The multiplication table says to repeat. Let's look at the main ways to quickly memorize

In life, people who are able to do mental calculations look like “super smart people,” although there is nothing complicated about it. A calculator is a calculator, but counting in your head is useful!
How to help your child learn the multiplication tables
Below are some simple techniques

Multiplying by 2 or doubling. Doubling is quite easy, just add something to yourself. At first, I showed one, two, three, four, five fingers on my left and right hand at the same time - this is how we got 2, 4, 6, 8, 10. Together with my student’s fingers, we reached twenty, and then I pointed to various things in the room, and suggested counting and doubling - the number of letters in a poster, the number of symbols on a watch dial, counting the number of spokes on one side of a bicycle wheel, and checking whether the total number matches the double, and so on.

Multiplying by 4 and 8, 3 and 6

When you know how to multiply by two, this is mere nonsense. Multiplying by four is the same as doubling the answer for something that has already been doubled, for example, 7x4 is 7x2x2, and we already remembered well that 7x2 is 14 in the previous lesson about doubling, so turn 14 itself into 28 will not be difficult. Once you've figured out the four, it's not so difficult to figure out the large numbers eights. Along the way we noticed that, for example, 16 is both 2x8 and 4x4. So we learned that there are numbers consisting entirely of twos: 2, 4, 8, 16, 32, 64.

By multiplying by 3 and 6, we learned the old pirate method of "dividing by three." If you add the digits of a number multiplied by 3, 6, or any other number that is divisible by three, then the result of adding the digits of the answer is always a multiple of three. For example, 3x5 = 15, 1+5 = 6. Or 6x8 = 48, and 4+8 = 12, a multiple of three. And you can add the numbers into 12, you also get 3, so if you get to the end like this, you always get one of three numbers: 3, 6 or 9.

So we turned it into another game. I would ask a number, even a three- or four-digit one, and ask if it was divisible by 3. To answer, just add the numbers, which is quite simple. If the number was divisible by 3, then I asked - “and by 6?” – and then you just had to see if it was even. And then (in the special case of small numbers from the table) sometimes I also wanted to find out what would happen when dividing by 3 or 6. It was a very fun activity.

Multiplying by 5 and 7, prime numbers
And now we are left with multiplication by five, seven, and nine. This means that we learned to multiply them by many other numbers - by 1, 2, 3, 4, 6, 8 and 10. We figured out five very quickly - it’s easy to remember: at the end there is either a zero or five, just the same as a number to be multiplied: either even or odd. A clock dial is a great object to use with A's; you can come up with many problems about traveling in time and space. At the same time, I explained why there are sixty minutes in an hour, and we understood why this is convenient.

We saw that it is convenient to divide 60 by 1, 2, 3, 4, 5, 6, but it is inconvenient to divide by 7. Therefore, it was time to take a closer look at this number. From multiplication by seven, the only things left to remember were 7×7 and 7×9. Now we knew almost everything we needed. I explained that seven is simply a very proud number - such numbers are called prime, they are divisible only by 1 and themselves.

Math can be fun and easy. Check out this cute table.
If you study it thoughtfully, there is not much to learn. There are 36 positions in total. The rest are either simple (1 x 10) or reversible (2 x 4 = 4 x 2). Minus 10 positions from the multiplication table by 9. It can be learned in 5 minutes. There is this trick:

So, let's go.

First, let's put our hands on the table and mentally number our fingers from left to right from 1 to 10. To perform the multiplication action, let's say 9 x 3 = ?, bend the third finger from the left. All! The answer is ready: the remaining uncurled fingers on the left form the number of tens in the answer, and the uncurled fingers on the right form the number of units. We count and say the answer: 27!


This way you can get the answer for any number. Here, for example, is an example 9 x 7 = 63

watch multiplication by 9 in the video:

Why haven’t I seen this technique before?!

And now I don’t understand why the school forces them to cram it, for a long time and painfully, instead of teaching children how to use the multiplication table so easily and cheerfully?!

During the summer holidays it is very convenient to learn the multiplication table. Simple and logical rules will help your child understand and remember the result for a long time.

