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Ways to quickly learn the multiplication table. How to quickly learn to multiply two-digit numbers in your head? Long multiplication in the mind

How to help your child learn the multiplication table

easy, fast and interesting

How to learn the multiplication table quickly, efficiently and easily?Thousands of schoolchildren, parents and even grandparents are worried about this issue from year to year. Unfortunately, not everyone can boast of excellent knowledge of the multiplication table.

Multiplication table (Pythagoras table) Is the most popular and most requested mathematical tool for computing. It is used by almost everyone at every step. It is impossible to assume successful schooling without a solid knowledge of the multiplication table.

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

I bring to your attention several proven ways to learn the multiplication table quickly, easily and even interestingly.

1) Use games.

For a child to be able to learn the multiplication table, he needs to be stimulated. You can find board math games, buy arithmetic loto and play with your child in the family. There are multiplication table games on the Internet that you can offer your child. Memorization during gameplay goes better.

2) Train daily.

The multiplication table is a great memory trainer. But, like any workout, it must be regular in order to achieve a good result. Learn the multiplication table gradually and don't try to cover all the numbers at once. If you want to learn the multiplication table quickly and easily, study with your child a little every day.It is better to start training even before studying the table, and they should not consist in simple memorization. Just casually ask your child about, for example, how much candy should be given to him and his friend to get them 3. Ask any questions that could develop his knowledge or could help in acquiring them. A creative approach is the path to success, the child must go through the multiplication table in practice.

3) You use different types of child's activities.

The more varied the ways your child plays the multiplication table, the more durable and easier he will learn it. Invite your student to write examples from the multiplication table, tell the table aloud, whisper the answers of the table for 3, sing the table for 6.

4) Be active and interested in learning the spreadsheet

Use playful techniques. Offer to check your multiplication table. Tell it to the child with mistakes. Let him correct you. You can take turns with the child to write any column of the table and check each other's work. Give your kid the opportunity to correct your mistakes, make sure that he has already well memorized many cases of table multiplication. You can write several two-digit numbers and ask your child to circle the answers of the multiplication table in a red pencil, for example, by 8.

5) Use hints while studying the table.

HERE ARE SOME OF THEM:

1) Multiplication by 1 and 10

It's worth starting with this to reassure the child: multiplication by one is the number itself, and multiplication by 10, the number and zero after it. Now he already knows the answers to the first and last examples in all columns.

2) Multiplication by 2

Multiplying a number by two means adding two of the same number.

3 × 2 = 3 + 3

6 × 2 = 6 + 6

3) Multiplication by 3

To memorize this column, mnemonic techniques are suitable, for example, short rhymes. You can invent them together with your child or search for “ready-made” ones on the net:

Come on, my friend, look

What is three times three?

Nothing to do!

Well, of course, nine!

Or

All the guys need to know

How much is three times five,

And don't be wrong!

Three times five - fifteen!

Or poetry A. Usacheva "Multiplication table in verse"

What is Multiplication?
It's a smart addition.
After all, smarter is to multiply once,
Than putting it all together for an hour.
1x1
One penguin was walking among the ice floes.
Once one - one.
1x2
There is safety in numbers.
Once, two, two.
2x2
Two athletes took weights.
This: two times two - four.
2x3
The rooster sat down before dawn
On a high pole:
- Kukareku! .. Twice three,
Twice three - six!

A pair of forks stuck into the cake:
Two by four - eight holes.
2x5
We decided to weigh two elephants:
Twice five - we get ten.
That is, each elephant weighs
Approximately five tons.
2x6
Met crab with cancer:
Twice six - twelve paws.
2x7
Twice seven mice -
Fourteen ears!
2x8
The octopuses went for a swim:
Twice eight legs - sixteen.
2x9
Have you seen such a miracle?
Two humps on the back of a camel.
Nine camels began to be reckoned:
Twice nine humps - eighteen.
2x10
Twice ten - two dozen!
Twenty, to put it briefly.
3x3
Two insects drank coffee
And they broke three cups.
What is broken cannot be glued together ...
three times three - nine comes out.
3x4
All day he repeats in the apartment
Talking Cockatoo:
- Three times four,
Three times four ...
Twelve months a year.
3x5
The schoolboy began to write in a notebook:
How much is "three times five"? ..
He was terribly neat:
Three times five - fifteen spots!
3x6
Foma began to eat pancakes:
Eighteen - three times six.
3x7
Three times seven - twenty one:
There's a hot pancake on my nose.
3x8
The mice gnaw holes in the cheese:
Three times eight is twenty four.
3x9
Three times nine - twenty seven.
Everyone should remember this.
3x10
Three maidens by the window
Dressed up in the evening.
The maidens measured the rings:
Three times ten - it will be thirty.
4x4
Four cute pigs
danced without boots:
Four times four - sixteen bare legs.
4x5
Four learned monkeys
They leafed through books with their feet ...
Each foot has five toes:
Four times five - twenty.
4x6
Went to the parade
Jacket Potatoes:
Four times six - twenty four!
4x7
Chickens are counted in the fall:
Four times seven - twenty eight!

