How to help your child learn the multiplication table

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

After a fairly clear addition and subtraction, cramming the multiplication table often looks like a boring ritual, devoid of any clarity. Therefore, many schoolchildren quickly lose interest and know it poorly, and this is reflected in all education. I am sure that learning to multiply is a very important experience, which affects a person’s general confidence in his own knowledge and abilities of the mind, and maybe even a rational choice of profession.
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The described techniques are quite simple, and, strictly speaking, have long been known. Memorization in my story also happens through frequent repetitions of examples, but all of them are just different events of the same game in which these multiplications come to life. I summarized the techniques known to me and made such a schedule for my student so that a little more complicated alternated with simple. Due to the amusement of such learning, at the same time memorizing the table, the child learns other interesting things from the world of arithmetic and in general mathematics: primes, the sign of division into 3, powers of two, and so on.

Also indirectly, the story mentions some ways of motivation. Our very learning, as will become clear from the narrative, was a game. I am sure that in the comments you will be able to supplement my story with your own interesting ideas and methods, which I did not know that would help make the story more complete for someone who bumps into it in search of an answer to the question of the article’s title.

Test

I taught one boy this table so. During her study, we had a lot of fun. Without cramming it is quite easy! And still, when in a few days my young friend was able to tell her completely 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 map-table that all people more or less know and keep in memory, and the one who knows it better than others, sends his knowledge of the heir. It is with the help of this map that pirates collect and share their treasures, so that in the lives of pirates, these cards are actually on a par, but since this is even more secret, they are less likely to talk about it. And so I chose him as such a student, as I pin great hopes on him. But first of all I had to check it, to conduct a test. The boy became very interested and agreed. I asked a few puzzles for addition, and made sure that he was able to put up quite well. So he passed the test, and we got down to the bottom line.

Treasure Map and Multiplication by 1, 10 and 2

Now we had to draw this table. I said that I would only draw it 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 in your mind imagine it . Just as I do.

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

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

before the tenth

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

I decided not to exclude multiplication 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, this is the easiest thing, this is the simplest, the number itself. And multiplying by ten is the same as taking something ten times. For example, 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 multiplying, we noticed that the number 10 acts like this: the unit again does nothing, and zero goes to the end, so it is enough just to assign it.

Together we decided that this is quite simple, and we will not dwell on this anymore. But in subsequent exams, I checked if he had 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 would be 11 by 1 or 10 by 10, and then he would come to life again.

Then we went to the doubling. Doubling is pretty easy, just add something to yourself. At the beginning, I showed one, two, three, four, five fingers on my left and right hands at the same time - so we got 2, 4, 6, 8, 10. Together with corsair fingers we reached twenty, and then I showed 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 face, count the number of spokes on one side of the bicycle wheel, and check if the total number converges with doubled and so on.

When I decided that we managed to cope with this column in the table, we moved to the table itself, and I proposed a circle around what we already know. Quickly circled the first and tenth column, and the second I gradually opened with each correct answer. Then I offered to see if something else could be circled. Together we noticed that in the other columns there is also multiplication by one, and ten, and two, and the answers are exactly the same. So we understood that the answer will not change from the rearrangement of numbers. So the work we have significantly diminished, 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 can multiply by two, this is utter nonsense. Multiply by four is the same as doubling the answer for something that has already been doubled, for example, 7x4 is 7x2x2, and 7x2 is 14 we already remembered well in the previous lesson about doubling, so 14 itself will not be difficult to turn into 28. When figured out with the four, it is not so difficult to figure out with large numbers of eight. Along the way, we noticed that, for example, 16 is both 2x8 and 4x4. So we learned that there are numbers, consisting entirely of twos: 2, 4, 8, 16, 32, 64. Then I remembered the story of one shipwreck, when sixty-four crew members had to be scattered around four old boats, about some of the sailors and about the ship itself.

After this lesson, there are still fewer non-listed cells in the table. Multiplying by 3 and 6, we learned the old pirate method of "sharing by three." If you add the numbers in the number multiplied by 3, 6 or any other, which is divided into three, 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 it is possible to add in 12 digits, it will turn out to be 3 too, so if you reach the end like this, you always get one of three numbers: 3, 6 or 9

So we turned it into another game. I asked some number, even a three- or four-digit number, and asked if it was divisible by 3. To answer, you simply add the numbers, which is pretty 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 know what happens with such a division by 3 or 6. It was a very fun exercise.

Multiplication by 5 and 7, prime numbers

And now we have multiplication by the five, the seven, and the 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 either zero or five, just as well as a multiplied number: either even or odd. As a subject on which it is convenient to deal with the fives, the watch face fits perfectly, you can come up with many tasks about time and space travel. At the same time I told why in an hour sixty minutes, 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 multiplying by seven, only 7x7 and 7x9 remained to be remembered. Now we knew almost everything we needed. I explained that seven are just a very proud number - such numbers are called simple, they are divisible only by 1 and into themselves. Simple numbers for our map are land, on which we can hardly navigate on our ship, but we can outline it, get into the harbor.

In order to better understand this, I began to ask various coordinates — numbers — and ask whether it was possible to get there by land, or only by water, that is, by our multiplication map. For example, 56 is 7x8, you can swim, and 17 is a prime number, we get up to the port. This is a very good way to learn how to divide 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 twain itself, but there are other composite numbers, so you can swim a lot where.

Multiplication by 9 and the table of Pythagoras

Nine I left at the very end, this is another one of the old pirate traditions. Earlier in the most brutal times, it was the Nine who checked how the young man learned the table that every pirate should know. If a 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 would remember the multiplication by nine forever. Now you understand how. The nine itself means ten minus one. :)

Both palms are pulled out so that ten fingers line up, and in order to multiply by some number, bend a finger that corresponds to this number. For example, you need to multiply 9x3, so the third finger is bent on the left hand, two fingers are to the left of it, seven to the right, and the result is 27. Similarly, for any number from 1 to 10. So, you used to firmly multiply by nine.

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