Multiplication table a simple way. How to explain multiplication and division to a child: simple techniques for parents

Any parent, sooner or later, will definitely be faced with the fact that the child will have to make enormous efforts to learn the multiplication table, which can greatly simplify counting, and, consequently, life in the future. In fact, this is not at all easy, although at the age of eight or nine, when the school offers to study the Pythagorean tablet, children have an extremely well developed mechanical memory. It is she who helps to memorize any text, table, poem, and so on. However, cramming is, by definition, boring and uninteresting, and the task of parents is to enliven this process, simplify it, and perhaps even turn it into a fun and exciting game. So how can you help your child learn the multiplication table and what needs to be done to ensure that it remains forever in memory, popping up just at the moment when it is absolutely necessary.

Multiplication tables: how to learn easily and quickly, without much effort

It is clear that the first thing the child must do is understand the essence of the task at hand, in our case it is multiplication, so first you need to explain to him how everything happens and why, fortunately, mathematics is an exact science and all the definitions in it are clear and intelligible. Moreover, when it comes to studying the multiplication table, it means that the basics of counting have already been given and, apparently, understood and studied. Addition and subtraction are the simplest mathematical operations, the basics, which are taught to children in kindergarten.

You need to explain to your child that you shouldn’t be afraid of a large and incomprehensible table, because in essence, everything is completely simple there. The essence of multiplication is adding a number as many times as indicated in the task. Does it seem difficult even to you? Let's make it simple by using simple examples. To multiply 2 by 4, for example, you just need to add the twos four times.

This makes everything much simpler, and this understanding will definitely help in the future. Moreover, many adults, even after studying at university, continue to add numbers in their heads in order to simplify the task. In addition, without a doubt, it is also necessary to give the child the opportunity to understand how that very Pythagorean table “works,” which anyone can handle if they understand the basics. Moreover, there is nothing difficult at all in using such a table, which was actually discovered by the brilliant ancient Greek mathematician and philosopher Pythagoras: find the number at the intersection of the columns of numbers, this will be the result. For example, 6 multiplied by 8 will be 48 and nothing else.

Simple Multiplication table: a game to quickly learn- a way out for many

Children of all ages simply love to play, because it is through play that they learn about the world around them. That is why it is worth trying to turn such a boring and routine process, which is the study of the multiplication table, into an entertaining and even exciting game. The game will help you not to think about fatigue, boredom, and will make studying very fun and enjoyable. Reluctance and laziness will immediately fade into the background if the baby becomes interested and he delves into the process, giving more and more correct answers.

The most popular and sought-after device that will help your child master the multiplication table in a playful way are cards that can be bought in the store.

In addition, similar cards with mathematical operations, and this may not only be multiplication, but also division, can be easily downloaded from the Internet and printed. If the situation with this is completely sour, then such cards can simply be cut out of paper and numbers written on them by hand. If you involve a child in this activity, you will most likely end up with a fun and entertaining game.

You should just start from the beginning: how to easily teach a child the multiplication table

Cards, of course, are a good and interesting thing, but they are based on simple cramming, that is, on the same rote memorization, and if we want to get not a robot that simply jabbers the columns of the multiplication table in a row, but understands the essence of the action itself, we will have to act a little differently. It is clear that you need to start giving material to a small child, starting with the simplest, so it would definitely be better to plan the study of the tablet, dividing the whole process into several main sub-stages.

First stage: one is as simple as a stick

It is clear that the simplest thing is the multiplication table by one, unless, of course, you do not take zero into account. Perhaps it’s worth explaining that you can’t multiply or divide by zero, it should be quickly and easily stored in memory, and then it’s worth starting, after all, with one. Draw some signs with examples, and clarify that whatever number needs to be multiplied by one, it will remain the same. Eg:

Second stage: ten, almost one, but with a zero

Next, we move on to another simple operation - multiplying by ten. You should definitely understand for yourself, and also explain to your child, that multiplying by ten is the same as by one, only at the end of the result you just need to add a zero. In fact, everything is quite simple, but you need to remember to let the child know that now he fully knows all the outer lines or columns of the plate. Moreover, multiplication by one and ten will be an open book for him, and then - more.

Third stage: multiplication table by two

If one day your child has enough strength to comprehend such problems, and a fun game of cards confirms the acquired knowledge, you can continue, slowly moving from simple to complex. However, experienced teaching specialists strongly recommend giving your child rest, so the next classes should be rescheduled to the next day, when he gets up with renewed vigor.

Most often, multiplication by a pair is given to all schoolchildren and even preschoolers quite easily and simply, since in fact, everything is really elementary. To multiply by two means to add a number to itself, that is, to add two given numbers. Moreover, when the need arises to learn the multiplication table, simple counting, such as addition, the child should already know, so let him add, especially since with small numbers it is quite simple. Next, you will have to memorize it mechanically, that is, the sign for three, four, six, seven, and so on, it’s better to try to learn it by heart, it will be easier and faster.