4x8
4x9
Baba Yaga's stupa broke:
"Four times eight" - thirty-two teeth! -
She has nothing to eat with bugs:
- Four times nine - thirty six!
4x10
We walked forty forty,
Found a curd cheese.
And the curd is divided into parts:
Four times ten - forty.
5x5
The hares went out for a walk:
Five five is twenty five.
5x6
A fox ran into the forest:
Five six is ​​thirty.
5x7
Five bears from the den
We walked through the forest without a road -
To sip jelly for seven versts:
Five seven - thirty five!
5x8
Climb a centipede
Difficult on a hillock:
Legs are tired -
Five eight is forty.
5x9
Cannons stood on the hillock:
Five eight - forty came out.
The cannons started firing:
Five nine is forty five.
5x9
If you sip cabbage soup with bast shoes:
Five nine - forty five ...
There will be this bast
Everybody drip on trousers!
5x10
We dug a bed of zucchini
Five dozen patches.
And piglets have tails:
Five ten - fifty!
6x6
Six old ladies were spinning wool:
Six six is ​​thirty six.
6x7
Six nets of six ruffs -
This is also thirty-six.
And the roach got caught in the net:
Six seven is forty two.
6x8
Hippos for buns are asking:
Six eight - forty eight ...
6x9
We do not mind the rolls.
Open your mouth wider:
Six nine will be -
Fifty four.
6x10
Six geese lead goslings:
Six ten - sixty.
7x7
Fools do not reap, do not sow,
Themselves are born:
Seven seven - forty nine ...
Let them not be offended!
7x8
Once the deer asked the elk:
- How many will be seven eight? -
The moose did not go into the textbook:
- Fifty, of course, six!
7x9
Seven nesting dolls
The whole family inside:
Seven nine crumbs -
Sixty three.
7x10
There are seven fox cubs in school:
Seven ten - seventy!
8x8
Vacuuming up the nose
Elephant carpets in the apartment:
Eight by eight -
Sixty four.
8x9
Eight bears were chopping wood.
Eight nine - seventy two.
8x10
The best score in the world
New Year is coming ...
The toys hang in eight rows:
Eight ten - eighty!
9x9
The piggy pig decided to check:
- How many "nine by nine"?
- Eighty - oink - one! -
So the young pig answered.
9x10
The sandpiper is small, but the nose:
Nine ten - ninety.
10x10
There are a dozen moles in the meadow,
Each one digs ten beds.
And for ten ten - one hundred:
The whole earth is like a sieve!

4) Multiplication by 4

Multiplication by 4 can be represented as multiplication by 2 and again by 2. This column will not cause difficulty for students who have mastered multiplication by two.

5) Multiplication by 5

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

6) Multiplication by 6, 7, 8

These columns, as well as the column of multiplication by 9, traditionally cause difficulties for schoolchildren. You can reassure the students by explaining that they have already learned most of the examples from these columns and that the terrifying 8 × 3 is the same as the already learned 3 × 8. By swapping the factors, you can remember what the product is equal to.

This means that children will only have to remember 6 "unfamiliar" examples:

6 × 7 = 42

6 × 8 = 48

6 × 9 = 54

7 × 8 = 56

7 × 9 = 63

8 × 9 = 72

These examples can be written on cards, hung on the wall, and memorized mechanically.

7) Multiplication by 9 on the fingers.

On fingers:
Place both hands on the table, palms down. Then let the little finger of the left hand be the first finger, the ring finger the second, the middle finger the third, etc., the thumb of the right hand — the sixth, etc., the little finger of the right hand — the tenth finger of both hands.
These fingers are an unmistakable counter
9 × 5 = 45
To solve this on your fingers, you only have to look how many fingers are from the 5th finger to the left and how many to the right: to the left 4 fingers is 4 tens, to the right 5 is 5 units, which means that the answer will be 45.
9 × 7 = 63
From the 7th finger to the left 6, to the right 3 fingers, which means 63.

For schoolchildren, the table seems boring and useless. Often children get angry, upset, trying to figure out a set of numbers that they do not understand. Parents can make the learning process easy and fun by preparing in advance.

The basic rule in learning the multiplication table is to get the child interested. Like adults, they perceive information in different ways. Some children enjoy learning poetry and songs. Others can sit quietly with their parents at the table and look at the Pythagorean table.

How to teach a child the multiplication table (picture)

It is easy for a child to remember the multiplication table:

• Cards;
• Counting figures, sticks;
• Special programs for tablet and phone;
• Educational videos and cartoons;
• Poems and songs;
• Images;
• Child's fingers.

