Printable math simulator for multiplication and division tables. This simple trick will teach your kids multiplication in no time! Vacations are not ruined

The multiplication table or Pythagorean table is the basis that the child will need in the future to quickly and correctly perform any mathematical operations. According to the school curriculum, students master it in the second grade, when they have already become familiar with the simplest mathematical operations - addition and subtraction.

Learning the multiplication tables is difficult for a small schoolchild. This is quite a large amount of information, which he cannot cope with on his own.

If you are seriously puzzled by the question of how to explain multiplication to a child, this article may be useful for you.

Studying the multiplication table is one of the most common and difficult problems encountered by primary schoolchildren. How much effort parents make to quickly teach their children how to multiply correctly in their heads. If the learning process is not paying off, then you are using the wrong approach.

Calm, just calm!

In this article we will present several effective ways to help children master multiplication faster.

A child will not be able to learn the table in five minutes, but in just a couple of lessons it is possible to achieve good results. Don't try to force a student to memorize a table like a mantra. To better remember it, you should first of all understand it. Time, patience and goodwill are your main allies in this matter.

When trying to help a child learn the multiplication tables, parents should follow a number of the following rules:

• It’s better to start learning when you and your child are completely ready for the lesson, without being distracted by other things. Exercises in the morning will be more productive, since brain activity is more active at this time.
• Information should be presented in small portions. Take frequent breaks while studying.
• It is worth assessing the abilities of a small schoolchild objectively, without exaggerating the requirements.
• For every success, even if it’s not a big one, be sure to praise the child.
• Raising your voice and scolding your child is completely unacceptable. This will not affect your study of the table in any way. Be patient if some examples are difficult for him. Take a break, rest, and return to the task with renewed vigor.
• Try to turn a boring learning process into a fun, exciting game. You will notice how your child will learn and remember the material much better in a playful way.

Help your child learn the multiplication tables

To study the multiplication tables productively, you should approach your home lesson in stages:

• Preparation;
• consideration of the order of multiplication;
• memorization through games and visual examples;
• repetition of the covered material.

Some children easily remember new material using rote memory. At the age of 7-9 years, in most junior schoolchildren it is quite well developed. Another category of children perceive information coming to them through visual channels. It will be easier for them to remember the table using additional visual aids.

When teaching your child, focus on his strengths.

The following will help to demonstrate and explain to your child the principle of multiplication:

• cut cards;
• posters;
• illustrations;
• counting sticks, figures;
• pencils and markers;
• songs and poems;
• educational cartoons;
• audio CDs;
• baby fingers.

"Magic" table of Pythagoras

Place in front of you a sheet of paper with a printed table of Pythagoras. She looks like this:

The Pythagorean table has a more simplified form than the table with examples in a column. It does not contain unnecessary information, which only confuses and complicates memorization.

So that the child understands the principle of multiplication<, попробуйте для начала объяснить его на простом примере.

2 × 3 - similar to the action of 2 + 2 + 2, that is, adding the number 2 three times.

Show how the table works: the number at the intersection of the column and the top row is the correct answer. The baby only needs to remember 36 combinations. The remaining actions are repeated or very easy.

Tricks, secrets, patterns

By examining the table independently, the child begins to think and analyze logically, and find interesting patterns.

Teaching children the multiplication tables should begin from simple to complex information.

It's easy to learn the multiplication table by 1. Any number multiplied by 1 remains unchanged.

The multiplication table by 2 should also not cause difficulties. Multiplication by 2 is the addition of two identical numbers.

Multiplying by 10 produces a number 10 times larger. To get the result, add a zero to the number being multiplied.

Multiplying by 5 is also easy to remember. If 5 is multiplied by an even number (2,4,6,8), the result is also an even number ending in zero. For example, 5 x 2 = 10. If the number multiplied by 5 is not an even number (3, 5, 7, 9), then the answer will be odd with the number 5 at the end. For example, 5 x 9 = 45.

It is not difficult to explain to a child multiplication by 4. When multiplying any number by 4, we multiply it by 2 twice. For example, 4 x 3. First, we take the number 3 and multiply it by 2, we get 6. Then, we multiply the resulting result by 2 again. The result of all operations is the number 12 - this is the correct answer in our example.