Parents of schoolchildren often ask: How to quickly and easily learn the multiplication table? People study the table by various reasons, but most often simply because it is required for school. Why is this required?

The multiplication table is used:


  • To carry out calculations with multi-digit numbers in your head or on paper without a calculator. Example: to multiply 42*78, you need to use four “facts” from the multiplication table, plus knowledge of the decimal system

  • To see deep connections in mathematics and develop your “mathematical intuition”

Both goals (but at a much higher level than traditional memorization of tables allows) can be achieved along pleasant, mathematically interesting and pedagogically sound “roads.” The speed of this journey is, of course, better to choose individually. “Four days” from the content is an approximate estimate calculated according to the following conditions:


  • The student understands quantitative relationships within the first two hundred, knows how to add and subtract, and understands what multiplication is (for example, sees 3 * 4 as three groups of four objects), but does not remember the table by heart

  • Children play with a mentor individually or in small groups

  • All students are interested in learning this topic

If children do not yet know what multiplication is, or are just learning to operate with large numbers, our materials can be used, but it is better to modify the approach and speed.

From hundreds of existing tricks and methods related to the multiplication table, we chose according to two criteria. 1 - the trick is short, no more than two steps (because of this, for example, the Trachenberg system was eliminated); and 2 - there is a mathematically accessible explanation/proof for the trick. What's left is easy to remember, easy to understand, and easy to use!

The problems are designed for discussion with the mentor or with other students and the mentor, rather than independent decision. They can lead to quite advanced mathematics, which the student himself may either not notice or be unable to put into words.

Day 1

Let's start learning the multiplication table. Free cells...and 36 examples remain!

Here regular table multiplication for integers from zero to ten:

It looks a bit scary to learn by heart. One hundred individual facts! Cramming them is so long and boring... But in reality, how many facts do you need to remember in order to know this entire table? Not a hundred, that's for sure. Study the table carefully and for a long time until you get bored, and you will find many interesting ideas for tricks and techniques quick memorization.

Problem 0. After studying the table, find as much as possible more ways learn to use the facts from it without cramming. Many mathematicians, and not only them, have worked on finding such methods, so in reality you will have to cram much less than a hundred facts. How much, according to your estimates? Remember your answer...

We begin to look carefully and see that the table is symmetrical. After all, 4*8=8*4, a 9*6=6*9, and so on. In order not to list everything, let’s write down this observation in words:

If one number is multiplied by a second, the answer is the same as if the second number is multiplied by the first.

That is, part of the table is given to us completely free of charge! Which part? If you said “half”, you almost guessed right. In fact, symmetry gives us 45 free “facts.”

Problem 1. Why 45? Find 3 different ways to count. How many “free” facts will the symmetry of the multiplication table up to 20*20 give? Up to 30*30?

There are two more numbers that are very easy to multiply by. These are 1 and 10.

Problem 2. Why multiplying by 1 is easy, understandable, right? Why is it so easy to multiply by 10? Hint - think about other number systems, such as hexadecimal.

Let's cross out multiplication by these numbers from the list of those that need to be memorized. On the table these "free" facts are now shown in very light grey. And this is what remains:

At the end of the first day, using one of the methods from Task 1, we calculate how many facts we have left to learn. Well, isn't it so scary anymore? Then look forward to the next multiplication day!

Day 2

Two times two equals four...and that leaves 21 facts!

It's easy to double. Scientists even believe that doubling is “hardwired” in the human (and some animals) brain, just like the distinction between big and small or one and many. Kids learn to double by dividing candy into two, counting shoes and gloves, looking at objects in the mirror... To multiply by two, add the number to itself! How about multiplying by four? Multiplying by four is the same as multiplying by two twice. That is, to multiply by four, we double the number (this is easy), and then double the result.

Problem 3. How can you use the same principle to multiply by 8, by 16, etc.? The numbers in this "etc." are called "powers of two". The first degree is 2, the second is 4, the third is 8... Continue this series until you get tired. What power of two is the number 64? The answer to this question is called, in mathematical parlance, “finding the base 2 logarithm of 64.”

