Preparation for school

How to remember the multiplication table by 4. Four methods of multiplication without a calculator. Poems, songs, stories

Almost all parents whose children went to school face early and late with the need to remember long-forgotten school disciplines to help the child understand them or learn something.

And one of the first serious tasks, as well as one of the first problems, becomes a multiplication table, which is often asked for children for self-study for the summer after the first class.

In this case, the task of parents is to explain to the child the basic principle of mathematical action and correctly convey to it the essence of multiplication so that he learned the table calmly, easily and quickly without monotonous and boring jar.

Sometimes it happens that the baby also did not go to school, but Mom wants him to multiply in the mind, at least three-digit numbers. Of course, among children there are small adderkinds, which are really capable of it and can assimilate not only the multiplication table at an early age, but also begin to extract the root square or solve complex equations from numbers. However, it is rather an exception to the rules.

Basically, even the younger schoolchildren table multiplication is not easy and creaked, because it usually explains it as an incomprehensible and boring set of numbers that for some reason must be remembered. What to say in this case about reoxoys.

So, if your baby is not a mathematical genius, then it is not necessary to prematurely download it to studying the multiplication table. Since the development of this skill is required only in the second grade school, it is recommended to acquaint a child with a multiplication table and the principle of its action not earlier than seven-eight-year-old age.

Nevertheless, you can prepare a baby, explaining to him the mathematical meaning of multiplication after it fell down addition and subtraction.

Every child is mastering mathematics in his own way: someone has a good mechanical memory, therefore he remembers everything faster and memorizes, others need to reinforce information with a visual or emotional perception, that is, to use for training cards with drawings, items, toys, poems and songs. The same applies to the filing for a child multiplication table.

In order for the baby to be not difficult in the middle of the school year, the table is usually set for independent acquaintance of the summer holidays.

Be sure to help the child understand, but be prepared for what you need to make a lot of work, as well as to be patient.

Some nuances and important moments

It is also necessary to understand that it is possible to start studying the table only when the child is already creating basic mathematical actions. That is, he knows how well and confidently:

consider at least to one hundred - in the usual and reverse order;
distinguish simple numbers, numbers and dozens;
understand the number of numbers;
fold and deduct
to understand the principle of multiplication, be able to replace addition by multiplication and vice versa.

Modern children do not always understand why they generally memorize the table, which is often served in schools, like mathematical abracadabra, is easy and quickly calculating on the calculator or get the answer from the computer / tablet / phone.

Your task is to find a significant motivation for the child, explain to him, for which such knowledge, skills and skills are needed, how can they help later in their studies and in life, what benefit can be learned.

Try to find your arguments on the example of the following eloquent arguments:

the principle on which the multiplication table is being built, and having learned it, the child will quickly carry out any calculations, operate with large and multigalous numbers in the mind - this will give him an advantage in school and will make it possible to cope with mathematics tasks much faster;
even at first he will need a crib or paper to make a calculation, then the result will be found only with your own knowledge and memory - without the use of assistance in the form of an electronic device;
such knowledge helps to develop and improve "mathematical intuition", train memory, strengthen the intelligence and speed of brain reactions;
the multiplication table is one of the basic mathematical operations, so without it it will not be possible to master more "deep water" in this discipline.

How to learn? Go to practice

Deciding with the age and readiness of the child, you can select the methodology for which you want to train it.

In order for the choice to be the most optimal and effective for your baby, it is worth introducing the most basic techniques and methods of studying the table, and also to understand what rules should be adhered to to obtain a good result.

