Let's look at how we can multiply two digit numbers using the traditional methods we are taught in school. Some of these methods can allow you to quickly multiply two-digit numbers in your head with enough practice. Knowing these methods is helpful. However, it is important to understand that this is just the tip of the iceberg. In this lesson, the most popular tricks for multiplying two-digit numbers are considered.

The first way is the layout into tens and ones

The easiest way to understand how to multiply two-digit numbers is the one we were taught in school. It consists in splitting both factors into tens and ones, followed by multiplying the resulting four numbers. This method is quite simple, but requires the ability to keep up to three numbers in memory at the same time and at the same time perform arithmetic operations in parallel.

For example: 63*85 = (60+3)*(80+5) = 60*80 + 60*5 +3*80 + 3*5=4800+300+240+15=5355

It is easier to solve such examples in 3 steps. First, tens are multiplied by each other. Then add 2 products of units by tens. Then the product of units is added. Schematically, this can be described as follows:

• First action: 60 * 80 = 4800 - remember
• Second action: 60*5+3*80 = 540 - remember
• Third action: (4800+540)+3*5= 5355 - answer

For the fastest effect, you will need a good knowledge of the multiplication table of numbers up to 10, the ability to add numbers (up to three digits), as well as the ability to quickly switch attention from one action to another, keeping the previous result in mind. It is convenient to train the last skill by visualizing the arithmetic operations performed, when you have to imagine a picture of your solution, as well as intermediate results.

Conclusion. It is not difficult to make sure that this method is not the most effective, that is, it allows you to get the right result with the least amount of effort. Other methods should be taken into account.

The second way is arithmetic fittings

Bringing an example to a convenient form is a fairly common way of counting in the mind. Customizing an example is useful when you need to quickly find an approximate or exact answer. The desire to adjust examples to certain mathematical patterns is often brought up in mathematics departments at universities or in schools in classes with a mathematical bias. People are taught to find simple and convenient algorithms for solving various problems. Here are some fitting examples:

Example 49*49 can be solved like this: (49*100)/2-49. First, 49 is counted by one hundred - 4900. Then 4900 is divided by 2, which equals 2450, then 49 is subtracted. Total 2401.

The product 56*92 is solved like this: 56*100-56*2*2*2. It turns out: 56*2= 112*2=224*2=448. We subtract 448 from 5600, we get 5152.

This method can be more effective than the previous one only if you own a mental account based on multiplying two-digit numbers by single-digit ones and can keep several results in mind at the same time. In addition, one has to spend time searching for a solution algorithm, and also takes a lot of attention for the correct observance of this algorithm.

Conclusion. The method when you try to multiply 2 numbers by decomposing them into simpler arithmetic procedures perfectly trains your brain, but is associated with great mental costs, and the risk of getting an incorrect result is higher than with the first method.

The third way is mental visualization of multiplication in a column

56 * 67 - count in a column.

Probably, the column count contains the maximum number of actions and requires you to constantly keep auxiliary numbers in mind. But it can be simplified. In the second lesson, it was said that it is important to be able to quickly multiply single-digit numbers by two-digit ones. If you already know how to do this automatically, then counting in a column in your mind will not be so difficult for you. The algorithm is

First action: 56*7 = 350+42=392 - remember and don't forget until the third step.

Second action: 56*6=300+36=336 (or 392-56)

Third action: 336 * 10 + 392 = 3360 + 392 = 3 752 - it’s more complicated here, but you can start calling the first number that you are sure of - “three thousand ...”, but for now, add 360 and 392.

Conclusion: counting in a column is directly difficult, but you can, if you have the skill of quickly multiplying two-digit numbers by single-digit ones, simplify it. Add this method to your arsenal. In a simplified form, the column count is some modification of the first method. Which is better is an amateur question.

As you can see, none of the methods described above allows you to count in your mind fast enough and accurately all examples of multiplication of two-digit numbers. It must be understood that the use of traditional methods of multiplication for counting in the mind is not always rational, that is, allowing you to achieve the maximum result with the least effort.

