The multiplication table is the foundation of mathematics. To learn how to perform complex mathematical and algebraic operations in high and high school, you need to know the multiplication and division of numbers.
How to quickly learn the multiplication table? Indeed, in adulthood, every person often encounters it: making purchases in a store, distributing the family budget, at work (accountant, economist, estimator and others), taking readings of electricity meters (gas, water) appliances and paying for utilities and so on .
About everything - in this article.
History
The most ancient multiplication table is considered to be one that was created back in Ancient Babylon - about 4 thousand years ago (that is, before our era).
The table of Pythagoras, the author of which revered the numbers and believed that the knowledge of the world means the comprehension of the numbers that govern it, or the modern table of multiplication, was compiled by him in the VI century of our era.
It is through it that schoolchildren are trained for more than a dozen generations in the countries of Europe and in Russia to the present.
If you look closely and find certain patterns on your own, then the question "How to quickly learn the multiplication table?" (and also in the opposite direction - division) can be resolved extremely quickly and without unnecessary effort. What children just like.
In Soviet times, the table was already asked for students after grade 1, and in the 2nd thoroughly fixed. Currently, in fact, nothing has changed - the child must learn this fundamental material by the age of 8.
Although, according to the provision on school education in the UK, it is important for each child to master the multiplication table up to 11 years. It can be earlier or at this age, but not later.
Interesting Facts
One modern school teacher of mathematics for their children specifically bought, when they were in elementary grades, cell notebooks on the cover of which a multiplication table was printed - not in columns:
2 x 1 = 2,
2 x 2 = 4 and so on (as in the photo above).
She chose the option designed precisely by the table. This is a multiplication table game to quickly learn it with minimal effort (from children and parents).
Why does she have such a look?
- It just looks like a real Pythagorean table, and all the other presented forms are derivatives.
- This arrangement of numbers is very interesting for children. And therefore, they unconsciously begin to play with this tablet: look for patterns, draw a diagonal, see geometric shapes, and so on.
- Thanks to this multiplication table, children without excessive labor and edification, faster and without the intervention of adults, memorize all mathematical operations (multiplication, division).
Therefore, you should not "strain" the child, forcing him to thoughtlessly memorize the hated columns that have literally been imposed on children since Soviet times.
It is better to submit the necessary material in an interesting form for the child, so that, if possible, he himself will try to figure out what's what.
Logical study of the multiplication table
According to the school curriculum, in mathematics lessons, the table is studied sequentially: starting from the number 2 and up to 9 (elementary school). In the middle and senior - they perform these mathematical actions in a more complicated version (multiply four-digit by four-digit and so on).
And studying each subsequent number, multiplied by a series from 1 to 9, there is no sense in learning the previous ones, because they are learned. For example, a table of 4 begins with the fact that this number is multiplied by itself, and the answers are already known by 1, 2 and 3.
This is still a famous relocation law, which states that 2 x 4 = 4 x 2 or 3 x 4 = 4 x 3 and so on.
As for the reverse process - division, then it is generally not necessary to specifically teach it. This is due to the fact that if the multiplication is learned, the division is remembered by itself.
It is especially easy to understand this material in practice through solving problems or examples.
Score
Another entertaining way to memorize the multiplication table is the simulator for grade 3. This is the score: deuces up to 20, triples up to 30, fours up to 40, fives up to 50 and so on.
By the way, such an approach very well develops and imaginative thinking, which will be discussed further.
If we consecutively represent all the numbers from 1 to 100 in the form of tens: the first, second, third ten, and so on, then it is easy to carry out the calculation.
For example, deuces to 20:
- two deuces are 4;
- three to 6;
- four to 8;
- five to 10;
- six to 12;
- seven to 14;
- eight to 16;
- nine to 18;
- ten - 20.
At the same time, it is possible to imagine, together with a child or children, how these deuces “train” move one after another. This is a very good game to quickly learn the multiplication table.
And it is important that students memorize the results of this count - sequentially, and then randomly.
A little more logic ...
Also, to learn the multiplication table some mathematical laws help:
- Distribution - by the amount. One of the factors can be represented as the sum of two numbers and alternately multiply the second by them (6 x 9 = 6 x 5 + 6 x 4). It works in the opposite direction - when another factor is expanded.
- Distribution - by difference. One of the factors is represented as the difference between a larger number (more memorable) and a smaller (simple) one. Then the second is multiplied with these numbers and the difference of the obtained products is determined (6 x 7 = 6 x 10 - 6 x 3). The law works in the opposite direction.
- Combinative - one of the factors is presented in the form of 2 factors, then the second is multiplied sequentially, you can put brackets for a clear presentation of the example (7 x 6 = 7 x 2 x 3).
Reference analyzers
But the most important thing to remember when studying the Pythagorean table is the reference analyzers: auditory, motor, visual, tactile, verbal.
They help to divide the entire amount of information into blocks and put their own reference points, making it easier to remember each information block.
Then learn the multiplication table with a child - this is a game made up of their interesting blocks, which have their own associations and signals. Mastering will be much faster and easier. And the process will be more interesting.
Game ways to study the multiplication table
Modern pedagogical techniques in the study of any sciences, including mathematics, involve game forms of learning when a child learns the multiplication table, without even realizing it.
It is also permissible to use poems, songs, pictures, which serve as hints and well-remembered images, so that in the future the baby could easily restore any fragment in his memory.
Basic teaching methods: visualization, game, memorization, associations.
