Cube multiplication table. Talk about making mistakes
Learning the multiplication table is easy if you use a game learning methodology.
It is difficult for a primary school student to immediately master such a mathematical operation as multiplication. Persistent classes will certainly bear fruit, but first you need to understand the reasons for the difficulties of the baby.
It often happens that a child who successfully masters the elementary school program experiences difficulties in completing the topic “Multiplication”. Parents do not need to panic and do not scold the baby.
Tip: Do extra activities to help your son or daughter remember these simple steps.
How to teach a child to multiply, how to explain?
Second grade students have difficulty memorizing the multiplication table, as children do not understand the essence of the mathematical operation "multiplication". How to teach a child to multiply, how to explain:
- Take counting sticks and place them on the table in pairs. For example, 4 pairs. The child must count how many sticks are on the table
- Let the kid write down the addition as an example: 2+2+2+2=8. Explain to the child the features of this action: the same numbers are added
- Continue the series of terms and place two or three more pairs of sticks on the table. Write down an example on paper: 2+2+2+2+2+2= 12
- Explain to the child that this action can be written as a multiplication: 2x6 = 12
- Now invite the child to perform one more action. Lay out on the table, for example, 8, 9 or 10 pairs of counting sticks. Let the kid independently compose the multiplication action. You will see with what interest he will do it.
Important: When the multiplication "by 2" is mastered, you can move on to more complex actions.
Multiplication table simulator
Important: It is good for children's memory when a child sees a visual mathematical action. Buy posters with the multiplication table or draw it yourself on a piece of A1 paper.
Explain to the child that he only needs to memorize 36 combinations. Other steps are repetitive or very simple.
When the baby understands the peculiarity of these actions, the entire multiplication table will seem easy for him. The simulator will help the memory to remember complex actions and memorize simple actions without spending a lot of time on them.
Video: Multiplication table
Video: Teaching a child the multiplication table is very easy and simple
Video: Visual multiplication table. Video clip counting.
It is easy to multiply any number by "2", since this is the addition of this number twice.
2x1=2(2 is repeated 1 time - it turns out 2)
2x2=4(2 is repeated 2 times - it turns out 4)
2x3=6(2 repeated 3 times = 6)
2x4=8(2 repeated 4 times = 8)
2x5=10(2 repeated 5 times = 10)
2x6=12(2 repeated 6 times = 12)
2x7=14(2 repeated 7 times = 14)
2x8=16(2 repeated 8 times = 16)
2x9=18(2 repeated 9 times = 18)
2x10=20(2 repeated 10 times = 20)
Explain to the child with a good example how the multiplication by "3" takes place, so that he understands. Then he will be able to quickly remember this action.
3x1=3(3 is repeated 1 time - it turns out 3)
3x2=6(3 is repeated 2 times - it turns out 6)
3x3=9(3 repeated 3 times = 9)
3x4=12(3 repeated 4 times = 12)
3x5=15(3 repeated 5 times = 15)
3x6=18(3 repeated 6 times = 18)
3x7=21(3 repeated 7 times = 21)
3x8=24(3 repeated 8 times = 24)
3x9=27(3 repeated 9 times = 27)
3x10=30(3 repeated 10 times = 30)
The fourth column of the multiplication table is still easy and the child will easily remember it. Help the baby with your tips and support in the form of words of encouragement and praise, and he will definitely be able to do everything.
4x1=4(4 is repeated 1 time - it turns out 4)
4x2=8(4 is repeated 2 times - it turns out 8)
4x3=12(4 repeated 3 times = 12)
4x4=16(4 repeated 4 times = 16)
4x5=20(4 repeated 5 times = 20)
4x6=24(4 repeated 6 times = 24)
4x7=28(4 repeated 7 times = 28)
4x8=32(4 repeated 8 times = 32)
4x9=36(4 repeated 9 times = 36)
4x10=40(4 repeated 10 times = 40)
The fifth column of the multiplication table is easy mathematical operations. To get the result, you need the number by which "5" is multiplied, first multiply by "10", and then divide in half.
Important: When a child understands how numbers are multiplied by "5", a logical chain of each action from this column will appear in his head over time. Thanks to this, he will already be able to multiply by "5" instantly.
5x1=5(5 is repeated 1 time - it turns out 5)
5x2=10(5 is repeated 2 times - it turns out 10)
5x3=15(5 repeated 3 times = 15)
5x4=20(5 repeated 4 times = 20)
5x5=25(5 repeated 5 times = 25)
5x6=30(5 repeated 6 times = 30)
5x7=35(5 repeated 7 times = 35)
5x8=40(5 repeated 8 times = 40)
5x9=45(5 repeated 9 times = 45)
5x10=50(5 repeated 10 times = 50)
With multiplication by "6" the first difficulties appear: actions are difficult to remember, and the numbers are large.
