This article is about how to learn the multiplication table without torment and cramming. In it we tell how to learn how to multiply numbers up to 10 by each other, remembering only 36 examples instead of 100. We also show 5 useful games and a couple of life hacks that will help you learn the multiplication table not only quickly, but also fun.
Help your child understand the meaning of multiplication
The first thing to do is explain the convenience of multiplication. You can start studying the multiplication table long before it appears in the school curriculum. For example, tell us in advance that there is such a magical mathematical action that allows you not to add the same numbers in turn, but to get the result in one action.
Psychological bonus. Such advanced training will not only help the child better understand mathematics, but also slightly increase self-esteem, because he will know a little more than his classmates.
A clear miracle
Suppose a family has a tradition of calculating monthly expenses. Have your child take part in home accounting. After all, he is already so adult and even goes for bread himself!
The task: calculate how much money is needed to buy bread for 20 rubles a month. Take a simple desk calendar and write every day in the desired cell:
Let the young mathematician consider it a cumulative total every day or all month at once. And then just show him how the magic is the only action:
And I know one amazing mathematical secret:20 rubles x 30 days = 600 rubles per month
This technique is a kind of presentation of an important skill. As a result, parents get a good motivational tool for the child: “Let's learn the multiplication table so that you can easily and quickly count.”
School of Math Tricks
Tricks with numbers should not end with the calculation of the family budget. Now invite your second-grader to independently find the relationship between addition and multiplication. Assign the follow-up assignment to the student.
- For two days in a row, you and I bought lollipops for 9 rubles. How much money did we spend on them?
- 9 + 9 = 18 rubles, - the student will answer.
“And if I buy you such sweets all week, how much money will I spend?”
-. There are 7 days in a week, which means: 9 + 9 + 9 + 9 + 9 + 9 + 9 = ..., - he will think it over and take a long time to count. Let him finish the example and get 63.
- And let's try to calculate according to the multiplication table? Look (show the table on the back of the notebook) - how many days in a row do I buy sweets?
- 7! - select column by 7.
- And how much is each candy?
- 9 rubles! - find the line at 9.
- Look how much it turns out?
- The calculator also knows the multiplication table. Look: 7 times 9, equal to 63. You see how fast! Is it great?
Engage in dialogue, try to captivate the child, create intrigue, point out the “wonderful” properties of numbers.
Important! Do not ban games with a calculator. Ask questions yourself. The scatter of any. Let the baby calculate, for example, how many grams of flour in two glasses, if you know how much one can hold. Such tasks are taught to navigate in terms of factors, terms, sums and products.
Other amazing and simple patterns
Boys and girls quickly realize that multiplication is a lightweight addition. Immediately you can tell about other interesting patterns of works:
- Unit Multiplication: the number multiplied by one remains unchanged. Here it is convenient to count stars or one hundred thousand thousand. And even the largest number will not change when multiplied by one.
“Every day I give you one apple for school. How many apples a week? And in 30 days? And for 365? "
- Multiplication by zero: Even the largest number in the world will not be if you multiply it by zero. You can shift something from one box to another and use the word “Not once” synonymous with zero.
“You leave every day and don’t take apples with you. How many apples do you not eat at school in a week? And in 30 days? And for 365? "
- Multiplication by 10. It is important to explain where to add the toe. At school, children make out what categories are and why they add zero to the right. At home, just repeat the rule.
“The first factor is such-and-such, the second is 10. To get the value of the product, you need to add the zero to the first factor on the right.”
- Multiplication by 100, 1000 and more it is better to postpone for now, unless the child himself asks a question.
From practice to theory: table patterns
When the child is finally carried away by all kinds of calculations, we can proceed to the development of the theory. Typically, in the classroom above the blackboard hangs a Pythagorean table, which children study for a year in columns and rows. There are several points here, indicate them to the child:
- A row or column can be represented as a column of equalities, as on the back of a notebook. Be sure to teach you to switch from Pythagoras to the standard view and vice versa.
- In a row and a column with the same number, the products coincide. This is a visual representation of the translational law of multiplication. And actually only half the table needs to be taught.
- Add the row and column to zero in the Pythagorean table yourself. This will help to establish the rule of multiplication “not once”.
- Make a joint discovery - the Pythagorean table tells you only the answers within 100. And in the world there are so many other and very large numbers!
It is advisable to hang the table in several places in the house where you can look at it more often. The visual memory will work by itself, and if necessary, the baby will be able to turn to the cheat sheet when counting household items and toys.
