How to read the multiplication table on your fingers. Multiplication on fingers. Entertaining mathematics. Through educational cartoons and programs

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.

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 have well developed associative memory. If a child is shown a clear example of 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 an 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 and 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.

One more 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 etc.

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 is in a 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!

In modern elementary schools, the multiplication tables begin to be taught in the second grade and end in the third, and learning the multiplication tables is often assigned for the summer. If you didn’t study in the summer, and your child is still “floating” in multiplication examples, we’ll tell you how to learn the multiplication table quickly and fun - with the help of drawings, games and even your fingers.

Problems that children often have in connection with the multiplication tables:

Children don't know what 7 x 8 is.
They don’t see that the problem must be solved by multiplication (because it doesn’t directly say: “What is 8 times 4?”)
They don't understand that if you know that 4 × 9 = 36, then you also know what 9 × 4, 36: 4 and 36: 9 are equal to.
They don’t know how to use their knowledge and use it to reconstruct a forgotten piece of the table.

How to quickly learn the multiplication table: the language of multiplication

Before you start teaching the multiplication table with your child, it’s worth stepping back a little and realizing that a simple multiplication example can be described in a surprising number of different ways. Take the 3×4 example. You can read it as:

three times four (or four times three);
three times four;
three times four;
product of three and four.

At first, it is far from obvious to the child that all these phrases mean multiplication. You can help your son or daughter if, instead of repeating yourself, you casually use different language when talking about multiplication. For example: “So how much is three times four? What do you get if you take three times four?”

In what order should I learn the multiplication tables?

The most natural way for children to learn multiplication tables is to start with the easiest ones and work their way up to the most difficult ones. The following sequence makes sense:

Multiplying by ten (10, 20, 30...), which children learn naturally as they learn to count.

Multiplying by five (after all, we all have five fingers and toes).

Multiplying by two. Pairs, even numbers and doubling are familiar even to young children.

Multiplying by four (after all, this is just doubling multiplying by two) and eight (doubling multiplying by four).

Multiplying by nine (there are quite convenient techniques for this, more on them below).

Multiplying by three and six.

Why is 3x7 equal to 7x3

When helping your child remember the multiplication tables, it is very important to explain to him that the order of the numbers does not matter: 3 × 7 gives the same answer as 7 × 3. One of the best ways to show this clearly is - use array. This is a special mathematical word that refers to a set of numbers or shapes enclosed in a rectangle. Here, for example, is an array of three rows and seven columns.

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Arrays are a simple and visual way to help your child understand how multiplication and fractions work. How many points are there in a 3 by 7 rectangle? Three rows of seven elements total 21 elements. In other words, arrays are an easy-to-understand way to visualize multiplication, in this case 3 × 7 = 21.

What if we draw the array in a different way?

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Obviously, both arrays must have the same number of points (they do not have to be counted individually), since if the first array is rotated a quarter turn, it will look exactly like the second.

Look around, look nearby, in the house or on the street, for some arrays. Take a look at the brownies in the box, for example. The cakes are arranged in a 4 by 3 array. What if you rotate them? Then 3 by 4.

Now look at the windows of the high-rise building. Wow, this is also an array, 5 by 4! Or maybe 4 to 5, depending on how you look? Once you start paying attention to arrays, it turns out that they are everywhere.

If you've already taught your children the idea that 3 x 7 is the same as 7 x 3, then the number of multiplication facts you need to memorize decreases dramatically. Once you memorize 3 × 7, you get the answer to 7 × 3 as a bonus.

Knowing the commutative law of multiplication reduces the number of multiplication facts from 100 to 55 (not exactly half due to squaring cases such as 3×3 or 7×7, which have no pair).

Each of the numbers located above the dotted diagonal (for example, 5 × 8 = 40) is also present below it (8 × 5 = 40).

The table below contains one more hint. Children usually start learning their multiplication tables using counting algorithms. To figure out what 8 × 4 is, they count like this: 4, 8, 12, 16, 20, 24, 28, 32. But if you know that eight is four is the same as four times eight, then 8, 16 , 24, 32 will be faster. In Japan, children are specifically taught to “put the lowest number first.” Seven times 3? Don't do this, count better 3 times 7.

Learning squares of numbers

The result of multiplying a number by itself (1 × 1, 2 × 2, 3 × 3, etc.) is known as square of the number. This is because graphically this multiplication corresponds to a square array. If you go back to the multiplication table and look at its diagonal, you will see that it is all made up of squares of numbers.

