Now, many years later, when we had to study and master a lot, it seems to us very easy to study the multiplication table.
And remember yourself at the age of a student in the second or third grade, it seemed to you that it was impossible to learn the multiplication table.
But you had to teach, and everyone taught in different ways.
Let's look at the easiest way to study the multiplication table so that the child is interested and he quickly memorizes the multiplication table.
Consider a simple way to learn the multiplication table
Stage 1. Preparation for the study of multiplication tables.
The most important thing you can do to help your child learn the multiplication table is to find and print the multiplication table itself and tell the principle of multiplication.
When the child understands the principle of multiplication itself, then he will quickly be able to learn the multiplication table and it will be easy for him to learn it.
You can cut out the multiplication table from the notebook, it is located on the back of the notebook.
The multiplication table is of two types:
The most important thing is that you must correctly explain to the child the regularity of the multiplication table, if the child understands the principle of multiplication, then he will easily learn the multiplication table and he will not need to learn it and cram without understanding its meaning.
Stage 2. Principle of the multiplication table
Before you start learning the multiplication table, consider it with your child, find certain sequences, patterns that are in the table, explain to your child how and from what these patterns appear.
Try to focus the child's attention on the important points of the multiplication table. When children begin to study the multiplication table, they already have a little experience in mathematical operations, they can add, subtract and begin to multiply prime numbers.
Start studying the multiplication table by two and at the same time review addition with your child so that he understands the essence of multiplication itself.
For example: you need to learn the multiplication table by two, you and your child multiply 2 * 3 = 6, you and your child describe the same action in the form of addition 2 + 2 + 2 = 6.
That is, you take the number two and add it three times and you get the same answer.
Explain to your child that by multiplying only two numbers he will quickly find the answer, and if he adds two several times, he will spend a lot of time to get the answer.
Consider the following examples:
2 + 2 + 2 + 2 = 8
2 + 2 + 2 + 2 + 2 = 10
2 + 2 + 2 + 2 + 2 + 2 = 12
2 + 2 + 2 + 2 + 2 + 2 + 2 = 14
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 20
Based on these examples, the child will easily understand the essence of multiplication, he will not want to add the same number several times, he will clearly see the path of multiplication and its regularity.
Having dealt with the multiplication table by two and having learned it, the child can easily begin to study the multiplication table by three, and so on.
Stage 3. Learn the multiplication table by parts
It is not necessary to learn the multiplication table all at once, it is very difficult for a child and instead of knowledge, the child will have one mess in his head.
Always learn the multiplication table by parts, start with the simplest numbers first by two, three, then consolidate the learned multiplication table. Ask the child in disagreement, then you can start studying the multiplication table by four, then by five.
Learn the multiplication table step by step and be sure to reinforce the learned multiplication table with examples, interesting questions or in the form of a game, the child will not only be useful to learn the multiplication table, but also interesting.
You can print or draw several multiplication tables with empty cells, the child can practice and test his knowledge on the already learned multiplication table.
Step 4. Explain the rule of multiplication
The child must remember the main rule of the multiplication table: the product does not change from the rearrangement of the factors.
Consider with your child several examples from the multiplication table that relate to this rule.
For example:
There are many such examples in the multiplication table, and when the child remembers the rule, he will not need to learn every row of the multiplication table, because many examples are repeated in the following columns.
Stage 5. Never forget about the laws of the multiplication table
In the multiplication table there are a lot of patterns that you always need to remember and know with the help of these patterns, it is easy to learn and remember the multiplication table.
Consider several patterns of the multiplication table
Pattern 1. Multiplication by one
No matter what number you want to multiply by one, you always get the same number that you multiply, multiplying by one does not change the final result.
For example:
Pattern 2. Multiplication by five
All examples of multiplication by the number five always end with 0 or 5, if you consider the column of the multiplication table by five, you will see that the multiplication of odd numbers always ends with 5, and the multiplication of even numbers ends with 0.
For example:
Multiplication of even numbers
Multiplication of odd numbers
Pattern 3. Multiplication by ten
Consider a column of the multiplication table by ten, multiplying any number by ten ends in 0.
For example:
Pattern 4. Some examples are half the size
Consider examples of multiplication by five and examples of multiplication by ten, then we will see that examples are five less than examples by ten by half.
For example:
Pattern 5. Multiply by four or double the number twice
Consider an example of multiplying six by four and an example of doubling six by two. For example:
The answer is the same 24.
Let's look at a few more examples:
Pattern 6. Multiplication by nine
If we consider the multiplication table by nine and the answers that are obtained, then you will also see the pattern of the first and last numbers in the answer of each example. The first digit of the answer is always incremented by one, and the second digit of the answer is always decremented by one.