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

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

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

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

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

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

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

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

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

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Multiplication table system

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

7 rules for remembering information

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

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

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Card game

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

Cards containing examples and their answers

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

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

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

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

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The initial stage of memorizing the multiplication table

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

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

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

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

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

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

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

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

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2 multiplication table

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

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

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

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

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Targeted memorization

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

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

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

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

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

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

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

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Number squares

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

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3 times table

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

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4 times table

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

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5 multiplication table

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

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Multiplication table for 6, 7, 8 and 9

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

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Complex examples from the multiplication table

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

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Here are the most difficult products from the multiplication table

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

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

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Techniques for memorizing the multiplication table

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

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

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Here are some of them.

Application in practice

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

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

Complex examples

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

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Memorizing multiplication tables with fingers

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

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

Schoolchildren find the table boring and useless. Often children get angry, upset, trying to figure out a set of numbers they do not understand. Parents can make learning easy and fun by preparing ahead of time.

The basic rule in learning the multiplication table is to interest the child. Like adults, they perceive information differently. Some children like to learn poems and songs. Others can sit quietly at the table with their parents and look at the Pythagorean table.

How to teach a child the multiplication table (picture)

Easy to remember the multiplication table for a child help:

• Cards;
• Counting figures, sticks;
• Special programs for tablet and phone;
• Educational videos and cartoons;
• Poems and songs;
• Pictures;
• Child's fingers.

Game methods are captivating and give quick results. It is better to start classes in a good mood when the child is in school.

Learning the multiplication table: life hacks and videos

It is important to understand how it is more comfortable for a child to perceive information so that the process does not turn into “cramming”. Everything is very simple:

Auditory children it is better to learn new things in conversation. They like to memorize numbers by repeating examples out loud. A good option to remember the multiplication table is to learn poems, songs or watch educational videos.

Learning the multiplication table (video)

visual child learns more easily when vision and imagery are involved. They absorb information through bright drawings, coloring games that have large colored fonts and numbers.

Multiplication table coloring game (picture)

Also, with a visual child, you can watch educational cartoons in which your favorite characters act as a teacher.

9 times table with Fixies (video)

Kinesthetic children learn through the sensations and feelings that they have when they come into contact with a new object and information. In this case, you can try the card method.

Learning the multiplication table with cards (video)

It is important to consider how your child learns best so that the process of memorizing the multiplication table will be fun and easy.

How to learn the multiplication table in 5 minutes a day

Kukina Ekaterina Georgievna

mathematics teacher

You have probably heard the opinion more than once that the level of mathematical education is falling.

So, when my children were in the second grade, I clearly understood why the level of mathematical education at school was falling. It is in the second grade, when laying the very foundation of mathematical education, that such a gigantic irreparable hole arises that you can’t support with any crutches in the form of calculators.

Namely, the main problem is in the multiplication table. Look at the checkered notebooks that your schoolchildren have.

I went shopping for a long, long time looking for notebooks. And anyway, for everyone - here is such a picture.

Multiplication table (picture)

There are even worse notebooks (for high school students), where there are no multiplication tables, but there are a bunch of meaningless formulas.

So what's wrong with this notebook? The unsuspecting parent sees that the multiplication table is on the notebook. It seems that all your life there was a multiplication table on notebooks? What's wrong?

And the problem is just that the multiplication table is NOT on the notebook.

The multiplication table, my dear readers, is this:

Sometimes the same table is even called the beautiful word "Pythagorean table". The top and left columns can be omitted, only the main rectangle.

First, it's a table. Second, it's interesting!

No child in their right mind will consider the examples written out in columns.

Not a single child, no matter how brilliant he may be, will not be able to find interesting tricks and patterns in the written examples.

Well, in general, when a teacher says: “learn the multiplication table,” and the child doesn’t even see the table in front of him, he immediately understands that mathematics is such a science where ordinary things are named somehow differently and you need a lot, a lot cramming, but it is impossible to understand anything. And in general, it is necessary to do "as it is said", and not "as it makes sense".

Why is the Pythagorean table better?

Firstly, it does not contain garbage and informational noise in the form of the left side of the examples.

Secondly, you can think about it. It's not even written anywhere that this multiplication is just a table.

Thirdly, if she is constantly at hand and the child constantly stumbles upon her, he willy-nilly begins to memorize these numbers. In particular, he will never answer the question "seven of eight" with 55 - after all, the number 55 is not and never was in the table at all!

