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How to learn the multiplication table on your fingers. Finger multiplication. Entertaining mathematics

In the summer, Arina must learn the multiplication table. She already knows up to 5, and then the set of numbers is a little more complicated. Today we discovered a curious method of multiplication on the fingers. Understood. Arina is delighted, and I am somewhat surprised why the school did not know about this! I share.


Turn your hands with your palms facing you and assign the numbers 6 to 10 to each finger, starting with the little finger.

Now let's try to multiply, for example, 7x8. To do this, connect the number 7 finger on the left hand with the number 8 finger on the right.

And now we count the fingers: the number of fingers under the connected ones is tens.

And the fingers of the left hand, remaining on top, are multiplied by the fingers of the right - these will be our units (3x2 = 6). The total is 56.

Sometimes it happens that when multiplying “units”, the result is more than 9. In such cases, you need to add both results in a column.

For example, 7x6. In this case, it turns out that the "units" are equal to 12 (3x4). Tens equals 3.

3 (tens)
+
12 (units)
________
42

Multiply by 9

Again turn the palms towards you, but now the numbering of the fingers will go in order from left to right, that is, from 1 to 10.

Now we multiply, for example, 2x9. Everything that goes up to finger number 2 is tens (that is, 1 in this case). And all that remains after finger number 2 is units (that is, 8). As a result, we get 18.

Being able to multiply on your fingers is a valuable skill, and mankind has known how to count multiplication tables on your fingers since at least the 15th century. We may have mobile calculators, but in many cases, it's actually easier to keep your phone in your pocket and multiply on your fingers. This technique can also be helpful for toddlers who have trouble learning endless math formulas.

You can start learning the multiplication table on the fingers after the child knows the multiplication from one to five. Already on the basis of this knowledge, you can develop a skill in the literal sense of manual multiplication. So let's get started?

Multiplication table on fingers: nine

Hold your hands in front of you with palms up. Each of your ten fingers represents a number. Moving from the thumb of the left hand to the thumb of the right hand, count the numbers from one to ten.

Point the finger corresponding to the number you want to multiply by nine down towards your body. So, for example, if you want to decide how much 9x3 will be, you will need to hold the middle finger with your left hand. The middle finger represents the number three, because if you count your fingers from one to ten, starting with your left thumb, your middle finger is the third one.

We make a count

The problem is solved by counting fingers to the left and to the right. First, count the fingers to the left of your bent finger - in this case there will be two. Then count the fingers to the right of your bent finger - in this case it should be seven. The first digit of the answer is two, and the second digit is seven. So the answer is 27!

This is how the multiplication table for 9 works on the fingers. Try it with other multiples of nine. How would you multiply 9 by 2? How about 9 by 7? This method is incredibly simple and understandable even for kids. As practice shows, children are more willing and successful in learning mathematics, knowing this interesting way to calculate the product of two numbers!

Multiplication table on fingers for six, seven, eight and ten

Hold your hands so that your palms are facing your body and your fingers are facing each other. Again each finger will represent a number. Your little finger represents the number six. The ring finger will be seven, the middle finger eight. The index fingers of your hands will symbolize the nine, and your thumbs will symbolize the ten. So, how to learn the multiplication table on your fingers?

Calculation scheme

For example, if you want to calculate what 7 * 6 will be, you need to touch the ring finger of your left hand (since it represents the number on the left) with the little finger of your right hand, since it represents the number on the right. Again, remember that each finger represents a number, in which case your ring finger represents seven and your little finger represents six. Therefore, you need to connect them to solve this mathematical problem.

You may have to bend your wrist in weird ways to calculate the product of two numbers! Who said it would be easy?

In order to make sure that you have correctly understood the technique of the multiplication table on the fingers of six, seven, eight and ten, check yourself. If you need to calculate what the product of 9 and 7 will be, then which fingers would you connect? Think! The answer will be in the next sentence.