The multiplication table by 9 is fraught with a little secret - the numbers multiplied by 9 are mirrored:

9 x 2=18 / 9 x 9=81

9 x 3=27 / 9 x 8=72

9 x 4=36 / 9 x 7=63

9 x 5=45 / 9 x 6=54

There is a great way to explain multiplication by 9 to your child using his fingers.

Place both hands in front of you, palms up. Number your fingers from left to right from 1 to 10. For example, you need 9 x 7. We count the seventh finger from left to right. We find it and bend it.

All fingers on the left up to the bent one are tens. Further behind the bent finger - units. We count and connect our fingers, the final answer is 63.

Another interesting way to multiply a number by 9 is to round it.

When multiplying by a specific number, round 9 to 10 to make it easier to multiply. From the result obtained, subtract the number that you multiplied by 9.

For example:

9 x 2 = 10 x 2 – 2 = 18

9 x 3 = 10 x 3 – 3 = 27

9 x 9 = 10 x 9 – 9 = 81

Hang a poster with the multiplication table in a prominent place in the room, and your baby will, willy-nilly, gradually memorize the numbers. To the question: “how much is 4 x 7?” he will never answer 29 - after all, such a number is not in the table at all.

We teach children multiplication in the form of a game

Let's look at an example of a game with cards. Pre-prepare cards with examples of multiplication without answers and place them in a common pile on the table. Let the child draw any card and try to give an answer to this example. Cards with correct answers are removed from the pile and the game continues. If the answer is incorrect, the card returns to its original place. Do not forget to voice the correct answer. The child will be able to remember it and answer correctly the next time he comes across the same card. The game ends when all examples from the pile have been solved.

Teaching a child multiplication in a playful way is much easier and faster.

There are several reasons for this:

• During the game, visual memory is used to its full potential.
• “Repetition is the mother of learning.” It is the examples that are difficult for the child that will be returned to the pile and, accordingly, repeated.
• Seeing how the stack of examples gradually decreases, the child develops a feeling of pleasure from successfully completed work, an incentive and motivation to complete the task as quickly as possible.

Some more fun game options

You can play the Lotto game with the same example cards. Prepare fields on paper that are filled with only answers. Randomly drawing one card with an example from the pile, the child must put it in the cell with the correct answer.

Give your child an oral quiz. For example, say the number 28 and ask which numbers are multiplied to produce the same result.

Learning will be more productive if examples from the multiplication tables are used simultaneously in practice. The boy likes cars, ask him to count how many wheels 6 cars have in total. Each car has 4 wheels, which means we multiply this number by the number of cars. The result will be 24 wheels. For a girl, give an example of two pigtails on dolls. You need an elastic band for each braid. How many rubber bands do you need for 7 dolls?

Transport yourself and your child into the world of fairy tales and your favorite characters. Play out different situations. Imagine Carlson blowing the candles off three cakes at once. How many candles are there on the cakes? Or Little Red Riding Hood brings gifts to grandma. In each hand there is one basket of pies. How many pies are there in two baskets?

There are plenty of examples right next to you, you just need to look around. You are required to show observation and imagination, then your child will be able to learn the multiplication table not only with ease, but also with great interest.

When studying the multiplication table, use available materials for clarity, for example, pencils or counting sticks. Place 5 glasses on the table and place 3 sticks in each - 15 pieces in total. Explain to your young student that the total number of pencils is the number of pencils in each glass multiplied by the number of glasses themselves.

Place 4 plates on the table and place 5 candies in them. Invite your child to count the total number of candies.

The use of poetic form is an effective method in studying the multiplication table. It will be easier for a child to remember numbers by hearing and rhyming. There are a large number of poems on the Internet that will help your child learn the multiplication tables.

This technique will be useful, for example, for learning multiplication by 3. Difficulties often arise with this number.

The version with riddles in verse is no less fascinating. Leave the ending of the verse unanswered, the child will guess in rhyme what number we are talking about.

Seven monkeys began to eat eight bananas each. How many bananas did you eat in total? 56

Playing games with your baby will help consolidate the acquired knowledge. If the child still does not understand how the multiplication table works, then you may not get the expected effect.