We are looking for the right approach to the child

In any learning, the main thing is the systemality and sequence of actions. If you came up with a child behind the table, then study it regularly, repeating each time passed.
Do not make your baby learning and do not sit by force. Try to understand what his failure is connected - perhaps the child is just tired, wants to eat, it feels bad or sick. Then set aside the occupation or transfer it to another time.
Some kids are very hard for a long time to sit in one place - they love to move all the time and need a frequent change of classes. In this case, standard classes will not suit, but you can learn a sign and while walking or playing, and on a swing, and on the way home.
Motivate the child to study - find exactly the key that will become incentive for him.
In no case are not going around, do not shout and do not scold for mistakes or misunderstanding. It is impossible to blow a child with bad memory, inability to learn anything, etc. Moreover, it is unacceptable to resort to physical punishments.
Another common parent error is to scare bad estimates or compare the baby with other kids, exposing it in an unsightly light. It is completely wrong, because every child is a person with its individual pace and the peculiarities of development.
Objectively evaluate the knowledge and abilities of your baby - if he is not mathematical, and the humanitarian warehouse of the mind, then look for the approach and the methodology that it is optimally suitable for him and give the greatest effect.
For example, for children, easily stored poems, you can come up with or find thematic rhymes for each figure - this will help the child and simplifies the memorization process.
If the baby has a figurative or associative thinking, find the association with it to all cliffs, compose stories, make illustrations or sketches.
Young musicians will help songs - suggesting them, it will remember much easier and will remember that forty-eight will be forty, and the family three is twenty-one.
Make breaks often in class so that the child rested.
Do not understand the literally statements in some methods - "learn the table for three hours" or something like that. Remember how you were given a multiplication table at one time, and then proceed to classes with your own child.
Do not forget to praise the baby for every small or great success and progress.

We start quickly and easily learn by the methodology

Let's look at one of the most effective learning techniques, according to which the child will get acquainted with the multiplication table in four days, it will understand the principle of its action and will permanently go, what is multiplication and why it is necessary.

If you explain briefly, the specific meaning of multiplication is the simple replacement of the amount of the same terms in one action.

It is this approach that is correct, because if a child suddenly forget some table example, it will easily find a way out of the situation, oriented that you can simply add one more component to the previous example.

If the kid shave the incomprehensible set for him, the set of numbers and does not see their essence and meaning, he can at any time forget all this abrakadabra and he will not even be out of what to push out to remember one or another example.

It is worth clarifying that the timing of four days is exemplary and suggest special classes, the child's special interest in training, as well as its ability: the ability to operate in numbers within two hundred, possession of various mathematical operations, understanding the composition of the number and essence of multiplication - in fact, the child Must be able to multiply, but still not know the tables, as such, by heart.

In this video, it is clearly shown, as you can easily master the multiplication table in a fun, game form, making color cards.

First day

Based on the proposed method, first it is necessary to carefully examine the standard multiplication table.

If you take multiplication of all numbers from one to ten, then the child will have to learn as much as a hundred examples. At first glance, a rather frightening perspective is not true?

However, if you look even more carefully, you can find a very interesting fact that many just do not notice - the table is symmetric.

So, what you need to do with the child:

draw or print the table and enter all the examples of multiply from one to ten;

then find together the same examples, such as five to multiply four and multiply five to five - explain to the child that the response from the permutation, as in addition, the answer does not change;
the resulting symmetric examples are filled with any other color (light gray) - repeats should be forty-five;
next, also paint the first and last column - multiplication of units and dozens, since these examples are very lungs and they will not need to teach nor tool;
you must remain dedicated 36 cells or thirty-six mathematical facts - we will deal with their study.

Note that the selected examples should be located in the number of numbers - from less to more, and their quantity will increase by one in each column.

That is, if only one fact remains in the multiplication column, only one fact is - two examples will already be on the top three - three three times three and so on. Thus, you have a kind of inverted ladder from numbers.

Second day

The main task for the child is to understand and assimilate the principle of doubling. It is easiest to explain his child like this: for multiplication two two, you just need to add the number "two" with yourself - the result is four.

See how easy it is easy:

to multiply any number to four, it is necessary to simply produce a multiplication operation two twice, and if short, then multiplying four, you should first double the number, and then double the result;
complete with the child examples of multiplication by two and four for all numbers and fill them with light blue;
make sure that the baby understood the principle of doubles, which means that it can do without a cramp for the cases of multiplication by two and four.