09,18,27,36,45,54,63,72,81,90
Step 6. Repeat the learned multiplication table regularly
Constantly check the child's learned multiplication table, first ask the multiplication table in order, slowly, so that the child has time to think and remember, if the child answers correctly, then you can start asking randomly, gradually increasing the pace between questions.
Thus, your child will be well oriented in the multiplication table and will remember it well.
Stage 7. Multiplication table in the form of a game
It's no secret that children love to play from birth, they learn a lot of new and interesting things during the game.
Play different games with your child so that he or she learns the multiplication table better.
Each child in the class has friends and girlfriends invite them over and play together.
Game 1. Nimble ball
An adult takes the ball in his hands and stands in the center of the room, and the children stand around him in a circle or in a semicircle. The presenter asks questions on the multiplication table and throws the ball in any order; children catch the ball and answer.
If the child answered incorrectly, then you can repeat the question and throw the ball to him again. During the game, do not forget to praise the children for the correct answers.
During the game, children develop a spirit of competition, everyone tries to answer correctly.
Game 2. Cards
Prepare cards in advance according to the multiplication table, on which an example will be written, you show the card, and the child answers.
This game can be played with one child or several children at the same time.
The more children participate in the game, the more interesting your child will be.
This game can be played for a while, whoever answers more and correctly is considered the winner.
Game 3. Answer quickly
This game can be played together, but several people are better, a presenter is chosen, it can be an adult, he gives a task and whoever answers correctly first, that person scores points.
This game will teach your child to remember and respond quickly. If several people are playing, then the players have a competitive spirit, and everyone will try to answer faster and score as many points as possible.
Question 1. Eight two -?
Question 2. Five eight -?
Question 3. Family five -?
Question 4. Three times ten -?
Question 5. Six three -?
Question 6. Twice seven -?
Question 7. Nine four -?
Question 8. Seven six -?
Question 9. Eight nine -?
Question 10. Six four -?
Questions can be changed with meta ad infinitum, the more you ask such questions, the faster the child will remember the multiplication table and will be well oriented in it.
Stage 8. Calm environment
Parents need to know a few rules to help your child learn the multiplication table.
Rule 1. Motivation of the child
If your child does not want to study or learn the multiplication table, motivate the child. Each parent knows his child well and knows how and when to motivate the child to achieve the goal and result.
Rule 2. Do not scold
Never scold your child for poor grades, comments in the diary for mistakes, be sure to figure out why your child is not good at learning to be attentive not to repeat mistakes, and so on. Understand and help your child with kind words and advice.
Rule 3. Classmates
Never set classmates, relatives, friends as an example to your child, do not humiliate your child, value him, love him, do not forget that each child is a separate person, which has its own personality and peculiarity.
Learn to find the right approach to your child in any even the most difficult situation.
Rule 4. Calculate the strength of the child
Never put in front of the child over the bar that he must overcome, try to plan the child's education gradually, systematically, without overloading and a large amount of material.
Do not frighten the child with a large amount of material, teach him to work gradually, the child will gradually get involved and cope with the stress.
Rule 5. Praise your child
Do not forget to praise your child even if he has very little success, encourage him, then the child will try even more and he will have a desire to master more and more material.
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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.
And in everyday life, the multiplication table is in demand almost every day. That is why so much time is devoted to mastering it in elementary school.
However, the study of the Pythagorean table cannot be called easy: the skill of multiplication is mastered with difficulty, and it is also not easy for a child to remember all this considerable mass of numbers.
The task of parents is to help children learn the multiplication table, making the process interesting and at the same time productive.
Simple ways to teach children the multiplication table
Good old counting material, as well as a variety of "tips" in the form of rhymes, songs and interesting memorable pictures, too, has not been canceled.
Having an idea of the basic teaching methods: memorization, play, visualization - parents are able to independently teach the child the multiplication table.
Memorization
The task of “learning the table” also involves memorizing it literally. It has been noticed that memorizing material is much easier in poetic form or in the form of a song, especially when it comes to children.
If we streamline and rhyme the examples for multiplication, then all the necessary numbers will indeed be fixed in memory much faster.
You can use any poems (for example, you can learn with your child the words of the song "Twice two - four" by V. Shainsky and M. Plyatskovsky). And parents with imagination 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 not remembered in any way, there remains a routine, but proven method by more than one generation of schoolchildren - to memorize it. However, keep in mind that the kids don't like this method at all.
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 to solve complex multiplication examples.
Visualization
Another way of mastering 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 5 objects 6 times").
In addition, the kid can count the figures presented and make sure that the answer is exactly the same as in the Pythagorean table.
Using pictures
If the child loves to draw, this is a great reason to study the table using pictures.