Move on to complex examples with ease

Having dealt with the multiplication table for 1, 2, 3, 4, 5, 9 and 10, we move on to more complex examples - multiplication by 6, 7, 8. These columns traditionally cause difficulties for children.

Calm the baby down. After all, he had already learned most of the examples in these columns long ago without knowing it.

7 x 2 is the same 2 x 7. He will understand that rearranging the factors does not change the product.

Your student will only have to remember 6 “unfamiliar” combinations:

The child can easily learn these examples mechanically.

Your efforts are not in vain

As an auxiliary tool in learning the multiplication tables for your child, you can include interesting educational cartoons. They are easy to find on the Internet. The baby will well accept this form of presenting the material.

Simulators, educational programs, exciting online games, and mobile applications are designed to help primary school students study and improve their knowledge of the multiplication tables. Choose an exciting game that you think is suitable for your child, and let the child try his hand at it. And then he will show you his achievements.

This method can greatly facilitate the task for parents, if, of course, they are not against such a pastime for the baby.

All children are unique and individual. There is no universal recipe for helping a child master the multiplication tables faster. Parents have an important task - to find the right approach to their child, to interest and motivate him to achieve his goals.

The multiplication table can be a serious test, so you shouldn’t rush, put pressure on, or even scold your child when the learning process doesn’t go the way you wanted. Remember yourself as a child, you once started with the same simple and complex steps.

Hello, dear readers! I remember learning the multiplication table; for me it was a difficult and lengthy process. I did this in the summer at my grandmother’s, she gave me a task in a stern voice, for example, to learn the table for 2, 3 and 4, and then checked.

For any parent, sooner or later there comes a time when their child has to learn the multiplication table. According to the modern school curriculum, it is supposed to master the material in the second grade. So I thought that the table should be taught not to the child himself, but together with his parents. And so today I wanted to reveal some secrets on how to quickly learn the multiplication tables for a child.

We discussed it with you earlier, and now it’s time for the multiplication table.

Many of us remember the notes on the back of our school notebooks, where multiplication examples were written in columns. Have you ever wondered, dear readers, why these endless examples are called a table?

It turns out that the Pythagorean table (this is its second name) is really a square divided into cells. At the top and to the right are the factors, and at their intersection is the answer to the example for multiplication.

To solve a multiplication example, you just need to mentally draw horizontal and vertical lines from the factors. The square where they intersect will contain the answer.

Observing a child in this form of presenting material allows him to quickly and easily remember it. This method has many advantages:

• The work is really interesting and exciting!
• The student independently looks for patterns, training logical thinking.
• Realizing that in front of him is really a table, and not a set of examples named like that for some reason, the kid changes his attitude towards mathematics as a science.
• The manual does not contain information “garbage” (multiplication and equal signs, which are an eyesore in the examples).
• By constantly looking at the manual, the child visually remembers numerical values. For example, when asked what is five and six, the baby will not answer, say, 55. The fact is that such a number does not exist at all, so it could not catch the children’s eye.

So, the fastest way to learn the multiplication table is to hang it in sight and regularly give your child examples. Here's an example task:

Other methods

To make multiplication clear to your child, you need to explain its principle. Let's say we need to multiply 3 by two. Explain that we take the three twice, and for convenience we write it down: 3x2.

We back up the examples with real facts. We set a life example. Grandmother brought two sets of pencils: Vasya and Vova. Each set contains 5 pencils. How many pencils will there be? To avoid adding, multiply 5 by 2 and get 10.

The best way to help children “cope” with the Pythagorean table is a game. Take the cubes and place them two at a time in a box. Count how many pairs of cubes you have. Make up the problem, say 2x4=8 cubes. Now, for clarity, expand the example and imagine it in the form of addition: 2+2+2+2=2×4=8.

The easiest way to memorize multiplication by one. Just explain to the guys: the result is the same number by which one was multiplied.

At the next stage, it is easiest to remember the results of multiplying by 2. You just need to add two identical numbers.

It’s quite simple to teach how to multiply by 4. First, multiply the number by 2 (we already know how to do this), and then multiply the result by 2 again.