Additionally, it is possible to begin to explain to the child that the doubling principle can be used and for multiplication by eight, sixteen and other degrees of two. That is, the first degree is the deuce itself, the second - the number of four, the third - the number is eight.

This series can be continued to infinity. So the baby slowly get acquainted with the finding of logarithms, just studying the multiplication table.

The third day

The next step of learning will be mastered by the skill of multiplication by five. To learn to multiply five, there are several interesting ways:

if you double the number is easy enough, it will not be more difficult and split it equally or in half, that is, to obtain a result of multiplying any number to five, you just need to multiply it for ten, and then divided into two, for example, multiply five At six - equal half of the sixty, because we multiply at ten and divide for two, as a result, it turns out thirty, etc.;
you can use another way - for an even number to attribute zero to its half, and for odd - to attach five to half the previous digit, for example, when you multiply the five to seven, you need to add a five to the top three, that is, half of the six, which is The numerical row is facing the seven, and when you multiply five to eight - divide eight to two and to the resulting four to attribute zealik;
there is a completely universal way that is suitable for all numbers, but we still use it for the top five - just count with the child five times as you need to multiply this very number, for example, for the multiplication of five to six, consider - five, ten , fifteen, twenty, twenty-five, thirty - that's the result;
we use the same way to explain the multiplication of the troika and train with the baby;
if he understood everything and learned, paint all the examples of multiplication by five and three light-purple color - you should have only ten cells.

Day four

By this time, the child should be well understood and easy to solve examples with multiplication of numbers from two to five - without memorizing and combaling, simply applying all the proposed logical methods.

He should like the next and final learning step. To do this, you need to use your fingers. It is with their help that the technique proposes to learn the multiplication of numbers from six to nine.

So, make the numbering of your fingers and yourself, and the baby. You can write the numbers with a marker or marker, make applications on paper nozzles, make figures from felt, as in the finger theater - additional creativity with mathematical background will be only in plus.

Numbers need the fingers of both hands:

on large fingers should be five;
on guide - six;
on medium - seven;
on nameless - eight;
on Mizinza - nine.

That's what you need to do later.

Sit with a child at the table. Hands put on the table with palms down. All numbers must be well and clearly visible.
Set any example for multiplication, for example, try multiply nine to eight.
Cut together the little finger with the left hand with a number nine and the ring finger of the right hand with a number eight. They should touch each other on the edge of the table.
The remaining seven fingers hang out - four on the left and three on the right. We calculate them with dozens - that is, for each finger ten. As a result, we get seventy.
Now it is necessary to multiply the ones on the table - one on the left and two on the right - it comes out two, and together seventy two.
We try with other numbers by the same principle: thumbs with those numbers that need to multiply, fingers in front of them we consider dozens, and the rest with the rest with each other and fold the result.
Go through all the remaining examples so that the child understands this principle and caught so multiply.
Ten remaining cells fasten with light orange.

So we passed the entire table, the study does not join the material, but to understand its meaning and logically arguing.

Other ways and methods in the form of games and poems

In addition to the proposed methodology, there are many other ways to non-standard learning multiplication table.

Very popular and efficient in work is, the so-called Pythagore table - you can purchase it ready or draw it with your child yourself. It is sufficiently simple - the numbers are located vertically and horizontally from one to nine in tabular form.

The essence of the use of the table is that the number from the left vertical column is multiplied by another of the horizontal top line. The task of the child is to hold the place of their intersection on the table and find the result.

With the table of Pythagora, you can invent various games and combinations so that the baby understand the principle of multiplication and trained the memory.

It is also worth using:

interactive sound posters;
cards with examples for the game;
poems - there are wonderful poems of Marina Kazarina "about multiplication" and "multiplication" of Alexander Usacheva;
online simulators and educational games for learning multiplication table on a computer;
practical examples with toys or surrounding objects;
didactic games - set the numbers in the houses, catch them like a fish, look for the right answers for the ray of the secrets of pirate treasures, form the compositions of trains, etc.