They have an interesting feature that you can explore with your child. When listing the squares of numbers, pay attention to how much they increase each time:

Squares of numbers 0 1 4 9 16 25 36 49...
Difference 1 3 5 7 9 11 13

This curious connection between squared numbers and odd numbers is a great example of how different kinds of numbers are related to each other in mathematics.

Multiplication table for 5 and 10

The first and easiest table to memorize is the 10 multiplication table: 10, 20, 30, 40...

In addition, children learn the multiplication table by five relatively easily, and they are helped in this by their arms and legs, which visually represent four fives.

It is also convenient that the numbers in the multiplication table for five always end in 5 or 0. (So, we know for sure that the number 3,451,254,947,815 is present in the multiplication table for five, although we cannot verify this using a calculator: on The device’s screen simply won’t fit such a number).

Children can easily double numbers. This is probably due to the fact that we have two hands with five fingers on each. However, children do not always associate doubling with multiplying by two. The child may know that if you double six you get 12, but when you ask him what six equals two, he has to count: 2, 4, 6, 8, 10, 12. In this case, you should remind him that six is two - the same as twice six, and twice six is double six.

So, if your child is good at doubling, then he essentially knows the two times table. At the same time, he is unlikely to immediately realize that with its help you can quickly imagine a multiplication table for four - for this you just need to double and double again.

Game: double adventure

Any game in which players roll dice can be adapted so that all rolls count as doubles. This gives several advantages: on the one hand, children like the idea of going twice as far as the dice shows with each throw; on the other hand, they gradually master the multiplication table by two. In addition (which is important for parents busy with other things), the game ends in half the time.

Multiplication table by 9: compensation method

One way to master the nine times table is to take the result of multiplying by ten and subtracting the excess.

What is nine times seven? Ten times seven is 70, subtract seven to get 63.

7 × 9 = (7 × 10) - 7 = 63

Perhaps a quick sketch of an appropriate array will help cement this idea in the child's mind.

If you have only memorized the nine times table up to "nine ten", then nine 25 will baffle you. But ten times 25 is 250, subtract 25, we get 225. 9 × 25 = 225.

Test yourself

Can you solve the 9 × 78 example in your head using the compensation method (multiplying by 10 and subtracting 78)?

There is another convenient way to master the nine multiplication table. It uses fingers and kids love it.

Hold your hands in front of you, palms down. Imagine that your fingers (including your thumb) are numbered from 1 to 10. 1 is the little finger on your left hand (the outermost finger to your left), 10 is the little finger on your right (the outermost finger to your right).

To multiply a number by nine, bend the finger with the corresponding number. Let's say you are interested in nine 7. Bend the finger that you mentally designated as the seventh number.

Now look at your hands: the number of fingers to the left of the curled one will give you the number of tens in your answer; in this case it is 60. The number of fingers on the right will give the number of ones: three. Total: 9 × 7 = 63. Try it: This method works for all single-digit numbers.

Multiplication table for 3 and 6

For children, the multiplication table by three is one of the most difficult. In this case, there are practically no tricks, and the multiplication table by 3 will simply have to be memorized.

The multiplication table for six follows directly from the multiplication table for three; here, again, it all comes down to doubling. If you know how to multiply by three, just double the result - and you get a multiplication by six. So 3 × 7 = 21, 6 × 7 = 42.

Multiplication table for 7 - dice game

So all we have left is the seven times table. There is good news. If your child has successfully mastered the tables described above, there is no need to memorize anything at all: everything is already in the other tables.

But if your child wants to learn the 7 times table separately, we will introduce you to a game that will help speed up this process.

You will need as many dice as you can find. Ten, for example, is an excellent number. Tell your son or daughter that you want to see which of you can add the numbers on the dice the fastest. However, let the children decide how many dice to roll. And to increase your child’s chances of winning, you can agree that he must add the numbers indicated on the upper faces of the cubes, and you – those on both the top and bottom.

Have each child choose at least two dice and place them in a glass or mug (they are great for shaking the dice to create a random roll). All you need to know is how many cubes the child took.

As soon as the dice are rolled, you can immediately calculate the total of the numbers on the top and bottom faces! How? Very simply: multiply the number of dice by 7. Thus, if three dice were drawn, the sum of the top and bottom numbers would be 21. (The reason, of course, is that the numbers on opposite sides of the die always add up to seven.)