Gambling methods are exciting and give quick results. It is better to start classes in a good mood when the child is in the mood for learning.

Learning the multiplication table: life hacks and videos

It is important to understand how the child is more comfortable to perceive information so that the process does not turn into “cramming”. Everything is very simple:

Audial children learn new things better in conversation. They enjoy memorizing numbers by repeating examples out loud. A good way to memorize the multiplication table is to learn poetry, songs, or watch instructional videos.

Learn the multiplication table (video)

Child visual learns more easily when vision and imagery are involved. They assimilate information through vivid drawings, coloring games, in which there are large colored fonts and numbers.

Multiplication table coloring game (picture)

Also, with a visual child, you can watch educational cartoons in which your favorite characters act as a teacher.

What is 9 multiplication table with Fixies (video)

Kinesthetic children learn through the sensations and feelings that they have when they come into contact with a new object and information. In this case, you can try the card method.

Learn the multiplication table using cards (video)

It's important to consider how your child learns best so that the process of memorizing the multiplication table will be fun and easy.

How to learn multiplication table in 5 minutes a day

Kukina Ekaterina Georgievna

math teacher

You've probably heard the opinion more than once that the level of mathematics education is falling.

When my children were in the second grade, I clearly understood why the level of mathematics education at school was falling. It is in the second grade, when laying the very foundation of mathematical education, such a giant irreplaceable hole appears, which cannot be supported by any crutches in the form of calculators.

Namely, the main problem is in the multiplication table. Take a look at the squared notebooks your school children have.

I went shopping for a long, long time in search of notebooks. And all the same, at all - this is the picture.

Multiplication table (picture)

There are notebooks that are even worse (for high school students), on which there is no multiplication table, but there are a bunch of meaningless formulas.

Well, why is this notebook bad? The unsuspecting parent sees that the multiplication table is on the notebook. It seems that all my life there was a multiplication table on notebooks? What's wrong?

And the problem is that the multiplication table is NOT on the notebook.

The multiplication table, my dear readers, is this:

Sometimes the same table is even called the beautiful word "Pythagoras table". The top and left columns can be omitted, only the main rectangle.

First, there is a table. Secondly, it's interesting!

No child in their right mind would consider columnar examples.

Not a single child, no matter how brilliant he is, will be able to find interesting features and patterns in the examples written out.

Well, in general, when the teacher says: "learn the multiplication table", and the child does not even see the table in front of him, he immediately understands that mathematics is a science where ordinary things are named somehow differently and you need a lot cram, but it is impossible to understand anything. And in general, it is necessary to do "as it is said," and not "as it makes sense."

Why is the Pythagorean table better?

Firstly, there is no garbage and information noise in the form of the left side of the examples.

Secondly, you can think about it. It is not even written anywhere that this multiplication is just a table.

Thirdly, if she is constantly at hand and the child constantly stumbles upon her, he willy-nilly begins to memorize these numbers. In particular, he will never answer the question "seven eight" with 55 - after all, the number 55 is not in the table at all and has never been!

Only children with abnormal memory are able to memorize columns of examples. In the "table" you need to memorize much less.

In addition, the child automatically searches for patterns. And he himself finds them. Even such patterns are found by children who do not yet know how to multiply.

For instance: numbers symmetric about the diagonal are equal. You see, the human brain is simply set to look for symmetry, and if it finds and notices it, it is very happy. And what does it mean? This means that the permutation of the places of the factors does not change the product (or that multiplication is commutative, in simpler terms).

Pythagoras table: multiplication (picture)

You see, the child notices it himself! And what a person invented himself, he will remember forever, in contrast to what he memorized or he was told.

Remember your high school math exam? You forgot all the theorems of the course, except for the one that you got, and you had to prove it to the evil teacher! Well, that's if you didn't cheat, of course. (I am exaggerating, but this is almost always close to the truth).

And then the child sees that it is not possible to learn the whole table, but only half. If we already know the line for multiplying by 3, then we do not need to memorize "eight by three", but it is enough to remember "three by eight". Already half the work.

And besides, it is very important that your brain does not accept dry information in the form of some incomprehensible columns of examples, but thinks and analyzes. Those. trains.

In addition to the commutativity of multiplication, one can observe, for example, another remarkable fact. If you poke at any number and draw a rectangle from the beginning of the table to this number, then the number of cells in the rectangle is your number.

Pythagoras table: multiplication (picture)

And here multiplication already acquires a deeper meaning than just an abbreviated notation of several identical terms. It makes sense for geometry - the area of ​​a rectangle is equal to the product of its sides)

And you have no idea how much easier it is to share with such a table!

In short, if your child is in the second grade, print him such a correct multiplication table. Hang a large one on the wall so that he looks at it when he does his homework or sits at the computer.