So, consider that you have learned the finger multiplication table for six, seven, eight and ten, if as an answer, which fingers you need to connect in order to calculate what the product of 9 and 7 is, you chose the index finger of your left hand and the ring finger finger of the right hand. It's a matter of small!

How to count?

The next step is to simply count the fingers that are touching as well as the fingers underneath. They will represent decimal numbers. In this case, you will count the ring finger on the left hand, the little finger on the left hand, and the little finger on the right hand. Each finger you count will equal 10. In this case, the total is 30.

Multiply the remaining fingers. The next step is to add up the number of fingers on each hand, not counting the fingers that touch each other. First count the number of fingers on the left hand that are above the touching fingers - in this case there will be 3. Then count the number of fingers of the right hand above the touching fingers - in this case there will be 4. 3 * 4 \u003d 12. Add the two numbers together, to find your answer. In this case, you need to add 30 to 12. The total will be 42. If 7 is multiplied by 6, then the answer will be 42!

The multiplication table on the fingers may seem complicated at first, however, if you carefully understand it, then learning it is much easier than the endless formulas in a real mathematical table.

Multiply by 10 using the same method. For example, if you want to find the answer, which is 10 times 7, then start by touching the thumb of your left hand to the ring finger of your right hand. Count the number of fingers under the connecting fingers, including fingers that touch each other. You should have a total of 7, which means 70. Then count the number of fingers above the touching fingers of the right and left hands. There should be 0 on your left and 3 on your right. Now multiply 3 by 0 = 0 and add 70 to 0 for the answer. The answer is 10 times 7 = 70!

Outcome

Try it with other multiples of six, seven, eight, and ten. How would you multiply 8 and 8 with your fingers? What about 8 and 10? If you are interested in the question of how to teach the multiplication table on the fingers of your child, then just try to include the practice of counting the product of various numbers in your daily routine. You will not even notice how the baby will begin not only to quickly count the product of two numbers, but also eventually remember the multiplication table.

This is the whole attraction of this method - it is fun, makes you think logically, turn on mathematical abilities and at the same time develops memory. What could be better for a child? Let's finally calculate what the product of 6 and 10 will be? What about 8 and 9? What about 7 and 8? Here's some fun math.

Not everyone needs higher mathematics in life. But if a child has mastered the multiplication table, then it simply cannot happen that it will not come in handy sometime and somewhere. At least in his youth, at least later, he will definitely need such knowledge. They may be required at any time at home when solving household problems, while going to shops and the market, when paying for utilities and other services. Whoever a child becomes when he turns into an adult: a laborer, a businessman, a production worker, a scientist, a minister, without such knowledge it is simply impossible to imagine the work process. And it is not always and everywhere convenient to carry a calculator with you. But how easy is it for a little person to memorize the multiplication table, and for adults to help him with this? Some fun tricks and exciting games allow you to optimize the process.

Cut the work in half

Everyone knows how to find the result according to the table, where the vertical left edge and the topmost line are cells filled with numbers from 1 to 10. And children learn to use it usually easily and without difficulty. For example, if we need to find out how much seven eight will be, we must first find 7 in the left vertical column and draw in our mind a horizontal imaginary line from it to the right. Next, you need to find 8 in the top row and lower the perpendicular down from it. At the intersection of such lines, the result will be visible. It is easy to verify that it is equal to 56, which is true. These tables are used frequently. They are convenient in that they allow you to compactly write down the multiplication table and easily find the result from it. This system of numbers is well known to elementary school students and is studied by them in the classroom.

Looking carefully at the multiplication table for numbers from 1 to 10 above, one can notice one interesting thing. It is a square, and if you draw an imaginary line from the left extreme corner at the top to the right extreme bottom, that is, the diagonal, then the numbers will be displayed into each other through it, as in a mirror. This shows a very important property of multiplication: when the factors are rearranged, the result of the calculation never changes. For example: 4 x 8 = 24, and also 8 x 4 = 24.

