contains examples of exercises, an analysis of the main mistakes that parents often make during classes.

Calculations are often harder for young students than reading. For a child to love mathematics, it is important for parents to know the basic rules and teaching methods. “But what about the school, the teachers?” many will ask.

Of course, the main burden falls on teachers, but when doing homework, parents must correctly explain certain rules and find errors. When adults understand how to instill a love of mathematics, classes are much easier.

You still have to pay attention to learning to count. Such is parental work, there is no escape from joint activities with a child. Even when visiting a tutor (children's development center), homework must be done. If parents know the basic techniques, modern teaching methods, it will be much easier for an adult and a child.

Teachers, parents give recommendations, offer proven algorithms, thanks to which a small student will understand what dozens are, how to learn more complex concepts. Always check whether the “young mathematician” has memorized the material covered, do not skip, even if the study takes not 2–3 days, but a week.

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Where to begin

Algorithm:

You will need two sets of cubes. Items must be the same;
the child must lay out 10 things in a row, always from left to right;
put another one on the first row of cubes. It turned out - 11 or one plus "twenty" \u003d eleven;
put two, then three, four dice on the twenty. It turned out: three - for - twenty, four - for - twenty and so on;
Did the child clearly remember the scheme for constructing numbers from 11 to 19? Proceed to the next step.

How is a hundred formed?

Algorithm:

most children who have mastered the formation of numbers up to 20 quickly understand how to make two, three, four tens to a hundred;
the beginning of the exercise is the same: lay out 10 cubes, say that it is a dozen or “twenty”;
next put the same row of ten cubes, it turned out two rows. Title: two plus "twenty" = twenty, three plus "twenty" = thirty;
Leave 40 (forty) and 90 (ninety) for later, say: these round numbers have a different name. Show that the ten always has a “0” at the end, because the number is round, the numbers 1, 5, 8, and so on are added to it;
50, 60, 70, 80 are even easier to remember. Ask how many tens are in the number 50. That's right, five. Let the children name the first number, add the word "ten" - it will turn out FIFTY. When the student understands the principle, ask, "How many tens did you find at 60, 70, and 80?" Sure, six, seven, eight. So new names will turn out: SIXTY, SEVENTY, EIGHTY.

Counting to 20 without going through ten

Algorithm:

take out the same cubes again;
let the child build a row of ten pieces;
put on top (required from left to right) two more cubes. It turned out 12;
explain to a small student how to quickly add 12 and 15. Add 1 + 1 ten, it turns out 2 tens or TWENTY;
add units: 2 + 5 = 7. Now there are TWENTY and SEVEN, together - TWENTY SEVEN;
back up the explanation with cubes. Let the child count if there are really 27 cubes on the table;
consolidate the lesson, let them try different options until the “young mathematician” understands the principle;
addition mastered? Proceed to subtraction: the principle is the same;
go through a dozen only after fully understanding the material with any numbers from 10 to 100.

Advice! By the beginning of training, the child must clearly understand where the tens are, and where are the units in a two-digit number, clearly know the concepts of “left - right”.

Ten counting rules

Use a table that shows the composition of the number. Children need to understand how to get numbers in different ways. For example, 8 = 3 + 5, 4 + 4, 6 + 2, 7 + 1, 8+ 0. Without the skills of quick counting, addition / subtraction from 0 to 10, you cannot move on to more complex exercises.

The task of parents: explain that one of the numbers needs to be decomposed by two to get 10, then add the remainder. The rule is easy to understand with an example.

See:

task: find how much will be 18 + 6;
18 is 10 and 8;
ask how much from 6 is missing to ten to add to 8;
right, 2 (the table “Composition of the number” is useful);
now write 6 as 2 and 4. That's 10 + 8 + 2 + 4, or 10 + 10 + 4. Two tens plus four ones equals TWENTY-FOUR;
when the child remembers addition, explain subtraction in the same way;
Always keep the Composition of Numbers table handy. Children will be less lost, easier to navigate.

Constantly conduct "training between cases" to better remember the composition of the number. Speak more often, connect the child, let him finish the phrase: “There are 3 plates on the table on the left, I put 3 more plates on the right. How many items in total? That's right, 6. Show another way: “I will put 2 plates on the left, 4 plates on the right, again 6 plates” and so on (1 + 5).

