Not everyone needs higher mathematics in life. But if a child has mastered the multiplication table, then it just cannot happen that it would ever come in handy to him somewhere. At least in his youth, at least later, he will definitely need such knowledge. They may be required at any time in the home environment when solving everyday problems, during shopping and market trips, and when paying for utilities and other services. Whatever the child becomes when he becomes an adult: a laborer, businessman, production worker, scientist, minister, without such knowledge it is simply impossible to imagine a work process. And it’s not always and everywhere convenient to carry a calculator. But how easy is it to remember the multiplication table for a small person, and for adults - to help him with this? To optimize the process allow some fun tricks and exciting games.
Halve the work
Everyone knows how to find the result from the table where the vertical left with the 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 many a family of eight will be, we must first find 7 in the left vertical column and draw a horizontal imaginary line to the right of it from the mind. Next, you need to find 8 in the upper row and from it lower the perpendicular down. At the intersection of such lines, the result will be visible. It is easy to verify that it is 56, which corresponds to reality. Such tables are often used. They are convenient in that they allow you to compactly write the multiplication table and easily find the result from it. This system of numbers is well known to primary school students and is studied by them in the classroom.
Carefully looking at the table of multiplication of numbers from 1 to 10 above, you 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 at the bottom, that is, the diagonal, then the numbers will be displayed in 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 calculations 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 to reproduce, changing the factors in places.
It will be easier for the child to find the result when multiplying the numbers 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 by 8 is much easier to calculate than taking 8 times by 4.
Sometimes it’s more convenient to start from the end
Multiplying the number by 1 in children usually does not cause problems, because as a result, this number will necessarily turn out. But when the child learns this simple rule, you should immediately explain to him that with a multiplication by 10 he also can’t have any difficulties, because doing it is almost as easy. Performing these calculations, you just need to ascribe 0 to the very number in the mind or on paper.
This convenience can be used a little later, helping to easily remember the multiplication table by 9. How to do this? We assign zero to the original digit and subtract this number from the resultant.
We give an example by multiplying 6 by 9. Assign 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 will help your fingers
Without difficulty, the fingers help to master this science. Starting the story about how easy it is to remember the multiplication table, namely its difficult part, when it comes to multiplying by 9, we put both hands on the table in front of us with our palms facing its surface. And number the fingers from left to right, assigning them numbers from 1 to 10.
Now imagine that you need 4 times 9. To do this, 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, we note that three fingers remained not bent on the left. It will be dozens of our number. And on the right we see six fingers. This will become the units of the desired result. Total we get the number 36. As you know, 4 x 9 and it will be exactly the same.
You can verify that this technique works in all other cases. That is, when multiplying 1 by 9, there will be no bent fingers on the left, and nine on the right. So, the desired number will be 9 (0 tens and 9 units), which is correct by all mathematical laws.
And one more example. Multiply 6 by 9. Bend the sixth finger to the left. This will turn out to be the thumb of the right hand. Five dozens remain on the left, and four units on the right. So, our number will be 54. And this is the correct answer.
Here is a way to make it easier for a child to remember the multiplication table with such a large and uncomfortable number of 9.
Squares of numbers
Considering the table at the beginning of the article, we pay special attention to its elements marked in red. They are located diagonally from left to right. These numbers are the result of multiplying the digits themselves from 1 to 10.
And this is expressed by all the 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 primary school do not yet know that such an action is tantamount to squaring. But if at this stage of training pay attention to this circumstance, then later it will be more convenient for them to assimilate it.
How easy is it to remember the multiplication table in such a case? We 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 clear that a square will be obtained, 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 peculiar 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 box. It reflects the number of cells and is simultaneously shown by the area of ​​the drawn square.
Row of square differences
What is more convenient to remember the squares of numbers? Note that the results of multiplying the numbers by yourself, given above, differ from each other as follows.
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; nine; eleven; 13; fifteen; 17; 19.
We found the differences, they are members of the resulting series. In this sequence, each number that follows goes from the previous one by 2. This means that the square of each next number increases compared to the square of the number, which is one less, by a certain difference. And she, in turn, changes in each subsequent case by two, becoming larger.
If you point out a similar property to your child, this will be another way of remembering the multiplication table quickly and easily. Numbers have interesting patterns, and knowing such interesting tricks in learning gives a much better result than dumb memorization of logically unrelated numbers. This can be presented to a child in the form of a game, which, incidentally, can not only turn out to be fascinating, but also help to practice the oral score.
Small numbers
How easy is it to remember the multiplication table by 2 and 3? This is usually easy to do with a child. Small numbers, as a rule, do not cause difficulties in children. If you multiply two by factors from 1 to 10, you still cannot 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 remember the multiplication table by 2.
In the same way, you should train with tripling the numbers by connecting another family member, 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 reception. And in this case, the process is facilitated by the fact that on each of the hands of a person there are five fingers. And this is convenient when calculating and forming the result in the student’s memory. Explaining this to a child, it is very appropriate 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.