Helpful advice!Buy a set of soldiers or get your old collections of toys from the "Kinder". Line them up in rows and columns, right on the printed table - one soldier per cage. So abstract and visual thinking will unite.
Fours, eights and fives
Fours are notable for being a pair of couples. It turns out that to multiply a number by 4, it is enough to multiply 2 times by 2: 2x2 = 4, 4x2 = 8.
And in the case of eights, the number doubles three times: 2x2 = 4, 4x2 = 8, 8x2 = 16.
The score by fives is not only a combination of twos and triples, but also a special result. Help the kid notice that all the pieces end in 0 for even numbers or 5 for odd ones. And even when multiplying the number by 5, the result is half as much as when multiplying the same number by 10.
"By-effect. When working with buttons and beads, fine motor skills will also be added to the study of the table, which in itself is the driving force of the child's intellectual development.
1. Get ready
First you need to do two things: print the multiplication table itself and explain the principle of multiplication.
For work, we 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:
So, this is not a table. These are just columns from examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make it easier for him, find or print this chart.
Turning 100 examples into 36
The multiplication table on the back of most notebooks looks like this:
It can take a whole summer to learn it. Mechanical memorization of the correct answers to a hundred examples is the most time-consuming way to remember the results of multiplying numbers up to 10 by each other.
The process will accelerate if we show the child how all these 100 combinations can be reduced to 36. In this case, the Pythagorean table is a much more successful visual aid:
Using her example, it is already possible to show the principles of multiplication through the areas of small rectangles:
• 3 * 5 = 15, because 15 small squares are placed in a rectangle with sides 3 and 5 squares long (we count them together to make sure),
• 5 * 3 = 15 for the same reason (counting together).
Here we clearly demonstrate the commutativity property: the product does not change due to a permutation of the places of the factors. Of course, the name of this property is best kept until Halloween, so as not to scare anyone ahead of time.
Because of this, the Pythagorean table is symmetrical with respect to its diagonal, so out of 100 examples for memorization there are already 55: the diagonal itself with values of 1, 4, 9, ... 100 and everything that is higher or lower.
This discovery can be done independently by filling out part of the empty Pythagorean table, in which only factors were initially marked:
A child can begin to fill it, even if he does not yet know the rules of multiplication - he already knows how to add, so he easily calculates first 2 + 2, then 4 + 2, then 6 + 2, and so on, up to 20. Then a row with triples, and so on.
Filling only part of the table (for example, a square of 6 * 6 cells), you can already see the same numbers and understand that you don’t need to cram it all at all.
After that, on the same Pythagorean table, we demonstrate two principles that allow us to “automate” another 19 operations on multiplication: multiplication by 1 and multiplication by 10:
• If you multiply a number by one, it does not change at all.
• If you multiply the number by 10, it will have a zero at the end.
Subtracting from the remaining 55 examples by multiplying another 19 “automated” ones, we get only 36 combinations that need to be remembered. Almost three times less than what they offer us on the covers of notebooks! Already easier, isn't it?
2. Explain the principle of operation
When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, in contrast to what he has learned or someone else told him. Therefore, try to turn the study of the table into an interesting game.
Starting to study multiplication, children are already familiar with simple mathematical actions: addition and multiplication. You can explain the principle of multiplication to a child with a simple example: 2 × 3 - 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 deal with the device of the table itself. Show that the numbers from the left column are multiplied by the numbers from the top row, and the correct answer is at the intersection. Finding the result is very simple: you just have to drag your hand along the table.
3. Teach in small portions
No need to try to learn everything in one sitting. Start with columns 1, 2, and 3. So you will gradually prepare your child to learn more complex information.
Good technique: take an empty printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count.
When he has figured out and mastered the simplest columns quite well, move on to more complicated numbers: first, multiply by 4–7, and then by 8–10.
5. Find patterns in the table
As we said earlier, in the multiplication table, you can find many patterns that will simplify its memorization. Here are some of them:
- When multiplied by 1, any number remains the same.
- All examples of 5 end with 5 or 0: if the number is even, we attribute 0 to half the number, if odd - 5.
- All 10 examples end with 0, and begin with the number by which we multiply.
- Examples are 5 times less than examples by 10 (10 × 5 = 50, and 5 × 5 = 25).
- 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.
- To remember multiplication by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. 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.
Repeat more often. First ask in order. When you notice that the answers have become confident, start asking randomly. Keep track of the pace: first, give more time to think, but gradually increase the pace.
Use not only standard methods of memorization. Education should fascinate, interest the child. Therefore, use visual aids, play, apply different techniques.