Stage four: five – what could be simpler?

The next step is to master the multiplication table by five, which will also be no more difficult than the notorious two. Just add five to the result if you study sequentially. It is clear that at first it will be a little unclear, but over time everything will become clearer and the easiest way is to explain it in detail, adding five kopecks to a certain amount, or subtracting it when dividing, but this is a separate topic for conversation.

Fifth stage: changing the places of multipliers is the key to good and high-quality memorization

You can learn anything by heart, and performing such a trick for most children will not be difficult at all. However, cramming, as already mentioned, is the first enemy of understanding, so it is worth giving the child conscious rules, one of which clearly states that changing the places of the factors will not change the result at all.

Stage six: conclusion and repetition - the mother of all teaching

Finally, it is worth saying that the entire Pythagorean tablet is usually given to children quite simply and studying it thoroughly will not be difficult for most of the tomboys. However, there are also nuances that should be taken into account when giving your child such complex material. First of all, you should understand that the more often you think about the sign in real life, for example, counting how many pancakes you need to bake for the whole family to have breakfast, and so on. That is, repeat the columns of the tablet in order and scattered constantly, reminding the child that it is fun and interesting, and most importantly, simple.

Among other things, there are positions in the multiplication table that are especially difficult to remember, and even many adults manage to get confused in the results, even those who graduated from school and two universities a long time ago. You will have to learn them so clearly that when you wake up at night, you can rattle off the result without even having time to think about what the child must be taught.

How can a child learn the multiplication table quickly?: alternative methods and creative approach

The process of learning the multiplication table is not at all easy and you should not be surprised if it takes you and your baby a lot of time. The main thing in this matter is patience, as well as thoroughness. There is no need to wait until the teacher at school explains everything herself, and you just walk around, all in white and assent, figure it out yourself first, especially since there is nothing complicated about it. Moreover, in addition to the traditional method of simple memorization, there are also several simple tips, as well as an original method that will help you multiply any number by nine, even without remembering at all what was there in the Pythagorean table.

Never, ever, under any circumstances, raise your voice while teaching. Studying for a child should not turn into a difficult, slavish task. Make it a fun game that can be easily put aside for later while doing something else.
Constantly review all the material you have covered, including the multiplication table. Moreover, you can apply new skills in real life. For example, ask your daughter how many candies you need to buy to give three to six girls, or how many wheels three cars have, counting the spare ones. The child should be interested, and not bored.
Easily follow your child’s lead, stopping classes at any time, but persistently and often give him examples of multiplication in real life. The more the child sees practical benefits from such an account, the faster and easier the memorization process will be.

Counting on fingers: the original method of multiplying by nine

Learning this “finger” counting method is not at all difficult. To do this, you only need the baby’s own hands, which you need to place in front of you, palms down. You will need to count your fingers from left to right, as is customary.

So, if you need to multiply nine by seven, you need to count seven fingers from the left, and bend the one where the count stopped.
Everything else is simple. Counting all the fingers that are not curled to the left of the seventh. This will be the number of tens in the answer.
The remaining fingers, which are to the right of what you have already folded, will be the response units.

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

And in everyday life, the multiplication table is in demand almost every day. That is why so much time is devoted to its development in elementary school.

However, studying the Pythagorean table cannot be called easy: the skill of multiplication is difficult to master, and remembering all this considerable mass of numbers is also not easy for a child.

The task of parents is to help children learn the multiplication tables, making the process interesting and at the same time effective.

Simple Ways to Teach Children Multiplication Tables

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

Having an idea of the basic teaching methods: memorization, play, visualization, parents are able to independently teach their child the multiplication table.

Memorization

The task of “learning a table” also involves literally memorizing it. It has been noted that it is much easier to remember material in poetic form or in the form of a song, especially when it comes to children.

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

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

As a last resort, if the table cannot be remembered in any way, there remains a routine method, but one that has been proven by more than one generation of schoolchildren - to memorize it. However, keep in mind that children do not like this method at all.

It should be remembered that memorization cannot be the only method of teaching a child the multiplication tables. 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 an older child 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!

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

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

Using pictures

If a child loves to draw, this is a great reason to study the table using pictures.

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

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

On fingers

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

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

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

In total, the answer is 27. Fast, easy and interesting!

Through educational cartoons and programs

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

Of course, all means are good for learning such a rebellious multiplication table, but remember that everything should be in moderation, and do not leave your child in the care of a gadget in this difficult task, but rather join him yourself.

A game

Playful learning always attracts children. It is good to learn the multiplication table using card games. Cards are made from cardboard for each example of the table; a numerical expression is written on one side (5 x 3 = ?), and the answer is written on the other.