Only children with abnormal memory can memorize columns of examples. In the "table" you need to remember much less.

In addition, the child automatically looks for patterns. And he finds them himself. Even such patterns are found by children who do not yet know how to multiply.

For example: numbers that are symmetrical about the diagonal are equal. You see, the human brain is just set to look for symmetry, and if it finds and notices, it is very happy. And what does it mean? This means that the product does not change from permutation of the places of the factors (or that the multiplication is commutative, to put it simply).

Pythagorean table: multiplication (picture)

You see, the child notices it himself! And what a person invented himself, he will remember forever, in contrast to what he memorized or was told.

Remember your high school math exam? You forgot all the theorems of the course, except for the one that you got, and you had to prove it to the evil teacher! Well, that's if you didn't cheat, of course. (I exaggerate, but almost always it is close to the truth).

And then the child sees that you can not learn the whole table, but only half. If we already know the line of multiplication by 3, then we do not need to memorize "eight by three", but just remember "three by eight". Half the work already.

And besides, it is very important that your brain does not accept dry information in the form of some incomprehensible columns of examples, but thinks and analyzes. Those. trains.

In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you poke at any number and draw a rectangle from the beginning of the table to this number, then the number of cells in the rectangle is your number.

Pythagorean table: multiplication (picture)

And here the multiplication already gets a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of ​​\u200b\u200ba rectangle is equal to the product of its sides)

And you have no idea how much easier it is to divide with such a table!

In short, if your child is in the second grade, print out such a correct multiplication table for him. Hang a large one on the wall so that he looks at it when he does his homework or sits at the computer.

And print and laminate a small one for him (or write on cardboard). Let him carry it to school with him, and just keep it conveniently at hand. (it does not hurt to highlight the squares diagonally on such a table so that you can see it better)

My kids have this one. And it really helped them in the second grade and still helps a lot in math classes.

Pythagorean table: multiplication (picture)

Here's my word of honor, immediately the average score in mathematics will increase, and the child will stop whining that mathematics is stupid. And in addition, in the future, your child will also be easier. He will understand that he needs to use his brains, and not cramming. And little that he understands, he also learns to do it.

And I repeat: there is nothing wrong with examples with columns. And the amount of information they contain is the same as in the "table". But there is nothing good in such examples either. This is informational garbage, from which you will not immediately find what you need.

Praise more often

Think of ways to reward your child. It could be the little things that make him happy.

Find an approach if the child is not in the mood

Forced to study, scream or completely deprive of entertainment - such methods beat off any desire to study. It makes sense to calmly explain the importance of classes and motivate the child.

Learn the multiplication table step by step

When a child first sees how many numbers he needs to remember, a protest arises. It is better to practice at a comfortable pace with rest breaks.

Remember that every child is an individual

As soon as children are compared with friends or classmates, they lose the desire to do anything. It must be remembered that each child has his own pace of learning and the careful attitude of parents is of great importance.

Talk about making mistakes

At the first failures, children lose interest, do not want to continue classes. It is important to explain that without mistakes there are no good results. Everything will surely work out.

Now you know everything about how to teach a child the multiplication table in different ways so that the stammering process is a joy.

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 so much time is devoted to its development in elementary school.

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 figures presented 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

Of course, educational cartoons, applications on mobile devices and programs on a PC can be used as visualization tools, 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.

A 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 the back 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 a 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 tables and, outside school hours, simply hang Pythagorean tables in different places at home so that the child can repeat the material at any time.

A good way to consolidate knowledge is the 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 in every possible way to 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 interchanged: 3 x 7 \u003d 21 and 7 x 3 \u003d 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, 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 the source material by heart - 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 some time, not without the help of the 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 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 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.

How to help your child learn the multiplication table

easy, fast and fun

How to learn the multiplication table quickly, efficiently and easily?This question worries thousands of schoolchildren, parents and even grandparents from year to year. Unfortunately, not everyone can boast of excellent knowledge of the multiplication table.

Multiplication table (pythagorean table) is the most popular and most demanded mathematical tool for calculations. It is used by almost everyone and at every turn. It is impossible to assume successful schooling without a strong knowledge of the multiplication table.

How can you help your child learn the multiplication table easily and quickly?