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conduct classes in a playful way. Preschoolers and younger schoolchildren react sharply to boring tasks, "gray", inexpressive pictures;
give simple examples, look for characters to count, understandable by age. A small student should easily recognize objects, animals that need to be counted. For example, a cat is suitable, a porcupine is not (many kids think that this is a hedgehog with long spines, they do not immediately recognize and call the animal). Orange is suitable, kiwi is not (an exotic fruit is somewhat reminiscent of a potato, you can make a mistake) and so on;
Dominoes, lotto, a labyrinth that you can travel with the help of chips, cubes with a large image are suitable. Buy games, make cardboard cards yourself;
interest the child, tell how important the account is in everyday affairs. Count the steps in the entryway, the chairs near the table, the windows in the store, the blue or white cars on the road. When shopping in a supermarket, ask your child to serve 1 carton of milk, 2 bagels, 3 packs of cottage cheese, and so on from the shelf. Say: "There are 4 bananas in the basket, I will put 1 more, it will be 5 bananas." Speak all numbers clearly. Such conversations often "strain" parents, often seem boring, empty, but it is difficult to overestimate the benefits of classes for children;
workout in between. This technique clearly demonstrates what numbers and calculations mean to people. Unobtrusively teach your baby to the world of mathematics. When setting the table for dinner or lunch, say: "I put 5 plates, I put 5 forks." Gradually, the little man will understand that each time the number of cutlery and dishes is different. Put one plate, sound it, add another one - call the number again and so on;
Conduct training in between times, invent fairy tales with a mathematical bias about surrounding objects (animate / inanimate).

ask for help from the "young mathematician", let him tell you how many cats are sitting near the entrance. Crumble bread, ask to count the pigeons that have flown in for food. Often 10, 20 or more birds fly together. Here is a good reason to show that "you counted to 10, but there are more numbers, for example, 11, 15, 20, and so on, to count all the birds";
game in a cafe/shop. Many parents and experienced teachers advise a simple technique for teaching counting, especially for adding and subtracting numbers through ten. By adding another 1, 2 or 5 rubles to 10 rubles, the child will understand what the number 15 \u003d 10 + 5, 20 \u003d 10 + 10 is. Make paper money from dense material. You will need "coins" and "banknotes" of all denominations, even those that are not in real circulation. Draw 3,4,7,8 rubles: you will get any number when added to 10. What size of "money" to choose? To clearly see the denomination;
school. Another useful game. Children love to be teachers. Give them this opportunity, solve examples, sometimes with errors, so that the "teacher" can correct you, test your knowledge. If the little teacher himself made a mistake, gently tell me, do not laugh. Check the correctness of the solution on cubes, apples, counting sticks, think together who is right. Praise for knowledge, promise to correct the grade, pull up mathematics;
to add numbers within 20, use visual aids, counting sticks, cubes. To study numbers from 0 to 100, a regular soft meter, which is used when sewing, will help. The “young mathematician” will see all the numbers, understand which one is to the left, which one is to the right. It is convenient to explain that 12 is less than 17 because it is to the left. You can measure 12 and 17 cm of fabric, cut off, compare pieces, confirm the correctness;
introduce the concepts of "plus" and "minus" later, when the rules of addition / subtraction up to 10 are learned;
always explain every word in the problem. Until the student understands what the condition means, he is unlikely to solve the problem. At first, come up with examples yourself, look for good textbooks with interesting, understandable tasks;
in case of difficulties, do not hesitate to ask for advice from a tutor, teacher of the children's center or teacher. The main thing: to find a person who understands not only mathematics, but also child psychology. The task is quite difficult, but solvable;
psychological contact with a small student is a prerequisite for successful learning. Shouts, humiliation, constant reminders of failures discourage study, provoke self-doubt, heavy complexes.

Arm yourself with the advice of teachers, parents, try to teach children to count correctly up to 20. In some cases, the material is easily absorbed, in others, perseverance, patience, and long explanations are required. Do not despair, do not scold the "young mathematician", consult with teachers, psychologists. Only regular classes, encouraging the slightest achievements will bring results.

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How to teach to add and subtract numbers | Mathematics

“One, two, three… there are six apples here.” What we just didn’t count - the steps in the entrance, and the Christmas trees in the yard, and the bunnies in the book ... It looked something like this. “How many bunnies? Point with your finger. One two Three. Three bunnies. Show three fingers.

Good girl! Right!" At first, my son was not interested in counting; he liked searching more. The game of hide and seek is also not superfluous: “One, two, three ... ten. I'm going to look. Ready or not, here I come!" At the age of 3, we could not count to 10, instead of numbers, we uttered unknown words with a similar intonation.

But later, due to the fact that it was often required to show the number of fingers, the numbers were associated with the number of objects.

Knows numbers

“One, two, three… there are six apples. The number "six" is written like this "6." I don't remember any special exercises that we would do. Everything happened in a flash. “What floor are we on? On the second. Look, here's his number written on the wall. "2". Show two fingers. Well done.

” In the elevator: “Which floor does grandma live on?” - “On the 3rd” - “Which button should I press?” - “This one” - “I didn’t guess a little. Here's a trio." In the store: “We have the key to the box at number 9. See, there is a tag on the key. On what box is such a figure written? Something like a wardrobe number.

In line to the doctor: “What is the office number? Here's the number." - “Two” (as far as I understand, at random) - “No, this is the number “5”. Show 5 fingers. Fine!". “When is dad coming?” - "In one hour. Look, it's a short hand at 6 now. When this arrow is on the 7th measurement, right here, then it will come.” “Please switch to Channel 1.

