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At one time, almost every person tried to learn the multiplication table, unless, of course, we are talking about civilized countries. Obviously, the vast majority successfully coped with this task, although sometimes there are people who, in adulthood, do not remember the multiplication table. Most likely, such unique people never really knew it, since few will argue with the statement that knowing the multiplication table in childhood is about the same as learning to ride a bicycle, and if you have already mastered this skill, then it remains with you for life. Moreover, a person regularly in his Everyday life is faced with the need to calculate something in the mind, even though almost everyone in mobile phone today there is a calculator.

But agree that constantly use the help technical means, with elementary calculations, it looks strange and speaks, at least for many, of a person’s insufficient education. It's like looking into a dictionary while talking to find the right words or driving a car with the rules in front of your eyes. traffic. Many, probably, will not agree with such comparisons, considering them inadequate, but they will not dispute the fact that this table is very useful in life. And the fact that its compulsory memorization remains in the modern school curriculum confirms the usefulness of mastering the skill of mental counting, which, in addition to its obvious practical benefits, is also a wonderful tool for training memory.

By the way, it will be interesting to know that this table first appeared in the school curriculum in medieval England. At that time, it differed from the well-known to us in that the account in the table was (and is still being) up to 12, which is explained by the peculiarities of the English system of measures of length, where 1 foot is equal to 12 inches, in addition, and in the British monetary unit shilling contains exactly 12 pence. So it is much more difficult for English children than ours to quickly master the multiplication table, although this is unlikely to reassure parents who are trying to force their child to cram this boring set of numbers.

Therefore, we bring to your attention a few recommendations on how parents can help their children master the skill of mental multiplication, because for many this task seems simply overwhelming.

The right environment

For an efficient workflow, you need to choose the right time and place. So, if your child is too tired after school or is simply hungry, then he is clearly not ready to “nibble on the granite of science” and classes will not give the desired effect. It is important to approach the multiplication table memorization with as much energy as possible and, which will be quite useful, with enthusiasm.

To do this, it is advisable to use some incentives, but not of a material nature. Only parents can know how best to encourage their child for success in learning, and there can be no universal advice here, but it can be said that even if you simply express in words the joy of your child’s success, this can be a good incentive for him to succeed in the future.

It is probably not worth saying that for successful learning it is necessary to exclude all distractions, such as a TV or a smartphone, and study in complete silence so that the child is focused only on numbers. Do not forget about the pauses in your studies, if the appearance of fatigue becomes noticeable. After a break, the lesson should begin with a repetition of what has already been learned earlier.

In addition, you should not limit classes to time, you just need to constantly maintain an incentive to study in your child. To do this, it is necessary to arrange small exams for him throughout the day, asking questions on the material already learned. For example, if you mastered multiplication by three the day before, then check how the child learned the multiplication table only up to this digit, without being ahead of events and without trying to make him memorize examples with the next digit along the way. Go to it only when the child confidently and without hesitation answers the material already covered.

Basic Rules

Many parents start teaching their children the multiplication table as early as preschool age, but at school they will be taught according to their own method, most likely different from yours. Therefore, it is better to adhere to the school method at home, unless of course the child has already learned the table before school. It is advisable to resort to other methods of memorizing the multiplication table only when the way children are taught at school does not suit your child, and it is difficult for him to learn the material using the school method.

The following are examples to help you understand which path to take in learning:

• You should start from the smallest numbers, moving in order: 0, 1, 2, and so on, giving information gradually, without forcing learning, which will enable the child to remember the rules well. You need to understand that children first learn the table by heart and only eventually begin to understand the algorithm.
• Explain to the child the very principle of multiplication, while applying the form of addition, with which he is probably already familiar if he proceeded to the multiplication table. Example: 2x5 = 2+2+2+2+2. This will teach the child not only to memorize the table, but also to understand where the result of multiplication comes from.
• From the first lesson, you need to show the principle of commutativity by examples. Having a table in front of you, demonstrate clearly that the permutation of elements does not affect the result and 4x6 is the same as 6x4. Thus, the child will see that he will actually have to learn only half of the multiplication table, which will certainly give him more enthusiasm.
• In the process of studying the table, try to minimize the principle of rote memorization as much as possible, paying attention to various patterns. This also needs to be shown clearly. So, it immediately catches your eye that all multiplications by the number 10 end in zero and to get the result you don’t need to remember anything, but simply add 0 to the number multiplied by 10. The same applies to the number 5, the multiplication results also end with either 5 or 0. Thus, the child will see how the table, which at first seems incredibly large, and therefore difficult to remember, has significantly decreased, and it has become much easier to achieve success. Second example: multiplying 5 is half that of 10. It may be easier for your child to remember that 4x5=20 by first multiplying 4x10=40 and dividing the result in half. Another example: to multiply by 4, you can simply multiply twice by 2. So, to multiply 8 by 4, you can first multiply 8x2=16 and then multiply the result again 16x2=32. There are relatively many such patterns, and the more a child learns about them, the easier it will be for him to choose the most suitable one for him.
• It will be useful to explain to the child that if, for example, he forgot how much 7x8 will be, but remembers that 7x7 \u003d 49, then he does not have to strain his memory, but simply add one more seven to 49 and get 56. This method works especially well with table by 9, only in this case you need not add, but subtract. Example: 9x7=63 is quite difficult to remember, but 10x7=70 is elementary simple and to get the correct result, it is enough just to subtract 7 from 70 and get 63. But it should be borne in mind that such a method should be used as an additional and valid only in if the child cannot remember the table. It is much better if, after all, the multiplication results pop up in memory automatically, and do not require additional mathematical calculations. This is why we don't mention finger multiplication here. This method was quite popular in the past, and even today there are people who teach their children to multiply in this way. It may have a right to exist, but it is more like multiplication on a calculator than mental counting.

Consolidation of the result

It must be realized that in the case of memorizing the multiplication table, it is more important final result, not the learning rate. It is important that the table remains forever in the memory of the child, and the best way here is to repeat it many times.

You should not force the memorization process by making frequent pauses so as not to tire the child unnecessarily, which can cause an elementary feeling of disgust and then it will be even more difficult to achieve a result. You can try to turn the lesson into a kind of game, which will make learning fun and exciting. So an example, you can remember the game of bingo or loto, when a card divided into squares with numbers is filled with chips. Everyone has their own card with 36 squares and different numbers printed on them. If the host calls, for example, 3x5, and your card has the number 15, then you close the corresponding square and so on. The first person to cover their entire card wins.

Some may enjoy memorizing the multiplication table in the form of a poem. For example, you can recommend poems by M. Kazarina or D. Usacheva. You can use modern gadgets in your classes, because the network offers many different games and quizzes on this topic. Classes on a smartphone or laptop will certainly interest your child, especially if it takes place in the form of a game or competition.

And don't forget to praise your baby for achieved success which, of course, will stimulate him to achieve the ultimate goal. BUT final goal- this is the level of memorization when the child begins to confidently answer any question from the multiplication table and then you can already move on to two-digit numbers.

In any case, the success of the study will require patience and perseverance, both on the part of parents and children. Daily activities will certainly bring results and there is nothing wrong with the fact that if your child needs more time to memorize than one of his classmates. All children have different abilities and yours will surely give odds to the rest in something else. And in this case, it is more important that the multiplication table is deposited in a person’s memory for life, and not how quickly he learns it.

The multiplication table, without exaggeration, is one of the foundations of mathematical science. Without her knowledge, teaching mathematics and algebra will become very difficult, if not impossible at all.

And in everyday life, the multiplication table is in demand almost daily. That is why its development in primary school taking so much time.

However, the study of the Pythagorean table cannot be called easy: the multiplication skill is mastered with difficulty, and it is also not easy for a child to memorize all this considerable mass of numbers.

The task of parents is to help children in learning the multiplication table, making the process interesting and at the same time productive.

Easy Ways to Teach Kids the Multiplication Table

The good old counting material, as well as various “tips” in the form of poems, songs and interesting memorable pictures, have not been canceled either.