So you don’t need to cram anything to multiply by two and four. Same as multiplying by eight, but this already takes three steps (because eight is the third power of two, see Problem 3), so we'll save multiplying by 8 for another trick. In the meantime, let's color the facts that doubling and multiplying by 4 with doubling save us from cramming in light blue:

Look how few dark cells are left in the table - but there are many ahead interesting mathematics. See you on the third day.

Day 3

A universal method and multiplying by 5...and there are 10 cells left!

You can learn to quickly obtain the results of multiplying by five without cramming, and in just a few in different ways. That is, you can choose to use the method that suits you best.

Dividing in half (equally) is almost as easy as doubling. Conclusion: to multiply by five, multiply by ten and then divide by two. For example, five times eight equals half of eighty. Five times four equals half of forty.

Task 4. Why, exactly, do we “have the right” to do this? From a mathematical point of view...

Another way to multiply a number by five: if the number is even, add zero to half the number. If the number is odd, add five to half the previous number. For example, to multiply eight by five, we assign zero to half of eight. To multiply seven by five, we add five to half of six.

Task 5. Why does this method work? How does it differ from the first method? (Hint: nothing! From a mathematical point of view...)

And here is the promised one universal method multiplication. It works for any and all numbers, but is too slow for most of them. We simply count not one by one “One, two, three...” but by the number that we are multiplying, as many times as we are multiplying by. Try this for 7*8: “Seven, fourteen, twenty-one, twenty-eight, thirty-five, forty-two, forty-nine, fifty-six.” It’s difficult, isn’t it? And slowly... Now try 5*8: “Five, ten, fifteen... ...forty.” Simple and fast!

Problem 6, psychological. Why do you think people find it easy to count with A's?

By the way, it’s also not difficult to count in threes: three, six, nine... (why, do you think?). At the end of the third day, we will recolor the cells with light purple, which now you don’t have to cram: all multiplication by five and multiplication by three. This is what remains:

There are a few cells left, but these are the most difficult ones, you say? The next day you will deal with them in one fell swoop!

Day 4

Tricks on your fingers...And all the cells are filled in!

This very beautiful trick came from somewhere in the East, like many other wonderful mathematical ideas (for example, the idea of ​​zero). It is assumed that you already know how to multiply numbers from two to five (to learn, you can use the ideas of the first three days). We will multiply numbers from six to nine on our fingers.

Number the fingers of both hands: thumbs - 5, index fingers - 6, middle fingers - 7, ring fingers - 8, little fingers - 9. To start, you can write numbers on your nails with a felt-tip pen. Place your hands in front of you on the table, palm down, and “ analog computer" ready! Let's say we multiply 7*8: bring together finger number 7 on your left hand and finger number 8 on your right, placing these touching fingers along the edge. We count the dangling fingers (2 on the left hand and 3 on the right) as tens - 50.

We multiply the fingers on the table: 3 from the left hand multiplied by 2 from the right - it turns out 6, here is the answer: 7 * 8 = 56. Another example: 9*8. We touch fingers number 9 on the left and number 8 on the right hands. There are 7 fingers left in front of the touching fingers (4 on the left, 3 on the right) - this is 70. We multiply the rest: 1 on the left by 2 on the right - we get 2, and the answer is 72. That is, the fingers in front of the two touching are always counted as tens, and the rest multiply the left hand by the right. After the third or fourth multiplication it turns out very quickly and deftly.

Task 7. Why does this trick work? We know three different pieces of evidence—maybe you can find not only them, but other pieces of evidence as well?

Let's now recolor the cells with the results that we can get from the last trick light orange. Wow! There’s nothing left to cram - everything is painted over! This means that we have finally learned the multiplication table.

This game will help you learn the multiplication table quickly and without stress. Learning Multiplication- this is a mathematics program for grade 2, but you can (and even need) to start learning much earlier.

Rules of the game

An example of multiplying numbers is written on the school board. And several possible answers. Choose the correct one and drag it to the flashing area. You need to drag the ball while holding it left button mice. If you don't know the correct answer, you can use the "Hint".