And print and laminate a small one for him (or write on cardboard). Let him carry her to school with him, and just keep it conveniently at hand. (it does not hurt to select the squares diagonally on such a table so that you can see better)

My children have one like this. And it really helped them in the second grade and still helps a lot in math lessons.

Pythagoras table: multiplication (picture)

Honestly, the GPA in math will immediately increase, and the child will stop whining that math is stupid. And in addition, in the future it will be easier for your child too. He will understand that he needs to wiggle his brains, not cram. And little that he will understand, he will also learn to do it.

And I repeat: there is nothing wrong with the column examples. And the amount of information they contain is the same as in the "table". But there is nothing good in such examples either. This is informational garbage, from which you will not immediately find what you need.

Praise more often

Think of ways to encourage your child. These can be pleasant little things that make him happy.

Finding a way to approach if the child is not in the mood

Forcing to study, shouting or completely depriving of entertainment - such methods discourage any desire to study. It makes sense to calmly explain the importance of the activity and motivate the child.

Learn the multiplication table gradually

When a child first sees how many numbers he needs to remember, a protest arises. It is best to practice at a comfortable pace with rest breaks.

Remember that every child is a person

As soon as children are compared to friends or classmates, they lose the desire to do anything. It must be remembered that each child has his own pace of learning and the careful attitude of the parents is of great importance.

Saying that mistakes are okay

At the first setbacks, children lose interest, do not want to continue classes. It is important to explain that there are no good results without mistakes. Everything will definitely work out.

Now you know all about how to teach your child the multiplication table in different ways to make the stumbling process a joy.

Many children go to great lengths to learn the multiplication table. As a parent, it is your responsibility to help. After all, multiplication skills will help them in school, university, and in life. It will take time and patience to help your child master multiplication skills. Here's how to do it.

Steps

Skill training

1. Pick a time. Sit down with your child when both of you are ready to gnaw the granite of science. If you are busy with your own business, or your child is too tired or hungry, teaching will not be as effective as you would like. Sit down for 30 minutes and eliminate all distractions for both of you.

   • Energy and enthusiasm are very important to both of you. Turn off your cell phone, TV, sit down at the table and beat these numbers.

2. Start with a table on 0, 1, 2, and 3. It is better to memorize information in small portions than trying to memorize the entire table as a whole. Remember: your child does not count, he just remembers. Presumably he already knows the basic principle of multiplication.

   • If your child is not familiar with multiplication, write multiplication in addition. For example, 4 * 3 is 4 + 4 + 4.
   • Ask your child to bring you math books and other materials that they have. You will understand what he is studying and become familiar with the teaching method used in his school.
   • Draw a table or number axis showing numbers from 0 to 100. The table is useful for finding answers that match specific rows and columns. The table will be more convenient for beginners, as the answers can be found faster.
     • The number axis is more time consuming. You can mark numbers and their multipliers in different colors.

3. Explain to the child how the commutative property (independence of the result of an operation from the rearrangement of its elements) makes it easier to memorize the multiplication table. Show your child that each answer is repeated; in fact, he should only learn half of the chart. 3 * 7 is the same as 7 * 3. When he learns the table for 0, 1, 2 and 3, he will already know 4 examples of tables for 4, 5, 6, 7, 8, 9 and 10.

   • Once the child has mastered multiplication by 0-3, move on to multiply by 4-7 and then by 8-10. If you want to go further, take the multiplication by 11 and 12. Some teachers take more complex examples as a bonus or to rate each child.

4. Discuss patterns throughout the table. There should be no rote memorization. The table clearly shows what you need to pay attention to.

   • All examples with 10 end in 0.
   • All 5 examples end in 5 or 0 and half the size of 10 examples (10 * 5 = 50; 5 * 5 = 25 or half of 50).
   • All 0 examples are 0.

5. Little tricks. Fortunately, math is full of abbreviations. Teach your child these tricks and he will be grateful to you.

   • Use your fingers to memorize the table at 9. Extend both palms in front of you. 9 * 1, bend your left pinky. What are you showing? 9. 9x2, bend the ring finger on the left palm. What are you showing? 1 and 8. 18. Bend your middle finger - 2 and 7.27. This works up to 9x9 (8 and 1.81)
   • If the child knows how to double the number, it will be easier to multiply by 4. Just double the number twice. Let's take 6x4. Double the number 6, it will be 12. Double the number 12, it will be 24.6x4 = 24. Use this technique to make your responses automatic.
   • To multiply any number by 11, just duplicate it. 3 * 11 = 33. Two threes. 4 * 11 = 44. Two fours. The answer is in the question.
   • If your child is a genius in mathematics, teach him this trick of multiplying 11 by a two-digit number. Take a two-digit number and divide it by numbers. 11 * 17 = 1__7. Add up these numbers, and put the resulting number in the middle: 187.