The principle of operation is about the same as in the case of counting material, only instead of laying 5 sticks in front of the young mathematician 6 times, you can draw directly opposite the example of 6 squares / cakes / cars 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 your fingers. This kind of life hack will interest any child.
Place your hands in front of you, palms outward and mentally number them from 1 to 10, starting with the left little finger. Table examples for multiplication with the number 9 are very simple to solve: just bend the finger, the number of which coincides with the second factor.
So, multiplying 3 by 9, bend the middle finger on the left hand. The fingers, which are located to the bent one (there are two of them), indicate the number of tens, and the rest (there are seven of them) - 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 PCs can be used as visualization tools, if there is such an opportunity and the parents do not mind such a pastime for the child.
Of course, all means are good to study such a rebellious multiplication table, but remember that everything should be in moderation, and do not leave the baby in the care of the gadget in this difficult matter, but rather join it yourself.
The game
Learning in a playful way always attracts kids. Learning the multiplication table is good on the material of a card game. Cards are made of cardboard for each example of a table, a numerical expression (5 x 3 =?) Is written on one side, and the answer is on the other.
The players take turns drawing cards, solving an example and checking themselves by looking at the reverse side. If the answer is correct, the card remains with the player, if not, it is returned to the deck. The winner is the one with the most cards at the end of the game.
First steps in learning the table: the easiest numbers and mastering the principle
Some examples from the Pythagorean table are engraved in memory almost instantly, while others, no matter how hardcore, 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 the child to remember the column of examples with 1, since the answers will be identical to the changing multiplier. Next, you can start studying the column with the number 2, because such a multiplication can be easily illustrated by any means at hand, adding two each time.
After that, the column with a four will be well remembered, because in order to multiply by 4, you need to multiply by 2 and another 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, the multiplication of these numbers by 1, 2, 4 and 5) will already be mastered. And if you decide to use the finger multiplication method described above, 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 child so that it is clear to him. To begin with, it is worth telling the child that this mathematical action was invented to speed up and facilitate counting.
It would be nice to think of a bright 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 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 your child that multiplication is “take so many times for so many times”.
If you think your child will be more likely to understand digital notation, explain that the expression "5 x 6" is a short notation of the expression "5 + 5 + 5 + 5 + 5 + 5". Thus, multiplication not only makes it easier to count, but also makes it possible to concisely write down the sum of the same terms.
This means that homework in math will take much less time - what is not a great reason to remember the table?
How to consolidate the result?
The best reinforcement of 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 baby's new knowledge into practice.
On a walk, ask them to say how many wheels four cars have, how many legs five cats have. At lunchtime, find out how many plates to put on the table if each of the three diners needs two. Repeat the multiplication tables in verse from time to time.
Many parents advise, to memorize the multiplication table and after school hours, simply hang the Pythagorean tables in different places at home, so that the child can repeat the material covered at any time.
Playing is also a good way to consolidate knowledge. Use the cards mentioned above for her. Play with the whole family, let adults sometimes deliberately make mistakes so that the child can correct them, demonstrating their knowledge.
How can you help your child learn and memorize information faster?
Mastering the multiplication table is not a very quick 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 in all possible ways to help the child quickly understand and remember the information received.
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 = 21 and 7 x 3 = 21.
Having understood this, the child will quickly guess 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 memorized is much less than it seems at first glance! For clarity, duplicate 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 9. If you reduce the numbers in the column with the digit eight in this way, you get a sequence from 8 to 1 in order. In the column with six, the sequence 6, 3, 9 will be repeated three times, and in the column with three - 3, 6, 9.
You can show the little conqueror of big mathematics and such a trick: if you take the first answer for 09 (and not just 9) in the column with nine, then the numbers in the answers will line up in two columns, and the left one will be a series of numbers 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 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 the knowledge of "tricks", in extreme cases it is even permissible to perform addition quickly.
Or, for example, if you forgot how much 9 x 3 will be, then how much will 3 x 9 be, you will probably be able to remember? The ability to use different ways to solve a problem will come in handy for a baby in life.
How do you teach your toddler to deal with difficult 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 the form of a two-digit number by a single-digit number.
Explain to your child that in this case it is necessary:
- Write down the numbers in a column, two-digit - on top.
- Multiply by a single number, first two-digit units, then tens (then you can increase the 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 digit denoting the number of units of the resulting number is written under the line, and a digit denoting 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 one.
It sounds complicated, for example, everything is much simpler. After a while, 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 worthwhile to specifically ask the child too difficult tasks - everything has its time.
Interest, motivation, play - this is what is at the forefront of education today, especially when it comes to young children. It has been proven that if a child is passionate about a material, he assimilates it much faster and better.