Bring the remote. One is written here. Click on this button. Thank you." Mosaic pictures are interesting, where you need to stick small squares on the numbers. The numbers define any color. In addition to learning colors and numbers, fine motor skills are trained. The numbers mirrored by the child must be corrected.

There is a diagnosis of dysgraphia. To exclude it, you should contact a speech therapist.

Can decompose (name) numbers in ascending-descending order

“Baba Yaga came and mixed up all the numbers. Can you arrange them correctly?” Before the age of three or four, the child needs to be taught how to compare, namely: new, fast-slow, far-close, hot-warm-cold, strong-weak, etc.

Look for the smallest object, the longest ... 2) combine objects: by color, shape and other characteristics (dishes, clothes, furniture, pets), find differences in pictures.

4) remove an extra item in a row (for example, one green apple from several red apples), continue the row (for example, ▷ ☐ ▷ ☐ ▷ ☐ ?), name the missing element (for example, ▷ ☐ ▷ ? ▷ ☐ ▷), arrange in pairs (for example, ▷ ☐ ▩ ☐ ▷ ▩), name what happened first, what then (first put on a sweater, then a jacket, and not vice versa; first it’s autumn, then winter ...).

5) fold a pyramid, a puzzle, put beads in a certain sequence. Only I have at least 20 books with similar tasks for kids. Previously, with my son, now with my daughter, we look through them with enthusiasm and pronounce them. “Show all the fruits” - “Here” - “Well done!” (clap hands) - “What kind of fruit is this?” - “Orange” - “Uh-huh. There is also?"…

By the age of 4, board games can and should be introduced (there is already enough perseverance and attention): dominoes, cards, lotto, with chips (each player has a chip) and dice (the move is made by the number of dots dropped on the dice), where the winner becomes the first to reach the finish line on the drawn map. We used standard options, not children's ones.

The cards were played in the “Drunkard” with a full deck (with 2 and 3): the deck is divided equally among the players, in the stacks the cards are turned upside down and the top one is drawn, there are no suits, the one whose card is larger (7- ka beats 4-ku, 2-ka beats aces, two more cards are put on two equal cards: one is face down, the other is face down, for the second time the merits of only the top cards are evaluated: “Who takes?” - “I!” - “ How?! What's more: 5 or 10? Let's count ... "), she joins the general pile, the one who has the whole deck wins. There is no limit to joy if the whole family sits down to play (with dad, grandma, grandpa…). The child learns not only to play, but also to perceive defeat correctly. It is better to be able to cycle through the numbers from 1 to 10 and vice versa, from 10 to 1, than to count up to 100. When we were 5 years old, we confidently did both. The countdown can be said in the relay: “Who will collect the most cubes? Get ready! Ten, nine, eight... one. Start!". We organized such contests when it was time to clean up the scattered toys. To learn how to count up to a hundred, we were helped by pictures where you need to connect the dots in ascending numbers. If you speak, you get a good result. ""Forty nine". Then what's going on?" The appearance, pronunciation of the number and the order are remembered. It can be explained that in tens the numbers are the same, while writing the numbers as follows: 0 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 2930 31 32 33 34 35 36 37 38 3940 41 42 43 44 45 46 47 48 4950 51 52 53 54 55 56 57 58 5960 61 62 63 64 65 66 67 68 6970 71 72 73 74 75 76 77 78 7980 81 82 83 84 85 86 87 88 8990 91 92 93 94 95 96 97 98 99 And it is handy to fix the material on the way: “When will we arrive?” - “Not long left. Count to 100 and we'll be there. Let `s together. One, two…” We did not teach more than 100 before school. She answered questions only when the child himself was interested: “What comes after 100? How much will one thousand and one thousand be? Or if the numbers met in everyday situations: “We are waiting for the 205 bus. Two zero five. Tell me when you see the 205th.” It is also useful to name the numbers before or after a given number or in a certain interval. The game will help in this: “I guessed a number from 1 to 20, try to guess it from 5 attempts, and I will say more or less than the number you named. I guessed.” - “Three” - “More” - “Seven” - “Less” - “Five” - “Well done! Guessed! Now it's your turn to guess the number.”

Knows more and less

“Dad has 6 apples, mom has 8. Who has more apples?” - “At mom's.” The clubs explain that the number 22 is greater than 18, since it is closer to 100. This is true, but we laid out heaps of nuts in parallel, erected towers of cubes to connect the image of the number with the number of objects. More-less gradually becomes more complicated, as well as addition-subtraction.

Almost simultaneously with plus-minus-equal signs, greater-less-equals signs are introduced. My son was just over 5 years old at the time. “There are a lot of apples on one side [intonation is required!], the distance between the fingers is large, next to the open side of the sign there is a larger number.”

“On the other hand, there are few apples, the distance between the fingers is tiny, the corner is looking at a smaller number.” “Equal”, “equal”, “at the same time”, “equally”, “the same” is the same: “You and dad have the same mugs”, “I have the same amount of soup”, “Share the candy equally with my sister”. There are no problems with this concept when there are two children in a family.

