How to help your child learn the multiplication table

Recently, I was asked this question, and after my story, how I taught the multiplication table to one of my acquaintances of a boy, it turned out that on these tips another student quickly learned the multiplication table without monotonous memorization. Therefore, I thought it would be useful to tell you these simple tricks, and suddenly you will also face such a task, for example, when teaching your child.

After quite understandable addition and subtraction, cramming the multiplication table often looks like a kind of boring ritual, devoid of any clarity. Therefore, many schoolchildren quickly lose interest and do not know it well, and this is reflected in all education. I am sure that learning to multiply is a very important experience that affects a person’s general confidence in his own knowledge and capabilities of the mind, and maybe even a rational choice of profession.

The described techniques are quite simple, and, strictly speaking, have long been known. Memorization in my story also occurs through frequent repetition of examples, but all of them are just different events of one game in which this multiplication comes to life. I summarized the techniques I knew and compiled a schedule for my student so that a little more complicated alternated with simple. Due to the amusement of such training, while learning the table, the child will learn other interesting things from the world of arithmetic and mathematics in general: about prime numbers, the sign of division by 3, powers of two, and so on.

Also indirectly in the story are mentioned some ways of motivation. Our training itself, as it becomes clear from the narrative, was a game. I am sure that in the comments you will be able to supplement my story with your interesting ideas and methods that I did not know about, which will help make the story more complete for anyone who comes across it in search of an answer to the article title question.

Test

I taught one boy this table like that. During her study, we had a lot of fun. Without cramming, this is quite easy to do! And also, when a few days later my young friend was able to completely tell her without hesitation, we went to the zoo in honor of the holiday.

He turned out to be a very sensible guy, he really likes pirates at this early age, and at first I said that there is such a table card that all people more or less know and keep in mind, and the one who knows it better than others, passes on his knowledge to the heir. It is with this card that the pirates collect and share their treasures, so that in the life of the pirates these cards are generally on a par, but since this is even more secret, they talk less about it. And so I chose him as such a student, as I have high hopes for him. But first of all, I had to check it, conduct a test. The boy was very interested and agreed. I asked several problems for addition, and made sure that he was quite able to fold. So he passed the test, and we proceeded to the very essence of the matter.

Treasure map and multiplication by 1, 10 and 2

Now we had to draw this table. I said that I would draw it only once, this is an old pirate tradition - you can draw such a table only once, and memorize it forever, so that if you lose it, you can restore it on any piece of paper, or imagine it in your mind . Just like I do.

First, we drew a table of ten columns from the first such column

1x1 = 1
1x2 = 2
...
1x10 = 10

to the tenth of this

10x1 = 10
10x2 = 20
...
10x10 = 100.

I decided not to exclude multiplications by 1 and 10 precisely because they are very light. From them I began to explain: to multiply by 1 is the same as taking something once, it is easiest, it is the simplest, the very same number. And multiplying by ten is the same as taking something ten times. Say, if you put four rings on ten fingers, it will be forty. This is ten times more than four, and this is quite a lot, if you imagine. And when we multiply, we noticed that the number 10 acts like this: the unit does nothing again, and the zero goes to the end, so it’s enough to ascribe it.

Together we decided that it was very simple, and we won’t dwell on this anymore. But in subsequent exams, I checked if he learned these things. Especially after those cases when it was hard to remember something and Jack Sparrow was a little upset when his answer did not coincide with mine, I suddenly asked how much it would be 11 to 1 or 10 to 10, and then he came to life again.

Next, we proceeded to doubling. It’s quite easy to double, it’s enough to add something to yourself. First, I showed on my left and right hand one, two, three, four, five fingers at the same time - so we got 2, 4, 6, 8, 10. Together with the corsair's fingers we reached twenty, and then I pointed to different pieces in the room, and offered to count and double - the number of letters in the poster, the number of characters on the watch dial, count the number of spokes on one side of the wheel of the bicycle, and check whether the total number converges with doubled and so on.