Cramming is not a bad option, but its result is often short-lived: after writing an important test or passing an exam, we are happy to forget what we said 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 super ability to multiply numbers is useful to a child and how much better it is to multiply them quickly than to add slowly;
- stimulation, in other words, the promise of something pleasant when the result is achieved (but remember that this method cannot be abused, otherwise one day you simply will not financially pull another "nice");
- praise: for every even the smallest step forward, the child needs to be praised, and significant progress is well encouraged with an exciting walk, a joint game or a trip to the cinema or a museum, and along the way, you can repeat a couple of examples at the same time;
- learning in a playful way: use to test the child's knowledge not mathematical dictations or tests - they are enough for him 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 correctly solving an 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 not learn even half, and if he does, he will have time to forget. Let your homework not be too long, then the multiplication will not have time to bore the student.
It is important to take breaks during class so that the baby can warm up and change the type of activity. And in order not to deviate from the topic, you can spend a mathematical physics minute: a parent throws a ball to the child with a question, for example, "Five five -?", He catches and throws it back, voicing the answer.
What mistakes is it important not to make when dealing 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, having applied 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 unwillingness to study may arise;
- wait for a quick assimilation of a large amount of material and be upset when this does not happen (and it will not happen);
- compare the child's success with the success of his friends, classmates and brothers (in any case, one of the children will have to be elevated before another, 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. By engaging in boring material with interest, rather than boring material, children will learn multiplication more willingly and faster.
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Every parent at some point has to face one very difficult problem: how to help a child learn the multiplication table. Today on the Internet there are many different ways to help children memorize the so-called Pythagorean table:, songs, audio programs. However, not every method is really effective and allows you to easily and quickly teach a child the multiplication table. Each student needs his own approach, his own most effective methodology. This article will analyze the basic techniques and methods of studying the multiplication table, from which you can choose the ones that are right for your child.
It is important! First of all, you should explain to the child the essence of the multiplication action. As a rule, children starting to learn the multiplication table already have a concept of elementary arithmetic operations, such as addition and subtraction. It is this knowledge of the child that will help you explain to him the principle of multiplication: that 2 multiplied by 3 means adding 3 times the number 2, that is, 2 + 2 + 2. The child should be well aware of this in order to avoid many difficulties and misunderstandings in the study of the multiplication table in the future. In addition, you should explain how the multiplication table itself is arranged, that the number from the left column is multiplied by the number from the top line, and at the intersection of the line and column in which these numbers are located, you should look for the answer, that is, their product. For example, five is eight equals forty (5 × 8 = 40).
The game
In any even routine process, which are exercises for studying the multiplication table, there must be an element of the game, it is necessary for children! Learning using game techniques will make the child delve into the task, become truly interested in the subject of multiplication and forget about the unwillingness to learn. One of the main ones says: interesting things are remembered better and faster. If you can spark a child's interest in multiplication, you’re halfway done!
One of the popular games for studying the multiplication table is the card game. You can read more about the game "" in this, as well as download and print ready-made cards with examples and answers. The essence of this game multiplication table is that the child randomly draws a card from the pile and sees on each card an example of multiplication without an answer (for example, 7 × 7 =? Or 3 × 8 =?). If he gives the correct answer, then the card is "out of play", and if the answer is incorrect, then the card is returned to the very bottom of the pile and can be drawn again. The game continues until all the cards are over, that is, until the child gives the correct answer to all the examples. When there are few cards left, as a rule, these are difficult examples that the child has already tried to solve, then they are easy enough to remember, especially when the child develops excitement during the game.
This game is sometimes called the "multiplication table simulator". The entire gameplay can be carried out in stages, depending on the material learned. For example, you can start your impromptu lesson with cards "multiplication by 2", and then dilute them with new learned examples. There are many options for the game, in what you can.
In addition, you can add a game element to the study of the multiplication table using all kinds of programs, online games, special sound posters and much more, which can be found on the Internet without any problems. But the game "" is the simplest and most effective way to learn the Pythagorean table.
Having studied the special techniques of memorizing the multiplication table, we have developed a special game, which is posted below. Children will be able to open cards and memorize examples in a simple playful way.
Where to begin?
If you are just starting to teach your child the skills of multiplication, then we can recommend that you try the following techniques (go through the following steps).
Immediately explain to your child the simplest and most trivial examples from the multiplication table, which he can solve without any problems. When you look at the multiplication table, this big 10 by 10 grid with numerous numbers, the child can simply get scared. You should immediately make him feel that not everything is so difficult. And already part of the table, he can decide on his own:
A) Multiplication by 1 always gives the same number that we multiplied by 1. For example, 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, and even a million by 1 equals a million.