It is most difficult to compare numbers consisting of the same digits. Almost always we solved them.

“Dad has 3 apples. Extend three fingers. Mom has 2 apples. Extend two more fingers. How many apples are there? How many fingers? One two three four five. Mom and dad have five apples.”

“Dad has 3 apples. Extend three fingers. He shared one apple with you. Bend one finger. How many apples does he have left? One two. Dad has two apples left.”

“Dad had 2 apples. Show two fingers. Dad got hungry and ate both apples. Remove two fingers. How much does he have left? “Daddy ate everything.

Dad didn’t give me an apple 🙁 Dad needs to be put in a corner!” “Uh-huh, dad didn’t have any apples left. He has zero apples. Hee hee, and yes, it needs to be put in a corner.” The child must count all the objects.

Do not rush, the understanding that there are 5 fingers on one hand does not come immediately.

With things on paper

We had difficulties not with finding an answer, but with pronouncing the whole example with signs, with the correct declination of objects. "One two Three. Three sweets. PLUS. One candy. How much? One two three four. Four sweets. Come on one more time. Three candies PLUS one candy EQUALS four candies.”

With numbers on paper

Three examples per day is enough. In six months, their number can be increased to 5-7. Answers should not only be spoken, but already written down.

Number Composition

How many points do you need to draw to make points? The words “addition table”, which is crammed as “multiplication table”, make me itchy. The mind and logic of the child, in my opinion, at this moment is generally turned off.

Therefore, I tried to put my son in such conditions that he himself guessed that the result of adding different numbers could be the same number. "One plus two?" - “Three” - “Two plus one?” - “Three” - “That is, the sum does not change from a change in the places of the terms” (hmm, the last one was pulled out automatically: I didn’t explain to my son what a “term” is).

“Can you solve the examples: 2 + 3 = ?1 + 4 = ?” - “Easy! Five. Oh, there are also five. And there and there five!” You can also take seven spoons: “How many spoons are there?” “One, two, three… seven.” Put one spoon aside: “How many spoons are in each pile?” - “One and one, two, three ... six” - “And in total?” - “Seven” - “It turns out that 1 + 6 = 7”.

Move another spoon: “Now how many spoons are in each pile?” - “Two and five” - “And everything?” - "Seven" - "Look, the number of spoons in the piles changes, but the total number remains the same." Further in the club, he drew houses in which numbers live (already without my participation). There are two apartments per floor.

It is necessary to resettle all the tenants so that on each floor their number is equal to the number indicated by the owner on the roof. _ _ / \ / \ / \ / \ / 2 \ / 3 \/_______\ /_______\|_0_|_2_| |_0_|_3_||_1_|_1_| |_1_|_2_||_2_|_0_| |_2_|_1_| |_3_|_0_|

Without recalculation of the first number

“Dad has 3 apples. Mom has 2 apples. How many apples are there? There are already three. Extend three fingers. Now two more. Three four five." She herself did not notice how her son stopped counting all the items. Explained a couple of times, but did not insist.

According to the given condition, formulate, write down and solve the example yourself

"Look. There is a problem. “You have 7 games loaded on your tablet. You've already played at 5. How many unexplored games are left?” - “Two” - “That's right. It can be written as "7−5=2". I wonder if you can paint a similar problem yourself. “After dinner, you need to wash 10 dirty dishes. 4 have already been washed.

How many more are in the sink?” - “Six” - “How to write down?” - ““10−4=6”” - “Well done!” Tasks should be simple and mundane, with items from everyday life, with questions “how much”, “how much.” You have 3 cars. They gave you 3 more for your birthday.

How many cars have you got? (6) “You have 6 pencils, the girl you played with yesterday has 2. How many more pencils do you have?” (4)”You are 5 years old, Nikita is three years older than you. How old is Nikita? (8)”There are five dogs and three balls.

Is there enough ball for everyone? How many balls are missing? (no, 2)”2 pears and 4 bananas grow on a birch. How many fruits grow on a birch in total? (0, since fruits do not grow on a birch)

Relationship between addition and subtraction

Subtraction is the inverse operation of addition. In other words, in order to more comfortably find the unknown variable x (pronounced "x") in the equation x + 1 = 3, the notation is reduced to the form x = 3 - 1 (when the number is transferred too early, it changes its sign from plus to minus and vice versa ).

Full example: x + 1 = 3x = 3 - 1 = 2 This is the connection that needs to be conveyed to the child. That is, to show that 2+1=3 is the same as 3−1=2 and 3−2=1. Why can you suggest that he himself, based on what he saw, come up with 3 conditions for the problem (instead of points there can be bows, houses, cars, etc.

Total dots”What examples do you think you can write? Say 6 + 2 = 8 or 2 + 6 = 8 “How many dots?” 8 – 2 = 6 “How many green dots?” 8 – 6 = 2 “How many pink dots?” Now it’s your turn.” −=
+ =
+ =

Source: http://shpargalkablog.ru/2015/06/addition-subtraction.html

Parents often ask how to teach a child to count within 20. Sometimes a tiny student successfully performs calculations up to 10, but does not fully understand how to add / subtract large quantities.