Important: Explain to the child that the row "6x6" is a repetition of the works from the previous columns that have already been learned. It remains to learn only four complex actions.
6x1=6(6 is repeated 1 time - it turns out 6)
6x2=12(6 is repeated 2 times - it turns out 12)
6x3=18(6 repeated 3 times = 18)
6x4=24(6 repeated 4 times = 24)
6x5=30(6 repeated 5 times = 30)
6x6=36(6 repeated 6 times = 36)
6x7=42(6 repeated 7 times = 42)
6x8=48(6 repeated 8 times = 48)
6x9=54(6 repeated 9 times = 54)
6x10=60(6 repeated 10 times = 60)
The seventh column of the multiplication table is usually easier to remember than subsequent ones. It has a couple of complex actions that need to be memorized.
7x1=7(7 is repeated 1 time - it turns out 7)
7x2=14(7 is repeated 2 times - it turns out 14)
7x3=21(7 repeated 3 times = 21)
7x4=28(7 repeated 4 times = 28)
7x5=35(7 repeated 5 times = 35)
7x6=42(7 repeated 6 times = 42)
7x7=49(7 repeated 7 times = 49)
7x8=56(7 repeated 8 times = 56)
7x9=63(7 repeated 9 times = 63)
7x10=70(7 repeated 10 times = 70)
The last complex column of the multiplication table. If the child remembers the previous columns well, then it will not be difficult for him to learn the multiplication by "8". It has only two new actions: 8x8 and 8x9
8x1=8(8 is repeated 1 time - it turns out 8)
8x2=16(8 is repeated 2 times - it turns out 16)
8x3=24(8 is repeated 3 times - it turns out 24)
8x4=32(8 is repeated 4 times - it turns out 32)
8x5=40(8 repeated 5 times = 40)
8x6=48(8 repeated 6 times = 48)
8x7=56(8 repeated 7 times = 56)
8x8=64(8 repeated 8 times = 64)
8x9=72(8 repeated 9 times = 72)
8x10=80(8 repeated 10 times = 80)
The ninth column is one of the easiest. By "9" we have already multiplied all the numbers. Therefore, the baby will have to learn only one action: 9x9
9x1=9(9 repeated 1 time = 9)
9x2=18(9 is repeated 2 times - it turns out 18)
9x3=27(9 repeated 3 times = 27)
9x4=36(9 repeated 4 times = 36)
9x5=45(9 repeated 5 times = 45)
9x6=54(9 repeated 6 times = 54)
9x7=63(9 repeated 7 times = 63)
9x8=72(9 repeated 8 times = 72)
9x9=81(9 repeated 9 times = 81)
9x10=90(9 repeated 10 times = 90)
Multiplication table - game for kids
Multiplication table - game for kidsTo date, you can find many different methods for memorizing the multiplication table. Mathematics is a difficult science, but for a child it should not be so. If classes are carried out correctly with the baby, then he will easily perceive and remember any information.
The easiest way to learn the multiplication table is a game for kids. If the kid will willingly go to classes, then he will be able to remember everything that will be offered to him in these classes.
Important: If you see that the child is not in the mood to engage, for example, he is naughty. Postpone the lesson until a more appropriate time.
Games for kids to learn the multiplication table quickly:
Video: Educational online game for children to quickly learn multiplication tables
Video: MULTIPLICATION TABLE. DEVELOPING CARTOON!
Video: Educational lessons and cartoons for children. Arithmetic. Multiplication table
As mentioned above, the main rule for teaching a child the multiplication table is a playful form of lessons. You can use multiplication in verses for children.
Important: Poems are well remembered because of the rhyme, which means that the multiplication table will also be perfectly stored in the baby's mind.
Poems - multiplication by 8
Multiplying by 5 - verses
Multiplying by 8 - verses
Video: Verse Multiplication table in verse
To make classes not boring, buy your child books with multiplication tables. Read them with him, and positive emotions will help you quickly memorize mathematical operations that are difficult for the baby.
Video: We improve the child's performance in mathematics - Everything will be kind - Issue 481 -10.20.14-Everything will be fine
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The multiplication table is a basic concept in mathematics, which we get acquainted with in elementary school and which we then use all our lives, regardless of profession. But the children are in no hurry to memorize the endless columns by heart, especially if the task was on vacation.
website will give tips on how to easily learn the table with children and make this process fun.
Pythagorean table
Despite the fact that the task is to learn, that is, memorize, the table by heart, it is first of all important to understand the essence of the action itself. To do this, you can replace multiplication with addition: the same numbers are added as many times as we multiply. For example, 6×8 is 8 times 6.