This video presents another interesting method of learning in poetic form.

Conclusion

Be sure to ask how the table is studying at school in a child. You can use your learning method, but in parallel to introduce the baby and with the standard program.

The multiplication table may turn out to be a hard nut, so it is not worth a hurry and upset or scold a child if the learning process is not as easy and quick as you wanted.

Remember that if you go to the case with patience, excerpt, and also to act gradually and work according to the methodology, then you will definitely get a great result.

How to help the child learn multiplication table

easy, quick and interesting

How to learn multiplication table fast, high quality and easy? This question, from year to year, worries thousands of schoolchildren, parents and even grandparents. Unfortunately, not everyone can boast an excellent knowledge of the multiplication table.

Multiplication table (table Pythagora) - This is the most popular and most popular mathematical instrument for computing. It is used almost all and at every step. It is impossible to assume successful training at school without strong knowledge of multiplication table.

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

I bring to your attention a few proven ways, how to learn the multiplication table quickly, easily and even interesting.

1) Use games.

To the child can learn the multiplication table, it must be stimulated. You can find desktop mathematical games, buy an arithmetic lotto and play with a child in the family. There are games for memorizing multiplication tables on the Internet, which can be offered to the child. Memorization during the gameplay is better.

2) Train daily.

Multiplication table is an excellent memory training. But, like any training, it should be regular to achieve a good result. Learn the multiplication table gradually and do not try to cover all the numbers at once. If you want to learn the multiplication table quickly and easily, deal with the child every day gradually.Training is better to start even before studying the table, and they should not be imprisoned. Just negate ask the child about such a person, for example, how much you need to give candy to him and his friend, so that they succeed in 3. Set any questions that could develop his knowledge or could help in their acquisition. The creative approach is the path to success, the child must go through the multiplication table in practice.

3) Use different activities of the child.

The more diverse ways to reproduce the multiplication table by your child, the stronger it will learn it easier. Suggest your student to write examples from the multiplication table, tell the table out loud, whisper the answers of the table to 3, pass the table by 6.

4) Be active and interested in learning the table

Attract game techniques. Offer check the multiplication table. Tell her baby with errors. Let him fix you. You can take turns with the child to write any table of the table and check each other's work. Give your baby the opportunity to fix your mistakes from you, convince that he has already remembered well many cases of table multiplication. You can write a few double-digit numbers and ask the child to circulate in the circle of red pencil answers of the multiplication table, for example, 8.

5) Use tips when studying the table.

Here are some of them:

1) Multiplication by 1 and 10

From this it is worth starting to reassure the child: multiplication per unit is the number itself, and multiplication by 10, number and zero after it. So he already knows the answers to the first and last examples in all columns.

2) Multiplication by 2

Multiply a number of two is to fold two identical numbers.

3 × 2 \u003d 3 + 3

6 × 2 \u003d 6 + 6

3) Multiplication by 3

For memorizing this column, mnemotechnical techniques are suitable, for example, short poems. You can invent them with your child or look for "ready-made" online:

Well, my friend, look,

How much will it be three times?

Nothing!

Well, of course, nine!

All guys need to know

How much will it be three times

And not mistaken!

Three times five - fifteen!

Or poems A. Usacheva "Multiplication Table in verses"

What is multiplication?
This is a smart addition.
After all, it is smart - multiply times,
How to seen all the hour.
1x1
One penguin walked the medium of ice floes.
Loose one - one.
1x2
There is safety in numbers.
One two two.
2x2
Two athletes took Giri.
This is: twice two - four.
2x3
Slit cock to dawn
On high pole:
- Kukarek! .. Two three,
Twice three - six!