B) Multiplication by 10, this is the same as simply attributing zero to a number. How much is 2 * 10? That's right, 2 with zero, that is, 20.
Having learned the multiplication table by 1 and by 10, the child should understand that he now knows all the extreme columns and rows of the multiplication table (in the figure they are highlighted in green). 
If all this took a long time, and the child was tired, then it is better to postpone the study of the remaining Pythagorean table for the next time. If not, and the child is full of strength and desire to continue, then move on.
V) What is multiplication table 2 is usually given to children quite easily. Multiplication by 2 is the same as simply adding two identical numbers. If you teach your child the multiplication table, then, most likely, he already knows how to add small numbers and will cope with multiplication by two without problems.
G) Change of multipliers. Another important rule of multiplication, which is usually understood by an adult, but not always understood by a child, is the displacement (or commutative) law of multiplication. Simply put: the product does not change from the permutation of the factors. In other words, learning the multiplication table is easier knowing that: 2 * 3 is the same as 3 * 2.
The child needs to explain and show why the second row and the second column of the Pythagorean table contain the same numbers, exactly like the 3rd row and 3rd column, etc. Therefore, having learned the multiplication of 2 by any number, he will also know the multiplication of the remaining numbers by 2. Therefore, the task becomes 2 times easier.
Thus, by applying the techniques described above, you can help your child easily remember the values of the multiplication table, highlighted in green: 
Agree, it looks good already. Make it clear to your child that the multiplication table is not that big or difficult.
Purposeful memorization
After your child has mastered the simplest values of the multiplication table, you can proceed to more complex factors. Here it is important to use the elements of the game, and many other useful ones: test tasks, application in practice. Many of the examples will need to be memorized, memorized and repeated several times so that your child can then easily name the values of the multiplication table. Better to go in order and not try to learn everything at once. Better to start with squares and multiply by 3 and 4, gradually moving on to the rest of the numbers.
Some educators believe that the right way to start learning the multiplication table is from the end, from more complex examples to simpler ones. But it is better not to do this in order to avoid stressing the child from not understanding how these values were obtained. Multiplying 3 by 3, the child can check himself on his fingers, and see why the multiplication table is exactly 9. And if he is immediately offered to multiply 8 by 9, and say that the result just needs to be remembered, he will not be able to apply his knowledge in practice , which will impair memorization and may negatively affect his motivation.
Squares of numbers. The square of a number is its product by itself. There are only 10 squares in the Russian multiplication table that you need to remember. The squares before the example "six by six thirty six" are usually remembered with a bang, and the next 3 squares usually do not cause too much difficulty either. And 10 to 10 will be one hundred, which we have already gone through earlier in previous lessons.
What is 3 times table. It is at this stage that the first difficulties may arise. If it so happens that the child cannot remember some of the meanings, then it's time to start using the cards. And if this does not help, and you know that your child has a more humanitarian mindset, then you can try (more will be written about them) to memorize the multiplication table.
What is multiplication table 4. You can also use flashcards and verses here. In addition, let your child understand that multiplying by four is the same as multiplying by 2 and again by 2. These and other simple arithmetic patterns that can be useful for the development of oral counting, you will find in this article.
What is the multiplication table of 5. Multiplication by five is usually easy. Intuitively, it becomes clear to the child that all the values of this multiplication are located after 5 from each other and end in either 5 or 0. All even numbers multiplied by 5 always end in zero, and odd numbers end in 5.
What is the multiplication table of 6, 7, 8 and 9. There is a certain peculiarity of studying complex examples from the multiplication table. If the child has learned the squares, as well as the multiplication table up to 5, then in fact he has very little left to learn, since he already knows the rest of the examples. This is clearly seen on this multiplication table, where cells that have already been mastered by the child at this moment are highlighted in green. 
As a result, the remaining cells of the multiplication table contain only six products, which are the most difficult and worth paying close attention to.
- 6 × 7 = 42
- 6 × 8 = 48
- 6 × 9 = 54
- 7 × 8 = 56
- 7 × 9 = 63
- 8 × 9 = 72
To memorize these expressions of the multiplication table, it is better to use a card game to bring the answers to automaticity. It is most effective to use 12 cards (with reversal of the multipliers). As practice shows, schoolchildren, and often adults, often have some problems with these six works.
That's all! In just a few lessons, the entire multiplication table can be learned quickly and easily!
Other techniques for learning the multiplication table
Naturally, the only correct answer to the question "how to learn the multiplication table" does not exist. In each individual case, for each specific child, even for each specific lesson, certain most effective methods need to be selected. Try to use in your pedagogical arsenal, several techniques of working with your child, and then you can quickly and easily understand how best to teach him the multiplication table. These are the ways.