Highlight the same values
A great helper for learning multiplication is the Pythagorean table, which also demonstrates some patterns. For example, what about t changing the places of the factors, the product does not change: 4 × 6 \u003d 6 × 4. Mark such “mirror” answers with a certain color - this will help you remember and not get confused when repeating.
It is better to start studying the Pythagorean table with the simplest and most understandable parts: multiplication by 1, 2, 5 and 10. When multiplied by one, the number remains unchanged, while multiplying by 2 gives us twice the value. All answers multiplied by 5 end either in 0 or 5. But multiplying by 10, in the answer we get a two-digit number from the digit that we multiplied and zero.
Table for fixing the result
To consolidate the results, draw an empty Pythagorean table with your child and invite him to fill in the cells with the correct answers. To do this, you only need a piece of paper, a pencil and a ruler. You need to draw a square and divide it into 10 parts vertically and horizontally. And then fill in the top line and the leftmost column with numbers from 1 to 9, skipping the first cell.
Of course, all children are individual and there is no universal recipe. The main task of a parent is to find an approach and support his child, because we all once started with such simple and complex steps at the same time.
You can’t do without knowing the multiplication table, so it is included in the school curriculum already in the primary grades. It is very difficult for a student to memorize. Children are frightened when the teacher points to a spread of a notebook, where examples that need to be learned rise in columns.
Therefore, it is worth showing how to make memorization fast with the help of games, multiplication secrets and useful algorithms.
The multiplication table (a game to quickly learn the memorization algorithm, described below) was invented a very long time ago. There is an opinion that the Pythagorean table was developed by an ancient philosopher and mathematician. But no confirmation of this has been found. But it is known that they counted with it already in ancient Japan, where during excavations they found wooden planks with parts of a table (8th century).
Scientists suggest that the table came to Japan through China. In those days, the countries closely interacted. Japanese residents came to China to study sciences. The assumption that the table was created in China is confirmed by a find dating back at least 3 thousand years in the form of a separate fragment of the table.
Some experts express the idea that the table penetrated from China to India by trade caravans, and from there it spread to all other countries.
Another version says: tablets with numbers were found 5 thousand years ago in Mesopotamia. Perhaps that is where it was invented. In addition, it could have been invented in several countries at the same time, because already at that time the need for calculating large numbers was clear.
What class teaches the multiplication table
In Russian schools, they begin to study the table in the 2nd grade. And by the beginning of grade 4, teachers are trying to finish memorization. However, the most commonly used standard method is memorization. It is ineffective, so some students peek at the answers on the back of the notebook until graduation.
How to teach a child to multiply
First of all, the child must be interested. Moreover, it is worth starting the study together, and not just playing the role of an inspector. 
A few tips to help you memorize the Pythagorean table faster and better:
- It is worthwhile to prepare a printed multiplication table in advance and explain how the action takes place (the answer to multiplication is at the intersection), tell the basic terms: factors, product.
- Explain to the child how the table works (for example, explain that 3 x 2 is the same as 3 + 3).
- Learn the material gradually, in small parts. You need to start with the simplest examples.
- It should be explained to the child that by changing the places of numbers in multiplication, the result does not change (2 x 4 is the same as 4 x 2);
- Look for patterns in the table (for example, if you multiply any number by 1, you get the same number).
- Do more reps. Gradually covered material can be forgotten, so it is systematically worth refreshing in memory.
- Use memory techniques.
- Not every child manages to memorize material quickly, so parents should be calm and attentive. Even if the student fails to learn something, he should not be forced to sit over the lessons for longer.
Where to begin
First you need to make the child understand the meaning of multiplication. This is done on the simplest examples: 3 x 4 - means that the number 3 must be taken 4 times. Once the meaning is clear, it becomes much easier. On the back of notebooks, a table is usually written in columns. It is better to abandon it in favor of the Pythagorean one, where the result is at the intersection of multiplying numbers. The visual method works better.
Therefore, it is worth printing the table and hanging it above the table or anywhere where the child will look at it. Let it be bright and big enough. They start learning with the smallest numbers: by 2, then by 3. 
You should first think over all the ways of memorization. A combination of methods will help you remember faster: with the help of cards, games, poems, knowledge of patterns.
Useful Study Materials
When memorizing the multiplication table, it will not be superfluous to use educational materials.
- Shklyarova T. "How I taught my girl the multiplication table." This book is small, smaller than a notebook. The author begins it by crossing out half of the multiplication table - the law of displacement is in effect. The first part of the book talks about what multiplication and division are, even and odd numbers, the features of finding the product and the quotient by 1, 10 and 0, how to find an unknown factor and more. The second part tells how to multiply and divide by all numbers, explains the different nuances and ways of simple memorization.