Players take turns drawing cards, solving an example, and testing themselves by looking at the back. If the answer is correct, the card remains with the player; if not, it is returned to the deck. The winner is the one who has 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 etched in the memory almost instantly, while others, no matter how crammed they are, do not want to obey. It is logical that you need to start mastering the table with more accommodating numbers.

Thus, it will not be difficult for a child to remember a column of examples with 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 multiplication can be easily illustrated using any available means, adding two each time.

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

Well, you can figure out multiplication from 6 to 9 (plus the number 3) 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 method of multiplication on your fingers described above, then there will be no problems with nine.

When the approximate scope of work has been outlined, it remains to determine how to explain the essence of multiplication to the child so that he can understand it. To begin with, you should tell your child that this mathematical operation was invented to speed up and make counting easier.

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

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 you think that the child is more likely to understand digital notation, tell him that the expression “5 x 6” is a short version of the expression “5 + 5 + 5 + 5 + 5 + 5.” Thus, multiplication not only makes counting easier, but also makes it possible to briefly write down the sum of identical terms.

This means that math homework will take much less time - isn’t it a great reason to memorize the table?

How to consolidate the result?

The best way to consolidate a skill is to put it into practice. To make mastering the Pythagorean table successful, do not forget to put your child’s new knowledge to use.

While walking, 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. Review table multiplication cases in verse from time to time.

To memorize the multiplication tables and outside of school hours, many parents advise simply hanging Pythagorean tables in different places at home so that the child can repeat the material covered at any time.

A good way to consolidate knowledge is to play. Use the cards mentioned above for it. Play with the whole family, let adults sometimes make mistakes on purpose, so that the child can correct them, demonstrating his 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 require a certain result.

Therefore, parents need to help their child in every possible way to quickly understand and remember the information received.

When studying the Pythagorean table with your child, draw his attention to the fact that many examples are repeated in it, only the numbers in the first part of the numerical expressions are swapped: 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 child's attention to some interesting facts discovered during a detailed study of the Pythagorean table and related to the reduction of numbers (that is, following the method of Pythagoras himself, 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 equal to 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 the column with a six the sequence 6, 3, 9 will be repeated three times, and in the column with a three - 3, 6, 9.

You can show the little conqueror of big mathematics this 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 - from 9 to 0.

It will be nice if you can provide your child with a multiplication table in the form of a square, along the edges of which the numbers from 1 to 9 are written, and the results of their multiplication are written inside. 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 knowledge of “tricks”; in extreme cases, it is even permissible to quickly perform addition.

Or, for example, if you forgot how much 9 x 3 is, then surely you can remember how much 3 x 9 is? The ability to use different methods to solve a problem will be useful to your child in life.

How to teach your child to cope with complex examples?

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

Explain to your child what is necessary in this case:

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

It sounds complicated, but with an example everything is much simpler. After some time, with the help of the school curriculum, the child will master this action and will be able to move on to more complex calculations. Remember that there is no point in specifically asking your child too difficult tasks - everything has its time.

Interest, motivation, play - these are the cornerstones 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 results are often short-lived: after writing an important test or passing an exam, we happily forget what we repeated day and night a couple of days ago. That is why it is important to make the study of complex material, such as the Pythagorean table, interesting for children.

There are different ways to do this:

motivation - an explanation of where the child’s superpower to multiply numbers will come in handy and how much better it is to multiply them quickly than to add them slowly;
stimulation, in other words, the promise of something pleasant when achieving a result (but remember that this method cannot be abused, otherwise one fine day you simply will not be able to afford the next “nice thing”);
praise: for every small step forward, the child should be praised, and it is good to encourage significant progress with an exciting walk, a joint game or a trip to the cinema or museum, and at the same time you can repeat a couple of examples;
learning in a playful way: to test the child’s knowledge, use not mathematical dictations or tests - he has enough of them at school - but games (the same card or computer). Or arrange a family-wide educational quiz or even a quest with a search for objects using hints, which can only be obtained by solving the example correctly.

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

It is important to take breaks during classes so that the child can warm up and change the type of activity. And in order not to deviate from the topic, you can conduct a mathematical physical exercise: the parent throws the child a ball with a question, for example, “Five five -?”, He catches it 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 using the ability to think in time, we can protect ourselves and the child from our own rash words and actions.

So, under no circumstances should you:

rush your child if, in your opinion, he takes too long to solve an example (if, of course, he really solves it and is not distracted by drawing or something else);
scolding a child, and even more so giving him unflattering assessments and nicknames - this will not add motivation to him, but a reluctance to study may arise;
expect to quickly assimilate a large amount of material and be upset when this does not happen (and this will not happen);
compare the child’s successes with the successes of his friends, classmates and brothers (in any case, one of the children will have to be elevated over the other, which is unlikely to make the relationship between them better).

