This article is about how to learn the multiplication tables without suffering and cramming. In it we tell you how to learn 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 in a fun way.
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. It is clear that rote 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 speeds up significantly when we show 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, we can already show the principles of multiplication through the areas of small rectangles:
- 3 * 5 = 15, because a rectangle with sides 3 and 5 squares long fits 15 small squares (count them together to make sure).
- 5 * 3 = 15 for the same reason (we count together).
Here we clearly demonstrate the property of commutativity: rearranging the places of the factors does not change the product. Of course, it’s better to hold off the name of this property 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, only 55 remain to be memorized: the diagonal itself with the values 1, 4, 9, ..., 100 and everything that is above or below.
You can make this discovery yourself by filling out part of the empty Pythagorean table, in which only the factors are initially marked:
A child can start filling it out, even if he doesn’t yet know the rules of multiplication - after all, he already knows how to add, so he can easily count first 2 + 2, then 4 + 2, then 6 + 2, and so on, up to 20. Then the row with threes , and so on.
Having filled out only part of the table (for example, a square of 6 * 6 cells), you can already see the same numbers and understand that there is no need to cram it entirely.
After this, on the same Pythagorean table we demonstrate two principles that allow us to “automate” another 19 multiplication operations: multiplication by 1 and multiplication by 10:
- If a number is multiplied by one, it does not change at all. .
- When a number is multiplied by 10, it ends in a zero.
We subtract another 19 “automated” ones from the previously remaining 55 examples of multiplication and we get a total of 36 combinations that need to be remembered. Almost three times less than what is offered to us on the covers of notebooks!
It's easier now, isn't it?
Let's play and remember
It is difficult to remember something that cannot be applied in life. This is why it is important to show that multiplication tables can be useful. Games and fun activities will help with this.
Big snowfall
These puzzles will allow the child to experience situations where multiplication is indispensable. In the process of solving problems, the child understands that it is not necessary to count the square tiles every time - just multiply the length by the width!
Battle of the Rectangles
This is a simple game for two people to learn about multiplication and the area of a rectangle.
You will need 2 markers, a piece of checkered paper and 2 cubes. Each player chooses the color of pencil or felt-tip pen with which he will draw.
Players take turns. The first player rolls 2 dice. Then he must draw a rectangle or square on his side of the piece of paper, the sides of which are equal in number of cells to the numbers on the cubes. In the middle of the figure, its area is recorded - how many cells the figure occupies. The second player goes next, and so on.
The game ends when there is no more room for new pieces on the sheet. The one whose pieces occupy more squares on a sheet of paper wins.
Multiplication fishing game
With this game, children will easily understand the principle of multiplication: why two by four is eight, or three by three is nine. In the game, you can only catch a number of fish that is a multiple of 2 or 3. And to get them, you have to choose the right cards.
Preparation
To play, print out the game board, at least 4 pages of fish, and a net for each player. Prepare a dice, counters for each player, and paper and pen.
How to play
Players take turns rolling the dice and moving around the field. If a player stops at a cell with an animal, he does not receive any fish.
If a player stops on a square with words, then he catches the specified number of fish - takes the cards and puts them in his net.
When all players have reached the end, we count the catch. Whoever had more fish in the nets won.
Board game
There are many, many useful and entertaining things in this game. But the most important thing is that the main part of the multiplication table is in your pocket! Without tedious memorization, a child learns to multiply numbers from 1 to 5. The game is built on a unique technique that helps children 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.
The game set includes cards with pictures of houses, the windows in these houses are transparent - this is the main feature of the technique! By connecting two cards with the number of windows “two” and “three” you will get a house in which the number of windows will be “six”: 2x3=6.
The houses themselves are drawn very brightly and unusually; just looking at them is a special pleasure. The set also includes task cards, a game piece, a cute storage pouch made of waterproof fabric and detailed instructions with original illustrations.
“Many-Many” has two game options. Both have the ability to adjust the difficulty of the game to suit your child. Both versions of the game will be exciting both for those who are just starting to get acquainted with the multiplication table, and for those who already know it firmly.