Children will be so amazed at the speed of your calculations that they will also want to master this method so that they can use it someday in a game with their friends.

In the era of the so-called British Imperial system of measures and "non-decimal" money, everyone needed to own an account up to 12 × 12 (then there were 12 pence in a shilling and 12 inches in a foot). But even today, 12 comes up every now and then in calculations: many people still measure and count in inches (in America this is the standard), and eggs are sold by dozens and half-dozens.

Little of. A child who can freely multiply numbers greater than ten begins to develop an understanding of how large numbers are multiplied. Knowing the 11 and 12 multiplication tables helps you spot interesting patterns. Here is the complete multiplication table for up to 12.

Note that the number eight, for example, appears four times in the table, while 36 appears five times. If you connect all the cells with the number eight, you get a smooth curve. The same can be said about cells with the number 36. In fact, if a certain number appears in the table more than twice, then all places where it appears can be connected by a smooth curve of approximately the same shape.

You can encourage your child to explore on his own, which will keep him busy for (maybe) half an hour or more. Print out several copies of the table for multiplying the first twelve numbers by 12, and then ask him to do the following:

color all cells with even numbers red, and all cells with odd numbers blue;
determine which numbers appear there most often;
say how many different numbers are found in the table;
answer the questions: “What is the smallest number not found in this table? What other numbers from 1 to 100 are missing from it?”

Focus with eleven

The 11 multiplication table is the easiest to construct.

1 × 11 = 11
2 × 11 = 22
3 × 11 = 33
4 × 11 = 44
5 × 11 = 55
6 × 11 = 66
7 × 11 = 77
8 × 11 = 88
9 × 11 = 99

Take any number from ten to 99 - let it be, say, 26.
Break it into two numbers and move them apart to create a space in the middle: 2 _ 6.
Add the two digits of your number together. 2 + 6 = 8 and insert what you got into the middle: 2 8 6

This is the answer! 26 × 11 = 286.

But be careful. What do you get if you multiply 75 x 11?

Breaking down the number: 7 _ 5
Add: 7 + 5 = 12
We insert the result in the middle and get 7125, which is obviously wrong!

What's the matter? There is a little trick in this example that needs to be used when the digits used to represent the number add up to ten or more (7 + 5 = 12). We add one to the first of our numbers. Therefore, 75 × 11 is not 7125, but (7 + 1)25, or 825. So the trick is actually not as simple as it might seem.

Game: beat the calculator

The purpose of this game is to develop the skill of quickly using the multiplication table. You will need a deck of playing cards without pictures and a calculator. Decide which player will be the first to use the calculator.

The player with the calculator must multiply the two numbers drawn on the cards; he must use a calculator even if he knows the answer (yes, this can be very difficult).
The other player must multiply the same two numbers in his head.
The one who gets the answer first gets a point.
After ten attempts, players change places.

Rob Eastway

Then, with the ease of a magician, we “click” examples for multiplication: 2·3, 3·5, 4·6 and so on. With age, however, we increasingly forget about factors closer to 9, especially if we haven’t practiced counting for a long time, which is why we surrender to the power of a calculator or rely on the freshness of a friend’s knowledge. However, having mastered one simple technique of “manual” multiplication, we can easily refuse the services of a calculator. But let’s immediately clarify that we are only talking about the school multiplication table, that is, for numbers from 2 to 9, multiplied by numbers from 1 to 10.

Multiplication for the number 9 - 9·1, 9·2 ... 9·10 - is easier to forget from memory and more difficult to recalculate manually using the addition method, however, specifically for the number 9, multiplication is easily reproduced “on the fingers”. Spread your fingers on both hands and turn your hands with your palms facing away from you. Mentally assign numbers from 1 to 10 to your fingers, starting with the little finger of your left hand and ending with the little finger of your right hand (this is shown in the figure).

Let's say we want to multiply 9 by 6. We bend the finger with a number equal to the number by which we will multiply nine. In our example, we need to bend the finger with number 6. The number of fingers to the left of the bent finger shows us the number of tens in the answer, the number of fingers to the right shows the number of units. On the left we have 5 fingers not bent, on the right - 4 fingers. Thus, 9·6=54. The figure below shows in detail the entire principle of “calculation”.

