How to quickly multiply large numbers, how to master such useful skills? Most people have difficulty mentally multiplying two-digit numbers by single-digit numbers. And there is nothing to say about complex arithmetic calculations. But if desired, the abilities inherent in each person can be developed. Regular training, a little effort and the use of effective methods developed by scientists will achieve amazing results.

Choosing traditional methods

Proven decades methods of multiplying two-digit numbers do not lose their relevance. The simplest tricks help millions of ordinary schoolchildren, students of specialized universities and lyceums, as well as people involved in self-development, improve their computational skills.

Multiplication by factoring numbers

The easiest way to quickly learn to multiply large numbers in your head is to multiply tens and ones. First, tens of two numbers are multiplied, then ones and tens alternately. The four received numbers are summed up. To use this method, it is important to be able to memorize the results of multiplication and add them in your mind.

For example, to multiply 38 by 57, you need:

• split the number into (30+8)*(50+7) ;
• 30*50 = 1500 - memorize the result;
• 30*7 + 50*8 = 210 + 400 = 610 - remember;
• (1500 + 610) + 8*7 = 2110 + 56 = 2166

Naturally, it is necessary to know the multiplication table perfectly, since it will not be possible to quickly multiply in the mind in this way without the appropriate skills.

Multiplication in a column in the mind

The visual representation of the usual multiplication in a column is used by many in calculations. This method is suitable for those who can memorize auxiliary numbers for a long time and perform arithmetic operations with them. But the process is greatly simplified if you learn how to quickly multiply two-digit numbers by one-digit numbers. To multiply, for example, 47 * 81 you need:

• 47*1 = 47 - remember;
• 47*8 = 376 - we remember;
• 376*10 + 47 = 3807.

Remembering intermediate results will help pronouncing them out loud while summing up in your mind. Despite the complexity of mental calculations, after a short practice, this method will become your favorite.

The above methods of multiplication are universal. But knowing more efficient algorithms for some numbers will greatly reduce the number of calculations.

Multiply by 11

This is perhaps the easiest way and is used to multiply any two digit numbers by 11.

It is enough to insert their sum between the numbers of the multiplier:
13*11 = 1(1+3)3 = 143

If a number greater than 10 is obtained in brackets, then one is added to the first digit, and 10 is subtracted from the sum in brackets.
28*11 = 2 (2+8) 8 = 308

Multiplication of large numbers

It is very convenient to multiply numbers close to 100 by decomposing them into components. For example, you need to multiply 87 by 91.

• Each number must be represented as the difference between 100 and one more number:
  (100 - 13)*(100 - 9)
  The answer will consist of four digits, the first two of which are the difference between the first factor and the factor subtracted from the second bracket, or vice versa - the difference between the second factor and the factor subtracted from the first bracket.
  87 – 9 = 78
  91 – 13 = 78
• The second two digits of the answer are the result of multiplying those subtracted from two brackets. 13*9 = 144
• As a result, the numbers 78 and 144 are obtained. If, when writing the final result, a number of 5 digits is obtained, the second and third digits are summed up. Result: 87*91 = 7944 .

These are the easiest ways to multiply. After their repeated application, bringing the calculations to automatism, more complex techniques can be mastered. And after a while, the problem of how to quickly multiply two-digit numbers will cease to excite you, and memory and logic will improve significantly.

Parents of schoolchildren very often face a rather difficult problem: how to help a child learn the multiplication table? Children study the Pythagorean table in the second grade of elementary school. At this age, mechanical memory works great, so many simply “memorize” the material. But not all children manage to learn the multiplication table in this way. Today, the Internet presents an exhaustive list of various methods that allow you to learn the multiplication table with comfort for the child and with special attention to his individual characteristics.

There are various ways to memorize the Pythagorean table: proverbs, sayings, poems, songs, fairy tales, games, as well as various visual materials. However, no matter which way you choose to study, it is worth remembering one thing: the child must understand the very principle of the multiplication table!

It is important! By the time your child starts learning the multiplication table, he will already know the logic of such an arithmetic operation as addition. First of all, it is worth explaining to the child the process of multiplication. For example, 3 times 4 means to add the number 3 four times, or 3+3+3+3. Use associations, let it be not just the number 3, but three cars or three dolls. The child should understand well the arithmetic operation itself - multiplication. If you explain to a child that, in fact, multiplication is a shorthand for adding a specified number of identical terms.

