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.

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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 with a 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 himself will 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 become more cheerful.

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.

To easily memorize tables, various tools are used: poems, cards, online simulators, small 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 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!

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

To work, we will need the Pythagorean table. Previously, it was published on the back of notebooks. It looks like this:

You can also see the multiplication table in this format:

Now, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make his job easier, find or print the actual chart.

2. Explain the working principle

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When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike what he has memorized or what someone else told him. Therefore, try to turn studying the table into an interesting game.

When starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.

Explain that multiplication is a short and quick way to do calculations.

Next you need to understand the structure of the table itself. Show that the numbers in the left column are multiplied by the numbers in the top row, and the correct answer is where they intersect. Finding the result is very simple: you just need to run your hand across the table.

3. Teach in small chunks

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There is no need to try to learn everything in one sitting. Start with columns 1, 2 and 3. This way you will gradually prepare your child to learn more complex information.

A good technique is to take a blank printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count.

When he has figured it out and mastered the simplest columns well enough, move on to more complex numbers: first, multiplying by 4–7, and then by 8–10.

4. Explain the property of commutativity

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The same well-known rule: rearranging the factors does not change the product.

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

5. Find patterns in the table

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

1. When multiplied by 1, any number remains the same.
2. All examples of 5 end in 5 or 0: if the number is even, we assign 0 to half the number, if it is odd, 5.
3. All examples of 10 end in 0 and begin with the number we are multiplying by.
4. Examples with 5 are half as many as examples with 10 (10 × 5 = 50, and 5 × 5 = 25).
5. To multiply by 4, you can simply double the number twice. For example, to multiply 6 × 4, you need to double 6 twice: 6 + 6 = 12, 12 + 12 = 24.
6. To remember multiplication by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. You need to remember the first and last number. All the rest can be reproduced according to the rule: the first digit in a two-digit number increases by 1, and the second decreases by 1.

6. Repeat

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Practice repetition often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Watch your pace too: give yourself more time to think at first, but gradually increase the pace.

7. Play

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Don't just use standard methods. Learning should captivate and interest the child. Therefore, use visual aids, play, use different techniques.

Cards

The game is simple: prepare cards with examples of multiplication without answers. Mix them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, if he gives the wrong answer, we return it to the pile.

The game can be varied. For example, giving answers on time. And count the number of correct answers every day so that the child has a desire to break his yesterday’s record.

You can play not only for a while, but also until the entire stack of examples runs out. Then for every wrong answer you can assign the child a task: recite a poem or tidy things up on the table. When all the cards have been solved, give them a small gift.

From the reverse

The game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will result in 30 (for example, 3 × 10 and 6 × 5).

Examples from life

Learning becomes more interesting if you discuss with your child things that he likes. So, you can ask a boy how many wheels four cars need.

You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass multiplied by the number of glasses.

Poetry

Rhyme will help you remember even complex examples that are difficult for a child. Come up with simple poems on your own. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine is seventy two.”

8. Don't be nervous

Usually, in the process, some parents forget themselves and make the same mistakes. Here is a list of things that you should never do:

1. Force the child if he doesn't want to. Instead, try to motivate him.
2. Scold for mistakes and scare with bad grades.
3. Set your classmates as an example. When you are compared to someone, it is unpleasant. In addition, you need to remember that all children are different, so you need to find the right approach for each.
4. Learn everything at once. A child can easily be frightened and tired by a large volume of material. Learn gradually.
5. Ignore successes. Praise your child when he completes tasks. At such moments he has a desire to study further.

Multiplication table or the Pythagorean table is a well-known mathematical structure that helps schoolchildren learn multiplication, as well as simply solve specific examples.

Below you can see it in its classic form. Pay attention to the numbers from 1 to 20 that title the lines on the left and the columns at the top. These are multipliers.

How to use the Pythagorean table?

1. So, in the first column we find the number that needs to be multiplied. Then in the top line we look for the number by which we will multiply the first one. Now we look at where the row and column we need intersect. The number at this intersection is the product of these factors. In other words, it is the result of their multiplication.