Board game
Players will perform many interesting actions: plant flowers in flower beds, uproot them if necessary, arrange surprises for their competitors - pleasant and not so pleasant. But the main thing for the participants is to fulfill orders accurately: they need to grow exactly as many flowers in their flower beds as the buyer wants. During the game, children learn in practice that in order to complete an order for 18 flowers, they need to collect 3 flower beds of 6 flowers each. Such visual operations will be remembered quickly and for a long time.
The goal of the game is to earn as many coins as possible. The number of coins is indicated on the buyer’s card - some have more, some have less. Everything is like in life. Three square cards with buyers are laid out on the table, on which the required number of colors is indicated. During the game, participants plant three flower beds from cards with the same number of flowers in order to grow the required number of flowers for sale: three flower beds of seven colors to get “21”, six flower beds of nine colors to get “54” and so on.
In the game you can be mischievous - give other players moles and beetles, or, on the contrary, you can give gifts. The deck also contains cards with magic watering cans - they multiply the number of flowers in the flowerbed by 2 or 3. And sometimes this is simply invaluable help!
Life hack: multiplying by 9 using your fingers
Multiplying by 9 is often the hardest thing to do. To make this process easier and more fun, you can use a hint - your own palms!
Turn your hands with your palms facing 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 before the curve is tens, in our example it is “6”.
The number of fingers after the curved one is units, that is, “3”.
As a result, we get 63!
Colorful posters
To make the multiplication table easier, we have prepared bright posters for you that can be printed and hung in a visible place.
To make the process of studying the table more dynamic, you can paint over or cover with stickers values that are already well established in memory.
And finally
It’s not so important how exactly you learn the multiplication tables: the main thing is to do it with pleasure - because this way the knowledge is absorbed much better, and the process becomes enjoyable and interesting!
First you need to do two things: print out the multiplication table itself and explain the principle of multiplication.
To work, we will 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:
Now, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make his job easier, find or print the actual chart.
2. Explain the working principle
psyh-olog.ru When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike what he has memorized or what someone else told him. Therefore, try to turn studying the table into an interesting game.
When starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is 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 understand the structure of the table itself. Show that the numbers in the left column are multiplied by the numbers in the top row, and the correct answer is where they intersect. Finding the result is very simple: you just need to run your hand across the table.
3. Teach in small chunks
ytimg.com There is no need to try to learn everything in one sitting. Start with columns 1, 2 and 3. This way you will gradually prepare your child to learn more complex information.
A good technique is to take a blank printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count.
When he has figured it out and mastered the simplest columns well enough, move on to more complex numbers: first, multiplying by 4–7, and then by 8–10.
4. Explain the property of commutativity
blogspot.com The same well-known rule: rearranging the factors does not change the product.
The child will understand that in fact he needs to learn not the whole, but only half of the table, and he already knows some examples. For example, 4×7 is the same as 7×4.
5. Find patterns in the table
secretwomans.ru 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 in 5 or 0: if the number is even, we assign 0 to half the number, if it is odd, 5.
- All examples of 10 end in 0 and begin with the number we are multiplying by.
- Examples with 5 are half as many as examples with 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 multiplying by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. You need to 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.
6. Repeat
medaboutme.ru Practice repetition often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Watch the pace too: give yourself more time to think at first, but gradually increase the pace.
7. Play
utahpubliceducation.org Don't just use standard methods. Learning should captivate and interest the child. Therefore, use visual aids, play, use different techniques.
Cards
The game is simple: prepare cards with examples of multiplication without answers. Mix them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, if he gives the wrong answer, we return it to the pile.
The game can be varied. For example, giving answers on time. And count the number of correct answers every day 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 entire stack of examples runs out. Then for every wrong answer you can assign the child a task: recite a poem or tidy things up on the table. When all the cards have been solved, give them a small gift.
From the reverse
The game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will result in 30 (for example, 3 × 10 and 6 × 5).
Examples from life
Learning becomes more interesting if you discuss with your child things that he likes. So, you can ask a boy how many wheels four cars need.
You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass multiplied by the number of glasses.
Poetry
Rhyme will help you remember even complex examples that are difficult for a child. Come up with simple poems on your own. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine is seventy two.”