When multiplying by 5, it's easy to remember that the answer must end in 5 or 0. This makes it easier to find the result of the example.

The most difficult stage begins with studying examples in 3,6,7 and 8. You have to use other techniques:

• Flashcards. Choose a few hard-to-remember examples and write them on cards. Place them in front of the children and ask them to look carefully and remember. Then remove the benefits and ask your child to restore the multipliers and the result. Repeat this periodically, day after day, until the material is firmly memorized. At the end of the training you can arrange an exam. Write examples on separate pieces of paper and place them face down. The kid draws out an example and says the answer to it.

• Visual aids. Hang the table in the house in the places where the baby most often visits. Let her always be in sight. Occasionally give your child examples so that he pays attention to the manuals.
• Poetry. It is easier for humanities scholars to remember material in the form of rhymed quatrains. Suitable poems were written by M. Kazarina and A. Usachev.
• Cartoons. Today there are many cartoons in which the characters solve problems. One such technique is only good at the dating stage.

And one more trick: explain that changing the places of the factors will not change the result. In other words, 3x4 and 4x3 give the same answer: 12.

The list of described techniques solves the question of how easy it is to learn the Pythagorean table with your child.

When to start?

Most parents rush to teach their children the material when it comes to it at school. As a rule, the process begins at age 8: at this time, children move to second grade, where the program requires mastering the principles of multiplication. Children who started school after 7 years old begin the table at 9 years old.

Since the school curriculum involves intensive learning, parents are actively looking for an answer to the question of how to learn a table with their children in 5 minutes. Unfortunately, science has not yet come up with such a method. You can use the above methods, but they will still take time.

The advice of psychologists and teachers is to start studying before school or at least in the summer after 1st grade. With this approach, there is no rush; parents and children have enough time to master and consolidate the material.

Many parents consider it unnecessary to “clutter” their child’s head with knowledge that is not yet necessary for him. This decision is legitimate if the baby has a hard time with mathematics, he has not yet mastered addition and subtraction. In this case, you need to give your child a good foundation and then start multiplying.

But if the child finds math problems easy, the table can be hung in the room long before the child enters 1st grade. Thus, parents make things easier for themselves two years in advance.

It's never too late to study the table. It trains memory, logical thinking, and makes children think.

Assignment for parents

Well, now, dear parents, show your class. Before teaching your children, check whether you yourself know this multiplication table well. Decide quickly, don't think long.

We have looked at ways to quickly and effectively learn the table with your kids. If the article was useful to you, leave comments on it. See you again, dear friends!

Many parents whose children have completed first grade ask themselves the question: how can they help their child quickly learn the multiplication tables. During the summer, children are asked to memorize this table, and the child does not always show a desire to engage in cramming in the summer. Moreover, if you just mechanically memorize and do not consolidate the result, then you can later forget some examples.

In this article, read ways to quickly learn the multiplication table. Of course, this cannot be done in 5 minutes, but in a few sessions it is quite possible to achieve a good result.

Also read the article,

At the very beginning, you need to explain to your child what multiplication is (if he doesn’t already know). Show the meaning of multiplication with a simple example. For example, 3*2 - this means that the number 3 needs to be added 2 times. That is, 3*2=3+3. And 3*3 means that the number 3 needs to be added 3 times. That is, 3*3=3+3+3. And so on. Understanding the essence of the multiplication table, it will be easier for the child to learn it.

It will be easier for children to perceive the multiplication table not in the form of columns, but in the form of a Pythagorean table. It looks like this:

Explain that the numbers at the intersection of the column and line are the result of multiplication. It is much more interesting for a child to study such a table, because here you can find certain patterns. And, when you look carefully at this table, you can see that the numbers highlighted in the same color are repeated.

From this, the child will even be able to conclude (and this will already be the development of the brain) that when multiplying, when the factors are swapped, the product does not change. That is, he will understand that 6*4=24 and 4*6=24 and so on. That is, you need to learn not the whole table, but half! Believe me, when you see the entire table for the first time (wow, there’s so much to learn!), your child will feel sad. But, realizing that he needs to study half of it, he will noticeably cheer up.