As you can see, everything is quite simple. You can view this table on our website at any time, and if necessary, you can save it to your computer as a picture so that you can access it without an Internet connection.

2. And again, please note that below there is the same table, but in a more familiar form - in the form mathematical examples. Many people will find this form simpler and more comfortable to use. It is also available for downloading to any medium in the form of a convenient image.

And finally, you can use our calculator, which is present on this page, at the very bottom. Just enter the numbers you need for multiplication into the empty cells, click on the Calculate button, and immediately a new number will appear in the Result window, which will be their product.

We hope this section will be useful to you, and our Pythagorean table in one form or another it will more than once help you in solving examples with multiplication and simply for memorizing this topic.

Pythagorean table from 1 to 20

×	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
11	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220
12	12	24	36	48	60	72	84	96	108	120	132	144	156	168	180	192	204	216	228	240
13	13	26	39	52	65	78	91	104	117	130	143	156	169	182	195	208	221	234	247	260
14	14	28	42	56	70	84	98	112	126	140	154	168	182	196	210	224	238	252	266	280
15	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
16	16	32	48	64	80	96	112	128	144	160	176	192	208	224	240	256	272	288	304	320
17	17	34	51	68	85	102	119	136	153	170	187	204	221	238	255	272	289	306	323	340
18	18	36	54	72	90	108	126	144	162	180	198	216	234	252	270	288	306	324	342	360
19	19	38	57	76	95	114	133	152	171	190	209	228	247	266	285	304	323	342	361	380
20	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400

Multiplication table in standard form from 1 to 10

1 x 1 = 1 1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 10	2 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20	3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30	4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40	5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50
6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60	7 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70	8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80	9 x 1 = 9 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90	10 x 1 = 10 10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 10 x 6 = 60 10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x 10 = 100

Multiplication tables in standard form from 10 to 20

11 x 1 = 11 11 x 2 = 22 11 x 3 = 33 11 x 4 = 44 11 x 5 = 55 11 x 6 = 66 11 x 7 = 77 11 x 8 = 88 11 x 9 = 99 11 x 10 = 110	12 x 1 = 12 12 x 2 = 24 12 x 3 = 36 12 x 4 = 48 12 x 5 = 60 12 x 6 = 72 12 x 7 = 84 12 x 8 = 96 12 x 9 = 108 12 x 10 = 120	13 x 1 = 13 13 x 2 = 26 13 x 3 = 39 13 x 4 = 52 13 x 5 = 65 13 x 6 = 78 13 x 7 = 91 13 x 8 = 104 13 x 9 = 117 13 x 10 = 130	14 x 1 = 14 14 x 2 = 28 14 x 3 = 42 14 x 4 = 56 14 x 5 = 70 14 x 6 = 84 14 x 7 = 98 14 x 8 = 112 14 x 9 = 126 14 x 10 = 140	15 x 1 = 15 15 x 2 = 30 15 x 3 = 45 15 x 4 = 60 15 x 5 = 70 15 x 6 = 90 15 x 7 = 105 15 x 8 = 120 15 x 9 = 135 15 x 10 = 150
16 x 1 = 16 16 x 2 = 32 16 x 3 = 48 16 x 4 = 64 16 x 5 = 80 16 x 6 = 96 16 x 7 = 112 16 x 8 = 128 16 x 9 = 144 16 x 10 = 160	17 x 1 = 17 17 x 2 = 34 17 x 3 = 51 17 x 4 = 68 17 x 5 = 85 17 x 6 = 102 17 x 7 = 119 17 x 8 = 136 17 x 9 = 153 17 x 10 = 170	18 x 1 = 18 18 x 2 = 36 18 x 3 = 54 18 x 4 = 72 18 x 5 = 90 18 x 6 = 108 18 x 7 = 126 18 x 8 = 144 18 x 9 = 162 18 x 10 = 180	19 x 1 = 19 19 x 2 = 38 19 x 3 = 57 19 x 4 = 76 19 x 5 = 95 19 x 6 = 114 19 x 7 = 133 19 x 8 = 152 19 x 9 = 171 19 x 10 = 190	20 x 1 = 20 20 x 2 = 40 20 x 3 = 60 20 x 4 = 80 20 x 5 = 100 20 x 6 = 120 20 x 7 = 140 20 x 8 = 160 20 x 9 = 180 20 x 10 = 200

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Every parent at some point has to face one very difficult problem: how to help their child learn the multiplication tables. Today on the Internet there are many different ways to help children memorize the so-called Pythagorean table: songs, audio programs. However, not every method is truly effective and makes it easy and quick to teach a child the multiplication table. Each student needs his own approach, his own most effective technique. This article will discuss the basic techniques and ways to study the multiplication table, from which you can choose those that are suitable for your child.