From this we conclude: how to remember the multiplication table quickly and easily? It is possible to halve the effort by memorizing the numbers of only the upper of the formed triangles. And the rest of the data is reproduced by changing the multipliers in places.

It will be easier for the child to find the result when multiplying numbers up to 10, if the smaller of them is put in the first place. This is usually taught in Japanese schools. It is believed that 4 times 8 is much easier to calculate than taking 8 times 4.

Sometimes it's better to start from the end

Children usually have no problems multiplying a number by 1, because the result will necessarily be the number itself. But when the child learns this simple rule, you should immediately explain to him that he cannot have difficulties with multiplying by 10 either, because it is almost as easy to do. When making these calculations, you simply need to attribute 0 to the number itself in your mind or on paper.

This convenience can be used a little later, helping to easily remember the multiplication table for 9. How to do this? We assign zero to the original number and subtract this number from the resulting number.

Let's give an example by multiplying 6 by 9. We add zero to the six and get 60. Then we subtract 6 - and 54 comes out. And so with all the other numbers.

Multiply by 9 with your fingers

Fingers help to master this science without difficulty. Starting a story about how easy it is to remember the multiplication table, namely that difficult part of it, when it comes to multiplying by 9, let's spread out both hands on the table in front of us with palms to its surface. And let's number the fingers from left to right, assigning them numbers from 1 to 10.

Now imagine that you need to multiply 4 by 9. To do this, we bend the one of the fingers that has the fourth number, that is, the index on the left hand. This process is illustrated in the picture. To find the desired result, let's pay attention to the fact that three fingers remained uncurved on the left. These will be the tens of our number. And on the right we see six fingers. This will become the units of the desired result. In total, we get the number 36. As you know, 4 x 9 will be exactly the same.

It can be verified that this technique works in all other cases as well. That is, when multiplying 1 by 9, there will be no bent fingers on the left, and nine of them will remain on the right. This means that the desired number will be 9 (0 tens and 9 units), which is correct according to all mathematical laws.

And one more example. Multiply 6 by 9. Bend the sixth finger on the left. This will be the thumb of the right hand. There are five tens on the left and four ones on the right. So our number will be 54. And this is the correct answer.

Here is a way to make it easier to remember the multiplication table for a child with such a large and uncomfortable number 9.

Number squares

Considering the table given at the beginning of the article, let's pay special attention to its elements marked in red. They are arranged diagonally from left to right. These numbers are the result of multiplying by themselves the numbers from 1 to 10.

And this is expressed by all known equalities:

1 x 1 = 1; 2 x 2 = 4; 3 x 3 = 9; 4 x 4 = 16; 5 x 5 = 25; 6 x 6 = 36; 7 x 7 = 49; 8 x 8 = 64; 9 x 9 = 81; 10 x 10 = 100.

Children in elementary grades do not yet know that such an action is tantamount to squaring. But if at this stage of training attention is paid to this circumstance, then later it will be more convenient for them to learn it.

How easy is it to remember the multiplication table in such a case? Let's explain this clearly for the multiplication of 7 x 7.

You should draw a rectangle, the length and width of which are seven cells, and number each of them. It is quite clear that a square will turn out, and the number of cells will be its area. In life, it is measured in square centimeters, meters, kilometers, and so on, that is, also in a kind of squares, but of a different and different size. And the desired result of the action, that is, 7 x 7, will be written in the very last, lower right cell. It reflects the number of cells and is simultaneously shown by the area of ​​the drawn square.

Series of differences of squares

What is the best way to memorize square numbers? Note that the results of multiplying numbers by themselves, given above, differ from each other in the following way.

4 - 1 = 3; 9 - 4 = 5; 16 - 9 = 7; 25 - 16 = 9; 36 - 25 = 11; 49 - 36 = 13; 64 - 49 = 15; 81 - 64 = 17; 100 - 91 = 19.

Total, there is a sequence of numbers: 3; 5; 7; 9; eleven; 13; 15; 17; 19.