The material contains examples of exercises, an analysis of the main mistakes that parents often make during classes.

General Information
How to teach to count within 20
Where to begin
How is a hundred formed?
Counting to 20 without going through ten
Ten counting rules
Useful tips for parents

general information

Calculations are often harder for young students than reading. In order for a child to fall in love with mathematics, it is important for parents to know the basic rules and enrollment of education. “But what about the school, the teachers?” many will ask.

Of course, the main burden falls on teachers, but when doing homework, parents must correctly explain certain rules and find errors. When adults figure out how to instill a love of mathematics, classes are much easier.

You still have to pay attention to learning to count. Such is parental work, there is no escape from joint activities with a child. Even when a tutor (children's development center) visits, homework must be done. If parents are in charge of the basic techniques, modern teaching methods, it will be much easier for an adult and a child.

How to teach to count within 20

Teachers, parents give recommendations, offer proven algorithms, thanks to which a small student will comprehend what dozens are, how to learn more complex concepts. Always test whether the “young mathematician” remembered the material he studied, do not skip, even if the study takes not 2–3 days, but a week.

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Where to start

algorithm:

learn the names of the numbers of the second ten;
You will need two sets of cubes. the items must be the same;
the child must lay out 10 objects in a row, always from left to right;
say that 10 is ten, it is called "twenty";
put another one on the initial row of cubes. it turned out - 11 or one plus "twenty" \u003d eleven;
put two, then three, four dice on the twenty. it turned out: three - for - twenty, four - for - twenty, and so on;
let the little student put the cubes himself, add a familiar number to ten;
Did the child clearly remember the scheme for constructing numbers from 11 to 19? move on to the next step.

How is a hundred formed?

algorithm:

most children who have mastered the formation of numbers up to 20 quickly understand how to make two, three, four tens to a hundred;
start the exercise the same: lay out 10 cubes, say that it is a dozen or “twenty”;
put the same row of ten cubes side by side, it turned out two rows. name: two plus "twenty" = twenty, three plus "twenty" = thirty;
Leave 40 (forty) and 90 (ninety) for later, say: these round numbers have a different name. show that the ten always has a “0” at the end, because the number is round, the numbers 1, 5, 8 are added to it, and so on;
50, 60, 70, 80 are even easier to remember. ask how many tens are in 50. That's right, five. let the children name the first number, add the word "ten" - fifty will come out. when the student understands the principle, ask: “How many tens did you find in 60, 70, and 80?” Sure, six, seven, eight. so the newly minted names will turn out: sixty, seventy, eighty.

counting to 20 without going through ten

algorithm:

take out the same cubes again;
let the child line up a row of ten pieces;
put on top (required from left to right) two more cubes. came out 12;
next, according to the same principle, build the number 15;
explain to the little student how to quickly add 12 and 15. add 1 + 1 ten, it turns out 2 tens or twenty;
add units: 2 + 5 = 7. now there are twenty and seven, together - twenty-seven;
back up the explanation with cubes. let the child count whether the 27 cubes are really on the table;
fix the task, let them try different options until the “young mathematician” comprehends the principle;
addition mastered? start subtracting: the principle is the same;
go through a dozen only after fully understanding the material with any numbers from 10 to 100.

counting rules with the transition through ten

use a table that shows the composition of the number. kids need to figure out how to get numbers in different ways. for example, 8 = 3 + 5, 4 + 4, 6 + 2, 7 + 1, 8+ 0. Without the skills of quick counting, addition / subtraction from 0 to 10, you cannot move on to more complex exercises.

parent's task: explain that one of the numbers must be divided by two to get 10, then add the remainder. The rule is easy to understand with an example.

see:

task: find how much will be 18 + 6;
18 is 10 and 8;
write down in a new way (10 + 8) + 6;
ask how much from 6 is missing to ten to add to 8;
right, 2 (the table “composition of the number” is useful);
now write 6 as 2 and 4. it turned out: 10 + 8 + 2 + 4 or 10 + 10 + 4. two tens plus four ones equals twenty-four;
when the child remembers addition, explain subtraction in the same way;
always keep a table of "number composition" at hand. children will be less lost, easier to navigate.

constantly conduct "training between cases" so that the composition of the number is better remembered. say more, connect the child, let him finish the phrase: “there are 3 plates on the table on the left, I set 3 more plates on the right. how many items are there? right, 6. show another way: “I will put 2 plates on the left, 4 plates on the right, 6 plates came out again” and so on (1 + 5).