Another example: you need to calculate 9·8=?. Along the way, let’s say that the fingers cannot necessarily act as a “calculating machine”. Take, for example, 10 cells in a notebook. Cross out the 8th cell. There are 7 cells left on the left, 2 cells on the right. So 9·8=72. Everything is very simple.

Now a few words to those inquisitive children who, in addition to the mechanical application of what has been said, want to understand why it works. Everything here is based on the observation that the number 9 is only one unit short of the round number 10, in which the ones place contains the number 0. Multiplication can be written as the sum of identical terms. For example, 9·3=9+9+9. Every time we add the next nine, we know that another one in the answer will not reach the round number. Therefore, no matter how many times nine is added (or, in other words, by what number x the multiplication is performed), the same number of ones will be missing in the answer. Since the units digit counts no more than 10 numbers (from 0 to 9), and when multiplying 9 x =? If there are exactly x ones missing in the ones place, then the number in the ones place will be equal to 10-x. This is reflected in the example with hands: we folded the finger with number x and counted the remaining fingers on the right for the units place, but in fact, out of 10 fingers, we simply excluded fingers with numbers from 1 to x, thus performing the 10-x operation.

At the same time, with each added nine, the number in the tens place increases by 1, and initially this place was empty (equal to zero). That is, for the first nine the tens place is zero, adding the second nine increases it by 1, the third nine increases it by another 1, and so on. This means that the number of tens is x-1, since the counting of tens began from zero. In the example with hands, we bent the finger with number x, thereby providing the “minus one” action, and counted the number of fingers to the left of the bent one, and there are exactly x-1 of them there. This is the secret of this simple technique.

This leads to additional considerations. Not only is the example 9·x=? it is easy to calculate through the number x (the tens place is x-1, the units place is 10-x), and this example can also be calculated as x·10-x. In other words, we add one zero to the right of the number x and subtract the number x from the resulting number. For example, 9·5=50-5=45, or 9·6=60-6=54, or 9·7=70-7=63, or 9·8=80-8=72, or 9·9= 90-9=81. With this unusual step, we turn the multiplication example into a subtraction example, which is much easier to solve.

Multiplication for the number 8 - 8·1, 8·2 ... 8·10 - the actions here are similar to the multiplication for the number 9 with some changes. Firstly, since the number 8 is already two short of the round number 10, we need to bend two fingers at once each time - with number x and the next finger with number x+1. Secondly, immediately after the bent fingers, we must bend as many more fingers as there are remaining uncurled fingers on the left. Thirdly, this directly works when multiplying by a number from 1 to 5, and when multiplying by a number from 6 to 10, you need to subtract the five from the number x and perform the calculation as for the number from 1 to 5, and then add the number 40 to the answer. because otherwise you will have to go through tens, which is not very convenient “on your fingers,” although in principle it is not so difficult. In general, it should be noted that multiplication for numbers below 9 is more inconvenient to perform “on your fingers”, the lower the number is located from 9.

Now let's look at an example of multiplication for the number 8. Let's say we want to multiply 8 by 4. We bend the finger with number 4 and then the finger with number 5 (4+1). On the left we have 3 uncurled fingers left, which means we need to bend 3 more fingers after finger number 5 (these will be fingers numbered 6, 7 and 8). There are 3 fingers left not bent on the left and 2 fingers on the right. Therefore, 8·4=32.

Another example: calculate 8·7=?. As mentioned above, when multiplying by a number from 6 to 10, you need to subtract five from the number x, perform the calculation with the new number x-5, and then add the number 40 to the answer. We have x = 7, which means we bend the finger with number 2 ( 7-5=2) and the next finger with number 3 (2+1). On the left, one finger remains unbent, which means we bend another finger (numbered 4). We get: on the left 1 finger is not bent and on the right - 6 fingers, which means the number 16. But to this number you need to add 40: 16+40=56. As a result, 8·7=56.

And just in case, let’s look at an example with passing through ten, where you don’t need to subtract any fives first and don’t need to add any 40s afterwards either. Suddenly it will be easier for you. Let's try to calculate 8·8=?. We bend two fingers with numbers 8 and 9 (8+1). There are 7 uncurled fingers left on the left. Remember that we already have 7 tens. Now we begin to bend 7 fingers on the right. Since there is only one unbent finger left, we bend it (there are 6 more to bend), then go through the ten (this means that we unbend all the fingers), and bend 6 unbent fingers from left to right. There are 4 fingers left on the right that are not bent, which means that in the units place the answer will contain the number 4. Previously, we remembered that there were 7 tens, but since we had to go through a ten, one ten needs to be discarded (7-1 = 6 tens). As a result, 8·8=64.