A pair of plots stood in the cake:
Two four - eight holes.
2x5
Two elephants decided to weigh:
Twice five - we get ten.
That is, weighs every elephant
Approximately five tons.
2x6
He met Crab Cancer:
Twice six - twelve paws.
2x7
Twice seven mice -
Fourteen ears!
2x8.
Octopuses went swimming:
Twice eight legs - sixteen.
2x9
Have you seen a similar miracle?
Two humps on the back at the camel.
Steel nine camels to reckon:
Twice nine humps - eighteen.
2x10
Twice ten - two dozen!
Twenty, if we say briefly.
3x3
Coffee drank two bugs
And broke three cups.
What is broken, then do not glue ...
three three - goes nine.
3x4.
Singing all day in the apartment
Talking Cockada:
- Trri multiplied on four,
Trry multiplied on four ...
Twelve months a year.
3x5
The schoolboy began to write in the notebook:
How much will "three three"? ..
It was terribly accustomed:
Three times five - fifteen stains!
3x6
Became the froths are:
Eighteen - three six.
3x7
Three times seven - twenty one:
On the nose is hot pancake.
3x8.
Mouse hammered in cheese:
Three times eight - twenty-four.
3x9
Three times nine - twenty-seven.
It must be remembered to everyone.
3x10
Three maidens by the window
Dressed in the evening.
Graduate merry girls:
Ten three times - will be thirty.
4x4
Four cute pigs
danced without boots:
Four times four - sixteen bare feet.
4x5
Four scientists Modyshki
Legs flipped books ...
On each leg - five fingers:
Four times five - twenty.
4x6
Went to the parade
Potato-in-Mundire:
Four times six - twenty-four!
4x7
Chickens are considered to be autumn:
Four times seven - twenty eight!

4x8.
4x9
Baba Yaga broke the stupa:
"Four times eight" - thirty two teeth! -
Beige Zhubov She has nothing:
- Four times nine - "Thirty Schusht"!
4x10
Walked forty forty
Found curd cheese.
And they divide cottage cheese:
Tits ten - forty.
5x5
Zaiters went out:
Five five to twenty five.
5x6
Raced in the forest Fox:
Five six - it turns out thirty.
5x7
Five Bear Bears
Walked through the forest without the road -
For seven miles Kisel biting:
Five seven - thirty five!
5x8
To fit the village
Hard on the hillock:
Tired legs -
Five eight - forty.
5x9
The guns were stood on the hillock:
Five eight - came forty.
Guns began to shoot:
Five nine - forty five.
5x9
If the lapties are bruised:
Five nine - forty five ...
There will be this lap
All on the trousers drip!
5x10
Floored Curbank Kabachkov
Five dozen pyatadkov.
And tails in piglets:
Five ten - fifty!
6x6
Six old women hung wool:
Six six - thirty six.
6x7
Six networks of six rams -
This is also thirty six.
And came to the roach network:
Six seven - forty-two.
6x8
Hippos of the bull asking:
Six eight - forty-eight ...
6x9
We do not feel sorry for the bull.
Mouth open wider:
Six nine will be -
Fifty four.
6x10
Six geese are gouted:
Six ten - sixty.
7x7
Fools do not zaughty, do not sow
Themselves are emerging:
Seven family - forty nine ...
Let not be offended!
7x8
Once deer asked Elk:
- How much will the family eight? -
Elk did not become a textbook to climb:
- Fifty, of course, six!
7x9
Seven Matryshka
The whole family inside:
Family nine crumbs -
Sixty three.
7x10
Text in school Seven Lisyat:
Ten family - seventy!
8x8
Vacuuming nose
Elephant carpets in the apartment:
Eight to eight -
Sixty four.
8x9
Eight bears struck firewood.
Eight nine - seventy two.
8x10
The best account in the world
There is a new year ...
In eight rows of toys hang:
Eight ten - eighty!
9x9
Pig pigty decided to check:
- How much will "nine nine" cost?
- Eighty - Hrew - one! -
So answered the young pig.
9x10
Nonwork kulik, and the nose:
Nine ten - ninety.
10x10
In the meadow mobils dozen,
Everyone digs ten beds.
And ten ten - a hundred:
All the earth as a sieve!