The game is simple: prepare cards with examples of multiplication without answers. Shuffle them, and the child should stretch one at a time. If he gives the correct answer, put the card aside, the wrong one - return to the stack.
The game can be varied. For example, give answers on time. And every day, count the number of correct answers 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 whole pile of examples ends. Then for each wrong answer you can entrust the child with a task: to tell a poem or to tidy things up on the table. When all the cards are unraveled, give a small gift.
Life hack: multiply by 9 with your fingers
Multiplying by 9 is often the hardest. To make this process easier and more fun, you can use the hint - with your own hands!
Turn your hands with your palms toward you and mentally number your fingers in order from left to right, from 1 to 10.
Now we multiply, for example, 7x9. We bend the seventh finger in a row from left to right.
The number of fingers to the bent is tens, in our example it is “6”.
The number of fingers after bent is units, that is, “3”.
As a result, we get 63!
To make the multiplication table easier, we have prepared for you bright posters that can be printed and hung in a prominent place.
To make the process of studying the table more dynamic, you can paint over or glue stickers with values that are already well fixed in memory.
1. Great snowfall
These tasks will allow the child to visit a situation where multiplication is indispensable. In the process of solving problems, the child understands that it is not necessary to count square tiles every time - just multiply the length by width.
2. The battle of the rectangles
This is a simple game for two people to understand the multiplication and area of a rectangle.
You will need two felt-tip pens, a piece of paper in a box and two dice. Each player chooses the color of a pencil or felt-tip pen with which he will draw. Players take turns. The first player rolls two dice. Then he must draw a rectangle or square on the side of the sheet, the sides of which are equal to the number of cubes in the number of cells. In the middle of the figure, its area is recorded - how many cells the figure occupies. Next comes the second player and so on.
The game ends when there is no more space left for new figures on the sheet. The one whose figures took up more cells on a sheet of paper wins.
3. Board game "Many-Many"
This game has many, many useful and entertaining things. But most importantly - the main part of the multiplication table in your pocket! Without boring memorization, the child learns to multiply numbers from 1 to 5. The game is built on a unique technique that helps children to see with their own eyes what multiplication is, and even hold it in their hands. And this is so important for the first steps in arithmetic.
4. Board game "Tsvetarium"
Players will perform many interesting actions: plant flowers on flower beds, uproot them if necessary, and arrange surprises for their competitors - pleasant and not so. But the main thing for participants is to carry out orders with accuracy: you need to grow exactly as many flowers on your flower beds as the buyer wants. During the game, children in practice are convinced that to complete an order for 18 flowers, you need to collect 3 flower beds of 6 flowers. Such visual operations will be remembered quickly and for a long time.
5. Multiplication by 9 using fingers
Multiplying by 9 is often the hardest. To make this process easier and more fun, you can use the hint - with your own hands. Turn the brushes with your palms toward you and mentally number the fingers in order from left to right, from 1 to 10. Now we multiply, for example, 7 × 9. We bend the seventh finger in a row from left to right. The number of fingers to the bent is tens, in our example it is “6”. The number of fingers after bent is units, that is, “3”. As a result, we get 63!
Sixes and Nines
Using the table, it’s easy to figure out the score with sixes (a couple of triples).
The numerical score is easy to explain by the principle of the inverse: if we subtract the multiplied number from the product by 10, we get the result of multiplying by 9:
2x10 = 20, => 20-2 = 18.
Another way to manipulate nines is through the already well-known triples: three triples are a nine.
The self-esteem of a child at eight years old is very fragile. Be sure to remember to praise the young mathematician for his excellent memory and ability to navigate the multiplication table. When he succeeds in mastering a work of one or ten, arrange a small celebration. And then move on to the next columns.
There is no need to memorize the table in a strict order from 1 to 9. It is much easier for the child to master the discrepancy:
- one and ten,
- couples and fours
- triples and sixes,
Before each new step, fasten the previous material scatter. Хорошо, если ребенок самостоятельно придет к выводу о том, что семерка — это сумма произведений одного числа на 3 и 4. Упражняйтесь с наглядной таблицей до тех пор, пока память школьника не начнет выдавать ответы автоматически.
Закрашивайте или штрихуйте те ячейки в таблице, которые хорошо освоены, чтобы ученик видел свой прогресс. Лучше всего делать это после каждого занятия. Но возвращаться к упражнениям на уже изученные примеры — обязательно.