We have found the differences, and they are members of the resulting series. In such a sequence, each subsequent number differs from the previous one by 2. This means that the square of each next number increases compared to the square of the number that is one less, by a certain difference. And it, in turn, changes in each subsequent case by two, becoming larger.

If you point out a similar property to a child, this will be another way to remember the multiplication table quickly and easily. Numbers have interesting patterns, and knowing such interesting tricks in learning gives a result much better than stupid memorization of logically unrelated numbers. This can be presented to a child in the form of a game, which, by the way, can not only be exciting, but will help to practice mental counting.

small numbers

How easy is it to remember the multiplication table for 2 and 3? This is usually easy to achieve when working with a child. Small numbers, as a rule, do not cause difficulties for children. When multiplying two by factors from 1 to 10, you still won’t get more than 20. And here you just need to learn how to double. This can be achieved by sitting next to the child and counting using the fingers of two pairs of hands. Here's how easy it is to memorize the multiplication table by 2.

In the same way, you should train with tripling the numbers, connecting one more of the family members, as well as friends of the son or daughter, to a similar game.

Multiplying by five, it is most convenient and correct to also resort to the same kind of trick. And in this case, the process is facilitated by the fact that a person has five fingers on each of the hands. And this is convenient when calculating and forming the result in the student's memory. Explaining this to a child, it is very appropriate here to delve into the history of mathematics. You can talk about how the decimal system of calculus arose in ancient times. And that this is due to the number of human fingers counted on one and two hands.

Prime Factors and Divisibility Tests

The child should pay special attention to the fact that when multiplying by 5 any of the numbers, even if it is much more than 10, you always get a product that ends in 0 or 5 in its writing. This will later help the little student to learn the signs of divisibility by 5.

It is useful to do the same with the numbers 2 and 3. How easy is it to remember the multiplication table for these numbers? Constantly pointing out that when any number is doubled, the result of the calculation always ends with the number 2; 4; 6; 8; 0. And when tripled, a product comes out, the constituent figures of which in the sum are always divisible by three.

Then you can start multiplying by 6, proving to the child in practice that when performing this action, you first need to triple the original number, and then double it (or vice versa), because the number 6 itself is made up of factors 2 and 3.

How easy is it to memorize the multiplication table for 8? Here it is convenient to show that the correct answer is obtained by doubling any given number three times. Similarly, multiplying by four, doubling the original should be twice.

prime number 7

Among the numbers from 1 to 10, seven turns out to be unexpectedly difficult for many children, precisely because it is a prime number. Although such a statement seems like a pun. Yes, from the point of view of mathematics, seven is prime, like all other numbers that, apart from themselves and one, have no divisors. And, of course, in view of this, it is difficult to multiply it. After all, the principles that have just been applied to 6 and 8 are not suitable for 7.

But given what was said about the number 7, how easy is it to remember the multiplication table? The game will help the child cope with the recalcitrant number. But what is needed for this?

Consider a very interesting thing - a dice. It has six faces and is endowed with a remarkable property: the number of points on its opposite sides, when added, always gives seven. Therefore, to calculate the sum of the numbers marked on all faces, 3 x 7 is enough. This will be 21. If you take several dice, to calculate the number of points on its sides in the sum, it will be enough to multiply 21 by the number of these playing devices.

When working with a child, you should collect as many of these items as possible. When throwing dice, you must first offer the little student to count the numbers that fell on their upper and lower faces, adding them up. Then on the sides, all sides, and so on, comparing the results of each other during the game. At the same time, of course, in adults who know the secret of these mysterious objects, the calculations will be surprisingly fast, and the calculation of the answer will occur at magical speed. At the end of the competition, the secret should be revealed to the child, who will no doubt be surprised by such abilities. And explain at the same time how the calculation is made, inviting him to try it himself. This is the easy way to remember the multiplication table when it comes to a complex number like 7.