Every parent can help their child learn the multiplication tables. It is enough to show a little patience, imagination and interest - then the work will go like clockwork. By studying with interest, rather than cramming boring material under pressure, children will learn multiplication more willingly and quickly.

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All parents sooner or later find themselves in a difficult situation, from which it can be quite difficult to find a way out. This problem occurs when a child needs help learning the multiplication tables.

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Parents have been familiar with this problem since childhood, but previously 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 activities with your child, you can find rhymes, songs, video and audio lessons, game scripts on the Internet, which can help make the task of parents and children easier in this difficult matter.

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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 child’s character and abilities.

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

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Initially, attention should be paid to the fact that The child needs to explain the meaning of the arithmetic operation of multiplication.

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As you know, children who begin to study the multiplication table already have an understanding of such simple arithmetic operations as addition and subtraction.

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It is this knowledge of the child that should be relied upon 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 overcome all possible difficulties that arise during memorization of 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 located in the left column is multiplied by the number located on the top line, and the answer is that their product must be looked for 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 task for a child can be turned into an interesting activity by brightening it up with games. Learning the multiplication table is no exception. Game techniques will help with this, attracting the child’s attention to learning, revealing the meaning of multiplication and making the task easier for parents. When studying with a child, you should adhere to the rule that it is always easier and faster to remember interesting things, 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 your knowledge of this information.

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

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Game with cards

This is one of the most popular and effective methods of memorizing the multiplication tables using games. This article reveals the essence of the game and the sequence of actions, and in addition to the theory you can download ready-made cards for printing. Download in one file

Which provide 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 take 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 “equals” sign there is a question mark. If the child voices 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 to all the cards. When the game approaches the end, there are very few cards left and they, most often, turn out to be the most difficult ones, which the child could not answer easily. 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 learn if you break it 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. Various game options can be developed that can be chosen depending on the child’s abilities and knowledge.

Also, various special programs, online games (there is a game at the end of the article) and original sound posters that the Internet offers will help to reinforce the game while studying the multiplication tables. However playing cards considered the simplest and most effective.

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The initial stage of memorizing the multiplication table

When starting to teach your child the basics of multiplication, this process can be simplified by some special techniques.

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Yes, it is necessary start learning with the simplest and most basic examples of multiplication tables, which the child will solve without much difficulty. After all, if a child immediately sees the entire 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 reassure 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 they multiplied by. So, 1x1=1, 2x1=2 and so on.

2. Examples of multiplying by 10 are also simple. , 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 by 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 correctly distribute the child’s workload and if he is tired after the first stage of training, then further training should be postponed until next time. But if the child is now ready to continue learning, you can try to continue the lesson.

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

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4. The next stage of studying the multiplication table will be related to the rule for replacing the multiplier, 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 during school. It says that changing the factors does not change the product. In other words, the child should be explained that the example 2x4 is identical to the example 4x2.

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Multiplication table by 2

The child needs to clearly explain how it turned out 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, a child, knowing all the 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 significantly facilitate the child’s task in the process of memorizing numerous examples of the multiplication table.

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Completing each stage of training, 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 can clearly see his achievements and be convinced that there is nothing unrealistic in memorizing the multiplication table, and it will not seem to him as huge and incomprehensible as at the beginning of classes.

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Targeted memorization

After your child has mastered the basics of multiplication and the simplest table examples, you should move on to the next stages of learning with more complex factors.

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At this stage, it is necessary to use not only game techniques, but also various effective memorization techniques based on associations, the repetition method, dividing into parts, 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 repeat it many times to consolidate knowledge. them to achieve a result when the child can name examples and correct answers without hesitation. To do this, you need to 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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You can often hear the opinion of teachers that it is best and most correct to study the multiplication table moving from end to beginning, that is, from complex examples to simpler ones.

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However, this teaching option seems quite 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 the complex meanings that he sees in the answers to the examples were obtained.

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Therefore, you need to start with the 3x3 example, when solving which, the child will be able to independently test himself by counting the example on his fingers, as a result of which the child will understand how the number 9 is obtained in the answer. If the child is given the task of multiplying, for example, 8 by 7 and requiring him to simply memorize the correct answer, then this may simply frighten the child with the impossibility of testing this example in practice, and as a result of hiding the solution process from him, the child may lose motivation and interest in learning, since he will consider that he has no ability for mathematics.

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Number squares

At the next stage of training, you will need knowledge and application of this term. The child should be explained that it means multiplying a number by itself. The multiplication table contains 10 squares that are required to be memorized. Practice shows that children remember squares up to the example 6x6=36 just fine. The next 3 squares also most often do not present any particular difficulties.

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Multiplication table by 3

From this stage, the child begins to have difficulties remembering examples from the table. If difficulties of this kind arise, you should turn to playing with cards. However, even if these techniques turn out to be ineffective, for example, because the child has a humanitarian mindset, then you can use special rhymes for memorization, which will present the child with examples from the table in a simple form.