Visualization makes it easy to learn the multiplication table as information that can be represented. It assumes the presence of counting materials, pictures, counting on fingers and so on.
For children who like to draw, a great way to remember the multiplication table is to display objects: geometric figures (familiar to the child), favorite toys, fairy-tale characters, animals, plants, stars, suns and so on.
You can learn the Pythagorean table with the help of instructional videos, as well as cartoons or applications on gadgets (but under the supervision of parents).
First things first.
Imaginative study
You can learn the multiplication table by playing. Children especially like colored pictures, posters, which depict useful information, but in a non-standard way.
- A great way would be to print or write by hand the real Pythagorean table, laminate and hang it in a prominent place where the student most often spends time (above the desk, in the bathroom, near the mirror, on the doors and so on). Can be carried in miniature format. This will help the table to always be in front of the eyes of the child and gradually remember it whole.
- For a kid who is only getting acquainted with this material, it is good to purchase a large-format poster, where the entire multiplication table is presented in the form of images - pictures. Or draw it yourself. Gradually, in order to assimilate the material, invent together every detail and memorize. Well and most importantly, the child, too, with pencils or paints (wax crayons and other materials) helps to depict his favorite pictures.
- Modeling of objects (fairy-tale numbers, fruits, vegetables, animals) from plasticine, salt dough or clay. This is a great way to remember the images that were molded with your own hands, and thus remember the multiplication table from 2 to 9.
Mathematical laws (distributive, combinatory, translational) can also be explained and shown with the help of pictures, objects, toys.
Finger learning
One way to visually memorize the Pythagorean table is to study on the fingers. For example, at 9.
Designate each finger - from 1 to 10. And bending one at a time, play, calling sequentially, and then scattering each example of the multiplication table by 9.
You can learn more about the method by watching this short video.
Card games
Learn the multiplication table by playing. This will appeal to older children - 7-9 years.
There are several options for this method of storing this mathematical information.
- To buy cardboard cards (ready-made or made independently (together with the child) (sizes 10 x 15 centimeters or 8 x 12 cm). In quantity, as many examples as multiplication exist in the table from 2 to 9 (90 in total). On the one hand, an example is reflected, and on the other, an answer (for self-testing). You can play with such material as you like - for which there is enough imagination. Usually the children themselves suggest how they would like to use such cards. And most importantly, the game will remember - gradually and unobtrusively - the entire Pythagorean table.
- Cards - by the quantity of 90 pieces, by the size of 10 x 15 or 15 x 20 centimeters. This mathematical material will carry the following information: on one side, in large and bright print, write an example for multiplication, and on the other hand, it is only in the form of a sum (first side: 3 x 3; second side: 3 + 3 + 3; and etc). You can place a child or group of children on a rug, mix cards and let each one be named on one side (an example is read aloud and the answer is named) and, without turning over, on the other (then turn over and check).
Poems
How to quickly learn the multiplication table? Provide each example in verse.
This is a great way to remember any information, including mathematical information. And it is also important that some familiar association is attached to each example.
The multiplication table in verses can be found on the Internet, special textbooks (for example, “Non-standard mathematics” or “Learn mathematics by playing”), as well as come up on your own (with your child).
Mental arithmetic
But the most advanced way to study mathematics and its main operations, including multiplication, is mental arithmetic. It was founded in Ancient Rome, thanks to the count on the fingers (one hand represents units, the other - tens). This principle is laid in the basis of a special device - the account, widely used in the study of mental arithmetic. These abacus are also called abacus or soroban. Currently, this technique of studying numbers and actions with them is called Japanese or Eastern. On such accounts (abacus) you can not only add and subtract, but also multiply and divide. But the main secret is that in a child, while learning this art, the counts are included in both hemispheres of the brain. This helps to develop more fully in the exact sciences and in the humanities. Such a technique will be interesting to children who have mastered the multiplication table to 9. Then, using the account, you can learn how to carry out this operation with two-, three-, and four-digit numbers. And even more.
It is also a freeze multiplication table.
Grid method
A surprisingly simple and quick way to learn with a child the multiplication table from 2 to 9 is the grid method.
The principle is this: depending on the numerical value of the first factor in the example, so many horizontal lines need to be drawn. And which one - the second factor, so many vertical (intersecting with horizontal) lines need to be drawn.
The number of intersection points will be the answer.
For example, the action is 2 x 2: two horizontal lines and two vertical lines - there are four intersection points, which means the answer is 4.
Or 4 x 4: four horizontal lines and four vertical lines - as a result, 16 intersection points are visible. So the answer is: 16.
Educational cartoons, programs
Children are happy to consolidate material on the study of the multiplication table along with educational cartoons.
Or games in which favorite fairy-tale characters participate.
A good simulator for grade 3 is the multiplication table in special applications for children on gadgets. They can be downloaded and together with the baby to study and consolidate the multiplication.
How to remember information to children
It turns out that learning is still part of the story. The most difficult thing is to send new information to the long-term memory of the child.
How easy is it to learn a multiplication table? And remember her for life?
If you teach your child in any way (of the above), then the brain is so structured that in the first hour after contact with new information, almost 60% is forgotten (according to research data of the German scientist G. Ebbinghaus).
A fairly important aspect of the study is the repetition of the material.
There are several time steps that must be passed in order for new information to be consolidated:
- Repeat immediately after studying.
- In 20 minutes.
- After 8 hours.
- In a day.
And if you adhere to this sequence when studying the multiplication table (each part: by 2, 3, 4, and so on), then guaranteed over time all the material will be successfully remembered and assimilated forever.