Having an idea about the basic teaching methods: memorization, game, visualization - parents are able to independently teach the child the multiplication table.

memorization

The task of "learning a table" involves, among other things, its literal memorization. It has been noticed that it is much easier to memorize material in a poetic form or in the form of a song, especially when it comes to children.

If you arrange and rhyme the multiplication examples, then all the necessary numbers will really be fixed in memory much faster.

You can use any verses (for example, you can learn with your child the words of the song by V. Shainsky and M. Plyatskovsky “Twice two - four”). And parents with fantasy can connect it and come up with their own rhymes, it's easy, for example: "six seven - forty-two, an owl flew to us."

In extreme cases, if the table is no longer remembered in any way, there remains a routine, but proven by more than one generation of schoolchildren, method - to memorize it. However, keep in mind that this method is not at all like the kids.

It should be remembered that memorization cannot be the only method of teaching a child the multiplication table. It is important not only to remember the sequence of numbers, but also to understand the essence of the action itself. This is what will help a child at an older age solve complex multiplication examples.

Visualization

Another way to master the Pythagorean table is its visualization, which involves the use of all kinds of visual materials.

It can be:

• counting materials;
• Pictures;
• and even fingers!

With the help of counting material, whether it be sticks, geometric figures or something else, you can show the child the essence of multiplication (“6 x 5” means “take 6 times 5 objects”).

In addition, the kid can count the presented figures and make sure that the answer is exactly the same as in the Pythagorean table.

With the help of pictures

If a child likes to draw, this is a great opportunity to study the table with the help of pictures.

The principle of operation is approximately the same as in the case of counting material, only instead of laying out 6 times 5 sticks in front of a young mathematician, you can draw directly opposite the example of 6 squares / cakes / wagons with 5 dots / cherries / bunnies inside each.

True, it will be difficult to draw whole pictures when multiplying large numbers.

On fingers

A good option would be to study part of the Pythagorean table, namely the column with a nine, on the fingers. Such a kind of life hack will interest any child.

Place your hands in front of you with your palms out and mentally number them from 1 to 10, starting with the left little finger. Tabular examples for multiplication with the number 9 are solved very simply: just bend your finger, the number of which matches the second factor.

So, multiplying 3 by 9, we bend the middle finger on the left hand. The fingers that are located before the bent one (there are two of them) indicate the number of tens, and the rest (there are seven) - the number of units.

In total, we get 27 in the answer. Fast, easy and interesting!

Through educational cartoons and programs

As a means of visualization, of course, you can use educational cartoons, applications on mobile devices and programs on a PC, if there is such an opportunity and parents are not against such a pastime for the child.

Of course, to study such a recalcitrant multiplication table, all means are good, but remember that everything should be in moderation, and do not leave the baby in the care of the gadget in this difficult matter, but rather join it yourself.

The game

Learning in a playful way always attracts kids. Learning the multiplication table is good on the material of the card game. Cards are made of cardboard for each example of a table, a numerical expression is written on one side (5 x 3 \u003d?), And on the other - the answer.

Players take turns drawing cards, solving an example and checking themselves by looking at reverse side. If the answer is correct, the card remains with the player, if not, it is returned to the deck. The winner is the one with the most cards at the end of the game.

First steps in learning the table: the easiest numbers and mastering the principle

Some examples from the Pythagorean table are burned into memory almost instantly, while others, no matter how hard they work, do not want to obey. It is logical that you need to start mastering the table with more accommodating numbers.

So, it will not be difficult for a child to remember a column of examples with a one, since the answers will be identical to the changing factor. Next, you can begin to study the column with the number 2, because such a multiplication is easy to illustrate by any means at hand, adding two each time.

After that, the column with four will be well remembered, because in order to multiply by 4, you need to multiply by 2 and another by 2. Experienced parents noticed that children easily master multiplication by 5, since the answers in this column end only in 0 and 5.

Well, with multiplication from 6 to 9 (plus the number 3) you can figure it out a little later, especially since some of them (namely, multiplying these numbers by 1, 2, 4 and 5) will already be mastered. And if you decide to use the multiplication method described above on the fingers, then there will be no problems with the nine.

When the approximate scope of work is outlined, it remains to determine how to explain the essence of multiplication to the baby, so that he understands. To begin with, it is worth telling the child that this mathematical action was invented to speed up and facilitate the calculation.