Multiplication by numbers greater than 5

Especially difficult for young children, of course, are numbers greater than 5 and their multiplication. But to easily cope with this task, fingers can again come to the rescue. It should be assured that there are ways to always find the answer to any question posed, solve examples and accurately find out the product of two indicated numbers, starting from 6 and ending with 10.

So how easy is it to remember the multiplication table on your fingers? They should be numbered again, but in a different way, not as in the application of the technique of multiplying only by 9, which was discussed earlier. Here, the thumbs on both hands are assigned the number 6, the index fingers - 7, the middle fingers following them - 8, the ring fingers - 9, and the little fingers - 10. The numbering scheme is shown in the picture below.

To find the product, fingers with the numbers of the desired numbers are connected. The number indicating the tens of the desired number is calculated as follows: two connected fingers plus the lower ones from them. And the units are found by multiplying the upper ones.

In the illustration below, you can see in more detail: how to multiply 8 by 9. Fingers with the corresponding numbers are connected. Next, the number of tens is counted, there are seven of them. Units are found by multiplying the number of upper fingers. So: 2 x 1 \u003d 2. In total, the number 72 comes out in the answer, which is correct.

There are also more difficult cases. For example, let's try to calculate 6 x 6. In this case, you have to connect your thumbs, and the number of tens seems to be 2, although this is not true. But the main difficulties in counting immediately become apparent when you have to determine the units and multiply the numbers of the upper fingers of both hands. Here 4 x 4 = 16, which is no longer a number, but a two-digit number. To get the correct answer, add two tens and the number 16. As a result, we get 36, which is the correct answer. This should be done every time when multiplying the upper fingers turns out to be a number greater than 9.

If the child learns the techniques described, he will immediately understand how easy it is to memorize the multiplication table.

We write mathematical poems

All children are known to be different. And they all have their own abilities. Some of them perfectly operate with numbers and learn their laws. Others are lyricists by nature. And no matter how much you explain the logic of multiplying numbers to them, they are little able to understand and remember. Therefore, there are small students for whom it is easy to remember the multiplication table in verse. How to do it better?

First of all, the child's attention should be drawn to the fact that some problems with multiplication and the answers to them rhyme on their own.

Here are some examples of this:

    five five - twenty five;

    six six - thirty six;

    seven five - thirty five;

    nine five - forty five.

But even if the tasks do not immediately add up to rhymes, then you can add them, that is, add phrases, thereby creating a poem out of them.

Here, as an example, consider the multiplication table for 7. And the rhyme can be like this:

Family two - fourteen, I want to become a scientist;

A family of three - twenty-one, we will sit stubbornly;

Family four - twenty-eight, we will decide for ourselves, we will not ask anyone;

A family of five - thirty-five, a hundred times I will repeat again;

A family of six - forty-two, help me learn words;

Family seven - forty nine, the main thing is to do the work;

Seven eight - fifty-six, I'm sure it is;

Seven nine - sixty three, and that's right, whatever you say.

The most important thing in implementing this method for parents is to understand that children should not be offered ready-made rhymed lines, forcing them to mindlessly memorize them. It is better to try to compose your own poems together and pick up good rhymes. Only then can we talk about the confidence that the child will perfectly memorize the multiplication table and remember it for the rest of his life.

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

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

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

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

Easy Ways to Teach Kids the Multiplication Table

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

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

memorization

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

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

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

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

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

Visualization

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

It can be:

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

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

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

With the help of pictures

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

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

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

On fingers

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

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

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

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

Through educational cartoons and programs

Of course, educational cartoons, applications on mobile devices and programs on a PC can be used as visualization tools, if there is such an opportunity and parents are not against such a pastime for the child.

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

A game

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

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

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

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

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

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

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

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

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

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

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

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

How to fix the result?

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

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

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

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

How to help your child learn and remember information faster?

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

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

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

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

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

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

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

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

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

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

How to teach a child to deal with complex examples?

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

Explain to the child what is necessary in this case:

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

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

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

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

There are different ways to do this:

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

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

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

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

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

So, in no case should you:

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

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

I welcome you to this page! Today we will talk about multiplication...Oh, this multiplication table.