   Memorizing Answers

   1. Make learning fun. From this point of view, you may be surprised that there is something in these squiggles. Bring an element of play and competition to your learning.

      • Ask your child to make a set of cards. Write an example, 4x9, on one side and the answer, 36, on the back. Writing examples is another repetition opportunity. Use the timer to see how many cards your child can get through in a minute. Will he be able to beat this score tomorrow?
        • You can also do this on an empty table. The table allows you to track down weaknesses that still need to be worked on.
      • "Capture a deck of cards" - This game is similar to war, but with multiplication. Each of you takes half a deck and places it face down in front of you. Don't look at the cards! Players turn over their first card at the same time - the first person to say their answer by multiplying the numbers on the two cards gets both cards (the goal of the game is to collect all the cards). If you flip 7 and 5, the answer is 35. For jacks, queens, and kings, you can use 11, 12, and 13, use them as 0, or remove them altogether.
      • Say the number. For example, 30. Can the child name all possible cases when the result is 30? 5 * 6? 3 * 10 =?
      • Say the number and ask to do the next multiplication. For example, start at 30 and ask for the next multiplication by 6. Or start at 18 and ask for the next two multiplications by 9. You can even start at 22 and ask the next multiplication by 4, even though 22 is not a multiple of 4. Be cunning.
      • Try a bingo game. Your child fills in the six by six square with any numbers. You name the example, "5 * 7." If he has the number 35 on the card, then he crosses it out. Continue until someone crosses out all the numbers on their card. What kind of prize can he win?

   Encourage your child

   1. Use incentives. You should not use money or material values ​​as an incentive - this can kill the craving for knowledge.

      • Save awards for school tests. If the child can handle examples under pressure, you are successful.

   2. Praise your child. Remember to pause and rest between serious activities. If you are happy with your child's success, they will want to be successful next time. Express in words how great the child is doing.

      • If he is practicing slower than he could, take a break. Negative emotions can lead to the termination of classes. A bad mood can negate all efforts. Encourage the child to make an effort.
   3. Be kind and patient. If necessary, just work with one combination for several days until the child fully understands.
   4. Examining a large volume too quickly will create confusion and frustration. Work gradually to make learning multiplication easier, but move forward firmly by constantly and consistently improving your multiplication skills.
   5. Note that addition can be done in two ways: 2 + 1 = 3 and 1 + 2 = 3. It's the same with multiplication.
   6. Leave the hard for later: 10 squared is very similar to 1 squared. 1 squared is 1, 10 squared is 100. It's easy to see that 20 squared is 400, 30 squared is 900, 40 squared 1600, and so on.

   Warnings

   • Never, never do not use the words "stupid", "lousy" or any other labels. Do not use them with a child, yourself, or the material.
   • Understand that your child is not a calculating machine. A quick answer is achieved only by memorization. Oral counting is useful initially, but becomes unnecessary once the spreadsheet is firmly understood.
   • Not tire your child by learning too many lines or patterns at one time - remember to smile and take short breaks between classes.

   Almost all parents, whose children went to school, sooner and later face the need to remember long-forgotten school disciplines in order to help their child understand them or learn something.

   And one of the first serious tasks, as well as one of the first problems, is the multiplication table, which is often asked to children for independent study for the summer after the first grade.

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

   Sometimes it also happens that the kid has not gone to school yet, but mom wants him to multiply at least three-digit numbers in his mind. Of course, there are little geeks among children who are really capable of this and can learn not only the multiplication table at an early age, but also start to extract the square root from numbers or solve complex equations. However, this is rather an exception to the rule.

   Basically, even for younger schoolchildren, the multiplication table is not easy and difficult, because it is usually explained as an incomprehensible and boring set of numbers that for some reason need to be remembered. What can we say in this case about preschool children.

   So, if your kid is not a mathematical genius, then you should not prematurely load him with the study of the multiplication table. Since mastering this skill will only be required from him in the second grade of school, it is recommended to acquaint the child with the multiplication table and the principle of its operation no earlier than seven to eight years of age.

   However, you can prepare your little one by explaining the mathematical meaning of multiplication after he has mastered addition and subtraction.

   Each child learns mathematics in his own way: someone has a good developed mechanical memory, so he remembers and memorizes everything faster, others need to reinforce information with the help of visual or emotional perception, that is, use cards with pictures, objects, toys for learning, poems and songs. The same goes for filing the multiplication table for the child.

   So that it is not difficult for the child in the middle of the school year, the table is usually set for self-familiarization for the summer holidays.

   Be sure to help the child figure it out, but be prepared for the fact that it will take a lot of work, and also be patient.

   Some nuances and important points

   It is also necessary to understand that it is possible to start studying the table only when the child has already mastered the basic mathematical actions. That is, he is good and confidently able to:

   • count to at least a hundred - in the usual and reverse order;
   • distinguish between simple numbers, numbers and tens;
   • understand the composition of numbers;
   • add and subtract;
   • understand the principle of multiplication, be able to replace addition by multiplication and vice versa.