Only after the child understands the essence of the arithmetic operation, proceed to the study of the table itself.

1	2	3	4	5	6	7	8	9	10
2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50
6	12	18	24	30	36	42	48	54	60
7	14	21	28	35	42	49	56	63	70
8	16	24	32	40	48	56	64	72	80
9	18	27	36	45	54	63	72	81	90
10	20	30	40	50	60	70	80	90	100

Learning the multiplication table with your child

Teach your child to understand the Pythagorean table. Explain that when a number from the leftmost column is multiplied by any of the numbers, their product is obtained, which is at the intersection of the desired row and column. When the child learns to easily navigate the table itself, it is necessary to proceed to the most important thing - memorizing the table itself.

Playfully memorize the multiplication table!

Unfortunately, it is rather difficult for many children to approach the issue of memorizing the table with all responsibility. It is much easier to conduct training using the element of the game. It will be much easier for children to remember the information that they really find interesting.

A fairly simple and effective game is an activity with cards. Draw or print with your child various examples from the multiplication table of the form:

• 3x7=?
• 2x4=?
• 5x8=?

Start your workout. Those cards that the child answered without difficulty and the first time, put aside. Set the examples that your student has difficulty at the bottom of the pile so that the child can pull them out again later. Continue the game until your student answers all questions. Such a quiz can be held daily, for example, after dinner. No need to force the child or scold him for the wrong answers. Together come up with a special reward that awaits your son or daughter if they answer all the questions absolutely right.

There are a lot of options for such a game. For example, your child has learned all the examples of multiplication by 2 and 3. Make only these cards together with the baby, and then dilute them with new ones. Another option for better memorization of the table can be drawing up cards of the form:

• 3x?=15
• ?х2=6
• 10x?=10

It is interesting! Turn on your imagination! It will be much easier for a child, and most importantly, more interesting to remember the material if the cards with examples are bright and colorful. Instead of boring questions, funny little animals or favorite fairy-tale characters of the baby will appear. Dream up, and then your child will be happy to guess what number is hidden behind the noble Puss in Boots or funny Carlson.

Memorizing the multiplication table with a child - the basic rules!

So that it is not difficult for a child to memorize the Pythagorean table, and the information received does not turn into a mess, you need to follow a few simple rules:

1. Seeing the Pythagorean table, even the smartest kid can get scared. Explain to the child that there is nothing difficult in understanding this information, and at one time, both mom and dad, and grandparents, taught this table.
2. Learn first a simple multiplication, for example, by one. Explain to your child that when you multiply by 1, you always get the same number that we multiplied by 1. For example, 1x1=1, 5x1=5, 10x1=10, etc. Multiplication by ten is also easy to convey to a child: it is the same as adding zero to a number every time. For example, 2x10=20, 3x10=30. The main thing is that the association with the appearance of zero in the number is deposited in the child’s head, and he can solve examples not only on paper, but also in his mind.
3. When you have learned and repeated the most simple examples, begin to move with the baby further down the table.
4. After each memorization of an arithmetic operation - multiplication by 2,3,4,5,6, etc. do not forget to repeat the material covered with the child (it can be in the form of a game that was described above).
5. Very often, a child, having learned multiplication by 2, begins to get lost if an adult asks him: “how much is 2x5”? In such a situation, one must be careful when explaining to the student the communicative rule of multiplication: when the places of factors are changed, the product does not change.

Finger games - learning the multiplication table is fun!

If your child is having a hard time learning the multiplication table. You can use the fingers of a young accountant. A great example would be learning to multiply by 9. Have the child place both hands on the table, palms down. Each finger will represent a number from one to ten. For example, we want to multiply 9 by 4. We count from left to right to 4 - we get the index finger of the left hand. We bend it, and count the number of fingers on the left. There are only 3 of them - that's dozens. Pure fingers on the right - 6 - units. Answer 36. This memorization option will add a bit of magic to the learning process, and your young accountant will definitely be carried away by such an interesting learning process.

association game

Many children have well-developed motor and figurative memory, so it will be easier for them to remember tabular examples using various associations. For example, the number 2 looks like a swan, and the number 1 looks like a gnome with a curious nose. For example, in the case of multiplication 2x1=2, you can come up with the following story: One beautiful swan was very lonely. He wanted to find a friend so much that he looked for him everywhere, everywhere. And then one day he met a dwarf with a funny hooked nose. However, the dwarf was very cunning and treacherous that the swan barely escaped him. And so the swan remained in splendid isolation ...