It would be nice to come up with a bright situation to illustrate this statement. For example: “You have 10 bags and each contains 8 sweets. It will take a few minutes to count the sweets in order. And if you know tricky way- multiplication - you will spend only a couple of seconds. Usually such motivation is to the liking of children.

The essence of multiplication is simple, it can be explained both visually and with the help of numbers. In the first case, using counting material, explain to the child that multiplication is “taking so many times so many times.”

If it seems to you that the child is more likely to understand the digital notation, tell them that the expression "5 x 6" is a shorthand for the expression "5 + 5 + 5 + 5 + 5 + 5". Thus, multiplication not only facilitates counting, but also makes it possible to briefly write down the sum of identical terms.

And this means that homework in mathematics will take much less time - what is not a great reason to memorize the table?

How to fix the result?

The best way to master a skill is to put it into practice. In order for the development of the Pythagorean table to be successful, do not forget to put the new knowledge of the baby into action.

On a walk, ask them to tell you how many wheels four cars have, how many legs five cats have. At dinner, find out how many plates to put on the table if each of the three diners needs two pieces. From time to time repeat the cases of tabular multiplication in verses.

Many parents advise to memorize the multiplication table and just hang it in after school hours. different places Pythagorean tables at home, so that the child can repeat the material covered at any time.

in a good way consolidation of knowledge is also a game. Use the cards mentioned above for her. Play with the whole family, let adults sometimes make mistakes on purpose so that the child can correct them, demonstrating their knowledge.

How to help your child learn and remember information faster?

Mastering the multiplication table is not a very fast process. However, at school, the number of hours for any material is limited, and, of course, the teacher in the next lesson (and mathematics lessons in elementary school are usually daily) will already demand a certain result.

Therefore, parents need all possible ways help the child understand and remember the information received.

When studying the Pythagorean table with the baby, pay attention to the fact that many examples are repeated in it, only the numbers in the first part of the numerical expressions are reversed: 3 x 7 = 21 and 7 x 3 = 21.

Having understood this, the child will quickly realize that he will not have to learn about half of the table at all, and in fact, the number of examples that need to be remembered is much less than it seems at first glance! For clarity, repeating examples can be highlighted in the table with the same color.

You can draw the attention of the child to some Interesting Facts, discovered during a detailed study of the Pythagorean table and associated with the reduction of numbers (that is, following the method of Pythagoras himself, by adding the numbers that make up the two-digit numbers of the table).

So, in the column with nine, the sum of the digits of each two-digit number in the answer will be 9. If you reduce the numbers in the column with the number eight in this way, you get a sequence from 8 to 1 in order. In a column with a six, the sequence 6, 3, 9 will be repeated three times, and in a column with a triple - 3, 6, 9.

You can show the little conqueror of big mathematics the following trick: if you take the first answer in the column with nine as 09 (and not just 9), then the numbers in the answers will line up in two columns, and the left one will be a series of numbers arranged in order from 0 to 9 , and the right one is from 9 to 0.

It will be nice if you can provide the baby with a multiplication table in the form of a square, along the edges of which numbers from 1 to 9 are written, and inside the results of their multiplication are recorded. By drawing lines from the factors above and to the left, at their intersection you can see the desired number.

It is important to explain to the child that the result of a numerical expression can be found in any way: you can remember the result, or you can count on your fingers or apply the knowledge of “tricks”, in extreme cases it is even possible to quickly perform addition.

Or, for example, if you forgot how much it will be 9 x 3, then how much will it be 3 x 9, you will surely be able to remember? The ability to use different methods to solve a problem will be useful to the baby in life.

How to teach a child to deal with complex examples?

Before proceeding to complex examples, you need to make sure that the child knows by heart the source material - the Pythagorean table. If you managed to cope with this, you can start multiplying the form of a two-digit number by a one-digit number.