   Modern children do not always understand why they even need to memorize a table, which is often served in schools as a mathematical gibberish, because you can easily and quickly calculate on a calculator or get an answer from a computer / tablet / phone.

   Your task is to find significant motivation for the child, explain to him what such knowledge, skills and abilities are needed for, how they can help later in school and in life, what benefit can be derived from them.

   Try to find your reasons for the example of the following eloquent arguments:

   • having understood the principle on which the multiplication table is built, and having learned it, the child will quickly carry out any calculations, operate with large and multi-digit numbers in his mind - this will give him an advantage in his studies and will allow him to cope with math tasks much faster;
   • even if at first he needs a cheat sheet or paper to make a calculation, the result will still be found only with the help of his own knowledge and memory - without the use of outside help in the form of an electronic device;
   • such knowledge helps to develop and improve "mathematical intuition", trains memory, enhances intelligence and quickness of brain reactions;
   • the multiplication table is one of the basic mathematical operations, so without it you will not be able to master deeper waters in this discipline.

   How to learn? Let's go to practice

   Having decided on the age and readiness of the child, you can select the method according to which you want to teach him.

   In order for the choice to be the most optimal and effective for your baby, you should get acquainted with the most basic techniques and methods of studying the table, as well as understand what rules should be followed to get a good result.

   We are looking for the right approach to the child

   • In any training, the main thing is the consistency and consistency of actions. If you took a table with your child, then study it regularly, each time repeating what you have passed.
   • Do not force your toddler to teach or force him to sit down. Try to understand what is the reason for his refusal - perhaps the child is simply tired, hungry, feeling unwell or sick. Then postpone the lesson or reschedule it to another time.
   • Some children find it very difficult to sit in one place for a long time - they like to move all the time and need to change activities frequently. In this case, standard activities will not work, but you can learn the sign while walking or playing, and on a swing, and on the way home.
   • Motivate your child to study - find exactly the key that will stimulate him.
   • Do not under any circumstances break loose, shout or scold for mistakes or misunderstandings. You cannot reproach a child with a bad memory, an inability to learn something, etc. Moreover, it is unacceptable to resort to physical punishment.
   • Another common mistake parents make is scaring them with bad grades or comparing their baby to other children, making them look unattractive. This is completely wrong, because every child is a person with his own individual pace and developmental characteristics.
   • Objectively evaluate the knowledge and abilities of your kid - if he has not a mathematical, but a humanitarian mindset, then look for the approach and the method that suits him best and will give the greatest effect.
   • For example, for children who easily memorize rhymes, you can come up with or find thematic rhymes for each number - this will already help the child and simplify the memorization process.
   • If the kid has figurative or associative thinking, find an association with all the numbers with him, compose stories, make illustrations or sketches.
   • Songs will help young musicians - singing them, he will remember much easier and faster that five eight will be forty, and seven three - twenty one.
   • Take frequent breaks from class to help your child rest.
   • Do not take literally the statements in some methods - “learn the chart in three hours” or something like that. Remember how the multiplication table was given to you at one time, and then start studying with your own child.
   • Remember to praise your little one for every small or big success and progress.

   We start to learn quickly and easily according to the methodology

   Let's look at one of the most effective teaching methods, according to which a child will get acquainted with the multiplication table in four days, understand the principle of its operation and will forever learn what multiplication is and why it is needed.

   In short, the specific meaning of multiplication is a simple replacement of the sum of the same terms with one action.

   It is this approach that is correct, because if a child suddenly forgets some kind of tabular example, then he will easily find a way out of the situation, orienting himself that it is possible to simply add one more term to the previous example.

   If the kid cramps a set of numbers incomprehensible to him and does not see their essence and meaning at all, then at any moment he can forget all this gibberish and he will not even have something to push off from in order to remember this or that example.

   It is worth clarifying that the terms of four days are approximate and suggest the presence of special classes, the child's special interest in learning, as well as his ability: the ability to operate with numbers within two hundred, mastery of various mathematical operations, understanding the composition of a number and the essence of multiplication - in fact, a child should already be able to multiply, but not yet know the table, as such, by heart.

   This video shows you how you can easily master the multiplication table in a fun, playful way by making colored cards.
   

   First day

   Based on the proposed methodology, you should first carefully study the standard multiplication table.

   If we take the multiplication of all the numbers from one to ten, then the child will have to learn as many as one hundred examples. At first glance, this is a rather daunting prospect, isn't it?

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

   So what you need to do with your child:

   • draw or print a table and write in it all the examples of multiplication from one to ten;

   

   • then find the same examples together, such as multiply five by four and four multiply by five - explain to the child that the answer does not change from permutation, as in addition;
   • fill in the obtained symmetrical examples with some other color (light gray) - there should be forty-five repetitions;
   • further, we also paint over the first and last column - multiplying one and tens, since these examples are very easy and they do not need to be taught or crammed;
   • you should have 36 cells or thirty-six mathematical facts selected - we will study them exactly.