Print out the Pythagorean table and hang it in a visible place. Every time, looking at it, the child will remember and repeat some examples. This point is very important.

You need to start studying the table from simple to complex: first learn multiplication by 2, 3, and then by other numbers.

To easily memorize tables, various tools are used: poems, cards, online simulators, small multiplication secrets.

Flashcards are one of the best ways to quickly learn the multiplication tables

The multiplication table needs to be learned gradually: you can take one column per day to memorize. When multiplication by any number is learned, you need to consolidate the result with the help of cards.

You can make the cards yourself, or you can print ready-made ones. You can download the cards from the link below.

Download cards for studying the multiplication tables.

The numbers to be multiplied are written on one side of the card, and the answer on the other. All cards are folded face down. The student draws cards from the deck one by one, answering the given example. If the answer is correct, the card is put aside; if the student is wrong, the card is returned to the general deck.

This way, your memory is trained, and the multiplication table is learned faster. After all, while playing, it is always more interesting to learn. When playing with cards, both visual and auditory memory works (you need to voice the equation). And also the student wants to “deal with” all the cards as quickly as possible.

When we learned a little about multiplying by 2, we played cards with multiplication by 2. We learned multiplication by 3, played cards with multiplication by 2 and 3. And so on.

Multiplying by 1 and 10

These are the easiest examples. You don’t even need to memorize anything here, just understand how numbers are multiplied by 1 and 10. Start studying the table by multiplying by these numbers. Explain to your child that multiplying by 1 will result in the same number being multiplied. Multiply by one means take a number once. There shouldn't be any difficulties here.

Multiply by 10 means you need to add the number 10 times. And the result will always be a number 10 times larger than the one being multiplied. That is, to get the answer you just need to add zero to the number being multiplied! A child can easily turn units into tens by adding a zero. Play flashcards with your student to help him remember all the answers better.

Multiply by 2

A child can learn multiplication by 2 in 5 minutes. After all, at school he had already learned to add units. And multiplication by 2 is nothing more than the addition of two identical numbers. When a child knows that 2*2 = 2+2, and 5*2 = 5+5 and so on, then this column will never become a stumbling block for him.

Multiply by 4

After you have learned multiplication by 2, move on to multiplying by 4. This column will be easier for your child to remember than multiplying by 3. To easily learn multiplication by 4, tell your child that multiplying by 4 is multiplying by 2, only twice . That is, we first multiply by two, and then the resulting result by another 2.

For example, 5*4 = 5*2 *2 = 5+5 (as when multiplying by 2 you need to add the same numbers, we get 10) + 10 = 20.

Multiply by 3

If you have any difficulties studying this column, you can turn to poetry for help. You can take ready-made poems, or you can come up with your own. Children have well developed associative memory. If a child is shown a clear example of multiplication on any objects from his environment, then he will more easily remember the answer that he will associate with any object.

For example, arrange the pencils in 3 piles of 4 (or 5, 6, 7, 8, 9 - depending on which example the child forgets) pieces. Come up with a problem: you have 4 pencils, dad has 4 pencils and mom has 4 pencils. How many pencils are there in total? Count the pencils and conclude that 3*4 = 12. Sometimes such visualization is very helpful in remembering a “difficult” example.

Multiply by 5

I remember that for me this column was the easiest to remember. Because each subsequent product increases by 5. If you multiply an even number by 5, the answer will also be an even number ending in 0. Children remember this easily: 5*2 = 10, 5*4 = 20, 5*6 = 30 and etc. If you multiply an odd number, the answer will be an odd number ending in 5: 5*3 = 15, 5*5 = 25, etc.

Multiply by 9

I write 9 immediately after 5, because multiplying by 9 has a little secret that will help you quickly learn this column. You can learn multiplication by 9 with your fingers!

To do this, place your hands palms up, fingers straightened. Mentally number your fingers from left to right from 1 to 10. Bend the finger by which number you need to multiply 9. For example, you need 9*5. Bend your 5th finger. All the fingers on the left (4 of them are tens), the fingers on the right (5 of them) are ones. We combine tens and ones and get 45.