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Multiplication table by 4

When studying examples from the multiplication table by 4, you will probably also have to use cards and poems in classes. 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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Multiplication table by 5

This stage of learning the multiplication table usually goes without difficulties, since examples for 5 are memorized quite simply. The child should be explained that all values of this multiplication series are 5 in relation to each other, and the extreme number will be either 5 or 0, also that when multiplying even numbers by 5, the result is 0, and when multiplying odd numbers, the result is 0. 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, it is necessary to explain to the child that after he has learned squares and the multiplication table up to 5, he will have to put in 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, the child just has to learn the most difficult examples from the multiplication table, there are 6 of them and they should be given special attention, make the final push 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 most effective way is to play cards so that the child can give an answer to any example without thinking. In this case, it is best to use The game contains 12 cards containing products with multipliers swapped.
Thus, using special methods and techniques, you can quickly and easily learn the multiplication table, which initially seemed incomprehensible to children and parents to memorize.

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Methods for memorizing multiplication tables

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

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Therefore, parents should master several techniques and know more than one way to memorize the multiplication tables 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, when studying examples on 5, a boy can be asked how many wheels are needed for 5 cars. So, the child will imagine a car with four wheels and will successfully remember the example 5x4=20. You can ask the girl how many ribbons it will take to give three dolls two tails. With the help of such an illustration, the child will remember that 3x2=6.

Complex Examples

While studying the multiplication table, a child may have some problems when trying to memorize the most complex examples, which should be emphasized by the child and helped him learn them, thereby overcoming the most difficult stages of the task.

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Memorizing multiplication tables using your fingers

To simplify the process of memorizing individual products from the multiplication table, you can tell your child that they can be counted 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 multiplication by 9. For this you will need both hands. When multiplying any number by 9, you should bend your straightened fingers under the number of the number being multiplied. Thus, the number of fingers before the curved one is tens, and after it - units.

Link to the game multiplication table - easy to learn!
This game will help you learn the multiplication table quickly and without stress.

Hello, dear relatives and friends of elementary school students! First grade is already behind us, and the complexity of school assignments is steadily increasing, isn’t it? Now it's time to find out how to learn the multiplication tables with your child without long and boring cramming. "Eureka" knows several ways!

Game with cards

In a playful way, a child learns much faster. Of course, because this way he feels calm and relaxed, and is also passionate about the process. It’s especially fun to play if a small prize awaits the winner.

To turn learning the multiplication table into a fun game, you need to buy or make cardboard cards with examples of multiplying single-digit numbers. At the beginning of the game, they need to be laid out face down in front of the child.

All players take turns drawing cards and calling out the answer. For each correct answer the player is awarded 1 point. All participants must have an equal number of attempts. The one who scored the most points won. You cannot think for a long time - for example, longer than 15 seconds, otherwise the point will not be counted.

In this game, you can use a little trick and let your child win. To do this, you need to agree with him that for correcting another player’s mistake he will receive an additional point. During the game, from time to time it is worth giving incorrect answers, which the child must notice and correct.

This game needs to be played regularly - then the student will learn the multiplication table quickly and will give the correct answers without hesitation.

Multiplication table through addition

When studying the multiplication table, it is important that the child understands the logic of this action. Therefore, each example of a multiplication table should be written through the addition of identical numbers.

2 × 2 = 2 + 2 + 4;

2 × 3 = 2 + 2 + 2 = 6;

2 × 4 = 2 + 2 + 2 + 2 = 8;

An extended version of the multiplication table can be hung in a visible place in front of the table where the child learns his lessons. In this case, he will not have to memorize most of the examples; he will simply calculate them in his head until the answer is permanently stored in his memory.

Multiplication on fingers

It is worth introducing your child to multiplication using fingers. This works well in the early stages of learning the multiplication tables. Let's look at an example: 4 × 5. Let's imagine that each finger is equal to 5. We leave 4 fingers straight and bend the rest. Now we simply count straight fingers, adding up the fives: 5, 10, 15, 20.

Multiplication tables in music videos and cartoons

All children love cartoons, so take a couple of “mathematical” cartoons and show them to your child from time to time. This method is good because you will be free at this time.

Also effective are clips in which multiplication examples with correct answers are heard instead of ordinary words. Such clips are a godsend for musical children. Let the child calmly do his favorite thing: draw or put together a construction set, and in the meantime you just play him a “mathematical” song for the background.

Soon you will be surprised to notice that the baby hums the words from the song, easily remembering examples of multiplication.

Fun ways to multiply with number 9

The number 9 is special, even magical. Tell your child about this and easily multiply any other number by 9.

Multiply by 9 with fingers

Have your baby place his palms on the table and straighten all his fingers. Now you need to assign a serial number to each finger from left to right. We demonstrate the wonders of mathematics: for example, we find the answer for the example “9 × 3”:

find finger number 3;
We count how many fingers are to the left of the third. These are dozens of our answer;
We count how many fingers to the right of the third. These are response units.