   

   Please note that the highlighted examples should be located in the table in order of numbers - from smallest to largest, and their number will increase by one in each column.

   That is, if in the multiplication column of two, only one fact remains highlighted - twice two, then there will already be two examples for three - twice three and three times three, etc. Thus, you get a kind of inverted ladder of numbers.

   Second day

   The main task for a child is to understand and master the principle of doubling. The easiest way to explain it to a child is this: to multiply two by two, you just need to add the number "two" to yourself - the result is four.

   See how easy and simple it turns out:

   • to multiply any number by four, you just need to perform the operation of multiplying two by two, and in short, multiplying by four, you must first double the number, and then double the result;
   • go with the child examples of multiplication by two and four for all numbers and paint them in light blue;
   • make sure that the kid understands the principle of doubling, which means that he can do without cramming for cases of multiplication by two and four.

   

   Additionally, you can begin to explain to your child that the doubling principle can be used to multiply by eight, sixteen, and other powers of two. That is, the first degree is the two itself, the second is the number four, the third is the number eight.

   This series can be continued indefinitely. So the kid will slowly get acquainted with finding logarithms, simply by studying the multiplication table.

   The third day

   The next stage of training will be mastering the skill of multiplying by five. There are several interesting ways to learn how to multiply by five:

   • if doubling the number is easy enough, then it will not be more difficult to divide it equally or in half, that is, to get the result of multiplying any number by five, you just need to multiply it first by ten, and then divide by two, for example, multiply five by six - equal to half sixty, because we multiply six by ten and divide by two, the result is thirty, and so on;
   • you can use another method - for an even number, assign zero to its half, and for an odd number, assign five to the half of the previous digit, for example, when multiplying five by seven, you need to add five to the three, that is, to half of the six, which is the number row is in front of the seven, and when multiplying five by eight, divide eight by two and assign a zero to the resulting four;
   • there is still a completely universal method that is suitable for all numbers, but for now we use it for fives - just count fives with the child as many times as you need to multiply this same number five, for example, to multiply five by six count - five, ten , fifteen, twenty, twenty-five, thirty - that's the result;
   • we use the same method to explain the multiplication of the three and train with the baby to count;
   • if he understood and mastered everything, paint over all the examples of multiplication by five and by three with light purple color - you should have only ten cells left.

   

   Day four

   By this time, the child should already well understand and easily solve examples with the multiplication of numbers from two to five - without memorizing and memorizing, simply applying all the logical methods proposed above.

   He should like the next and final stage of training. To do this, you need to use your fingers. It is with their help that the technique offers to learn how to multiply numbers from six to nine.

   So, make the numbering of the fingers for yourself and the baby. You can write numbers with a felt-tip pen or marker, make appliqués on paper nozzles, make numbers out of felt, like in a finger theater - additional creativity with a mathematical background will only be a plus.

   The fingers of both hands must be numbered:

   • there should be fives on the thumbs;
   • on the indexes - sixes;
   • on the middle - sevens;
   • unnamed - eights;
   • on the little fingers - nines.

   Here's what to do next.

   • Sit down with your child at the table. Place your hands on the table, palms down. All numbers should be well and clearly visible.
   • Give any example for multiplication, for example, try multiplying nine by eight.
   • Bring the little finger of your left hand together with the number nine and the ring finger of your right hand with the number eight. They should touch each other at the edge of the table.
   • The other seven fingers hang down - four on the left and three on the right. Let's count them in dozens - that is, ten for each finger. As a result, we get seventy.
   • Now you need to multiply those on the table - one on the left and two on the right - two come out, and together seventy-two.
   • We also try with other numbers according to the same principle: he brings his fingers together with those numbers that need to be multiplied, the fingers in front of them are counted in tens, and the rest we multiply among ourselves and add the result.
   • Go through all the remaining examples so that the child understands this principle and gets the hang of multiplying.
   • Fill in the ten remaining cells with light orange.

   

   So we went through the entire table, learning not to memorize the material, but to understand its meaning and reason logically.

   Other ways and methods in the form of games and poetry

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

   The so-called Pythagorean table is very popular and effective in work - you can purchase a ready-made one or draw it with your child yourself. It is quite simple - the numbers are arranged vertically and horizontally from one to nine in tabular form.

   The essence of using the table is that the number from the left vertical column is multiplied by another one from the horizontal top row. The child's task is to move his hand to the place of their intersection on the table and find the result.

   With the Pythagoras table, you can come up with various games and combinations so that the kid understands the principle of multiplication and trains his memory.