Practical example
It will be easier to learn any work from the Pythagorean table if you demonstrate it in practice. For example, boys can be asked how many wheels are needed for 5 cars (5 × 4 = 20). And the multiplication table for girls may have examples in style of how many elastic bands are needed to braid three dolls in two braids (2 × 3 = 6).
Complex examples
Some examples from the multiplication table may be easier for your child, and some more difficult. Try to train him with complex examples so that he concentrates especially on them.
Finger multiplication table
Some examples from the multiplication table can be easily calculated using fingers, "natural human". And this applies not only to the simplest works, but also, for example, multiplication by 9. To do this, put our hands, palms down next to each other, fingers need to be straightened. Now, to multiply any number by 9, just bend your finger under the number of this number (counting from the left). The number of fingers before the curved one will be tens of the answer, and after - the ones. 
Poetry
Another memorization of the multiplication table is the use of poems (rhymes). If your child finds it difficult to memorize a certain value of the Pythagorean table, then this method will probably seem interesting to you. It may turn out that it is much easier for a child to memorize poetry than "dry" numbers. Today on the Internet you can find several large (even gigantic) multiplication tables in verse.
It will hardly seem to you that learning such a poem can be easier than just a multiplication table, but rhyme can be used in especially difficult cases. For example, multiplying by 7 and 8 is often difficult. And here the poems of Marina Kazarina "About multiplication" and Alexander Usachev "Multiplication" can come to the rescue. Below are 6 excerpts from a poem by Alexander Usachev about multiplication of the six most difficult examples of the multiplication table.
6 × 7
Six nets of six ruffs -
This is also thirty-six.
And the roach got caught in the net:
Six seven is forty two.
6 × 8
Hippos for buns are asking:
Six eight - forty eight ...
6 × 9
We don't mind the buns.
Open your mouth wider:
Six nine will be -
Fifty four.
7 × 8
Once a deer asked a moose:
- How many will be seven eight? -
The moose did not go into the textbook:
- Fifty, of course, six!
7 × 9
Seven nesting dolls
The whole family inside:
Seven nine crumbs -
Sixty three.
8 × 9
Eight bears were chopping wood.
Eight nine - seventy two
Parents of schoolchildren very often face a rather difficult problem: how to help a child learn the multiplication table? Children study the Pythagorean Table in the second grade of elementary school. At this age, mechanical memory works great, so many people simply "memorize" the material. But not all children manage to learn the multiplication table this way. Today, an exhaustive list of various techniques is presented on the Internet that allow you to learn the multiplication table with the comfort of a child and with special attention to his individual characteristics.
There are various ways of memorizing the Pythagorean table: proverbs, sayings, poems, songs, fairy tales, games, as well as various visual materials. However, whichever way you choose to study, it is worth remembering one thing: the child must understand the principle of the multiplication table!
It is important! By the time your child begins to study the multiplication table, he will already know the logic of such an arithmetic operation as addition. First of all, it is worth explaining the process of multiplication to the child. For example, 3 times 4 means adding 3 four times, or 3 + 3 + 3 + 3. Use associations, let it be not just the number 3, but three cars or three dolls. The child must understand well the arithmetic operation itself - multiplication. If you explain to your child that, in fact, multiplication is a short notation of the addition of the specified number of identical terms.
Only after the child understands the essence of arithmetic operations, start studying the table itself.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |
| 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
| 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
| 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
| 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
| 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
Studying the multiplication table with your child
Teach your child to understand the Pythagorean table. Explain that when you multiply the number in the leftmost column by any of the numbers, you get their product, which is at the intersection of the row and column you are looking for. When the child learns to easily navigate in the table itself, it is necessary to proceed to the most important thing - memorizing the table itself.
Playfully memorize the multiplication table!
Unfortunately, it is quite difficult for many children to approach the issue of memorizing the table with full responsibility. It is much easier to teach using the element of the game. It will be much easier for children to remember the information that they really find interesting.
A rather simple and effective game is to play with cards. Draw or print with your child different versions of examples from the multiplication table of the form:
- 3x7 =?
- 2x4 =?
- 5x8 =?
You can think of a great variety of options for such a game. For example, your child has learned all the examples of multiplication by 2 and 3. Make only these cards with your baby, and then dilute them with new ones. Another option for better memorization of the table can be drawing up cards of the form:
- 3x? = 15
- ? x2 = 6
- 10x? = 10
It is interesting! Use your imagination! It will be much easier for the child, and most importantly, it will be more interesting to memorize the material if the cards with examples are bright and colorful. Instead of boring questions, funny animals or favorite fairy-tale characters of the kid will appear. Imagine, and then your child will be happy to guess which number is hidden behind the back of the noble Puss in Boots or the funny Carlson.