We put 2 numbers side by side and get the correct answer - 27.

We look at the second factor when multiplying by 9

There is another interesting way to multiply any single-digit number by 9. Consider the example “9 × 3”. Let us perform the following metamorphoses with the number 3:

let's take 3 tens;
subtract 3 units from them;
we get 30 − 3;
answer: 27.

Multiplication table in verses

Many teachers use poetry to memorize multiplication tables. When you need to give the correct answer, the lines of the poem themselves pop up in your memory. Remember the song “Twice two is four”? The same principle applies to memorizing multiplication examples.

What is "multiplication"?
This is a smart addition.
After all, it’s smarter to multiply times,
How to put everything together for an hour.

1 × 1 = 1
One penguin was walking among the ice floes.
Once alone - alone.

1 × 2 = 2
There is safety in numbers.
Once two is two.

2 × 2 = 4
Two athletes took weights.
This is: two and two are four.

2 × 3 = 6
The rooster sat before dawn
On a high pole:
- Crow!.. Twice three,
Twice three is six!

2 × 4 = 8
A pair of forks stuck into the pie:
Two by four - eight holes.

2 × 5 = 10
They decided to weigh two elephants:
Two times five equals ten.
That is, every elephant weighs
Approximately five tons.

2 × 6 = 12
Met a crab with cancer:
Twice six equals twelve paws.

2 × 7 = 14
Twice seven mice -
Fourteen ears!

2 × 8 = 16
The octopuses went for a swim:
Twice eight legs is sixteen.

2 × 9 = 18
Have you seen such a miracle?
Two humps on the camel's back!
Nine camels began to be counted:
Twice nine humps equals eighteen.

2 × 10 = 20
Twice ten is two tens!
Twenty, to put it briefly.

3 × 3 = 9
Three insects drank coffee
And they broke three cups.
What is broken cannot be mended...
Three times three equals nine.

3 × 4 = 12
He talks all day in the apartment
Talking cockatoo:
- Trrr multiplied by four,
Trrr multiplied by four -
Twelve months a year.

3 × 5 = 15
The schoolboy began to write in his notebook:
What is "three times five"?
He was terribly careful:
Three times five equals fifteen spots!

3 × 6 = 18
Thomas began to eat pancakes:
Eighteen is three times six.

3 × 7 = 21
Three times seven is twenty one:
There's a hot pancake on my nose.

3 × 8 = 24
Mice gnawed holes in the cheese:
Three times eight is twenty four.

3 × 9 = 27
Three times nine is twenty seven.
Everyone needs to remember this.

3 × 10 = 30
Three maidens by the window
Dressed up in the evening.
The girls tried on the rings:
Three times ten is thirty.

4 × 4 = 16
Four cute pigs
They danced without boots:
Four times four equals sixteen bare legs.

4 × 5 = 20
Four scientist monkeys
They leafed through books with their feet.
Each foot has five toes:
Four times five is twenty.

4 × 6 = 24
I went to the parade
Jacket potato:
Four times six is twenty four!

4 × 7 = 28
Chicks are counted in the fall:
Four times seven is twenty eight!

4 × 9 = 36
Baba Yaga's stupa broke.
Four times eight equals thirty-two teeth!
She has nothing to eat between her teeth:
Four times nine is “thirty six”!

4 × 10 = 40
Forty forty walked
We found curd cheese.
And divide the cottage cheese into parts:
Four times ten is forty.

5 × 5 = 25
The hares went out for a walk:
Five five is twenty five.

5 × 6 = 30
A fox ran into the forest:
Five six makes thirty.

5 × 7 = 35
Five bears from a den
We walked through the forest without a road -
For seven miles to slurp jelly:
Five seven is thirty five!

5 × 8 = 40
Climb the centipede
Difficult up the hill:
Legs are tired -
Five eight is forty.

The guns stood on the hill:
Five eight - that's forty.

5 × 9 = 45
The guns started firing:
Five nine is forty five.

If you slurp cabbage soup with a bast shoe:
Five nine is forty five.
There will be this bast shoe
Drip on everyone's trousers!

5 × 10 = 50
Digging a bed of zucchini
Five dozen patches.
And the piglets' tails:
Five ten is fifty!

6 × 6 = 36
Six old women were spinning wool:
Six six is thirty six.

6 × 7 = 42
Six networks of six ruffs -
This is also thirty-six.
And a roach got caught in the net:
Six seven is forty two.

6 × 8 = 48
Hippos of buns ask for:
Six eight is forty eight.

6 × 9 = 54
We don't feel sorry for the buns -
Open your mouth wider:
Six is nine
Fifty four.

6 × 10 = 60
Six geese leading the goslings:
Six ten is sixty.