There are a lot of stories like this. Let the child dream up himself, the main thing is that the story unites two multiplier characters, and the work is the logical conclusion of this plot. The more emotional and exciting the stories are, the easier it will be for the child to remember this or that example.

As soon as the causal relationships are worked out with the help of a fairy tale, the most important thing can be singled out: “The swan met the dwarf, did he make friends with him or was he left alone?” If your child answered everything correctly, then you need to ask him to compose this example in numbers.

Poems, songs, stories

This way of memorizing the multiplication table is suitable for children who perfectly memorize poems and songs. Children can be offered to memorize examples from the multiplication table with the help of verses. An excellent option are the works of A. Usachev "Multiplication" and M. Kazarina "About multiplication". Thus, when solving this or that example, the child will associate with a rhyming line.

No matter how you explain the multiplication table to your child, the main thing is to never get angry with your baby if something is not clear to him! Show patience, as well as your imagination, and then your child will be happy to learn the multiplication table!

At some point, parents will definitely face the question: how to quickly learn the multiplication table for a child? He will not be able to do this on his own, he needs the help of adults. And also - correctly chosen methods of memorization.

Basics of learning

To help your child quickly learn the multiplication table, it is best to first explain to him the essence of this action. He already has the concept of addition and subtraction. We explain that 2 multiplied by 2 means adding two deuces, that is, 2 + 2.

You can give more complex examples: 3 times 4 means to add three 4 times - 3+3+3+3.

It is good to support your explanations with real, understandable examples for the child: “Grandfather brought 2 sets of felt-tip pens to you and Ksyusha. Each has 5 pieces. And just how many felt-tip pens will it make? How do we count: 5 plus 5 or 2 times 5? And so, and so we get 10.

Game tricks

How to quickly learn the multiplication table for a child? Of course, use game visual techniques. We take a box and balls. I put them in a box in pairs. Then the next two balls, then another and another. It turned out like this:

Methods for studying the multiplication table

Different methods will help a child quickly learn the multiplication table. The fact is that some of the children memorize numbers well simply mechanically (at this age, this type of memory is quite well developed in them).

Some will need visual reinforcement: videos, drawings, emotional nourishment, games work well, and tools such as online games and poetry.

Multiplication table - where to start?

The child needs to explain how the Pythagorean table is arranged: there are numbers in columns and in rows, and where they intersect, we look for the answer - the product of numbers, for example, six by eight will be forty-eight (6x8 = 48).

You can start studying the table with its usual version. Immediately explain to the child - do not be afraid that it is so big at first glance. Many examples there are already known and do not require memorization.

For example, multiplying by 1 and by 10. What does it mean to multiply a number by 1 - take it 1 time. Two will remain a deuce, four will remain a four, and so on. That is, the number will not change. And multiplying by 10 is also easy - just add a zero to the number: 5x10=50.

Multiply by 2, by 5 and learn the squares of numbers

How to quickly learn the multiplication table for a child - remember at first simpler options. Multiplying by 2 is usually not difficult for children. It's like adding another one to a number.

After that, you can learn how to multiply by 5. Answers will end in either 0 (even numbers) or 5 (odd numbers).

The next step is memorizing the squares of numbers. Repetition and consolidation is indispensable here. The child will just have to remember that 8 by 8 is 64, and 9 by 9 is 81.

Usually the first difficulties begin with multiplying by 3. Here it is time to introduce additional memorization methods - visual techniques, for example, playing cards or associations using poetry. About them - a little lower.

How to multiply by 6, 7, 8 and 9

This stage is the most difficult, and some examples just need to be remembered. You will have to repeat these few of the most difficult works with your child constantly until the numbers reach automatism.

The main thing is to show the child that he already knows almost the entire table, and there are mere trifles left. Here are those tricky values ​​that are so hard to remember:

6x7=42
6x8=48
6x9=54
7x8=56
7x9=63
8x9=72

On the change of factors

Adults understand that 4x3 = 3x4. But the child needs to be explained that if you swap the factors, the result will not change.