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while away the lessons in a playful way. Preschoolers and younger schoolchildren react sharply to sad tasks, "gray", inexpressive pictures;
give simple examples, look for characters to count, understandable by age. A small student should easily recognize objects, animals that need to be counted. For example, a cat is suitable, a porcupine is not (many kids think that this is a hedgehog with long spines, they do not immediately recognize and call the animal). Orange - suitable, kiwi - no (an exotic fruit is somewhat reminiscent of a potato, you can miss) and so on;
math games are a great option for developing activities. You will have dominoes, lotto, a labyrinth through which you can travel with the help of chips, cubes with a large image. Buy games, make cardboard cards yourself;
interest the child, tell how significant the score is in everyday affairs. Count the steps in the entryway, the chairs near the table, the windows in the store, the blue or white cars on the road. When shopping in a supermarket, you ask your child to serve 1 carton of milk, 2 bagels, 3 stacks of cottage cheese, and so on from the shelf. Say: “There are 4 bananas in the basket, I will put 1 more, it will come out 5 bananas.” Speak all numbers clearly. Such conversations often "strain" parents, often seem boring, empty, but it is difficult to overestimate the benefits of classes for children;
training in between. This technique clearly demonstrates what numbers and calculations mean to people. Unobtrusively teach your baby to the universe of mathematics. When setting the table for dinner or lunch, say: "I put 5 plates, I put 5 forks." Gradually, the little man will understand that every time the number of cutlery, dishes happens to be different. Put one plate, voice it, add another one - name the number again and so on;
regularity, perseverance - one of the main rules. Whilst the training between times, invent fairy tales with a mathematical bias about encircling objects (animate / inanimate).

ask for help from the "young mathematician", let him tell you how many cats are sitting near the entrance. Crumble bread, ask to count the ghouls who have flown in for food. Often 10, 20 or more birds fly together. Here is a good reason to show that "you counted to 10, but there are more numbers, like 11, 15, 20 and so on, to count all the birds";
game in a cafe / shop. Many parents and experienced teachers advise a simple technique for teaching counting, especially for adding, subtracting numbers through a dozen. By adding another 1, 2 or 5 rubles to 10 rubles, the child will comprehend what the number 15 \u003d 10 + 5, 20 \u003d 10 + 10 is. Make paper money from dense material. “Coins” and “banknotes” of all denominations will be required, even those that are not in real circulation. Draw 3,4,7,8 rubles: you will get any number when added to 10. What size of "money" to choose? To clearly see the denomination;
school. Another useful game. Kids love being teachers. Give them this opportunity, solve examples, sometimes with mistakes, so that the "teacher" can correct you, test your knowledge. If the tiddly teacher himself made a mistake, gently tell me, do not laugh. Check the correctness of the solution on cubes, apples, counting sticks, think together who is right. Praise for knowledge, promise to correct the grade, sum up the math;
to add numbers within 20, use visual aids, counting sticks, cubes. Learning numbers from 0 to 100 will help the usual soft meter, which is used when sewing. The “young mathematician” will see all the numbers, comprehend which one is to the left, which one is to the right. It is convenient to explain that 12 is less than 17, because it is to the left. You can measure 12 and 17 cm of fabric, cut off, match the pieces, confirm the correctness;
the concepts of "plus" and "minus" are introduced later, when the rules of addition / subtraction up to 10 are learned;
always explain any word in the problem. Until the student understands what the condition means, he is unlikely to solve the problem. At first, come up with examples yourself, look for good textbooks with interesting, understandable tasks;
in case of difficulties, do not hesitate to ask for recommendations from a tutor, teacher of the children's center or teacher. The main thing: to find a person who understands not only mathematics, but also child psychology. The task is quite difficult, but solvable;
psychological contact with a tiny student is a prerequisite for successful learning. Shouts, humiliation, continuous reminders of failures discourage study, provoke uncertainty in their urine, heavy complexes.

Reading, writing, counting are the basic skills necessary for a child to master knowledge, so they need to be developed from early childhood, and not wait until the baby goes to school. By teaching your baby to read, write and count, you will greatly facilitate his life in an educational institution. One of the most difficult tasks can be learning to count, but do not be afraid and give up when you fail: the main thing is patience and work.

Learning features

It is difficult to focus the attention of a small child on something serious. You should start learning in a playful way to interest the baby. It is not necessary to sit down with the baby at the table, like at a school desk. You can learn in different ways: moving, sitting on the floor, even jumping in place.

With preschool children, you can proceed to more serious, focused activities. The time spent on counting may also increase. For example, it is advisable to practice with kids for 10 minutes about three times a day. With preschool children - 20 each (at best 30 minutes).

Create a favorable atmosphere. You will not achieve anything by shouting, you will only discourage the baby from learning. In this case, patience and calmness are important factors.
Connect surrounding objects to learning, show your child that the ability to count is vital. You can count plates on the table, birds flying in the park, children on the playground, fruits, cars, toys, steps in the entrance and much more.
Do not demand more from a small child than he can. All children are individual in their development, each new skill comes in due time.

If the baby does not succeed, do not get annoyed. Wait, return to the task after some time (for example, in a week, a month).