Additional considerations: Examples here can also be calculated simply in terms of the number x in the form of a subtraction expression x·10-x-x. That is, we add one zero to the right of the number x and subtract the number x from the resulting number twice. For example, 8·5=50-5-5=40, or 8·6=60-6-6=48, or 8·7=70-7-7=56, or 8·8=80-8-8 =64, or 8·9=90-9-9=72.

Multiplication for the number 7 - 7·1, 7·2 ... 7·10. Here you can’t do without going through a dozen. The number 7 only needs three to reach the round number 10, so you will have to bend 3 fingers at a time. We immediately remember the resulting number of tens by the number of fingers not bent to the left. Next, as many fingers as there are dozens are bent on the right. If, while bending your fingers, a transition through ten is required, we do it. Then the same number of fingers are bent a second time, that is, one operation is performed twice. And now the number of uncurled fingers remaining on the right is recorded in the units category, the number of previously counted tens (minus the number of transitions through the ten) is recorded in the tens category.

You see how it becomes more difficult to count “on your fingers” than to extract this information from memory. And then, for the numbers 7, 8 and 9, forgetting the elements of the multiplication table is somehow justified, but for the numbers below it is a sin not to remember. Therefore, at this point we will stop the story in the hope that you have grasped the very thread of “calculations” and, if absolutely necessary, you will be able to independently go down to numbers below 7, although a person who counts “on his fingers” something like “five five "must look extremely stupid.

If my memory serves me correctly, the multiplication table up to 5 inclusive was quite easy. But with multiplication by 6, 7, 8 and 9, certain difficulties arose. If I had known this trick before, my homework would have been completed at least twice as fast ;)

Multiplying by 6, 7 and 8

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

Now let's try to multiply, for example, 7x8. To do this, connect finger No. 7 on your left hand with finger No. 8 on your right.

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

(picture clickable)

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

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

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

3 (tens)
+
12 (units)
________
42

Multiply by 9

Turn your hands again with your palms facing you, but now the numbering of your fingers will go in order from left to right, that is, from 1 to 10.

Now we multiply, for example, 2x9. Everything that goes up to finger No. 2 is tens (that is, 1 in this case). And all that remains after finger No. 2 is units (that is, 8). As a result we get 18.

This method is often called the grandma method. It should be said right away that this is the worst of the proposed ways to study multiplication - it leads to a dead end, and the method given below is recommended more for familiarization than for practical use.

Finger multiplication technique.

Description and preparation.

The child is required to be able to add, know the multiplication table from 1 to 5 and be able to multiply by 10. To multiply by 6, 7, 8, 9 and 10 we use the fingers of both hands.

First you need to place both hands with your palms facing you and number all your fingers sequentially from 6 to 10. The numbering of the fingers is as follows:

Little finger – 6,

Nameless – 7,

Average – 8,

Index – 9,

Big – 10.

At the initial stage, fingers can be numbered with a pen. During the multiplication process, you will need to touch the necessary fingers of both hands. More details immediately with examples.

Example 7 * 6.

First you need to touch the ring finger of your left hand (number 7) to the little finger of your right hand (number 6). This matches the numbers in the example.

Multiplying 7 by 6

The touching fingers and the fingers below them are called lower, the fingers above are called upper.

To multiply 7 * 6, first calculate the sum of the lower fingers. In our case it is 3. Then multiply by 10, we get 30.

Now add 30 and 12 and get the answer 42.

Example 8 * 9.

To begin, you need to touch the middle finger of your left hand (number 8) to the index finger of your right hand (number 9).

Multiplying 8 by 9

First, let's calculate the sum of the lower fingers. In this case it is 7. Then multiply by 10, we get 70.

Adding 70 and 2, we get the answer 72.

Advantages of the method

Quite easy to use.

Disadvantages of the method

Dead end method. Multiplying on your fingers will not allow you to count anything more than the multiplication table, that is, you will still have to relearn how to multiply normally.
Inferior. Requires basic training in multiplication.
Inconvenient. Requires the use of both hands.
Impractical. It is unlikely that you will be able to pass the multiplication table by counting on your fingers in front of the teacher.
Not serious. A child counting on his fingers may become an object of ridicule from classmates.