Simple factors and signs of divisibility
You should pay special attention to the fact that if you multiply by 5 any of the numbers, even if it is much more than 10, you always get a product that ends in writing 0 or 5. This will further help the little student to learn signs of divisibility by 5.
The same thing is useful to do with numbers 2 and 3. How easy is it to remember the multiplication table for given numbers? Constantly indicating that when doubling any number, the calculation result all the time ends with the numbers 2; 4; 6; eight; 0. And when tripling comes out a work, the constituent digits of which in the sum are always divided by three.
Then you can start multiplying by 6, proving to the child in practice that, by 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 remember the 8 times table? It is convenient to show here that the correct answer is obtained by triple doubling any number taken. Similarly, multiplying by four, double the original should be doubled.
Prime number 7
Among the numbers from 1 to 10, for many children, the seven is unexpectedly difficult, precisely because it is a prime number. Although such a statement and looks like a pun. Yes, from the point of view of mathematics, seven is simple, like all other numbers that, except themselves and ones, have no divisors. And, of course, in view of this, it is difficult to multiply by it. Indeed, for 7 those principles that have just been applied for 6 and 8 are not suitable.
But given the number 7 indicated, how easy is it to remember the multiplication table? The game will help your child deal with a rebellious number. But what is needed for this?
Consider a very interesting thing - a dice. It has six faces and is endowed with a wonderful property: the number of points on its opposite sides always add seven when added. Therefore, to calculate the sum of the numbers marked on all faces, 3 x 7 is enough. This will be 21. If you take a few cubes, to calculate the number of points on its sides, it will be enough to total 21 times the number of these playing devices.
When dealing with a child, you should collect such items as much as possible. Throwing the cubes, 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, on all sides, and so on, comparing each other's results during the game. At the same time, of course, in adults who know the secret of these mysterious objects, the calculations will be performed surprisingly quickly, and the answer will be calculated at a magic speed. At the end of the competition, a secret should be revealed to the child who will no doubt be surprised at such abilities. And at the same time explain how the calculation is made, inviting him to try it himself. This is an easy way to remember the multiplication table when it comes to a complex number like 7.
Multiplication by numbers greater than 5
Of particular difficulty in young children, of course, are numbers greater than 5 and their multiplication by each other. 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 correctly recognize the product of the two indicated numbers, starting from 6 and ending with 10.
So how easy is it to remember the multiplication table on the fingers? They should be numbered again, but in a different way, not as when applying the method of multiplying by only 9, which was considered earlier. Here, the thumbs on both hands are assigned the number 6, the index - 7, the next middle - 8, the nameless - 9, and the little fingers - 10. The numbering scheme is shown in the picture below.
To find the product, fingers are connected with the numbers of the desired numbers. A figure indicating dozens of the desired number is calculated as follows: two connected fingers plus the lower ones from them. And units are found by multiplying the upper ones.
In the illustration below, you can consider in more detail: how to multiply 8 by 9. The fingers with the corresponding numbers are connected. Next, the number of tens, seven of them, is calculated. Units are found by multiplying the number of upper fingers. And that means: 2 x 1 = 2. Total in the answer is the number 72, which is true.
There are more complicated cases. For example, try to calculate 6 x 6. In this case, you have to connect your thumbs, and the number of tens should seem to be 2, although this is not true. But the main difficulties in the calculation immediately become apparent when you have to determine units and multiply the numbers of the upper fingers of both hands. Here 4 x 4 = 16, which is no longer a digit, but a two-digit number. To get the correct answer, add two dozen 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, the number is greater than 9.
If the child learns the described techniques, he will immediately understand how easy it is to remember the multiplication table.
Writing math 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 by nature lyrics. And no matter how much they explain to them the logic of multiplication of numbers, they are little able to understand and remember. Therefore, there are little students for whom it is easy to remember the multiplication table in verse. How to do it better?
First of all, you should pay attention to the child that some problems with multiplication and the answers to them rhyme on their own.
Here are some examples of this:
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 from them.
Here, as an example, consider the table of multiplication by 7. And the rhyme may be like this:
A family of two - fourteen, I want to become a scientist;
Family of three - twenty-one, we will persistently sit;
A family of four - twenty eight, we will decide for ourselves, we won’t ask anyone;
A family of five - thirty-five, a hundred times I will repeat again;
A family of six - forty-two helps me learn words;
A family of seven - forty-nine, the main work to do;
A family of eight - fifty six, I'm sure it is;
A family of nine is sixty-three, and rightly so, whatever you say.
The most important thing when implementing this method for parents is to understand that children do not need to offer ready-made rhymed lines, forcing them to memorize them thoughtlessly. It is better to try to compose your poems together and pick up successful rhymes. Only then can we talk about the belief that the child will perfectly memorize the multiplication table and remember it for the rest of his life.