4) multiplication by 4

Multiplication by 4 can be represented as a multiplication by 2 and once again at 2. This column for students who have mastered the multiplication of a twice, difficulties will not cause.

5) Multiplication by 5

This is the easiest to memorize the column. All values \u200b\u200bof this column are located after 5 units from each other. Moreover, if an even number is multiplied by 5, the product will end with 0, and if odd - by 5.

6) Multiplication by 6, 7, 8

These columns, as well as a multiplication column by 9, traditionally cause difficulties from schoolchildren. It is possible to reassure the students, explaining that most of the examples of these columns they have already learned and frightening 8 × 3 is the same as the already studied 3 × 8. By changing places multipliers, you can remember what is equal to the work.

So, children will remember only 6 "unfamiliar" examples:

6 × 7 \u003d 42

6 × 8 \u003d 48

6 × 9 \u003d 54

7 × 8 \u003d 56

7 × 9 \u003d 63

8 × 9 \u003d 72

These examples can be written on cards, rave on the wall and learn mechanically.

7) Multiplication by 9 on the fingers.

On fingers:
Put both hands on the table with palms down. Then the little finger of the left hand would be the first finger, Unnamed - the second, the middle-third, etc., the thumb with the right hand is sixth, etc., the little finger of the right hand is the tenth finger of both hands.
These fingers are an error-free counter
9 × 5 = 45
To solve it on the fingers, you only have to see how many fingers from the 5th finger to the left and how much to right: left 4 fingers - it is 4 dozen, right 5 - this is 5 units, it means that the answer will be 45.
9 × 7 = 63
From the 7th finger to the left 6, right 3 fingers, it means 63.

Multiplication of double-digit numbers - skill, extremely necessary for our daily life. People constantly face the need to multiply anything in mind: price tag in the store, a lot of products, or a discount size. But how to multiply two-digit numbers quickly and without problems? Let's figure it out.

How to multiply a two-digit number on unambiguous?

Let's start with a simple task - how to multiply two-digit numbers to unambiguous.

For a start, a two-digit number is a number that consists of a certain number of tens and units.

In order to multiply a two-digit number on an unambiguous in the column, you need to write the desired two-digit number, and the corresponding one-valued. Next, it should be multiplying to a specified number first, and then dozens. If the multiplication of units turned out to be more than 10, then the number of dozens need to be simply transferred to the next discharge by adding them.

Multiplication of double digits for tens

Multiplying two-digit numbers per dozens - the task is not much more complicated than multiplying to unambiguous numbers. The main procedure remains the same:

To write down the numbers in each other into the column, while the zero should be as it were for the "side" in order not to interfere with arithmetic action.
Multiply a two-digit number on the number of dozens, do not forget about the transfer of some numbers to the following discharges.
The only thing that distinguishes this example from the previous one - at the end of the resulting answer you need to add zero, so dozens that have been omitted at the beginning become accounted for.

How to multiply two double numbers?

After you completely figured out the multiplication of double-digit and unambiguous numbers, you can begin to think how to multiply the two-digit numbers on each other. In fact, this action should also not require much effort from you, since the principle still remains the same.

We write these numbers in the column - units under units, dozens are under dozens.
We begin multiplication from the unit in the same way as in the examples with unambiguous numbers.
After you received the first number, multiplying the units on this number, you need to multiply dozens on the same figure in the same way. Attention: the answer must be recorded strictly under dozens. The empty place under units is unaccounted zero. You can write it if you are so more convenient.
Alternating and dozens, and units and receiving two numbers recorded one under one, they need to be folded into the column. The resulting value is the answer.

How to multiply two-digit numbers? It is not enough to just read or learn the instructions. Remember, in order to master the principle, how to multiply two-digit numbers, first of all you need to constantly practic - to solve as many examples as possible, as you can easily use the calculator.

How to multiply in mind

Having learned brilliantly multiplied on paper, you can wonder how to quickly multiply two-digit numbers in the mind.