For each correct answer you will receive one point. For an incorrect one, two points will be deducted from you.

How to learn the multiplication table. Simple technique

From the beginning, try to score 10 points on the simulator. For the first day, this result will be enough.

In the next days, try to improve your results and gain one or two points more than yesterday. If you want to learn the multiplication tables, then study regularly! Best of all - every day for 5 - 10 minutes. Use the exercise machine two to three times a day. Press "CTRL" and "D" keys simultaneously and bookmark this page. And you will always have easy access to this free online game.

When you can quickly and almost without errors gain 25 points, your knowledge of the multiplication tables can already be assessed as “good.” Well, getting 50 points is an excellent result! We can consider the test passed!

If you liked this game, be sure to share it with your friends. After all, they might like it too :-)

This game is designed and extremely useful for children from 3 to 10 years old. It helps to learn the multiplication tables in game form. But not only! During the game, the child’s attention and memory also develop. And also our Multiplication table"develops fine motor skills and strengthens hand muscles in children.

Without the multiplication table, just like without the alphabet, there’s nowhere! You learn it once and you will use it all your life - we need it in everyday life And professional activity! Let's look at effective techniques that will help your child learn the multiplication tables quickly and easily.

How to learn the multiplication table with your child: useful tips

Not every child succeeds in memorizing the multiplication table mechanically, and there is little point in it. Such memorization will not help in understanding and manipulating more complex mathematical operations, will not ensure the development of mental activity. That is why studying the table should be started only after understanding the very principle of multiplication.

Where to start mastering the multiplication table?

  1. At the first stage, you can explain to your child that multiplication is simply faster addition. Knowing that 3 x 2 can be replaced by addition (take 3 2 times), i.e. to 3 + 3, the child can easily calculate in his head.
  2. Explain to your child the principle of multiplication by 0 and 1. Children easily learn to multiply 0 and 1 by any number. After all, whatever number you take 0 times, 0 will remain (for example, 5×0=0), and if you take a number 1 time, it will be the same number (8×1=8).
  3. Introduce your child to the rule of multiplying by 10. Explain to him that when multiplying by 10, you just need to add a zero after performing the operation with one (for example: 5 x 10 = 5 x 1 and add 0, or 5 multiplied by one ten will be 5 tens). Over time, the answers will become ingrained in memory and there will be no need to calculate them every time. But for this you need to exercise regularly.
  4. Help your child master counting in twos, threes, fives (2,4,6...), (3,6,9...), (5,10,15...) . By practicing this type of counting, your child will easily be able to remember examples of multiplication by 2,3 and 5. These basic cases will help him master more complex options.
  5. The technique of adding the required multiplier to the previous answer . If the child remembers how much 3 x 5 is, he will add the answer with a factor of 3 and get the following example of a multiplication table for 3.
  6. A technique for subtracting a number from a familiar product. Knowing the table for 10, you can calculate any example for 9. For example, 6 x 10=60, which means 6 x 9 is 60-6=54.

After the principle of multiplication is understood by the child, he can be introduced to the Pythagorean table.

Pythagorean table

How to use the Pythagorean table?

  • Explain to your child that in the table, the rows and columns are headed by factors, and their products are in the table cells. Practice him in quickly finding works different numbers up to 10 using a table. And let it always be at hand. There is no need to prohibit using it until all the examples are fully learned. Then the table will “remember itself.”
  • If the baby understands principle commutative property of multiplication , there will be no need to memorize a significant part of the examples. It sounds like this: “The product does not change by rearranging the factors.” This means that 2×6 will be 12 and 6×2 will also be 12. And then the Pythagorean table will no longer seem so scary and big.

How to learn the multiplication table: games, cards

During school lessons, children are not allowed to play, jump, have fun, and often even move. The minutes of the lesson become painful for them, and learning becomes only a duty. Dry and uninteresting information is difficult to remember. It's much better to do it in a game, it's fun. One has only to show a second grader the attributes and tell the rules of the game, and his eyes immediately light up. Emotional memory is more effective than voluntary memory. There are many interesting games and exercises for painless and effective memorization of examples of multiplication according to the table. They arouse the child’s interest, motivate him and unobtrusively help develop his memory. Let's give a few examples with which you can achieve the desired goal without quarrels and tears.