It is important! First of all, you should explain to your child the essence of the operation of multiplication. As a rule, children who begin to learn the multiplication table already have an understanding of basic arithmetic operations, such as addition and subtraction. It is this child’s knowledge that will help you explain to him the principle of multiplication: that multiplying 2 by 3 means adding the number 2 3 times, that is, 2+2+2. The child must be well aware of this in order to avoid many difficulties and misunderstandings in learning the multiplication table in the future. In addition, you should explain how the multiplication table itself works, that the number from the left column is multiplied by the number from the top line, and at the intersection of the row and column in which these numbers are located, you should look for the answer, that is, their product. For example, five equals forty (5×8=40).

A game

In any even routine process, such as exercises for studying the multiplication tables, there must be an element of play; it is necessary for children! Learning using game techniques will force the child to delve into the task, become truly interested in the subject of multiplication and forget about his reluctance to learn. One of the main ones is: interesting things are remembered better and faster. If you can spark a child's interest in multiplication, you've already done half the job!

One of the popular games for learning multiplication tables is playing cards. You can read more about the game “” in this, and also download and print ready-made cards with examples and answers. The essence of this game multiplication table is that the child randomly draws a card from a pile and sees on each card an example of multiplication without an answer (for example, 7 × 7 =? or 3 × 8 =?). If he gives the correct answer, then the card “goes out of the game”, and if the answer is incorrect, then the card returns to the very bottom of the pile, and can be drawn again. The game continues until all the cards are gone, that is, until the child gives the correct answer to all the examples. When there are few cards left, as a rule, these are difficult examples that the child has already tried to solve, then they are easily remembered, especially when the child becomes excited during the game.

This game is sometimes called a "multiplication table simulator." The entire gameplay can be carried out in stages, depending on the material learned. For example, you can start your impromptu lesson with cards “multiplication tables by 2”, and then dilute them with new learned examples. There are many options for the game, whatever you can do.

In addition, you can introduce an element of play into learning the multiplication tables by using all kinds of programs, online games, special sound posters and much more, which can be easily found on the Internet. But the game "" is the simplest and most effective way to learn the Pythagorean table.

Having studied special techniques for memorizing the multiplication tables, we developed a special game, which we posted below. Children will be able to open cards in a simple playful way and remember examples.

Where to begin?

If you are just starting to teach your child multiplication skills, we recommend that you try the following techniques (go through the following stages).

Immediately explain to your child the simplest and most trivial examples from the multiplication table, which he can solve without any problems. When looking at a multiplication table, that big 10 by 10 grid with numerous numbers, a child can simply get scared. You should immediately make him feel that not everything is so difficult. And he can already solve part of the table on his own:

A) Multiply by 1 always gives the same number that we multiplied by 1. For example, 1*1=1, 2*1=2, 3*1=3, and even a million times 1 equals a million.

B) Multiply by 10, this is the same as simply adding a zero to a number. What is 2*10? That's right, 2 followed by a zero, that is 20.

Having learned the multiplication table by 1 and 10, the child should understand that he now knows all the outer columns and rows of the multiplication table (they are highlighted in green in the figure).


If all this took a lot of time and the child is tired, then it is better to postpone the study of the remaining Pythagorean table until next time. If not, and the child is full of strength and desire to continue, then we move on.

IN) Multiplication table by 2 It usually comes quite easily to children. Multiplying by 2 is equivalent to simply adding two identical numbers. If you teach your child the multiplication table, then most likely he already knows how to add small numbers and can handle multiplication by two without problems.