Of course, this is not the easiest task. It requires some concentration, good memory, as well as the ability to keep a certain amount of information in the head. However, this can be learned, putting enough effort, especially if you choose the correct algorithm. Obviously, it is easiest to multiply on round numbers, so the easiest way is the decomposition of numbers for multipliers.

To begin with, one of these two-digit numbers should be divided into dozens. For example, 48 \u003d 4 × 10 + 8.
Next, you need to multiply the units first, and then dozens with the second number. These are quite complex for performing operations in the mind, as you need to multiply the numbers at each other at the same time and keep the result in the mind. Most likely, it will be difficult for you to cope with this task from the first time, but if you can be quite diligent, this skill can be developed, because it can be understood how to multiply two-digit numbers in the mind correctly in practice.

Some tricks when multiplying double digits

But is there an easier way to multiply two-digit numbers in your mind, and how to do it?

There are several tricks. They will help you easily and quickly multiply double-digit numbers.

When multiplying, eleven you need to simply put the amount of tens and units in the middle of this two-digit number. For example, we needed to multiply 34 to 11.

We put 7 in the middle, 374. This is the answer.

If the number is obtained by more than 10, then you should simply add a unit to the first number. For example, 79 × 11.

Sometimes it is easier to decompose the number of multipliers and consistently multiply them. For example, 16 \u003d 2 × 2 × 2 × 2, so you can simply multiply the initial number 4 times.

14 \u003d 2 × 7, so when performing mathematical operations, you can multiply first by 7, and then 2.

In order to multiply the number in numbers, multiple 100, for example, 50 or 25, you can multiply this number 100, and then divided by 2 or 4, respectively.
You still need to remember that sometimes you do not add to multiply, but take numbers from each other.

For example, in order to multiply the number 29, you can first multiply it by 30, and then take away the number from the resulting number once. This rule is valid for any dozens.

The usual school mathematics can be very practical in everyday life, because it makes it possible to conduct serious arithmetic calculations in the mind. We will tell you several techniques that help multiply double-digit numbers quickly without using a calculator or sheet of paper and handles.

How to multiply two-digit numbers in the mind?

It may seem that multiplied in the mind such large numbers is impossible, but it is not. There is a way that will be understood even to schoolchildren.

For example, take numbers 96 and 97.

Calculate the difference between these numbers relative to 100. In our case, it is 3 and 4. Their work will be the second part of the multiplication solution of numbers 97 and 96 (3 * 4 \u003d 12).

The first part will be the difference of the first number and the difference of 100 and the second number. In our example, it is: 97-4 \u003d 93.

Thus, we get 97 * 96 \u003d 93 12

How to quickly multiply in the mind?

The essence of this simple and usual way is to decompose multipliers per units and dozens. Then follow their alternate multiplication. Make it just, in the mind you will have to keep no more than 3 numbers at the same time.

Here is a standard method of such multiplication:

64*86 = (60+4)*(80+6) = 60*80 + 60*6 + 4*80 + 4*6 = 4800 + 360 + 320 + 24 = 5504

But the method calculated by only 3 actions.

1 ) Multiply dozens of 60 and 80. Result 4800, remember it.
2 ) Fold the works 60 * 6 and 80 * 4. It turns out 680. Remember this number.
3 ) Multiply units 4 * 6 \u003d 24 and fold all three numbers. 4800 + 680 +24 \u003d 5504.

See how easy you can multiply in your mind!

First you need to do two things: print the multiplication table itself and explain the principle of multiplication.

To work, we will need a table of Pythagora. Previously, she was published on the turnover of notebooks. She looks like this:

You can also see the multiplication table in such a format:

So, this is not a table. It's just the columns from examples in which it is impossible to find logical connections and patterns, so the child has to teach everything by heart. To make it easier for it, find or print a real table.

2. Explain the principle of work

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When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike the fact that he came down or what someone said to him. Therefore, try to turn the study of the table in an interesting game.