When I decided that we coped with this column in the table, we moved on to the table itself, and I proposed to frame what we already know. Quickly circled the first and tenth column, and the second I gradually opened with each correct answer. Then I suggested to see if something else could be circled. Together we noticed that in the other columns there is also a multiplication by one, ten, and two, and the answers are exactly the same. So we realized that from a rearrangement of numbers the answer will not change. So the work was significantly reduced for us, and we learned not so little.

Multiplication by 4 and 8, 3 and 6

The next day we started multiplying by four and eight. When you know how to multiply by two, these are utter nonsense. Multiplying by four is the same as doubling the answer for what has already been doubled, for example 7x4 is 7x2x2, and what 7x2 is 14 we already remembered well in the previous lesson about doubling, so turning 14 into 28 is not difficult. When I figured out the four, it's not so difficult to deal with the big numbers of the eight. Along the way, we noticed that, for example, 16 is both 2x4 and 4x4. So we learned that there are numbers consisting entirely of twos: 2, 4, 8, 16, 32, 64. Then I recalled the story of one shipwreck, when sixty-four crew members had to be scattered across four old boats, about some of the sailors and about the ship itself.

After this lesson in the table there are even fewer non-circled cells. Multiplying by 3 and 6, we learned the old pirate method of "dividing into three." If you add the numbers in a number multiplied by 3, 6 or any other that is divided by three, then the result of adding the answer numbers 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 up to 12 digits, it will also be 3, so if you get to the end this way, you always get one of three numbers: 3, 6 or 9.

So we turned it into another game. I asked a number, even a three- or four-digit number, and asked if it was divisible by 3. For the answer, it’s enough to add the numbers, which is quite simple. If the number was divided 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 with such a division by 3 or 6. It was a very fun lesson.

Multiplication by 5 and 7, prime numbers

And now we have left the multiplication by five, seven, and nine. And this means that we learned to multiply them by many other numbers - by 1, 2, 3, 4, 6, 8, and 10. We figured out the five very quickly - it is easy to remember: at the end there is either zero or five, exactly the same as a multiplied number: either even or odd. As a subject that is convenient for practicing with fives, the watch dial is excellent, you can come up with many tasks about traveling in time and space. At the same time, I told why it was sixty minutes in an hour, and we understood how convenient it is.

We saw that 60 is convenient to divide by 1, 2, 3, 4, 5, 6, and 7 is inconvenient to divide. Therefore, it was time to look at this number. From multiplication by seven, it remained only to remember 7x7 and 7x9. Now we knew almost everything we needed. I explained that seven is simply a very proud number - such numbers are called prime, they are divided only by 1 and by themselves. The prime numbers for our map are the land on which we can’t swim on our ship in any way, but we can outline it, get into the harbor.

In order to better understand this, I began to set various coordinates - numbers - and ask whether it is possible to get there by land, or only by water, that is, on our multiplication table map. For example, 56 is 7x8, you can swim, and 17 is a prime, get up to the port. This is a very good way to learn division at the same time, to recall what already learned numbers consist of. It turned out that the sea is much larger, if only because every second number is even, it is divided into two, which means it is not simple except for the two itself, but there are other composite numbers, so you can swim a lot where.

Multiplication by 9 and the Pythagorean table

I left nine at the very end, this is another of the old pirate traditions. Previously, in the most cruel times, it was the nine who checked how the youngest had learned the table that every pirate should know. If the sailor was mistaken somewhere, then he failed this first of the exams, and his finger was cut off at the place where he was wrong, so that he forever remembers the multiplication by nine. Now you will understand how. The nine itself means ten minus one. :)

Both palms are extended, so that ten fingers are lined up in a row, and in order to multiply by some number, they bend the finger that corresponds to this number. For example, you need to multiply 9x3, which means that the third finger is bent on the left hand, - you get two fingers to the left of it, and seven fingers to the right, the total is 27. In the same way, for any number from 1 to 10. So before, the multiplication by nine was firmly learned.

The next day I told how the Pythagoras table is built, and we drew it on a large sheet. My friend is numbers, and I am around them - boats. So we coped with the task and went to look at the animals.