G) Changing multipliers. Another important rule of multiplication, which is usually understandable to an adult, but not always clear to a child, is the commutative (or commutative) law of multiplication. Simply put: rearranging the factors does not change the product. In other words, it is easier to learn the multiplication table if you know that 2*3 is the same as 3*2.

The child needs to explain and show why the second row and second column of the Pythagorean table contain the same numbers, exactly like the 3rd row and 3rd column, etc. Therefore, having learned the multiplication of 2 by any number, he will also know the multiplication of other numbers by 2. Therefore, the task becomes 2 times easier.

Thus, by applying the techniques described above, you can help your child easily remember the multiplication table values ​​highlighted in green:


Agree, it already looks good. Let your child know that the multiplication tables are not that big or complicated.

Targeted Memorization

Once your child has mastered the simplest multiplication table values, you can move on to more complex factors. Here it is important to use game elements and many other useful ones: test tasks, practical application. Many of the examples will need to be memorized, memorized and repeated several times so that your child can then easily recite the values ​​of the multiplication table. It's better to go in order and not try to learn everything at once. It is better to start with squares and multiplication by 3 and 4, gradually moving on to other numbers.

Some teachers believe that the right way to start learning the multiplication table is from the end, from more complex examples to simpler ones. But it is better not to do this in order to avoid the child’s stress from not understanding how these values ​​were obtained. By multiplying 3 by 3, a child can test himself on his fingers and see why it is 9 in the multiplication table. And if he is immediately asked to multiply 8 by 9 and told that the result just needs to be remembered, he will not be able to apply his knowledge in practice , which will worsen memorization and may negatively affect his motivation.

Squares of numbers. The square of a number is its product with itself. In the Russian multiplication table there are only 10 squares that need to be memorized. The squares up to the example “six by six thirty-six” are usually memorized with a bang, and the next 3 squares usually do not cause any particular difficulties either. And 10 by 10 will be one hundred, which we have already covered earlier in previous lessons.

Multiplication table for 3. It is at this stage that the first difficulties may arise. If it happens that the child cannot remember some meanings, then it’s time to start using cards. And if this doesn’t help, and you know that your child has a more humanitarian mindset, then you can try (more will be written about them) to memorize the multiplication tables.

Multiplication table for 4. You can also use cards and poems here. In addition, let your child understand that multiplying by four is the same as multiplying by 2 and again by 2. You will find these and other simple arithmetic patterns that can be useful for the development of mental counting in this article.

Multiplication table for 5. Multiplying by five is usually easy. Intuitively, it becomes clear to the child that all values ​​of this multiplication are located through 5 from each other and end in either 5 or 0. All even numbers multiplied by 5 always end in zero, and odd numbers end in 5.

Multiplication table for 6, 7, 8 and 9. There is a certain peculiarity of studying complex examples from the multiplication table. If a child has learned squares, as well as the multiplication table up to 5, then in fact he has very little left to learn, since he already knows the rest of the examples. This is clearly visible on this multiplication table, where the cells that the child has already mastered at this moment are highlighted in green.


As a result, the remaining cells of the multiplication table contain only six products, which are the most complex and worth paying close attention to.

1. 6×7=42
2. 6×8=48
3. 6×9=54
4. 7×8=56
5. 7×9=63
6. 8×9=72

To memorize these multiplication table expressions, it is better to use a card game to bring the answers to automaticity. It is most effective to use 12 cards (with multipliers swapped). As practice shows, schoolchildren, and often adults, often have some problems with these six works.

That's all! In just a few lessons, the entire multiplication table can be learned quickly and easily!

Other tricks for learning multiplication tables

Naturally, there is no single correct answer to the question “how to learn the multiplication tables correctly.” In each individual case, for each individual child, even for each individual lesson, it is necessary to select certain most effective methods. Try using several techniques in your teaching arsenal to work with your child, and then you can quickly and easily understand how best to teach him the multiplication table. These are the methods.

Case Study

It will be easier to learn any work from the Pythagorean table if you demonstrate it in practice. For example, you can ask the boys how many wheels are needed for 5 cars (5×4=20). And the multiplication table for girls can have examples in the style of how many elastic bands are needed to braid two pigtails for three dolls (2 × 3 = 6).