Another example. What is 9*7? Bend the seventh finger. There are 6 fingers left on the left, 3 on the right. We connect, we get - 63!

To better understand this simple way to learn multiplication by 9, watch the video.

Another interesting fact about multiplying by 9. Look at the picture below. If you write the multiplication by 9 from 1 to 10 in a column, you will notice that the products will have a certain pattern. The first digits will be from 0 to 9 from top to bottom, the second digits will be from 0 to 9 from bottom to top.

Also, if you look closely at the resulting column, you will notice that the sum of the numbers in the product is 9. For example, 18 is 1+8=9, 27 is 2+7=9, 36 is 3+6=9 and so on.

The second interesting observation is this: the first digit of the answer is always 1 less than the number by which 9 is multiplied. That is, 9 × 5 = 4 5 - 4 is one less than 5; 9×9 =8 1 - 8 is one less than 9. Knowing this, it is easy to remember what number the answer begins with when multiplied by 9. If you forgot the second digit, then you can easily count it, knowing that the sum of the numbers in the answer is 9.

For example, how much is 9x6? We immediately understand that the answer will begin with the number 5 (one less than 6). Second digit: 9-5=4 (because the sum of the numbers is 4+5=9). That makes 54!

Multiplying by 6,7,8

When you and your child begin to learn multiplication by these numbers, he will already know multiplication by 2, 3, 4, 5, 9. From the very beginning, you explained to him that 5x6 is the same as 6x5. This means that he already knows some answers; he does not need to learn them first.

The remaining equations need to be learned. Use the Pythagorean table and playing cards for better memorization.

There is one way to calculate the answer when multiplying by 6, 7, 8 on your fingers. But it is more complex than multiplying by 9, it will take time to count. But, if some example does not want to be remembered, try counting on your fingers with your child, perhaps it will be easier for him to learn these most difficult columns.

To make it easier to remember the most complex examples from the multiplication table, solve simple problems with the necessary numbers with your child, give an example from life. All children love to go to the store with their parents. Give him a problem on this topic. For example, a student cannot remember how much 7x8 is. Then simulate the situation: it’s his birthday. He invited 7 friends to visit. Each friend needs to be treated to 8 candies. How many candies will he buy at the store for his friends? He will remember the answer 56 much faster, knowing that this is the number of treats for friends.

You can memorize the multiplication tables not only at home. If you and your child are on the street, then you can solve problems based on what you see. For example, 4 dogs ran past you. Ask your child how many paws, ears, and tails do dogs have?

Children also love to play on the computer. So let them play profitably. Turn on an online trainer for your student to memorize the multiplication tables.

Study the multiplication tables when your child is in a good mood. If he is tired and begins to be capricious, then it is better to leave further training for another time.

Use the methods that are most suitable for your child, and everything will work out!

I wish you easy and quick memorization of the multiplication tables!

Specify table ID

Studying the school mathematics course in the primary grades involves studying the multiplication tables. Tips and techniques prepared by our consultants - psychologists, teachers - will help you remember the necessary array of information in a matter of minutes.

Learning the multiplication table

When we have figured out the processes of memorization, determined the main directions and methods that are most suitable for a particular child, we begin to study the Pythagorean table.

First of all, there is no need to frighten the child with the amount of information that he must remember. Explain that, despite the large number of numbers and mathematical symbols, you will only have to remember half. After all, 5x2 will correspond to the value of 2x5, etc. And the process of multiplication itself is the addition of a certain number a selected number of times. So 4x2 means the same as 4+4, and 2x3 means 2+2+2. Having understood these simple truths, it will be easier for the child to study the material in the future. As a visual aid, print out the table and attach it to the wall in the nursery so that the baby’s gaze constantly “bumps” into it, stimulating the repetition of the material.

What you need to print is the Pythagorean Table, where the product of two numbers is located at the intersection of horizontal and vertical lines corresponding to the factors.

History of appearance

To this day, there is a debate among historians about the true “inventor” of this numerical grid. Among those not privy to the historical vicissitudes, the nuances of the dispute are considered to be the author of the ancient Greek mathematician Pythagoras (570–490 BC). However, there are no records from the “author” himself on this matter. And conclusions are drawn on the basis of his biographies, which were written by his followers, after the death of this Great Scientist of his time.