   Also worth using:

   • interactive sound posters;
   • cards with examples for the game;
   • poems - there are wonderful poems by Marina Kazarina "About multiplication" and "Multiplication" by Alexander Usachev;
   • online simulators and educational games for studying the multiplication table on a computer;
   • practical examples with toys or surrounding objects;
   • didactic games - place numbers in houses, catch them like a fish, look for the correct answers to solve the mystery of pirate treasures, form trains, etc.

   This video presents another interesting teaching method in poetic form.
   

   Conclusion

   Be sure to ask how the child is studying the table at school. You can use your own teaching method, but at the same time introduce the baby to the standard program.

   The multiplication table can be a tough nut to crack, so do not rush and get upset or scold your child if the learning process is not as easy and fast as you would like.

   Remember that if you approach the matter with patience, endurance, and also act gradually and work according to the method, then you will definitely get an excellent result soon.

   Some quick ways oral multiplication we have already sorted it out with you, now let's take a closer look at how to quickly multiply numbers in your head, using various auxiliary methods. You may already know, and some of them are quite exotic, for example, the ancient Chinese way of multiplying numbers.

   Layout by category

   It is the simplest technique for fast multiplication of two-digit numbers. Both factors must be divided into tens and ones, and then all these new numbers must be multiplied by each other.

   This method requires the ability to keep in memory up to four numbers at the same time, and to do calculations with these numbers.

   For example, you need to multiply the numbers 38 and 56 ... We do it as follows:

   38 * 56 = (30 + 8) * (50 + 6) = 30 * 50 + 8 * 50 + 30 * 6 + 8 * 6 = 1500 + 400 + 180 + 48 = 2128 It will be even easier to do oral multiplication of two-digit numbers in three steps. First you need to multiply tens, then add two products of ones by tens, and then add the product of ones by ones. It looks like this: 38 * 56 = (30 + 8) * (50 + 6) = 30 * 50 + (8 * 50 + 30 * 6) + 8 * 6 = 1500 + 580 + 48 = 2128 In order to successfully use this method, you need to know the multiplication table well, be able to quickly add two-digit and three-digit numbers, and switch between mathematical operations, not forgetting intermediate results. The latter skill is achieved with help and visualization.

   This method is not the fastest and most effective, therefore it is worth exploring other methods of oral multiplication.

   Fitting numbers

   You can try to bring the arithmetic calculation to a more convenient form. For example, the product of numbers 35 and 49 can be imagined like this: 35 * 49 = (35 * 100) / 2 — 35 = 1715
   This method may turn out to be more effective than the previous one, but it is not universal and is not suitable for all cases. It is not always possible to find a suitable algorithm to simplify the task.

   On this topic, I remembered an anecdote about how the mathematician sailed along the river past the farm, and told the interlocutors that he was able to quickly count the number of sheep in the pen, 1358 sheep. When asked how he did it, he said that everything is simple - you need to count the number of legs and divide by 4.

   Visualizing long multiplication

   This is one of the most versatile methods of verbal multiplication of numbers, developing spatial imagination and memory. First you need to learn how to multiply two-digit numbers by single-digit numbers in a column in your mind. After that, you can easily multiply two-digit numbers in three steps. First, a two-digit number must be multiplied by tens of another number, then multiplied by units of another number, and then sum up the resulting numbers.

   It looks like this: 38 * 56 = (38 * 5) * 10 + 38 * 6 = 1900 + 228 = 2128

   Number placement visualization

   A very interesting way to multiply two-digit numbers is as follows. You need to consistently multiply the numbers in numbers to get hundreds, ones and tens.

   Let's say you need to multiply 35 on the 49 .

   First multiply 3 on the 4 , you get 12 , then 5 and 9 , you get 45 ... Write down 12 and 5 , with a space between them, and 4 remember.

   You get: 12 __ 5 (remember 4 ).

   Now multiply 3 on the 9 , and 5 on the 4 , and summarize: 3 * 9 + 5 * 4 = 27 + 20 = 47 .

   Now you need to 47 add 4 that we have memorized. We get 51 .

   We write 1 in the middle and 5 add to 12 , we get 17 .

   Total, the number we were looking for 1715 , it is the answer:

   35 * 49 = 1715
   Try to multiply in your head in the same way: 18 * 34, 45 * 91, 31 * 52 .

   Chinese or Japanese multiplication

   In Asian countries, it is customary to multiply numbers not in a column, but by drawing lines. For eastern cultures, the striving for contemplation and visualization is important, therefore, probably, they came up with such a beautiful method that allows you to multiply any numbers. This method is complicated only at first glance. In fact, greater clarity allows you to use this method much more efficiently than long multiplication.

   In addition, knowledge of this ancient oriental method increases your erudition. Agree, not everyone can boast that they know the ancient multiplication system, which the Chinese used 3000 years ago.

   Video on how the Chinese multiply numbers

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