Then it will be much easier for your student to remember how much it will be, for example, 7 by 4. If you forgot, let him remember the multiplication of 4 by 7. This is an important point in learning the multiplication table.

Different methods of studying the multiplication table

A variety of ways to study the multiplication table helps you find the right one for your child.

Memory cards

All kinds of online games on the Internet also contribute to memorization, but the most reliable and proven method remains a visual method that uses memory cards.

Make cards with examples: for example, on one side write 7x8, and on the other - the answer. How we play - the child takes a card, answers the question and turns it over to see the answer. He answered correctly - he keeps the card for himself, if not - he takes another card. The one with the most cards wins. During the game there is repetition and memorization, but in a fun way.

One such option is digital lotto. Enter the answers from the table into the cards, make cards with example tasks. The gameplay stimulates memorization.

Multiply with fingers

There is such a way of counting - on the fingers. Suitable for multiplying by 9. You need to put your hands down with your palms and straighten your fingers. We need to multiply 7 by 9. We bend the 7th finger in a row and look - the number of fingers before it will be equal to tens in the answer - 6, and after the 7th finger - units, that is, three. We get 63.

There is another interesting method for multiplying by 9. It is necessary to multiply a given number, for example 6, by 10 (6 by 10 \u003d 60). And now we subtract 6, we get 54.

Repetition is the key to memory

To make it easier for your child to remember, make visual aids for him. He must constantly see examples before his eyes and repeat them. You can brightly and colorfully decorate the table and hang it in the children's room and in the kitchen. This will make the information easier to remember.

Teaching verses

For many children, especially humanists, it is much easier to memorize the table using a poetic form. The most famous similar poems were written by Marina Kazarina and Alexander Usachev:

Multiply five by six
As a result, we get THIRTY.
And five seven - easy to count -
Short answer: THIRTY-FIVE!

Once the deer asked the elk:
How old is seven eight? —
The moose did not climb into the textbook:
- Fifty, of course, six!

Cartoons to remember

If you set a goal, you can find a lot of interesting cartoons to help those who study the basics of multiplication. Children always perceive this form of presentation well, so we advise you to actively use it. An example is in this video:

Take it, tell your friends!

Read also on our website:

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Do you think it is difficult to depict people on paper, and this art is only available to the gifted? Nothing like this! We will tell you how to draw a person, breaking down the process into stages and simplifying it as much as possible. Following our instructions, even a child can portray homo sapiens.

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All parents sooner or later find themselves in a difficult situation, a way out of which is quite difficult to find. This problem occurs when a child needs help learning the multiplication table.

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Parents have known this problem since childhood, but before it was much more difficult to cope with it. After all, the modern Internet provides parents and children with a variety of methods for mastering the Pythagorean table, helping to remember the multiplication table in a playful way. For classes with a child on the Internet, you can find rhymes, songs, video and audio lessons, game scripts, which can help facilitate the task of parents and children in this difficult task.

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But among the proposed methods, parents will have to choose the most suitable and effective one for their child, since each child requires an individual approach to learning, so the methods used should be based on the characteristics of the character and abilities of the child.

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This article analyzes the most popular methods for memorizing the multiplication table, among which each parent will find the one suitable for their child.

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Initially, attention should be focused on the child needs to explain the meaning of the arithmetic operation of multiplication.

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As you know, children starting to study the multiplication table already have an idea about such simple arithmetic operations as addition and subtraction.

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It is on this knowledge of the child that one should rely when explaining to him the principle of multiplication, that is, that the arithmetic operation 2x3 is identical to the example 2 + 2 + 2.

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It is necessary to ensure that the child learns this rule, which will help to overcome all possible difficulties that arise in the course of memorizing table examples.

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It is also necessary to explain to the child what the system of the multiplication table is, that the number in the left column is multiplied by the number located on the top line, while the answer is that their product must be sought at the intersection point of the column and row where these numbers are located.

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Multiplication table system

A game
You should always remember that even the most boring and tedious thing for a child can be turned into an interesting activity by brightening it up with a game. Learning the multiplication table is no exception. This will help game techniques that will draw the child's attention to learning, reveal the meaning of multiplication and facilitate the task of parents. When studying with a child, one should adhere to the rule that it is always easier and faster to remember something interesting, that is, initially you need to interest the child in the subject of study and concentrate his attention on the arithmetic operation of multiplication.