Disputes about authorship are based on the results of archaeological excavations of ancient cities. Thus, at the site of excavations of the city-states of Mesopotamia, clay tables with systematized numerical sequences were discovered, the age of which, according to the most conservative estimates, exceeds 5 thousand years.

China is not far behind in terms of artifacts - the records found there date back to 1000-1500. BC It is possible that it was from Ancient China that knowledge spread to India, Japan, and other countries of that time.

And the share of the ancient Greek thinker can be attributed to the collection of knowledge available at that time and its systematization. Dissemination and popularization of mathematical knowledge already in the European part of the continent.

Multiplication table

It is a systematic grid - numbers are located vertically and horizontally, and the internal cells contain their product. It is currently the most popular must-learn tool for computational behavior. The only difference between the school curriculum of different countries is the number of factors required for memorization:

• in our country, schoolchildren learn the multiplication table up to the number 10;
• in the UK - up to 12, which is due to the peculiarities of the calculation systems and measures used in Foggy Albion;
• in India up to 20, etc.

The structure of the table itself is quite unique. Includes symmetry of numbers, which is quite easy to see. It is enough to analyze the numbers you encounter and consider their location. So, if we reduce two-digit numbers to simple, single-digit numbers, by subtracting a smaller number from a larger number (for example, the number 27 can be represented as 7-2=5) we get a unique picture.

Exactly in the center of the diagram there will be 4 values, the difference between their component parts will be 3. Next, 8 cells will be placed around this block, the difference of which will be 2. And even further - 16 with the result of “simplification” equal to 1.

One more, but not the last, unusual property of the table is the following. If all two-digit numbers are reduced to single-digit numbers (as indicated earlier) and then alternately subtract the adjacent ones horizontally and then vertically, the result will be 0.

In addition to the main, mathematical function, the table is used by representatives of non-traditional sciences - predictors, numerologists. Shifting the “laws of numbers” to human destiny. Forming both a description of a person’s character and predictions of his fate, based on his date of birth. But that's a completely different story.

Memory development - important aspects

Before you begin practical exercises in studying the multiplication table, you need to make a small but important digression. The affected aspect is necessary for understanding, correcting further study, and memorizing any material. By shaping the process taking into account the specifics of the child, parents will make learning moments comfortable both for themselves and, first of all, for the child.

First, let's remember a simple thing - human memory can be characterized by several important processes:

• The process of memorizing knowledge and events. The most labor-intensive process. It represents the ability to store information in a person’s memory using certain procedures that contribute to its “development.” With the development of memory, the process of memorization becomes more and more easier, and further “extraction” of the studied material becomes more and more simple.
• The process of reproducing stored information. It is an indicator of the quality of the previous process.

If parents encounter problems at this stage, then it is necessary to reconsider the methods used at the initial stage. Find for your child an integrated approach to learning the material that will give the best results. It’s easier to spend time honing a technique once than to waste it in the future using ineffective methods.

The next important point to understand is the types of memory. There are also 2 of them, short-term and long-term. As is clear from the definition, they are distinguished only by the period of time during which the received information can be “extracted.” Therefore, priorities for development must be given to the long-term. Although developed short-term memory is also necessary for humans.

The classification would not be complete without mentioning the effort involved in memorizing.

Types of memory

In this aspect, memory can be highlighted:

Involuntary

“It happens naturally” and does not require additional effort on the part of a person. It is most developed in preschool children, who “consume” the necessary information for development from all possible sources. Representatives of the older generation lose this opportunity with age, unless, of course, they keep themselves “in shape.”

free

It involves making a certain effort to memorize an array of information. Requires constant development, while at each new level the amount of effort expended decreases. Thus, there is an inverse relationship between indicators of memory development and the effort spent on memorization.

Methods of memorization are the “whale” on which the learning process rests. Conventionally, 4 main directions can be distinguished:

• visual– uses visual, associative images to remember the necessary information (pictures, faces, texts, etc.);
• sound– includes information for memorization received through the auditory organs (sounds, phrases, music, etc.);
• motor– is responsible for remembering the sequence of actions in certain circumstances (dance steps, techniques of various martial arts, etc.);
• emotional– it is not the action itself or the reaction to the process that is remembered, but the emotional “color” that accompanied it.