7 × 7 = 49
Fools are not reaped, fools are not sown,
They themselves are born:
Seven seven - forty nine...
Let them not be offended!

7 × 8 = 56
Once a deer asked an elk:
“What is seven eight?”
Elk did not bother to look into the textbook:
“Fifty, of course, six!”

7 × 9 = 63
Seven nesting dolls
The whole family is inside:
Seven nine crumbs -
Sixty three.

7 × 10 = 70
Seven fox cubs are taught at school:
Seven ten - seventy!

8 × 8 = 64
Vacuuming with his nose
Elephant carpets in the apartment:
Eight by eight -
Sixty four.

8 × 9 = 72
Eight bears were chopping wood:
Eight nine is seventy two.

8 × 10 = 80
The best score in the world:
New Year is coming!
Toys hang in eight rows:
Eight ten is eighty!

9 × 9 = 81
The little pig decided to check:
- How much does “nine by nine” turn out to be?
- Eighty - oink - one! -
So answered the young pig.

9 × 10 = 90
The sandpiper is small, but his nose is great!
Nine ten is ninety.

10 × 10 = 100
There are a dozen moles in the meadow -
Each person digs ten beds.
And at ten ten - a hundred:
The whole earth is like a sieve!

It is not necessary to memorize all the verses. You can choose only those examples that are difficult for your child to remember.

Just without fanaticism: computer games

Even children who don't like math will enjoy playing a computer game. If your teaching abilities are not up to par, then let Baba Yaga or some other character take over.

By completing simple tasks and gradually increasing the complexity of the game, the child will not even notice how quickly he will learn the multiplication table by heart.

Approach the learning process creatively - then it will bring only positive emotions to you and your child. These simple tips from Eureka will make learning the multiplication tables easier:

Hang examples where you can see them.
Learn to multiply and divide at once.
Once you've mastered multiplying by 2, move on to multiplying by 4 and then multiplying by 8.
After multiplying by 3, move on to multiplying by 6 and 9.
While multiplying by 5, it is convenient to study the clock face.
Give praise and be patient.
Your helpers are cartoons, music videos, educational videos and games with a mathematical bias.

Well, now the multiplication table doesn’t seem like a punishment to you? We believe that your positive attitude will be passed on to your child. Eureka wishes you an easy learning experience! See you again in a wide circle of our readers!

After the first year of schooling, parents face the problem of how to teach their children the multiplication tables. Moreover, make sure that young students have a desire to remember it, and not because it is necessary. Simple rote learning gets boring too quickly, and continuing this process will be quite difficult.

Also, it has already been proven that simply memorizing examples over time leads to the fact that some of them are forgotten too quickly. Let's try to give simple techniques that will help you learn the multiplication table easily and quickly.

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Where to start

When answering the question of how to explain the multiplication table to a child, one correct technique should be noted. It is necessary to clearly explain what the principle of this action is.

By the time it comes time to start learning multiplication table examples, children already have a good understanding of addition and subtraction. That is, the action of multiplication is replaced adding identical terms.

For example, 3 multiplied by 2 means that the number 3 must be added twice - 3+3. If you multiply 5 by 3, then add the fives three times 5+5+5.

It would be very nice if, during the explanation, the examples on the table were reinforced with visual examples: “Mom bought Vova and Masha 2 boxes of pencils. Each box contains 6 pieces. How many pencils are there in two boxes? How can you calculate? 6 plus 6 is equal to or 6 multiplied by 2. In both the first and second cases we get 12.”

A few learning techniques

Learn the multiplication table with your child possible with different techniques. We rely on the fact that at this age most children have well-developed mechanical memory. Some require visual perception such as sketches, videos, emotional poetry or game moments. Let us provide the essence of several of them.

Pythagorean table

One answer to the question of how to help a child learn the multiplication table is Pythagorean table. There are columns and lines with numbers from 0 to 9. If you connect the line and column in which the factors are written with your finger, you will get a number - the result of multiplication.

Despite the fact that at first glance the table seems cumbersome, you should not be scared. You need to immediately explain to your child that examples of multiplication by column are very easy to remember. Basic simple rules:

Written diagonally the simplest and easy products of identical numbers.
The last line and the outermost column contains multiplication by 10, in which . is simply added to the multiplier.
The first column and first row shows the result of multiplying by one, the result of which is the same.
The child needs explain the basic principle using the Pythagorean table, which involves finding a number. The result is located at the intersection of the column and row with the necessary factors.

Note a number of advantages of studying the table Column multiplication using the Pythagorean method:

children enjoy forming squares from horizontal and vertical lines, looking for the correct answer;
when performing these actions, the logic of mathematical thinking develops;
contemplating a table in front of oneself, and not just written down examples that do not tell him anything, helps to more significantly understand the material being studied;
the absence of extraneous signs allows you to more effectively visually remember the numbers written in the table;
using the method on an ongoing basis For example, when finding answers to questions that adults ask him, a child quickly remembers the location of the number and the number itself, while he does not subsequently reproduce results that are not in the table.