Learn the multiplication table with your child - basic rules!
So that it is not difficult for a child to memorize the Pythagorean table, and the information received does not turn into a mess, you need to follow a few simple rules:
- Seeing the Pythagorean table, even the smartest kid can get scared. Explain to your child that there is nothing difficult in understanding this information, and at one time, both mom and dad, and grandparents learned this table.
- First, learn a simple multiplication, for example, by one. Explain to your kid that when you multiply by 1, you always get the same number that we multiplied by one. For example, 1x1 = 1.5x1 = 5, 10x1 = 10, etc. Multiplication by ten is also easy to convey to a child: it is the same as attributing zero to a number every time. For example, 2x10 = 20, 3x10 = 30. The main thing is that the association with the appearance of zero in a number is deposited in the child's head, and he can solve examples not only on paper, but also in his mind.
- When you have learned and repeated the simplest examples, start moving with the baby further along the table.
- After each memorization of an arithmetic operation - multiply by 2,3,4,5,6, etc. do not forget to repeat the material covered with the child (it can be in the form of a game that was described above).
- Very often a child, having learned multiplication by 2, begins to get lost if an adult asks him: "How much will 2x5 be?" In such a situation, you need to be careful when explaining to the student the communicative rule of multiplication: when you change the places of the factors, the product does not change.
Finger games - learning multiplication table fun!
If your child finds it difficult to study the multiplication table. You can use the fingers of a young bookkeeper. A great example would be learning how to multiply by 9. Have the child place both hands on the table, palms down. Each finger will represent a number from one to ten. For example, we want to multiply 9 by 4. We count from left to right to 4 - we get the index finger of the left hand. We bend it, and count the number of fingers on the left. There are only 3 of them - there are dozens of them. Purely fingers on the right - 6 - units. Answer 36. This type of memorization will bring a drop of magic into the learning process, and your young accountant will definitely be carried away by such an interesting learning process.
Association game
Many children have well-developed motor and figurative memory, so it will be easier for them to remember tabular examples using various associations. For example, the number 2 looks like a swan, and the number 1 looks like a gnome with a curious nose. For example, in the case of multiplication 2x1 = 2, you can think of the following story: One beautiful swan was very lonely. He so wanted to find a friend for himself that he was looking for him everywhere, everywhere. And then one day he met a gnome with a funny hooked nose. However, the dwarf was very cunning and cunning that the swan barely escaped from him. So the swan remained in splendid isolation ...
You can think of a great variety of such stories. Let the child dream up himself, the main thing is that the story unites two multiplier characters, and the work is the logical conclusion of this plot. The more emotional and exciting the stories are, the easier it will be for the child to remember this or that example.
As soon as the causal relationships with the help of a fairy tale are worked out, you can isolate the most important thing: "The swan met a gnome, did he make friends with him or was he left alone?" If your child answered everything correctly, then you need to ask him to compose this example in numbers.
Poems, songs, stories
This way of memorizing the multiplication table is suitable for children who perfectly memorize poems and songs. Children can be encouraged to memorize examples from the multiplication table using verses. An excellent option are the works of A. Usachev "Multiplication" and M. Kazarina "About multiplication". Thus, solving this or that example, the child will associate with a rhymed line.
No matter how you explain the multiplication table to your child, the main thing is to never get angry with your baby if he does not understand something! Show patience, as well as your imagination, and then your child will be happy to learn the multiplication table!
After the first year of schooling, parents face the problem of how to teach their children the multiplication table. Moreover, to make sure that young students have a desire to remember it, and not because it is necessary. Simple memorization get bored too quickly, and it will be rather difficult to continue this process.
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 tricks that will help you quickly and easily learn the multiplication table.
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Where to start
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 studying examples for the multiplication table, children already understand well what addition and subtraction are. That is, the multiplication action is replaced by addition of the same terms.
For example, 3 multiplied by 2 means that the number 3 must be added twice - 3 + 3. If 5 times 3, then we add fives three times 5 + 5 + 5.
It would be very nice if during the explanation the examples on the table were fixed with illustrative examples: “Mom bought Vova and Masha 2 boxes of pencils. Each box contains 6 pieces. How many pencils are in two boxes? How can you count? 6 plus 6 is equal to 6 or multiplied by 2. And in the first and in the second case we get 12 ".
Several learning techniques
Learn multiplication table with your child possible with different techniques. We rely on the fact that at this age, most children have a well-developed mechanical memory. Some require visual perception, such as sketches, videos, emotional poetic presentation or game moments. We will provide the essence of several of them.
Pythagoras table
One of the answers to the question of how to help a child learn the multiplication table is Pythagoras table... There are columns and lines with numbers from 0 to 9. If you connect a line and a column in which the factors are written with your finger, we get a number - the result of multiplication.
