Understanding the multiplication table lays the foundation for further study of mathematics. Without such knowledge, learning will become problematic. Therefore, already in elementary school it is required to learn the multiplication table.
Who invented the multiplication table?
For the first time in the usual form, the multiplication table appeared in the work of Nikomakh Gerazsky (I-II centuries AD) - “Introduction to Arithmetic”.
So who invented the multiplication table? It is generally accepted that the first to discover it is Pythagoras, although there is no direct evidence for this. Only indirect evidence is present. As, for example, Nikomakh Gerazsky refers to Pythagoras in his essay.
At the same time, there is one of the oldest multiplication tables, given on clay tablets, whose age is about 4-5 thousand years, and it was discovered in Ancient Babylon. It was based on the six-decimal system of calculus. A table with a decimal system of calculus was found in China, in 305 BC. Therefore, to clearly answer the question: “Who invented the multiplication table”, it will not work.
Today, the multiplication table is called the "Pythagorean table" and looks like a square, the sides of which are indicated by factors, and their product is in the cells.
Start training
Parents whose children went to school, sooner or later will have to help the child learn and understand the multiplication table. Starting to study it, the child already knows how to add and subtract, has an idea of mathematical actions.
The multiplication table for children should be based on motivation, an explanation of why this is necessary. It is necessary, with the help of an example, to lead the child to the fact that knowledge of the table can facilitate us to complete some tasks. For example, if there are three packages of sweets in a store and each package contains 6 sweets, then in order to quickly find out how many sweets are in total, you must not count them individually, but multiply three by six and immediately find out the result.
To begin to study the table, the child must have a good understanding of the essence of the action of multiplication. You must first explain the principle of counting. That is, for example, if you need 3 * 8, then it will be equal to the same as 8 + 8 + 8. On the basis of such examples, the child must well learn and understand the principle of multiplication.
When the basis is disassembled and the child has learned the procedure, we must begin to learn the multiplication table
Learning easy and simple
Memorizing a table is hard. The child needs to be interested, then the learning process will go easier. So, we learn the multiplication table with interest and joy. There are several types of games related to learning tables. Depending on which channel of perception the child is better and faster to absorb information, a study takes place. The multiplication table in a game form will be interesting and easy to understand.
There are 3 channels of perception:
If the child has a more developed visual channel of perception, then he needs to look at the table when studying it. You can hang a homemade table in the room. Visual perception will speed up the process and memorization will be easier.
The audio channel is more of an auditory perception of information. To date, many songs and poems have appeared that are aimed at learning. Therefore, it will be easier for the child to learn the table if it is present in his auditory perception.
With kinesthetic perception, you need to touch everything, feel it in your hands. The same is with the table; its study is better represented visually. For example, put cubes or any other objects on plates and explain the principle of multiplication.
Secrets of the multiplication table
A multiplication table in a game form is a great option for elementary school children. Remembering it will be easier if the elements of the game are added to the study. When memorizing a table, mechanical memory is more involved. However, for simple memorization it is better to use the associative method.
Studying the multiplication table will be easier if you use:
- poems;
- songs;
- cards;
- audio and video materials;
- online simulators.
There are also secrets when multiplying, for example, by the number 9, knowing which, you can study the table faster.
Poems and Songs
The multiplication table for children will learn with interest if the child is interested. There are many verses and songs, the memorization of which is the multiplication table. In such verses, the rhyme tells about the multiplication of two numbers and their result. In the future, poems will be the association, remembering which, you can find out the result.
By memorizing poems and songs, you can learn the multiplication table easier and faster.
Cards
A game of cards is effective when the table has already been learned and it is required to bring the acquired knowledge to automatism.
The meaning of the game: cards are made with examples, without answers. Turn over the clean side up, mix and stretch the children in turn. Having stretched out a card, the child should answer - solve an example. If the answer is correct, the card is removed, if the answer is incorrect or not given at all, then the card is returned to the game. As a result, at the end of the game there remain examples that caused difficulty in answering, therefore, solving them again, the children repeat and consolidate the material that is difficult for them.
The peculiarity of this game is that you can take cards with the entire multiplication table, and choose only one specific number, and then add more.
Playing in this way, children hone their knowledge and bring it to automatism.
Secret table of multiplication by 9
Multiply any number from 1 to 10 by 9 on your fingers. To do this, put both hands with straightened fingers side by side and mentally number the fingers in a row from 1 to 10. Now, to multiply, for example, 6 by 9, you need to raise (or bend) the sixth finger. We count the number of fingers until the sixth is raised - there will be 5 of them, and after that - 4, put the numbers next to and get 54. In the same way, you can calculate the result by any other number, within ten, multiplying by the number 9.
Learning from easy to hard
Learning the multiplication table is better to start from primes, that is, from one. Starting to learn the table with lighter numbers, the child will not lose interest in learning. And if you start with the numbers 10, 9, then, on the contrary, a loss of faith in one's own strength is possible and further training will be difficult.
When studying the multiplication by the numbers 1, 2, 3, the child is able in practice to check the correctness of the solutions, and starting to study from the number 9, practically checking the correctness will be problematic.
Using the square of Pythagoras, and having learned the table to a factor of 6, it is necessary to visualize the already learned examples in green and see that there are not so many left. Before this, draw the attention of the child that when changing places of the factors, the result will be the same, that is, if 2 * 9 = 18, then 9 * 2 = 18.
Be sure to praise and encourage when learning. Do not scold or punish - this will only turn the child away from the teaching of the table, and then it will be given to him with great difficulty.
Unusual and interesting
You can still return to the study of the Pythagorean table in high school and find out what the secret of the multiplication table is.
In the late 90s of the 20th century, the scientist A. A. Matveev invented a way to translate numbers into a graphic image. Based on his teachings, the graphic image of the multiplication table was created using the Katya method.
The essence of the method: numbers (a column of multiplication results) are reflected horizontally (in reverse order) and, by the principle of comparing numbers with each other, more or less, are encoded, respectively, with pluses or minuses.
Using this method, we can understand that in the multiplication table the logical construction of numbers is in the polar system, in which the pros and cons form two ellipses of different polarity. It turns out that the multiplication table is a holistic form with its graphics and polarity.
Learning and remembering the multiplication table is a mandatory and key step in completing the school curriculum. This knowledge will be necessary throughout the school and in the future will facilitate life at some points. So who invented the table? The table of multiplication and division, as many believe, was created by Pythagoras. However, the lack of documented works of this scientist calls into question the correctness of authorship. At the same time, doubts about who invented the multiplication table do not interfere with the use and application in her studies.