Играй и запоминай
Even the most ideal army of soldiers can bore a student of the second or third class. Therefore, stock up on other games and exercises. In the arsenal of parents there should always be fallback didactics in mathematics.
Mathematics is indeed a very fascinating science. The child will be much more interesting if you re-immerse yourself in the magic of numbers with him and play with the whole family.
You can buy ready-made or print and draw together with mom, dad, and an older child. Participants - cards with tasks, the leader - answers-works. Given that the same product can be obtained using different factors, someone closes the field faster if it counts faster:
18 = 1x18, 2x9, 3x6, 6x3, 9x2, 18x1.
Cards and Cards
You can start with simple, unanswered cards. If the child answers correctly, takes a point. If there is no answer or it is incorrect, the task returns to the deck. You can add one of the conditions:
- name more correct answers per unit of time,
- give the correct answer to at least seven out of ten tasks, etc.
You can complicate this game by turning it from a didactic into a card. Participants draw four cards from the deck. The right of the first move can be determined by lot or counting.
The task of the players is to calculate the values of the works (or any other mathematical actions). Whose work is greater, he takes the con.
See how great the game is to remember the multiplication table in the Brovchenko family.
The development of memory in children is easiest to stimulate with rhymes and songs. Moreover, at school they are rarely allowed funny ways to memorize the rules. What is studied in a positive mood, on an emotional upsurge, is remembered faster and more durable. Therefore, the baby will definitely appreciate the desire of mom and dad to fool around with everyone and read math words before dinner.
Pay attention to special manuals with ready-made verses. One of them is the verses of Marina Kazarina “About Multiplication” and Andrei Usachev “Multiplication”. You can also try to write some verses with your children yourself. They will definitely be remembered for a lifetime! Ready-made rhymes can be found on the Web, and children's imagination will tell the plots.
By the way. A song about “twice two - four” can only become a reference point in joint creativity. Writing and rhyme selection exercises will help to master the Russian language and literary reading simultaneously with mathematics. What is not intersubject communication?
Print the table of Pythagoras, shade the squares in it according to any pattern for cross-stitch. For the drawing to be completed, the student will have to fill in the colored squares with the product of numbers.
The reverse version of the exercise: specify the code in which the values of the works and color will be given, and the child needs to fill in the squares in accordance with the code.
Miracles Go On
Studying the multiplication table for longer than 5-10 minutes per day is a punishment for a second-grade student, but this must be done. Talk to him that there is no person in the world who does not use multiplication in ordinary life or work. Knowledge of numbers is the basis of many sciences. Give examples from biology and genetics, from history and art.
Half of Pythagoras
Once the relational law is mastered, you can halve the multiplication table exactly diagonally. The dividing line passes through the squares of numbers. And then another surprising property of the works is revealed to the child - the squares of numbers in the Pythagorean table are not repeated like the others. A number is multiplied by itself only once.
The smaller multiplier is forward. Tell the student the technique of quick counting: let him learn that three times six is considered faster than six times three.
Learning becomes more interesting if you discuss things with your child that he likes. So, you can ask the boy how many wheels four cars need.
You can also use visual aids: sticks for counting, pencils, cubes. For example, take two glasses, each with four pencils. And visually show that the number of pencils is equal to the number of pencils in one glass, multiplied by the number of glasses.
The rhyme will help to remember even complex examples that are in no way given to the child. Create simple verses yourself. Choose the simplest words, because your goal is to simplify the process of memorization. For example: “Eight bears chopped wood. Eight nine - seventy two. "
Finger Multiplication: The Magic Nine
For parents, this technique can be a revelation. It is customary to add and subtract on fingers, but not to multiply numbers. However, this technique of multiplying by 9 is much more entertaining than cramming equalities.
Ask the child to circle the left and right hands. Number each finger from the left little finger (1) to the right (10). To multiply a number by nine, circle the corresponding finger on paper. Now explain to the child the principle of counting: to the left of the circled is the number of tens, and to the right is the number of units. Check it out for yourself.
There are also gif animations and the video “Why They Didn’t Teach Us at School”. Show these videos to your child. He will appreciate it.
The best way to remember a large amount of information is to allow this information to flow through different channels: sound, image, actions with objects. Print bright posters. Hang them in significant parts of your home: on the fridge, the front door, on the TV screen or a note board above the desk.
Each new mention causes an electric impulse in the brain of the child. The more often it runs along its path, the stronger the connection becomes between an external stimulus (task, example) and an internal response to it (activation of a memory cell).
Periodically alternate the set of current cards and posters. It’s easier for the look to catch on to something new. The familiar landscape is not psychologically interesting, especially at the age of eight.