Despite the fact that at first glance the table seems cumbersome, you should not be intimidated. It is necessary to immediately explain to your child that examples for column multiplication are very easy to memorize. Basic simple rules:
- Diagonally written the simplest and easy products of the same numbers.
- The last line and the extreme column contain multiplication by 10, in which they simply add to the multiplier.
- The first column and first line show the result of multiplying by one, which results in the same thing.
- The child needs explain the basic principle using the Pythagorean table, which is to find the number. The result is located at the intersection of a column and a line with the required factors.
Note a number of advantages of studying the table multiplication in a column by the method of Pythagoras:
- children are happy to form squares from horizontal and vertical lines, looking for the right answer;
- when performing these actions, the logic of mathematical thinking develops;
- contemplation of the table in front of you, and not just recorded 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 permanently, for example, finding answers to the questions that adults ask him, the child quickly remembers the location of the number and the number itself, while he does not reproduce in the future the results that are not in the table.
Important! In order for the process of studying multiplication to be effective, it is necessary to place the Pythagorean table in a conspicuous place, and regularly work with the baby to find the correct answers.
Studying by cards
An easy way to remember the multiplication table is use of special cards. This process should be planned and the study is carried out gradually. You should start by making double-sided cards. An example for multiplication is written on one side of the card, and the answer to this example is on the other.
To begin with, they study with the baby, for example, the multiplication table by two. After the initial study, the material is consolidated with the help of 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.
Then the card is turned over and the correct answer is checked. If the result is correct, then the card is set aside. In the event that a mistake is made, the card is returned to the general pile.
The advantage of the proposed method is game form of study. While playing, it is always easier and easier to remember. In addition, children develop visual memory, auditory memory and speech, as it is necessary to read the example aloud. The mathematical terminology is remembered.
The learning process is best structured in this way:
- First, we study the table for two, and then we fix it with a card.
- Next, a table of three is studied. Then cards with these examples are added to the pile of previously studied ones. It is necessary to fix already examples for two and three.
- With the increase in the stock of knowledge, the number of cards increases.
Features of the study
At this stage, we present the features of studying the table for each factor. Each of them has its own flavor, knowing about which, you can help the child. quickly learn the multiplication table and ensure the firmness of its memorization. So, the tricks of the table are as follows.
Multiplication by 10 and by 1
The simplest methods of memorizing the multiplication table are contained in examples by 1 and 10. That is why experts recommend start training with these exercises. The features are as follows:
- when multiplying a number by 1, we get the same number;
- when multiplied by 10, we simply assign zero to the number.
Multiplication by 2
How to correctly and quickly learn the multiplication table by 2? First of all, we will explain to the child that multiplication is easily replaced by addition action... 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 pretty quickly.
Table for 4
Teachers recommend, after studying examples for 2, go to examples for 4. An easy way to learn the multiplication table - this is explained in detail and in an accessible way to the kid, what multiplying 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 apply a poetic form of study. You can compose poems yourself, or you can already take ready-made ones.
The next way is to explain to children with specific everyday examples. For example, the 3 × 4 example is solved using a practical problem. Mom had 4 apples, dad also had 4 and you have 4.
How many apples are there? Moreover, the tasks should be associative so that the child can easily imagine the situation and find the answer.
Multiplication by 5
These examples are always easy for children. The first sign by which it is 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, ends in zero;
- digits 1, 3, 5, 7, 9 are odd and their product with 5 gives a number that ends in 5.
Table for 9
A special trick is the table for 9. If you start to study it simply as examples, then the result will not always be successful. And the easiest way to remember it by bending the fingers. Its essence is as follows:
- Count your child's fingers and assign each their own number according to the score.
- Further, when multiplying 9 by any number, bend the finger with the corresponding number.
- We explain to the kid that the bent finger divides the rest of the fingers into two parts: the right and the left. The fingers on the left represent tens, and the fingers on the right represent the number of ones.
For example, 9x6. We bend 6 according to the number of the finger. To the left of it, 5 fingers remain unbent. Which means 50. On the right - 4 fingers, which means the number of units. Adding the numbers, we get 54. So, 9 × 6 = 54.
Multiply by 6, 7, 8
Starting to study these examples, we clearly explain to the little student that he already knows many examples. For example, if you need to multiply 6 by 4, that's the same as 4 × 6. 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 one is Pythagoras table.
There are many ways to help your child learn the multiplication table. It is especially easy to do this 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.
It is better to conduct training when the little student is in the right mood and, as it were, playing with him. Learning the table in a playful way will bring much more benefit than memorizing it in one tone, regardless of the class in which the multiplication takes place.