Complex Examples

Some examples from the multiplication table may be easier for your child, while others may be more difficult. Try to train him on complex examples so that he concentrates especially on them.

Multiplication table on fingers

Some examples from the multiplication table can be easily calculated using natural human fingers. And this applies not only to the simplest products, but also, for example, to multiplying by 9. To do this, we place our hands, palms down, next to each other, with our fingers straightened. Now, to multiply any number by 9, simply bend your finger under the number of this number (counting from the left). The number of fingers before the curved one will be tens of the answer, and after - units.

Poetry

Another way to memorize multiplication tables is to use poems (rhymes). If your child has difficulty remembering a certain value of the Pythagorean table, then you will probably find this method interesting. It may turn out that it is much easier for a child to memorize poetry than “dry” numbers. Today on the Internet you can find several large (even gigantic) multiplication tables in verse.

It is unlikely that you would think that learning such a poem could be easier than just the multiplication table, but the rhyme can be used in particularly difficult cases. For example, multiplying by 7 and 8 often causes difficulties. And here the poems of Marina Kazarina “About Multiplication” and Alexander Usachev “Multiplication” can come to the rescue. Below are 6 excerpts from a poem by Alexander Usachev about multiplication of the six most difficult examples of the multiplication table.

6x7

Six networks of six ruffs -
This is also thirty-six.
And a roach got caught in the net:
Six seven is forty two.

6x8

Hippos of buns ask for:
Six eight - forty eight...

6x9

We don't mind the buns.
Open your mouth wider:
Six will be nine -
Fifty four.

7x8

Once a deer asked an elk:
- What is seven eight? —
Elk did not bother to look into the textbook:
- Fifty, of course, six!

7x9

Seven nesting dolls
The whole family is inside:
Seven nine crumbs -
Sixty three.

8x9

Eight bears were chopping wood.
Eight nine is seventy two

Mathematics is one of the most important and necessary sciences for your child.

In mathematics there are four types of arithmetic operations: addition, subtraction, multiplication, division.

What is multiplication?

It's a smart addition

After all, it’s smarter to multiply times,

Than add everything up for an hour.

Today we will consider the arithmetic operation, multiplication, it is very important to explain and teach every child to multiply, for this we will look at how you can multiply different numbers by 4.

Multiplying different numbers by four

Let's consider what happens if you multiply the number four by different numbers.

Multiply the number four by two

Let's look at the next example, in this example there are two terms 4, 4. Let's add these two terms, what do we get? We will get the answer 8.

That is, the sum of two fours is equal to eight.

Now let's see how you can get the number eight by multiplication?

Look at the example written above. In the example, there are two terms, to get the number eight, you need to multiply the number four by the number of terms. That is, four times two is the sum of two fours.

Multiply four by two to get eight.

Four times two is eight

Multiply the number four by three

Let's look at the next example, in this example there are three terms 4, 4, 4. Let's add these three terms, what do we get? We will get the answer 12.

That is, the sum of three fours is equal to twelve.

Now let's see how you can get the number twelve by multiplication?

Look at the example written above. In the example there are three terms, to get the number twelve, you need to multiply the number four by the number of terms. That is, four times three is the sum of three fours.

Multiply four by three to get twelve.

Four times three is twelve

Multiply the number four by four

Let's look at the next example in this example there are four terms 4, 4, 4, 4. Let's add these four terms, what do we get? We will get the answer 16.

4 + 4 + 4 + 4 = 16

That is, the sum of four fours is equal to sixteen.

Now let's see how you can get the number sixteen by multiplication?

Look at the example that is written above, in our example there are four terms, to get the number sixteen, we need the number four, multiplied by the number of terms, that is, by four we get sixteen.

Multiply four by four to get sixteen.

Four times four sixteen

Multiply the number four by five

Let's look at the next example in this example there are five terms 4, 4, 4, 4, 4. Let's add these five terms, what do we get? We will get the answer 20.

4 + 4 + 4 + 4 + 4 = 20

That is, the sum of five fours is equal to twenty.