Important! In order for the process of learning multiplication to be effective, it is necessary to place the Pythagorean table in a visible place, and regularly work with the child to find the correct answers.

Studying with flashcards

An easy way to remember the multiplication tables - use of special cards. This process must be planned and the study is carried out gradually. You should start by making double-sided cards. On one side of the card there is an example for multiplication, and on the other - the answer to this example.

To begin with, the child learns, for example, the multiplication table by two. After the initial study, the material is reinforced using cards. The child picks up the cards that are laid out on the table examples down, one at a time, reads the example and names the result of the solution.

The card is then turned over and the correct answer is checked. If the result is correct, then the card is put aside. If a mistake is made, the card is returned to the general pile.

The advantage of the proposed method is game form of learning. When playing, it is always easier and easier to remember. In addition, children develop visual memory, auditory memory and speech, since it is necessary to read the example out loud. Mathematical terminology is memorized.

It is better to structure the learning process this way:

First we study the table for two, and then we fix it with a card.
Next, we study the table for three. Then cards with these examples are added to the pile with previously studied ones. It is necessary to consolidate examples in both two and three.
As the stock of knowledge increases, the number of cards increases.

Features of the study

At this stage, we will present the features of studying the table for each factor. Each of them has its own zest, knowing which you can help your child learn multiplication tables quickly and ensure the firmness of its memorization. So, the tricks of the table are as follows.

Multiplying by 10 and 1

The simplest methods for memorizing the multiplication tables are contained in examples for 1 and 10. That is why experts recommend start training with these exercises. Features are as follows:

when multiplying a number by 1, we get the same number;
When multiplying by 10, we simply add zero to the number.

Multiply by 2

How to learn the 2 multiplication table correctly and quickly? First of all, we explain to the child that multiplication can be easily replaced by addition. For example, 2×2 means that you need to add 2+2, and 3×2=3+3. So there is no difficulty in memorizing and you can learn it quite quickly.

Table for 4

Teachers recommend that after studying examples for 2, move on to examples for 4. A simple way to learn the multiplication table is to explain in detail and clearly to your child what multiplication by 4 means Multiply by 2 twice. That is, we multiply the number by 2, and then again by 2. For example, 3×4 means that 3×2=6, and then 6×2=12. This method will help you make calculations faster.

Multiply by 3

Memorizing the multiplication table by 3 causes some difficulties for kids. Therefore, in this case, experts advise use a poetic form of study. You can compose poems yourself, or you can take ready-made ones.

The next way is to explain to children using specific everyday examples. For example, the example 3x4 is solved using a practice problem. Mom had 4 apples, dad also had 4 and you had 4.

How many apples are there in total? Moreover, the tasks must be associative so that the child can easily imagine the situation and find the answer.

Multiply by 5

These examples are always easy for children. The first sign that makes it easy to teach children to multiply by 5 is the fact that each subsequent example differs from the previous one by five. It should be clarified:

the numbers 2, 4, 6, 8 are even and multiplying them by 5 we get a number that expresses the number of tens, that is, it ends with zero;
The numbers 1, 3, 5, 7, 9 are odd and their product with 5 gives a number that ends in 5.

Table for 9

Table 9 has a special trick. If you start studying it simply as examples, the result will not always be successful. And the easiest way to remember it is finger bending method. Its essence is as follows:

Count the child's fingers and assign each one a number according to the count.
Next, when multiplying 9 by any number, bend the finger with the corresponding number.
We explain to the baby that the bent finger divides the other fingers into two parts: right and left. The fingers on the left represent the number of tens, and the fingers on the right the number of units.

For example, 9x6. Bend finger number 6. To the left of it, 5 fingers remain uncurled. Which means 50. On the right are 4 fingers, which means the number of units. Adding the numbers, we get 54. So, 9×6=54.

Multiply by 6, 7, 8

When starting to study these examples, we clearly explain to the little student that he already knows many of the examples. For example, if you need to multiply 6 by 4, that is the same as 4x6. From this we conclude that there is very little left to remember.

To study the remaining examples, you must apply any of the above methods. The most practical of them is Pythagorean table.

There are many ways to help your child learn the multiplication tables. This is especially easy to do in the world of technology. You can offer online games to study this topic. In this case, the baby will spend time with some benefit.

Important! It should be remembered that each child requires an individual approach. And the method that suits one may cause difficulties for others.

How to easily learn multiplication tables

Learning the multiplication table in a playful way

Conclusion

The main rule: do not force your child under fire. It is better to conduct training when the little student is in the right mood and as if playing with him. Studying the table in a playful way will bring much more benefits than memorizing it monotonously, regardless of the class in which multiplication is taught.