As a rule, the greatest effect is achieved by combinations of these methods, selected in accordance with the character and abilities of each individual.

What affects memory

In addition to the above, memory development is influenced by:

If a child is inattentive and does not remember information well, this does not mean that he has “bad memory” or does not have the ability to do so. It’s just that the parents failed to interest their child in the process. He got bored. Change your approach - after all, this is your child. Only in your hands is the development of his abilities, and, as a result, the joy of achievements and the bitterness of disappointments.

Among the practical tips for developing memory, the most effective are the following:

Stimulating the perception of information

To recreate the most comfortable atmosphere for studying and, most importantly, memorizing the multiplication tables, you need to remember once again what kind of memory there is and use all the available opportunities.

1 Emotional component. An important aspect from the very beginning of studying. If a child, even when learning multiplication by 1, gets bored or feels “negative,” all further work will be 90% focused on eliminating negative emotions. And only 10% for mastering the material. Start building a “foundation” of knowledge on your child’s interest. This will save effort and time in the future.

1 Acoustic component. In addition to your voice giving explanations on the topic being studied, come up with or download small quatrains that describe the actions being studied. Do you remember from childhood, “twice two is four, everyone in the whole world knows this”? You don’t have to be a poet - rhyme simple words, creating vivid images for your child.

1 Visual and motor components. The “broadest layer” that provides opportunities for the implementation of the task.

When studying, you will only need a “flight of fancy” and available means - cubes, sticks, pencils, paper. Let's look at some gaming tips below. Let them, as examples, become the basis of your individual methods.

Cards

Option 1

To do this, you will need small pieces of cardboard, which reflect the recording of numerical multiplication, without a designated result (3x5 =?). The number of cards corresponds to the multiplication table from 1 to 10 (remember that some of them are paired - 3x6 is identical to 6x3). Progress of the game - the child pulls out a card and gives an answer to the question. If the result is negative, the card is returned to the unused pile. Encourage your child not only to answer the question correctly, but also to surpass his previous result in correct answers. In the future, the game can be complicated by limiting the time for giving the correct answer.

Option 2

The initial parameters are the same - cards with numbers. Here are just the answers to them. And the child must think carefully and name a bunch of numbers, multiplying which will give the following result (12 = 2x6 = 6x2 = 3x4 = 4x3). The correct answers can be placed on the back of the card. At the same time, the completeness of the answer should be appreciated.

This option is more difficult both for the child - to remember all possible combinations, and for the parents - they cannot “lose face in the mud” when making the game.

To do this, we will need cards with ready-made answers and a 10x10 playing field (analogous to the Pythagorean grid) with painted cells and marked markings. The student must correctly place the answer cards in the shaded cells.

Option 4

Reverse to option 3, except that the child must recreate the image on the playing field.

Both options are reminiscent of a Japanese crossword puzzle, the secrets of solving which can be read on our resource. There you can also find links to sites that will suggest possible fun images for the playing field. ( insert a link to the desired topic)

Life examples

Use real-life examples to teach. “How many legs do 2 giraffes have?” (4x2=?), “For the holiday, 3 girls were given 2 dolls. How many dolls did the girls have? (3x2=?), etc.

You can take a couple of mugs and put 5 cherries in them, asking your child to count the total number of cherries in the mugs. And so on.

With the best free game you learn very quickly. Check it out for yourself!

Learn multiplication tables - game

Try our educational e-game. Using it, tomorrow you will be able to solve mathematical problems in class at the blackboard without answers, without resorting to a tablet to multiply numbers. You just have to start playing, and within 40 minutes you will have an excellent result. And to consolidate the result, train several times, not forgetting about breaks. Ideally, every day (save the page so as not to lose it). The game form of the simulator is suitable for both boys and girls.

Result: 0 points

See the full cheat sheet below.

Multiplication directly on the site (online)

How to multiply numbers in a column (mathematics video)

To practice and learn quickly, you can also try multiplying numbers by column.