I bring to your attention several proven ways to learn the multiplication table quickly, easily and even interestingly.

1) Use games.

In order for a child to be able to learn the multiplication table, it must be stimulated. You can find board math games, buy an arithmetic loto and play with a child in the family. There are games for memorizing the multiplication table on the Internet that you can offer your child. Memorization during the gameplay is better.

2) Exercise daily.

The multiplication table is a great memory training. But, like any workout, it must be regular in order to achieve a good result. Learn the multiplication table gradually and do not try to cover all the numbers at once. If you want to learn the multiplication table quickly and easily, do a little bit every day with your child.It is better to start training even before studying the table, and they should not consist in simple memorization. Just casually ask the child about, for example, how many sweets to give him and his friend so that they get 3 each. Ask any questions that could develop his knowledge or could help in acquiring them. Creativity is the way to success, the child must pass the multiplication table in practice.

3) Use different activities of the child.

The more varied the ways your child reproduces the multiplication table, the stronger and easier he will learn it. Invite your student to write examples from the multiplication table, say the table aloud, whisper the answers of the table for 3, sing the table for 6.

4) Be active and interested in learning the table

Involve game techniques. Offer to check your multiplication table. Tell it to a child with mistakes. Let him correct you. You can take turns with the child to write any column of the table and check each other's work. Give your child the opportunity to correct your mistakes, make sure that he has already memorized many cases of tabular multiplication well. You can write several two-digit numbers and ask the child to circle the answers of the multiplication table in a red pencil, for example, by 8.

5) Use hints when studying the table.

HERE IS A FEW OF THEM:

1) Multiplication by 1 and 10

It’s worth starting with this to calm the child: multiplication by one is the number itself, and multiplication by 10, the number and zero after it. So he already knows the answers to the first and last examples in all columns.

2) Multiply by 2

Multiplying a number by two means adding two identical numbers.

3x2 = 3+3

6x2 = 6+6

3) Multiply by 3

To memorize this column, mnemonic techniques are suitable, for example, short rhymes. You can invent them with your child or look for "ready-made" ones on the net:

Well, my friend, look

What is three times three?

Nothing to do!

Well, of course, nine!

Or

All the kids need to know

What is three times five

And don't be mistaken!

Three times five is fifteen!

Or poetry A. Usacheva "The multiplication table in verse"

What is Multiplication?
This is smart addition.
After all, smarter - multiply times,
Than to add up everything for an hour.
1x1
One penguin walked among the ice floes.
Once one - one.
1x2
There is safety in numbers.
Once two two.
2x2
Two athletes took kettlebells.
It is: two times two is four.
2x3
The rooster sat before dawn
On a high pole:
- Crow! .. Twice three,
Two times three is six!

A pair of forks stuck into the pie:
Two by four - eight holes.
2x5
They decided to weigh two elephants:
Twice five, we get ten.
That is, each elephant weighs
Approximately five tons.
2x6
Met cancer crab:
Twice six - twelve paws.
2x7
Twice seven mice -
Fourteen ears!
2x8
Octopuses went for a swim:
Twice eight legs is sixteen.
2x9
Have you seen such a miracle?
Two humps on the back of a camel.
Nine camels began to be counted:
Twice nine humps is eighteen.
2x10
Twice ten is two tens!
Twenty, to put it briefly.
3x3
Two bugs drinking coffee
And they broke three cups.
What is broken, do not glue ...
three times three - comes out nine.
3x4
He keeps repeating in the apartment all day
Talking cockatoo:
- Three times four,
Three times four...
twelve months of the year.
3x5
The student began to write in a notebook:
What is "three times five"?
He was terribly careful:
Three times five - fifteen spots!
3x6
Thomas began to eat pancakes:
Eighteen is three times six.
3x7
Three times seven is twenty one:
Hot pancake on the nose.
3x8
Mice gnawed holes in cheese:
Three times eight is twenty-four.
3x9
Three times nine is twenty-seven.
Everyone needs to remember this.
3x10
Three maidens by the window
Dressed up in the evening.
The girls measured the rings:
Three times ten is thirty.
4x4
Four cute pigs
danced without boots:
Four times four is sixteen bare legs.
4x5
Four scientist monkeys
Flipping through books...
Each foot has five toes:
Four times five is twenty.
4x6
Went to the parade
Jacket-potato:
Four times six is ​​twenty-four!
4x7
Chickens are counted in autumn:
Four times seven is twenty-eight!