Getting Started by learning multiplication, children are already familiar with simple mathematical actions: addition and multiplication. You can explain the child the principle of multiplication on a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.

Explain that multiplication is a short and quick way to calculate.

Next, you need to deal with the device itself. Show that numbers from the left column are multiplied by numbers from the top line, and the correct answer is on the place of their intersection. It is very easy to find the result: you just need to spend your hand on the table.

3. Teach small portions

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No need to try to learn everything for one. Start from columns 1, 2 and 3. So you gradually prepare the child to absorb more complex information.

Good technique: Take an empty printed or drawn table and fill it yourself. At this stage, the child will not remember, but count.

When he figured out and understood quite well the simplest columns, go to the numbers more complicated: first to multiply by 4-7, and then at 8-10.

4. Explain the commutative property

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That is the most well-known rule: the work is not changing from the permutation of multipliers.

The child will understand that in fact he needs to learn not all, but only half of the table, and some examples he already knows. For example, 4 × 7 is the same as 7 × 4.

5. Find regularities in the table

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As we have said earlier, in the multiplication table, you can detect many patterns that will simplify its memorization. Here is some of them:

When multiplying on 1, any number remains the same.
All examples on 5 ends on 5 or 0: if the number is evenly attributed to 0 to half the number, if something is 5.
All examples on 10 end 0, and begin with the number that we multiply.
Examples of 5 half are smaller than examples of 10 (10 × 5 \u003d 50, and 5 × 5 \u003d 25).
To multiply by 4, you can just double double the number. For example, to multiply 6 × 4, you need to double 6 twice: 6 + 6 \u003d 12, 12 + 12 \u003d 24.
To remember multiplication by 9, write down a number of answers in the column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. Remember you need the first and last number. All others can be reproduced according to the rule: the first digit in the double-digit number increases by 1, and the second decreases by 1.

6. Repeat

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You are more likely to repeat. First ask in order. When notice that the answers became confident, start asking for a corrosion. Watch and beyond the tempo: first let's get a lot of time to think, but gradually increase the tempo.

7. Play

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Use not only standard methods. Training should pass, interest the child. Therefore, use visual funds, play, apply different techniques.

Cards

The game is simple: Prepare cards with examples of multiplication without answers. Mix them, and the child must pull one. If he gives the correct answer, lay the card to the side, wrong - we return to the stack.

The game can be diversified. For example, give answers for a while. And every day count the number of correct answers so that the child appears the desire to beat his yesterday's record.

You can play not only for a while, but also until the entire stack of examples end. Then, for each incorrect answer, you can assign a child to the child: to tell the poem or take things on the table. When all the cards are solved, hand a small gift.

From contrary

The game is similar to the previous one, only instead of cards with examples you are cooking cards with answers. For example, the number 30 is written on the card. The child should call a few examples, which will result in 30 (for example, 3 × 10 and 6 × 5).

Examples of life

Training is becoming more interesting if you discuss with the child the things that he likes. So, the boy can ask how many wheels need four cars.

You can also use visual funds: scores, pencils, cubes. For example, take two glasses in each of which four pencils. And clearly show that the number of pencils is equal to the number of pencils in one cup, multiplied by the number of glasses.

Poems

Rhyme will help remember even complex examples that are not given to the child. Independently invent uncomplicated poems. Pick up the easiest words, because your goal is to simplify the memorization process. For example: "Eight bears struck firewood. Eight nine - seventy two. "

8. Do not nervous

Usually, in the process, some parents are forgotten and commit the same mistakes. Here is a list of things that cannot be done in any way:

Make a child if he does not want. Instead, try to motivate it.
Scold for errors and frighten bad estimates.
Put in an example of classmates. When you compare you with someone, it's unpleasant. In addition, it is necessary to remember that all children are different, so everyone needs to find the right approach.
Learn everything immediately. The child is easy to scare and tire a large material volume. Learn gradually.
Ignore progress. Praise the child when it copes with the tasks. At such moments, he appears a desire to learn further.