A little trick. Try to make a mistake on purpose, and then be sure to praise the child when he informs you of her: “What a fellow you are! You see, I didn’t notice, and you are so attentive! ”
Books and toys for memorizing the multiplication tables have already been invented and went on sale. You can buy them at special stores or online. Pay attention to colorfulness, but choose manuals with a minimum of distracting details. To make educational pictures at home, you only need a fantasy, a printer and cardboard.
Take on board a short list of literature that you can use at home:
- Olga Uzorova and Elena Nefedova. “Quickly learn the multiplication table.” The author’s technique helps parents teach children, is designed for daily use and helps to improve all mathematical results in general.
- Another author, Olga Alexandrova, offers yet another way to learn multiplication and division by heart, and without tears and in a short time.
- It is possible to use the optional GEF manuals for homework (by Georgy Dorofeev).
- Yana Pligina - the author of the book “A Quick and Easy Way to Learn the Multiplication Table” - is known all over the world for mathematical games with a magic bookmark.
- Tatyana Shklyarova offers readers her book “How I Teached My Girl the Multiplication Table”. The allowance is intended for the summer holidays.
Toys and benefits
Give preference to such aids that combine presentation through different channels of perception. Cards should be pleasing to the eye, posters are better interactive, and electronic toys - talking and showing.
Well, if the game is designed for several participants. For example, in elementary school, children really like board games-walkers - with chips and a dice. Look for one for your child and his neighbors on the porch. Their joint games will immediately become useful, educational, and nobody forbids them to mix them with war or hide and seek!
One of the most famous and liked by children - uchi.ru. Here you can train for free for 20 tasks per day (about 20 minutes) or pay for unlimited access. As a bonus, the child gets the opportunity to study other subjects from among the compulsory ones: Russian, English, the world around him. Video lessons and olympiads are well motivated to learn.
You can learn the multiplication table on other school projects.
Uchi.ru is a fun application for mobile devices. You can play educational games, master both multiplication and division. A well-thought-out technique allows you to securely fasten the material in 5 minutes a day.
The kid will be able to learn a column a day if parents help him at every stage. At least a half-year is allotted to study this complex topic at school. Mathematical dictations, written puzzles, games - a teacher in the classroom, as she can, occupies children's memory. Try to keep your homework from tiring. The goal of parents is learning with passion.
- You need to gradually train your brain for loads. 3 minutes at the beginning of the study of the table is enough.
- Do not rush to make your child study - coercion has never been a good way.
- You can not mix organizational moments and assignments. Before the lesson, it will be correct to give the child time to prepare the workplace and prepare the pen, notebook and calculating material.
- You need to start and end the lesson only on a positive note.
- Any simulator is effective if used in dosage. Do not strive to learn everything at once, divide the information into small blocks.
- Information should be repeated many times, but not monotonouslyotherwise you will overwork the child and get the opposite result - poor appetite and sleep, memory loss.
- Game Memory Method - Best Choice for home exercises. Playfully, children do not notice that they are being taught. It is this perception of lessons that allows information to be firmly rooted in a child’s memory.
- The child needs help learning by heart. It is unlikely that a second-grader will be able to force himself to sit and cram. Try at least part of the lesson to speak equality out loud together. First in a row, then at random.
- Memory works better for the coming dreamfor the night. Before sending your baby to sleep, give some examples of the scatter.
- Try to task complications did not occur often or too early. Otherwise, the child will cease to understand the material.
- Change the order of tasks from lesson to lesson. Alternate mobility and concentration in games.
- Invite your child to record a table on the recorder. Own voice better than any simulator stores information in memory.
In Russia of past centuries, the multiplication table was studied through the drill, cramming and rods. Today, unique copyrighted teaching aids, tabular and pictorial stimulating material, electronic devices and applications help to master complex material effectively.
It has become easier to interest children in their studies, but they still need the presence and participation of parents, because any lessons are easier in communication and joint activities.
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8. Do not be nervous
Usually in the process, some parents are forgotten and make the same mistakes. Here is a list of things that should never be done:
- Make the child do it if he does not want to. Instead, try to motivate him.
- Scold for mistakes and scare bad grades.
- Set as an example classmates. When you are compared with someone, it’s unpleasant. In addition, you need to remember that all children are different, so everyone needs to find the right approach.
- Learn everything at once. The child is easy to scare and tire of a large amount of material. Learn gradually.
- Ignore success. Praise the child when he copes with the tasks. At such moments, he has a desire to learn further.