When training, try to follow the three steps. First, let the baby get used to the names, terms, the process itself. Then make sure that he understands the essence of what is being studied. Simple memorization is irrational, it is necessary that the child learns to understand, to realize the essence of each phenomenon. When the information is understood by the baby, he can retell and explain it, then you can proceed to memorization.
Do not forget that when you get acquainted with mathematics, you should pay attention not only to the score. Also teach the baby to recognize geometric shapes, navigate in space so that he can show where the "top", "bottom", "right", "left". By about three years old, the baby should be able to determine which object is shorter, longer, higher, lower, in which direction it is going.

Given the age

Children learn new things much more easily than adults. The need to acquire new knowledge arises in babies by the age of two. Fresh information is given effortlessly to babies, so they quickly learn some actions. But when learning to count, the age of the child should be taken into account:

You can start learning to count at 2 years old. During this period, children are able to master counting from 0 to 3. By the age of 2.5-3, you can learn to count up to 10. All this must be done with visual aids, objects, improvised means (for example, using cubes, sticks).

At 3-4 years old the child is able to learn to count up to 20. At this stage, visibility is still needed: it is worth using cards with numbers, objects that need to be counted.
If the kid has a mathematical mindset, at 4-5 years old he can learn to count up to 100. The main thing is to explain the principle of forming numbers from numbers. Do not despair if at this age your child does not count with tens. You can resume training at the age of 6.
Aged 5-6 years you need to move from visualization to mental arithmetic. During this period, the child must learn to count without the help of sticks, fingers, cards. You need to train the reverse count, as well as call the numbers in a chaotic manner.

Addition and subtraction

The ability to add and subtract is usually developed by the age of five. First, this should be done with the help of various objects, then train to solve the simplest examples in your head. When learning to count, you need to gradually introduce simple examples of addition and subtraction. It is too early to solve examples in a column, but it is quite possible to teach adding single-digit numbers.

Doing math with the baby is necessary so that he does not lose interest. Therefore, no boring examples like “3+5=? " it can not be. We teach, enticing, visually. Maybe in a joke way.

You need to start simple. For example, add one to each known digit and subtract it. It is worth using objects that are interesting to the child or important to him. It is better to present an example in the form of a question: “You have two cookies. You will share one with your mother. How much will you have left? » And all in the same spirit.

To move on to subtraction, make sure that the baby has mastered addition well. Use examples of addition and subtraction not only in class, but also on a walk, in a store, at lunch, when cleaning a room. Let the child pronounce the condition of the problem after you. Use special manuals and didactic materials with simple exercises. Pay attention to the presence of bright illustrations. Do not forget - the child needs to be lured.

To easily add and subtract, the baby needs to learn the composition of the number. He must learn that 5 is made up of the numbers 2 and 3, 1 and 4, 10 is made up of the numbers 1 and 9, 2 and 8, and so on. Before learning how to count correctly in the mind, the child must be good at solving problems with visual materials or on the fingers. It is better to start learning to count for yourself from the age of 4, not earlier. From this age, the time allotted for addition and subtraction affects the overall development.

It is important to learn the concepts of "more", "less". Scrolling through educational books, you can ask which animals are more on the page, which color is less. You also need to learn the term "equally". Be sure to explain to the child that the amount does not change from changing the places of the terms.

You should not miss the opportunity to ask the baby to count in his mind. This can be done anytime, anywhere and with anything: you can count at home, benches, flowers, chairs.

Impact on development

At 5-6 years old, most preschoolers already know how to decently count up to 20, or even up to 100. Teaching counting specifically and mathematics in general contributes to the intellectual development of the baby as a whole. Accounting in the mind stimulates the brain, makes it tense. Memorization of numbers, their composition develop memory.

Solving simple tasks where you need to count, add or subtract any objects, the kid connects the imagination, drawing various images in his head. Saying the conditions of the task aloud, the child trains speech. Therefore, it is important that adults pronounce the text correctly, because the baby will repeat it.

Knowing the numbers will give the baby the opportunity to participate to some extent in the lives of adults: he will be able to help set the table, knowing how many cutlery is needed, to carry out small instructions from his parents, which will teach him responsibility and much more. This is good preparation for school. Already in the first grade, the child will be able to count how many children are present at the lesson, name the date, and will know what it means to “prepare two pencils for work.”

Quick Techniques

Training should be done gradually. First you need to learn the numbers from 0 to 10. But even this can be difficult for a baby. Therefore, split the top ten, for example, into two fives and learn in stages. For learning, you can use various teaching aids, connect entertaining material (games, fairy tales, counting rhymes), make lessons fun, avoiding tedious memorization.

At home, you can easily diversify the learning process:

learn to count on your fingers;
choose tasks in the form of games;
connect counters;
show pictures, asking how many of these or other objects are shown;
watch educational programs with your child;
teach your child poems, fairy tales with quantitative and ordinal numbers;
constantly count everything that comes in your way.

The following methods and rules for teaching counting to preschool children are proposed. You can choose the most suitable method for your child. Better to combine several.