7 rules for remembering information

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• Arouse interest.
• Make associations.
• Remember in parts.
• Repeat what you remember.
• Try to understand.
• Set a goal to remember.
• Apply knowledge of this information.

For example, five times eight equals forty (5×8=40)

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Card game

This is one of the most popular and effective methods of memorizing the multiplication table with the help of a game. This article reveals the essence of the game and the sequence of actions.

Cards containing examples and their answers

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The meaning of the game multiplication table comes down to the fact that the child needs to be asked to get cards out of the pack in random order, on which he will find an example from the multiplication table without an answer, that is, after the “equal” sign there is a question mark. If the child gives the correct answer, then this card is no longer involved in the game, but if the answer is incorrect, the card is placed between other cards and the child will be able to draw it again.

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Thus, the game lasts until the child goes through all the cards and gives the correct answers for all the cards. When the game is nearing the end, there are very few cards left and they, most often, turn out to be the most difficult ones that the child could not answer with ease. If at the end of the game the child turns to them again and tries to find the correct answer, then he will remember these examples.

This game is actually a multiplication table simulator. The game becomes more interesting and easier to master if it is broken down into successive stages related to the educational material. So, you can start an impromptu lesson with the simplest cards of examples of multiplication by 2, and then gradually add new, more complex mastered examples to them. It is possible to develop different variants of the game, which can be chosen depending on the abilities and knowledge of the child.

Also, various special programs, online games and original sound posters offered by the Internet will help reinforce the game while studying the multiplication table. However playing cards considered the simplest and most effective.

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The initial stage of memorizing the multiplication table

Starting teaching a child the basics of multiplication, this process can be simplified by some special tricks.

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Yes, it is necessary start learning with the simplest and most elementary multiplication table examples which the child will solve without much difficulty. Indeed, if a child immediately sees the whole table, consisting of many complex examples, he may despair and think that it is unrealistic to learn this table. Therefore, the task of parents is to calm the child and show him that everything is actually much simpler and that he can immediately solve several simple examples.

1. The simplest examples are multiplication by 1 , which always result in the number by which they were multiplied. So, 1x1=1, 2x1=2 and so on.

2. Also simple are examples of multiplying by 10 , since this is the same as adding zero to the number that is being multiplied. So, the result of multiplying 3 by 10 is 30.
Thus, having learned the simplest examples of the multiplication table for 1 and 10, the child will understand that he has already mastered the most extreme columns and rows of the multiplication table.

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A simplified version of the multiplication table without examples for 1 and 10

Parents should be able to properly distribute the load of the child, and if he is tired after the first stage of training, then further training should be postponed for the next time. But in the case when the child is ready to continue learning now, you can try to continue the lesson.

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3. At the first stages of the lesson, we made sure that multiplication by 2 examples are the easiest for a child , since they are identical to the simple addition of two numbers. Usually, children who begin learning the multiplication table already have the skills to add numbers, so simple examples of multiplying by 2 will be easily mastered.

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4. The next stage in the study of the multiplication table will be associated with the rule for the replacement of the factor, based on the commutative law of multiplication, which may be understandable to parents, but very difficult for a child. This law is well known to parents, because they have already encountered it in the process of schooling. It says that the product does not change from a change in factors. In other words, the child should be explained that the example 2x4 is identical to the example 4x2.

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2 multiplication table

The child needs to clearly explain how it happened that the second row and second column of the table have the same numbers, like all other rows and columns that match in serial number.

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Thus, the child, knowing all examples of multiplication by 2, will know the multiplication of all numbers in the table by 2, that is, the child's task is extremely simplified.

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Based on this, as a result of applying the presented methods for studying the multiplication table, parents can greatly facilitate the task of the child in the process of memorizing numerous examples of the multiplication table.

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At the end of each stage of learning, as a result of which the child has learned a certain number of examples, parents are advised to highlight them in the table in green so that the child clearly sees his achievements and makes sure that there is nothing unrealistic in memorizing the multiplication table, and it will not be as huge and incomprehensible to him as at the beginning of classes.

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Targeted memorization

After the child has mastered the basics of multiplication and the simplest examples of the table, one should proceed to the next stages of learning with more complex multipliers.