8. Don't be nervous
Usually, in the process, some parents forget themselves and make the same mistakes. Here is a list of things that you should never do:
- Force the child if he doesn't want to. Instead, try to motivate him.
- Scold for mistakes and scare with bad grades.
- Set your classmates as an example. When you are compared to someone, it is unpleasant. In addition, you need to remember that all children are different, so you need to find the right approach for each.
- Learn everything at once. A child can easily be frightened and tired by a large volume of material. Learn gradually.
- Ignore successes. Praise your child when he completes tasks. At such moments he has a desire to study further.
Since childhood, the familiar song “2x2=4” brings a smile to adults. I immediately remember my school years and the multiplication table, which was given to many with great difficulty. Now nothing has changed and children also have to learn the table. There are many methods for learning the multiplication table, some even promise to learn the table in a few minutes.
How to learn the multiplication table in 5 minutes - a competent approach
Where do we start studying the table? From the basics, you will first have to explain to your child how to multiply a number by a number. That is, before you start cramming a table, you need to understand the principle of multiplication.
We explain to the child that the simple example of 2 multiplied by 3 means that the number 2 needs to be added 3 times. And we show him an example that he understands, write it like this: 2+2+2=6. Explaining the essence of multiplication. If it is difficult for a child to understand why this example is written as 2x3 = 6, then we take counting sticks, seeds, candies, cherries, etc. and with the help of these objects we show an example of multiplication.
If the child has mastered this, then you can move on to the next stage, actually studying the table.
Which multiplication table is easier to learn?
Teachers of the old school argue that the table, which is now presented on the back of the notebook in the form of columns, is not suitable for the first acquaintance. You can simply learn it, but not understand how to use it. And the real table, which opens up all the possibilities of multiplication, is the Pythagorean table. It was placed on every notebook during the Soviet years. Our mothers and grandmothers used this table.
The numbers in the tablet are arranged symmetrically and the child, without even thinking, will look for symmetry and quickly find the right answer.
And yet, if the child saw and understood the principle of how to use the hint board, then he will only need to learn half of the table. Because the rest is a repetition of the learned material. And yet, the columns and examples of a regular table are sometimes distracting and the student may get confused as to why the extra information is needed. He can learn the table in order, but using the learned material randomly is not an easy task.
How to learn the multiplication table in 5 minutes
The table for 2 and 10 is easy to learn even in 5 minutes! It is important to show the child so that he understands the principle of multiplication, and then simple mathematics. For example, to multiply a number by 10, you need to add it the same number of times, that is, 10 times. And so on. And to get the answer, you just need to add 0 to the resulting number and say the answer received. Children who have completed first grade can already count well within 100 and will be able to convert one into tens.
How to easily learn the table for 2? You can do this in literally 5 minutes. The child already knows how to add identical numbers; you just need to explain the principle to him and practice the learned material.
Have you learned the sign for 2? Feel free to move on to number 4, and leave the table for 3 for later. The child will remember the table for 4 faster if you explain to him that this is the same table as for 2, only all answers need to be doubled. If 2x2=4, then 2x4=8, etc. We multiplied by 2, got the answer, then multiplied the result again by 2.
Multiplying by 3 is sometimes harder than the whole table, so a simple count will help:
How to learn the multiplication table. The easy way
The multiplication table for 5 is as easy to learn as for 2 and 10. Simple answers, count within 5. A little hint: if even is multiplied by odd, the answer is always odd by 0. For example, 5 multiplied by 2 is 10, by 4 will be 20, 6 will be 30. And vice versa, if even is multiplied by 5, the answer will be a number ending with this digit: 5 by 3 = 15, etc.
After table 5, immediately jump to studying table 9. And learning the table is easy with the help of your fingers. When you master this number, all the others will be easy: the table for 6, 7 and 8. The child just needs to explain that he already knows the answers to these examples, only they are written in reverse. If 2 over 8 is 16, then 8 over 2 is also 16.
Now you know how to quickly learn the multiplication tables, and we advise you not to rush, not to force your child to do what he does not want, to study for pleasure anytime and anywhere, even on vacation and during transport, turning lessons into a game. Good luck!