Now let's see how you can get the number twenty by multiplication?

Look at the example that is written above, in our example we have five terms, to get the number twenty, we need the number four, multiplied by the number of terms, that is, by five we get twenty.

Multiply four by five to get twenty.

Four times five twenty

Multiply the number four by six

Let's look at the next example in this example there are six terms 4, 4, 4, 4, 4, 4. Let's add these six terms, what do we get? We will get the answer 24.

4 + 4 + 4 + 4 + 4 + 4 = 24

That is, the sum of six fours is equal to twenty-four.

Now let's see how you can get the number twenty-four by multiplication?

Look at the example that is written above, in our example there are six terms, to get the number twenty-four, we need the number four, multiplied by the number of terms, that is, by six we get twenty-four.

Multiplying four by six equals twenty-four.

Four times six twenty four

Multiply the number four by seven

Let's look at the next example in this example seven terms 4, 4, 4, 4, 4, 4, 4. Let's add these seven terms, what do we get? We will get the answer 28.

4 + 4 + 4 + 4 + 4 + 4 + 4 = 28

That is, the sum of seven fours is equal to twenty-eight.

Now let's see how you can get the number twenty-eight by multiplication?

Look at the example that is written above, in our example there are seven terms, to get the number twenty-eight, we need the number four, multiplied by the number of terms, that is, by seven we get twenty-eight.

Multiplying four by seven equals twenty-eight.

Four times seven twenty eight

Multiply the number four by eight

Let's look at the next example in this example there are eight terms 4, 4, 4, 4, 4, 4, 4, 4. Let's add these eight terms, what do we get? We will get the answer 32.

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32

That is, the sum of eight fours is thirty-two.

Now let's see how you can get the number thirty-two by multiplication?

Look at the example written above, in our example there are eight terms, to get the number thirty-two, we need the number four, multiplied by the number of terms, that is, by eight we get thirty-two.

Multiplying four by eight equals thirty-two.

Four times eight thirty two

Multiply the number four by nine

Let's look at the next example in this example there are nine terms 4, 4, 4, 4, 4, 4, 4, 4, 4. Let's add these nine terms, what do we get? We will get the answer 36.

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36

That is, the sum of nine fours is thirty-six.

Now let's see how you can get the number thirty-six by multiplication?

Look at the example written above, in our example there are nine terms, to get the number thirty-six, we need the number four, multiplied by the number of terms, that is, by nine we get thirty-six.

Multiplying four by nine equals thirty-six.

Four times nine thirty six

Multiply the number four by ten

Let's look at the next example in this example ten terms 4, 4, 4, 4, 4, 4, 4, 4, 4, 4. Let's add these ten terms, what do we get? We will get the answer 40.

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 40

That is, the sum of ten fours is equal to forty.

Now let's see how you can get the number forty by multiplication?

Look at the example that is written above, in our example there are ten terms, to get the number forty, we need the number four, multiplied by the number of terms, that is, by ten we get forty.

Multiplying four by ten equals forty.

Four times ten forty

We have looked at the entire multiplication table by four, now let's look at the entire multiplication table by four.

The multiplication table by four can be written in a different order; we swap the factors and get exactly the same answer.

To remember the four times table well, you can play the following games.

Games for memorizing the four times tables

Game one “Answer quickly”

This game can be played by two people, but several people are better, a leader is chosen, it can be an adult, he gives a task and whoever answers correctly first scores points.

This game will teach your child to remember and answer quickly. If several people play, then the players will develop a spirit of competition, and everyone will try to answer faster and score as many points as possible.

Question 1. Four times two - ?

Question 2. Four times eight - ?

Question 3. Four times five - ?

Question 4. Four times ten - ?

Question 5. Four times three - ?

Question 6. Four times seven - ?

Question 7. Four times four - ?

Question 8. Four times six - ?

Question 9. Four times nine - ?

Questions can be changed ad infinitum; the more you ask such questions, the faster the child will remember the multiplication table and will be well versed in it.