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At this stage, it is necessary to apply not only game techniques, but also various effective memorization techniques based on associations, on the repetition method, on dividing into parts, on solving test problems and applying the child's knowledge in practice.

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Most table examples the child will have to specifically memorize and to consolidate knowledge repeatedly repeat them to achieve such a result when the child can name examples and correct answers without hesitation. To do this, you must patiently follow the sequence and rush the child.

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It is most effective to start this stage of training with squares containing examples of multiplication by 3 and 4, gradually moving to the next numbers.

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Often you can hear the opinion of teachers that it is best and most correct to study the multiplication table moving from the end to the beginning, that is, from complex examples to simpler ones.

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However, this training option seems to be rather doubtful, since it may not be effective for every child, since certain difficulties may be associated with the child’s confusion due to a lack of understanding of how those complex values ​​that he sees in the answers to the examples turned out.

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Therefore, you need to start with an example 3x3, when solving which, the child will be able to independently check himself by counting the example on his fingers, as a result of which it will become clear to the child how the number 9 is obtained in the answer. If, however, the child is given the task to multiply, for example, 8 by 7 and demand that he simply memorize the correct answer, this may simply frighten the child with the impossibility of testing this example in practice, and as a result of hiding the decision process from him, the child may lose motivation and interest in learning, as he considers that he does not have the ability to mathematics.

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Number squares

The next stage of training will require knowledge and application of this term. The child should be explained that it means the product of a number by itself. The multiplication table contains 10 squares needed for memorization. Practice shows that the squares up to the example 6x6 = 36 are remembered by children just fine. The 3 squares that follow it also most often do not present any particular difficulties.

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3 times table

From this stage, the child begins to have difficulty remembering examples from the table. If you encounter difficulties of this kind, you should turn to the game with cards. However, even if these techniques turn out to be ineffective, for example, due to the fact that the child has a humanitarian mindset, then special rhymes can be used to memorize, which in a simple form will present the child with examples from the table.

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4 times table

When studying examples from the multiplication table by 4, you will probably also have to use flashcards and poems in class. To simplify the task for the child, you should explain to him that multiplying by 4 is the same as multiplying 2 times by 2.

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5 multiplication table

This stage of learning the multiplication table usually goes without difficulty, since examples for 5 are remembered quite simply. The child should be explained that all values ​​​​of this series of multiplication are 5 in relation to each other, and the extreme number will be either 5 or 0, also that multiplying even numbers by 5, as a result, we get 0 on the edge, and multiplying odd numbers - on the edge we get 5.

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Multiplication table for 6, 7, 8 and 9

Multiplying by 6.7, 8 and 9 are considered the most difficult to remember. Therefore, at this stage, the child needs to be explained that after he has learned the squares and the multiplication table up to 5, he will have to make very little effort, because he has, in fact, already learned all the subsequent examples.

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Complex examples from the multiplication table

So, it remains for the child to learn the most difficult examples from the multiplication table, there are 6 of them, and it is they who should be given special attention, make the last leap and complete this task to the end.

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Here are the most difficult products from the multiplication table

6×7=42
6×8=48
6×9=54
7×8=56
7×9=63
8×9=72

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To remember them The best way is to play cards so that the child can give an answer to any example without hesitation. In this case, it is best to use There are 12 cards in the game, containing products with changing places of multipliers.
Thus, using special techniques and techniques, you can quickly and easily learn the multiplication table, which initially seemed incomprehensible to children and parents to remember.

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Techniques for memorizing the multiplication table

Obviously, there is no one specific method of learning the multiplication table that is suitable for everyone. After all, when conducting classes with a child, it is necessary to approach them individually, based on the preparation of the child and his character.

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Therefore, parents should master several techniques and know more than one way to remember the multiplication table in order to choose the right one for their child.

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Here are some of them.

Application in practice

Learning will be simpler and more effective if all the examples from the multiplication table are illustrated to the child in practice.

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For example, studying examples for 5, a boy can be asked how many wheels will be needed for 5 cars. So, the child will imagine a car with four wheels and successfully memorize the example 5 × 4 = 20. You can ask a girl how many ribbons it will take to make two ponytails for three dolls. With the help of such an illustration, the child will remember that 3x2 = 6.