Explain to the child what is necessary in this case:

1. Write the numbers in a column, two-digit - on top.
2. Multiply by a single number, first two-digit units, then tens (further, you can increase the capacity of the first multiplier, mentioning that each larger digit is multiplied after the smaller one);
3. If, when multiplying one digit by a single-digit number, a two-digit number is obtained, then a number indicating the number of units of the resulting number is written under the line, and the number indicating the number of tens is written over the next digit of the first multiplier and added to the number obtained by multiplying this digit by a single-digit.

It sounds complicated, but the example is much simpler. After a while, not without help school curriculum the kid will master this action, and will be able to move on to more complex calculations. Remember that it is not worth it to specifically ask the child too difficult tasks - everything has its time.

Interest, motivation, play - this is what is at the forefront in education today, especially when it comes to young children. It has been proven that if a child is passionate about the material, he learns it much faster and better.

Cramming is a good option, but its result is often short-lived: after writing an important test or passing an exam, we are happy to forget what we repeated day and night a couple of days ago. That is why it is important to study complex material, which is the Pythagorean table, interesting for children.

There are different ways to do this:

• motivation - an explanation of where the superpower to multiply numbers comes in handy for a child and how much better it is to quickly multiply them than to add them slowly;
• stimulation, in other words, the promise of something pleasant when a result is achieved (but remember that this method cannot be abused, otherwise one fine day you simply will not materially pull another “pretty girl”);
• praise: for every even the smallest step forward, the child should be praised, and significant advancements should be well encouraged with an exciting walk, playing together or going to the cinema or museum, and at the same time you can repeat a couple of examples at the same time;
• learning in a playful way: use not mathematical dictations or tests to test the child's knowledge - they are enough for him at school - but games (the same card or computer games). Or arrange a family-wide educational quiz or even a hidden object quest with the help of hints, which can only be obtained by correctly solving the example.

Do not forget that it is impossible to load the baby with an excessive amount of material in one lesson, in the end the child will get bored and will not learn even half, and if he learns, he will have time to forget. Let your home lessons not be too long, then the multiplication will not have time to bother the student.

It is important to take breaks during classes so that the baby can warm up and change the type of activity. And in order not to shy away from the topic, you can hold a mathematical physical minute: the parent throws the ball to the child with a question, for example, “Five five -?”, He catches and throws it back, voicing the answer.

What mistakes are important to avoid when working with a child?

Memorizing the multiplication table is not an easy task. The efforts of children do not always bring results immediately, and the patience of parents and grandparents is not unlimited. However, by applying the ability to think in time, we can protect ourselves and the child from our own rash words and actions.

So, in no case should you:

• rush the child if, in your opinion, he solves the example for too long (if, of course, he really solves it, and is not distracted by drawing or something else);
• to scold the baby, and even more so to give him impartial assessments and nicknames - this will not add motivation to him, but a reluctance to engage in it may arise;
• expect a quick assimilation of a large amount of material and be upset when this does not happen (and this will not happen);
• compare the success of the child with the success of his friends, classmates and brothers (in any case, one of the children will have to be elevated in front of the other, which is unlikely to make the relationship between them better).

Every parent can help a child learn the multiplication table. It is enough to show a little patience, imagination and interest - then the work will go like clockwork. Studying with interest, and not boring boring material from a stick, children will more readily and quickly master multiplication.

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Learn multiplication table - game

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Multiplication directly on the site (online)

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Multiplication table (numbers 1 to 20)

×	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
11	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220
12	12	24	36	48	60	72	84	96	108	120	132	144	156	168	180	192	204	216	228	240
13	13	26	39	52	65	78	91	104	117	130	143	156	169	182	195	208	221	234	247	260
14	14	28	42	56	70	84	98	112	126	140	154	168	182	196	210	224	238	252	266	280
15	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
16	16	32	48	64	80	96	112	128	144	160	176	192	208	224	240	256	272	288	304	320
17	17	34	51	68	85	102	119	136	153	170	187	204	221	238	255	272	289	306	323	340
18	18	36	54	72	90	108	126	144	162	180	198	216	234	252	270	288	306	324	342	360
19	19	38	57	76	95	114	133	152	171	190	209	228	247	266	285	304	323	342	361	380
20	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400

How to multiply numbers by a column (mathematics video)

To practice and learn quickly, you can also try to multiply numbers by a column.