Game two “Correct orientation”

It is better to play this game with several children at the same time, we choose a leader, it can be an adult. The leader takes the ball and stands in a circle, asks a question on the multiplication table by four and throws the ball to the child, the child catches this ball, quickly answers the question and throws back.

If the child answered incorrectly, the presenter throws the ball to him again and asks another question.

If the child answers correctly, the child is praised and the ball is thrown to another child.

Sample questions:

how much does it get if we multiply six by four;

what is four times three?

what is five four?

Game three “Show me quickly”

For this game, you need to prepare cards with numbers from one to forty in advance and distribute them to each child who will participate in this game.

The presenter asks questions on the topic “multiplying by four,” and the children quietly answer from their seats using these cards, picking them up.

The presenter checks the correctness of the answers and asks further questions.

Sample questions for the game:

what is the answer if you multiply four by seven;

what is five four?

what is eight four?

what is the answer if you multiply four by six;

how much does it get if we multiply four by four;

what is four times three?

what is four times eight?

what is nine four?

how much will it be if we multiply seven by four and so on.

In this game, change the wording of the question so that the child thinks a little.

Game four "Quick answer"

In this game, the leader reads a verse on the topic “studying the multiplication table for the number four,” and the children must listen carefully and when the leader reads the verse in full or during the verse, the children must quickly give an answer.

Verse 1. Pigs

Four cute pigs

They danced without boots:

Four times four -

How many? Bare legs?

Answer: sixteen bare legs.

Verse 2. Monkeys

Four scientist monkeys

We were leafing through books with our feet...

Each foot has five toes:

Four times five – guess?

Answer: twenty.

Verse 3. Potatoes

Potato went to the parade - in - uniform:

Four times six is...

Answer: twenty-four.

Verse 4. Magpies

Forty forty walked

We found curd cheese.

And divide the cottage cheese into parts:

Four times ten -...

Answer: forty.

Homework

To consolidate the multiplication table by four, we suggest doing your homework.

Task one

After the equal sign, put the answer; thirty seconds are given to complete the task.

Task two

In this task you need to answer the questions posed.

what is four times nine?

what is seven four?

how much does it get if nine is multiplied by four;

what is four times three?

what is four times five?

what is four times six?

what is the value if eight is multiplied by four?

how much does it get if you multiply four by four?

what is six four?

how much does it get if you multiply four by ten?

Task three

This task contains several problems that must be solved quickly and correctly.

Four birds brought three berries in their beaks. How many berries did the birds bring?

Five squirrels each had four cones. How many cones did the squirrels have?

Each hedgehog had four mushrooms in its hole. I counted six hedgehogs. How many mushrooms did the hedgehogs have?

The four bunnies will be visited by the same number of squirrels today. How many animals will there be?

Sveta had four postcards, and her friends gave Sveta the same number of postcards. How many postcards does Sveta have?

Four girls came to sign up for the drawing club, and twice as many boys. How many children in total came to sign up for the drawing club?

Task four

Look at the next task, here are examples of multiplication; you need to put numbers instead of dots so that the equality turns out to be true.

Task five

In this task, two columns are given, the first column contains examples, and the second column contains answers. You need to solve the example correctly, and find the answer you need, connect the example and the answer with an arrow.

Task six

In this task the numbers given are 8, 12,16, 20, 28, 24, 32, 36, 40.

What number must be taken to obtain the following equality?

To better master mathematical counting and multiplication tables, we offer you several educational games for children.

Educational games for children

Game 1 “Comparing numbers from memory”

The game “Comparing numbers from memory” develops thinking and memory.

The main essence of the game is given a number; it must be compared with the previous number.

In this game, a number appears on the screen for a few seconds, you need to remember it, then the number disappears and another number appears, you need to compare it with the previous one and answer the question “more” or “less.” If you answered correctly, you score points and continue playing.

Game 2 “Mathematical comparisons”

The game "Mathematical Comparisons" develops thinking and memory.

The main essence of the game is to compare numbers and mathematical operations.

In this game you need to compare two numbers. At the top there is a question written, read the question carefully. At the bottom there are three buttons “left”, “equal”, “right”. You can answer with the mouse by clicking on the desired button with the mouse. If you answered correctly, you score points and play further .

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