Complex examples

During the study of the multiplication table, the child may experience some problems when trying to memorize the most difficult examples, which should be focused on the child's attention and help him learn them, thereby overcoming the most difficult stages of the task.

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Memorizing multiplication tables with fingers

To simplify the process of memorizing individual works from the multiplication table, you can tell the child that you can count them with your fingers.

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At the same time, examples that can be calculated in this way can be not only the simplest, but also, for example, from multiplying by 9. This will require both hands. It should be bent when multiplying any number by 9 straightened fingers under the number of the multiplied number. Thus, the number of fingers before the bent is tens, and after it - units.

First you need to do two things: print the multiplication table itself and explain the principle of multiplication.

For work, we need the Pythagorean table. Previously, it was published on the back of notebooks. It looks like this:

You can also see the multiplication table in this format:

So, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make it easier for him, find or print a real table.

2. Explain the working principle

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When a child finds a pattern on his own (for example, he sees symmetry in a multiplication table), he remembers it forever, unlike what he memorized or what someone else told him. Therefore, try to turn the study of the table into an interesting game.

Starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.

Explain that multiplication is a short and fast way to do calculations.

Next, you need to deal with the structure of the table itself. Show that the numbers from the left column are multiplied by the numbers from the top row, and the correct answer is at their intersection. Finding the result is very simple: you just need to swipe your hand across the table.

3. Teach in small chunks

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No need to try to learn everything in one sitting. Start with columns 1, 2, and 3. This will gradually prepare your child for more complex information.

A good technique is to take an empty printed or drawn table and fill it out yourself. At this stage, the child will not memorize, but count.

When he figured out and mastered the simplest columns well enough, move on to more difficult numbers: first to multiply by 4-7, and then by 8-10.

4. Explain the property of commutativity

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The most famous rule: the product does not change from permutation of factors.

It will become clear to the child that in fact he needs to learn not all, but only half of the table, and he already knows some examples. For example, 4×7 is the same as 7×4.

5. Find patterns in the table

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As we said earlier, in the multiplication table, you can find many patterns that will simplify its memorization. Here are some of them:

1. When multiplied by 1, any number remains the same.
2. All examples of 5 end in 5 or 0: if the number is even, we attribute 0 to half of the number, if odd - 5.
3. All examples of 10 end in 0 and start with the number we are multiplying by.
4. 5 examples are half as many as 10 examples (10 × 5 = 50, and 5 × 5 = 25).
5. To multiply by 4, you can simply double the number twice. For example, to multiply 6 × 4, you need to double 6 twice: 6 + 6 = 12, 12 + 12 = 24.
6. To remember multiplying by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. You need to remember the first and last number. All the rest can be reproduced according to the rule: the first digit in a two-digit number is increased by 1, and the second is decreased by 1.

6. Repeat

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Practice repetition more often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Keep an eye on the pace: at first, let's have more time to think, but gradually increase the pace.

7. Play

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Use not only standard methods. Education should be fun and interesting for the child. Therefore, use visual aids, play, use different techniques.

Cards

The game is simple: prepare cards with multiplication examples without answers. Shuffle them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, the wrong one - we return it to the stack.

The game can be varied. For example, give answers on time. And every day count the number of correct answers so that the child has a desire to beat his yesterday's record.

You can play not only for a while, but also until the whole stack of examples runs out. Then for each wrong answer, you can entrust the child with a task: recite a poem or clean up things on the table. When all the cards are solved, give a small gift.

From reverse

The game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will give 30 as a result (for example, 3 × 10 and 6 × 5).

Real life examples

Learning becomes more interesting if you discuss with the child things that he likes. So, you can ask a boy how many wheels four cars need.

You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass, multiplied by the number of glasses.

Poems

Rhyme will help to remember even complex examples that are not given to a child. Make up your own simple verses. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine - seventy two.

8. Don't be nervous

Usually in the process, some parents forget and make the same mistakes. Here is a list of things that should never be done:

1. Force the child if he does not want to. Instead, try to motivate him.
2. Scold for mistakes and scare bad grades.
3. Set an example for your classmates. When someone compares you to someone, it's unpleasant. In addition, you need to remember that all children are different, so you need to find the right approach for each.
4. Learn everything at once. The child is easily frightened and tired of a large amount of material. Learn gradually.
5. Ignore progress. Praise your child when they complete tasks. At such moments, he has a desire to study further.