Game "Fill in the colored squares"

During the game, the child must fill in the cells that make up a certain pattern on the Pythagorean table. For example, in the figure below you need to enter the products of numbers in the yellow cells that form the drawing of a dog. Have the student write down all the answers independently, not necessarily in order.

In the figure below, the form is divided into rectangles. different colors so that they do not merge into one. The exercise should be done daily until all multiplication cases are completely memorized. Incorrect answers must be written down on a draft and counted together with the baby.

Sherlock Holmes game

To play you will need:

  • form with the Pythagorean table;
  • simple pencils and colored pencils or markers.

The child needs to be given a code in the form of a sequence of multiplication examples, which, after filling in the answers in the table, will form some kind of picture. In order to solve the code, the child needs to find the works and color the square in which it is written.

Card game

On separate bright rectangles you need to write examples of table multiplication, and put a question mark instead of the answer. You can use ready-made cards by simply printing and cutting them.


The cut cards need to be mixed and pulled out one at a time. If the child counts the example on it correctly, then the card is eliminated from the game; if he makes a mistake, he is returned back.

Lotto

The game requires fields on which the answers and the examples themselves will be written in rectangles on separate cut cards. With these cards, the child must close the cells in the fields with the answers.

How to learn the multiplication table for 9 on your fingers?

Fingers are visual aids that are always “at hand.” With their help, a technique was invented for calculating multiplication by 9. To do this, you need to turn your hands with the backs of your hands towards you, mentally number your fingers, starting with the little finger of your left hand. When multiplying 9 by 1, we bend the finger at number 1 - 9 straightened remain, this is the answer. If you need to multiply 9 by 2, bend the finger at number 2. All fingers located to the left of the bent one will indicate the number of tens in the answer, and those to the right will indicate the number of units. One ten and 8 units is 18, the answer has been found! And so on.

Using your fingers, you can multiply by 2, alternately bending 1 finger on each hand, and after the fingers “run out”, start bending them again, but adding ten in your mind. In this case, first you need to count the fingers that are bent, and then those that remain straight.

Verses for memorizing the multiplication tables

More complex examples can be learned using rhyming lines. Good poems were invented for this by Marina Kazarina, Tom Sobakin, Andrei Usachev and many other authors.

Almost everyone can learn the multiplication tables. If a child is able to count the example 2 X 2 in his head, then he is capable of this. But the criterion for knowing the table is the speed of the answer. Therefore, it is important to bring this mechanism to automation.

On saucers for six eat
There are six crackers each.
But will they be able to eat them?
After all, six is ​​six -
Already thirty-six!

Multiplied tirelessly
Eastern sage,
And then to myself
Finally he whispered:
"May he remember forever
Your head:
SIX SEVEN –
FORTY TWO…
Seven six forty two..."

There lived a forester in the forest.
Even in severe frosts
Since childhood he was accustomed to counting
Fir trees, pines and birches,
Let's ask the forester:
How much will it be
SIX EIGHT?
He will answer:
FORTY EIGHT…
Either a Christmas tree,
Either pine trees.

The hippopotamus was spinning
In the hot summer sky
And a simple song
At the same time he sang:
"Let them know about it
Children around the world:
SIX IS NINE
FIFTY FOUR!"
T. Sobakin.

We hope that the tips in the article will help your children learn the multiplication tables quickly and easily! But what to do if a child has difficulty writing or reading, read the articles about and.

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

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

Also read the article,

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

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

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

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

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

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

For easy memorization, tables are used various instruments: poems, cards, online trainers, little multiplication secrets.

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

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

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

Download cards for studying the multiplication tables.

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

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

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

Multiplying by 1 and 10

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

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

Multiply by 2

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

Multiply by 4

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

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

Multiply by 3

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

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

Multiply by 5

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

Multiply by 9

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

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

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

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

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

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

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

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

Multiplying by 6,7,8

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

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

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

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

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

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

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

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

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