4x8
4x9
Baba Yaga's stupa broke:
"Four times eight" - thirty-two teeth! -
Bezh zhubov she has nothing to eat:
- Four times nine - "thirty six"!
4x10
Walked forty forty,
We found cottage cheese.
And divide the cottage cheese into parts:
Four times ten is forty.
5x5
The hares went out for a walk:
Five five - twenty five.
5x6
The fox ran into the forest:
Five six - thirty comes out.
5x7
Five bears from the den
We walked through the forest without a road -
For seven miles jelly slurp:
Five seven - thirty five!
5x8
climb centipede
Difficulty on a hillock:
Tired legs -
Five eight - forty.
5x9
Cannons stood on a hillock:
Five eight - came out forty.
The guns started firing:
Five nine - forty five.
5x9
If you slurp cabbage soup with bast shoes:
Five nine - forty five ...
There will be this bast
Drip everyone on your trousers!
5x10
Digging a bed of zucchini
Five dozen patches.
And piglets' tails:
Five ten - fifty!
6x6
Six old women spun wool:
Six six - thirty six.
6x7
Six networks of six ruffs -
This is also thirty-six.
And caught in the net of a roach:
Six seven - forty two.
6x8
Hippo buns ask:
Six eight - forty eight ...
6x9
We do not feel sorry for the rolls.
Mouth open wider:
Six nine will be -
Fifty four.
6x10
Six geese lead goslings:
Six ten is sixty.
7x7
Fools do not reap, do not sow,
They themselves are born:
Family seven - forty nine ...
Let them not be offended!
7x8
Once the deer asked the elk:
- How much will seven eight? -
The moose did not climb into the textbook:
- Fifty, of course, six!
7x9
At seven nesting dolls
Whole family inside:
Seven nine crumbs -
Sixty three.
7x10
Seven fox cubs are taught at school:
A family of ten - seventy!
8x8
Vacuuming the nose
Elephant carpets in the apartment:
Eight by eight -
Sixty-four.
8x9
Eight bears were chopping wood.
Eight nine - seventy two.
8x10
The best account in the world
New Year is coming...
Toys hang in eight rows:
Eight ten - eighty!
9x9
Pig pig decided to check:
- How much will it be "nine by nine"?
- Eighty - oink - one! -
So answered the young pig.
9x10
The sandpiper is small, but the nose is:
Nine ten is ninety.
10x10
There are ten moles in the meadow,
Each digs ten beds.
And ten ten - one hundred:
The whole earth is like a sieve!

4) Multiply by 4

Multiplication by 4 can be represented as a multiplication by 2 and again by 2. This column for students who have mastered multiplication by two will not cause difficulties.

5) Multiply by 5

This is the easiest column to remember. All values ​​in this column are located 5 units from each other. Moreover, if an even number is multiplied by 5, the product will end with 0, and if an odd number - with 5.

6) Multiply by 6, 7, 8

These columns, as well as the multiplication by 9 column, traditionally cause difficulties for schoolchildren. You can calm the students by explaining that they have already learned most of the examples from these columns and the awesome 8x3 is the same as the already learned 3x8. By swapping the factors, you can remember what the product is equal to.

This means that children will only have to remember 6 “unfamiliar” examples:

6×7=42

6×8=48

6×9=54

7×8=56

7×9=63

8×9=72

These examples can be written on cards, hung on the wall and memorized.

7) Multiplication by 9 on the fingers.

On fingers:
Place both hands on the table, palms down. Then let the little finger of the left hand be the first finger, the ring finger the second, the middle finger the third, etc., the thumb of the right hand the sixth, etc., the little finger of the right hand the tenth finger of both hands.
These fingers are the unmistakable counter
9 × 5 = 45
To solve this on your fingers, you only have to look at how many fingers from the 5th finger to the left and how many to the right: 4 fingers to the left is 4 tens, 5 to the right is 5 units, which means the answer will be 45.
9 × 7 = 63
From the 7th finger to the left 6, to the right 3 fingers, which means 63.