From year to year, both at school and now, as a tutor, I meet the same problem: students do not know the multiplication table. And this is not only an elementary school, but also students of the 9th, 10th and even 11th grades. And so today I decided to devote time to her - the Multiplication Table.

Students very quickly remember the table for 2, 3, 4, 5, but then - ... There are not so many ways to learn the table)) For example, you can learn the multiplication table for 6,7,8 and 9 with your fingers. And just don't say that it's a shame to count on your fingers))) IT'S NOT SHAME!!! After a long use, you will finally remember the entire table and you will no longer use fingers for counting ...

We'll be using both hands to study the table, so get rid of them and let's get started.

I'll start from the end Let's look at multiplying by 9:

To begin with, let's agree and designate the fingers with numbers, as in the picture:

9*2=18 Bend the finger at number 2. The number of fingers on the left is tens, the number of fingers on the right is ones. In our case, there is one finger on the left, eight on the right, and this is how we get the number 18.

9*3=27 (two fingers on the left and seven fingers on the right)

9*4=36 (three fingers on the left and six fingers on the right)

Etc. if you check the multiplication of nine or the rest of the numbers, make sure that this method works. And it's easy to remember.

Now let's talk about multiplying by the numbers 6, 7 and 8.

Let's number the fingers of our hands again, only in a slightly different order.

When multiplying, we connect the fingers of the corresponding numbers.

8*7=56 (we connect the 8th finger of the left hand and the 7th finger of the right hand, although vice versa is possible)

As a result, from below we get tens (connected fingers are also counted), and from above - the number of fingers of the left hand must be multiplied by the number of fingers of the right hand and add the resulting number to tens))

In our case, there are 5 fingers at the bottom, 2 * 3 = 6 at the top. Therefore 50+6=56

Let's try again:

6*9=54 (connect the 6th finger of the left hand and the 9th)

In our case, there are 5 fingers at the bottom, 1 * 4 = 6 at the top. Therefore 50+4=54

One more example: 6*6=36 (we connect the 6th finger of the left hand and the 6th)

In our case, there are 2 fingers at the bottom, 4 * 4 = 16 at the top. Therefore 20+16=36

  1. The process of studying the table needs to be turned into a game.
  2. In no case do not try to learn the table in one day.
  3. Start this process with interest and understanding why you need it.
  4. Celebrate your successes, praise yourself for each of your victories.
  5. If you don't feel like studying today, skip class. But do not forget, only your intention and regular training will give the desired result.
  6. 10-15 minutes every day the multiplication table will become your assistant when studying other topics in mathematics.

Make your own cards Write the example on one side and the answer on the other. Use colored cardboard for cards (to make it easier to separate cards by certain numbers). Shuffle the studied cards and, pulling out one by one, put the cards in two piles: in one - those that you answered correctly, in the other - answered incorrectly.

You can download here a blank for such cards (I printed it on colored self-adhesive paper, cut it out and glued it to cardboard). , .

If you are too lazy to make cards yourself - order them from us) In the near future we will upload a product description and price information.

You can apply for cards now. To do this, write in the comments to this article or through the form on the Contacts page.

Play with classmates, relatives and friends, the one who gave the most correct answers wins. Play for time, 5 minutes is a great result for the whole table. Play backwards, select cards with the same answers and name as a result of multiplying which numbers you can get this answer.

In general, it all depends on your imagination. If you have your own way of using cards - write in the comments, maybe your way will help someone cope with the table faster.

And of course there is many computer simulators, which can be downloaded not only to a computer, but also to a phone. You can find links to them on the Internet.

P.S. In the near future I will upload a link to one of these simulators, developed by my team. You may like this method better. Therefore, bookmark this page to be one of the first to try the simulator.

I wish you good luck in such an important matter as learning the multiplication table! And believe me, having learned it, many topics will be given much easier!