Sergey Polyakov's technique

According to this technique, you need to start teaching the child to count when he shows interest. As soon as parents notice that the baby is interested in numbers, training should begin. Not later than. Sergey Polyakov does not recommend using the method of learning to count, in which you need to add one by one. This slows down the learning process, prevents the child from developing.

He does not recommend starting learning with counting on sticks, fingers and rulers. It also does not contribute to intellectual development. According to Polyakov, classes are based on teaching oral counting. First, the baby lists everything that catches his eye (toys, books, steps), then he tries to count to himself, including adding and subtracting.

At the first stage, the child works with numbers within 10. To solve simple examples in the mind, the child needs to remember the composition of the numbers. At the second stage, the child solves examples already with two-digit numbers. At the same time, he does not retrieve ready-made solutions from memory, as happens at the first stage, but comes to understanding and memorizing the methods of addition and subtraction.

When teaching, the child must learn the concepts of "more", "less", "equally". Lessons according to the Polyakov method are accompanied by various games. For example, at the first stage, they use cubes and games with them “We put numbers on the cubes”, “Gnomes in the house”, “Divide in half”. You can use others.

Method Peterson

The technique of Lyudmila Georgievna Peterson teaches children to think logically. The method is not limited to learning to count, it includes many interesting game tasks that develop ingenuity. This technique is popular in preschools and primary schools. The learning system is a cycle that is called the “layer cake principle”.

Traditional teaching methods adhere to a linear concept: in the first grade we study addition and subtraction, in the second - the multiplication table, division and multiplication, in the third - fractions, and so on. It turns out that if a child was ill for a long time in the second grade and missed the main points of the topic, it will be difficult to catch up with them. Following this methodology, every year the same thing is studied, but with a different depth of complexity. For several years in a row, the themes are repeated, while each again and again appears in a new aspect.

This system involves a large number of games. Toddlers, for example, love the number line. The task before the baby is to find out how much 3 + 2 will be. The child stands at mark 3, takes two steps forward (to be added) and stops at mark 5. If it is necessary to subtract, the child takes 2 steps back. So the baby gradually remembers the composition of single-digit numbers.

At home, you can develop the logic of the baby by playing. Lay a row of cubes: 2 red-2 blue, 2 red-2 blue. Tell the child to continue the row so that the sequence is not broken. If the baby takes instead of a red cube, for example, a yellow one, you suggest that this is how the row changes, but it should be preserved.

Another interesting game. Draw a large blue square on a piece of paper. Give the kid a task - to draw a figure that differs from yours in only one way. Your child draws a small blue square. Then you draw a small blue circle. It is a small yellow circle. And so on ad infinitum, until you get bored.

It is appropriate to use tasks with the definition of more and fewer items. In two squares located opposite each other, you need to draw, for example, hearts - 6 and 5. The kid needs to determine where there are more. Of course, he immediately rushes to count hearts. But you can show him another way.

Show that the hearts are paired: connect one heart from the left square with a line with a heart from the right square. In the square where the heart was left without a pair, there are more of them. Here you can enter the signs "greater than" and "less than". It happens that there is not enough time to deal with the baby and draw tasks for him himself.

According to this technique, many printed notebooks are produced with interesting puzzles that can keep a child busy.

Training according to Zaitsev

Nikolai Alexandrovich Zaitsev has developed several games and sets of visual materials that make it easier to learn mathematics. For example, the game "One Hundred Account". It includes a set of cards with numbers in the transmission 100. This game will help develop the child.

Each card has one number. In addition to numbers, geometric figures are depicted in the number of tens and units of the number. For example, the number 75. Under the seven, a row of seven rectangles is depicted, each of which contains ten sticks (7 tens), and under the five - 1 with five sticks (5 units).

Gradually, the child needs to be introduced to each card, you can place them on the wall in the nursery. With the same cards, you can learn to add and subtract. Zaitsev’s methodology also includes such games as “It’s tight for me in a hundred” (studying numbers up to a thousand), “Platonic Solids” (geometric skills), “A Thousand Plus”, etc.

Soroban School

Mental arithmetic Soroban is a school of mental counting in the mind. These are precisely the official institutions located in several cities of Russia that teach children under this program. The Soroban school organizes classes in such a way that both hemispheres of the brain are involved. At the same time, various skills and abilities are formed:

speech;
imagination;
creative thinking;
analytical thinking;
memory;
Creative skills;
attention;
intuition.

Learning takes place on the accounts. The emphasis is on seeing and remembering the picture in motion. Then the child himself creates moving images, invents associations. This technique creates conditions for the rapid perception of information, teaches how to synthesize and analyze information, and contributes to quick mental arithmetic.

This program is open to children ages 5 to 11.

The technique of the Soroban school is based on three main principles:

regularity;
an exciting learning process;
strong motivation.

Until recently, the Soroban school methodology worked well only with gifted children. With children of an average level of development, classes did not work, they seemed too difficult.

In recent years, the school has developed a program suitable not only for "wunderkinds", but also for children with average abilities, which allows them to learn something more, develop average abilities to high results.