- Samsonova L. "Tabular multiplication to all current textbooks". This manual is built in a strict order of study: first multiply by 2, then by 3, by 4, and so on up to 9. The book contains many tests, tasks, interesting examples, coloring pages. After learning the multiplication by certain numbers, there is an independent work to check.
- Long Linnet "The Magnificent Multiplication".
The last tutorial is based on games, of which there are 28 pieces:
- multiplication on fingers;
- memorization with socks;
- pencils;
- corners of the room;
- playing cards;
- counting rhymes;
- inventing fairy tales;
- tic-tac-toe;
- digital lotto and more.
The book is divided into 3 parts - according to the level of difficulty. Boys and girls will be surprised that to memorize complex examples, you just need to decorate a teddy bear or learn a counting rhyme.
Cards
This is a simple but effective method. You should prepare cards with multiplication examples without entering answers. They are mixed (you can use a loto bag). The child draws one card at a time and tries to answer. If it is correct, then the card is removed to the side, the wrong one is returned to the bag.
Flashcards will help you quickly learn the multiplication table You can diversify the game like this: give answers for a certain period of time. Allocate 1 min. (or more), then count how many cards were guessed. The child will want to improve his result, which will be an incentive to memorize.
Another option is to play until all examples run out. For each wrong answer, entrust the child with a task: collect toys, dance, squat, recite a verse. If all the cards are correctly guessed, then you can give a prize in the form of sweets.
All children love to play, so once they learn that they can get points, win a chocolate bar, or beat someone (even themselves), they become much more interesting.
Therefore, you can offer your child to learn the material with the following phrase: “The multiplication table is a game. To learn faster, we will play "cards, sea battle, shop" (depending on what is taken). The goal is to score so many points, do it in that amount of time, reach level 3, and more.”
Poetic examples
With the help of short rhyming lines, you can remember the most difficult moments well.
You can compose simple rhymes that will speed up the child's memorization process. They don't have to be logical:
It is worth noting that some examples from the Pythagorean table are themselves rhyming phrases. These include:
- Six six - thirty six;
- A family of five - thirty-five and others.
Such variations do not cause much difficulty in memorization.
Counting on fingers
Often children resort to the turnover of a notebook with a multiplication table or even use a calculator when they forget complex examples. There is an easy way to count with your fingers.
Using this method, it is easy to multiply numbers by 9. Counting algorithm:
Example: you need to multiply 3 by 9. The hand is put forward, the third finger is bent. To the left of it are 2 fingers - they represent the number 20. To the right, there are 7 fingers, which means 7 units. The result was 27.
Multiply 9 by 9. The ninth finger is bent. 8 remain on the left (which means 80), on the right - 1. It turns out 81.
The following method will help you multiply numbers greater than 5. He's more difficult. Let's say you need to calculate how much 6 by 7 will be. To do this, one finger is extended on the left hand (6 is more than 5 by 1), the others are bent. On the right, 2 fingers remain (7 more than 5 by 2), the rest are hidden.
Visible fingers add up: 1 + 2 = 3 tens (i.e. 30). The bent ones are multiplied: 4 x 3 \u003d 12. It remains to add the resulting numbers: 30 + 12 \u003d 42. The answer is found.
The child should learn the multiplication table with pleasure, so you should interest him.
You can do this in the form of a trick game: give the kid a table and ask him to name any example from the desired column. He will ask, after that the parent will say that he can count with his own hand, quickly show the whole sequence. It is important that the student himself wants to learn multiplication. So the process will move much faster.
Use of toys
The multiplication table (a game to quickly learn the algorithm, you can offer the child instead of boring memorization) is better absorbed with the help of additional "tools". To do this, you will need your child's favorite toys.
The essence of the method is simple: cars, designer parts, furniture from a dollhouse are taken. Based on this, examples are built. Let's say you need to multiply 5 by 3. Then 5 details of the designer are laid out in front of the baby.
It is reported that you need to take 5 bricks 3 times to build a house. He takes these 5 parts, 5 more to them, and again the same number. Then he calculates that 15 bricks were brought to the construction site. With the help of such visual practice, the material is remembered faster.
If the method with toys is used, then it is not necessary to additionally burden the student with the counting method on the fingers. It is better to choose one option so as not to confuse the child.
Mobile or online games
Modern assistants are computer games. The memorization process is fun and imperceptible. 
Examples of online games:
- "Multiplication Table: Animal Puzzles". The child needs to collect a picture. You can do this only by solving the examples - they are below. At the top of the screen is a figure in the form of a table with numbers. After solving the example, a piece of the puzzle is dragged onto the square with the resulting number. As a result, the image of the animal should open. In the game, you can select the mode with multiplication by any number.
- "Multiplication Table: Jungle Adventure". The player is transported to the world of dangerous forests where an ancient tribe lives. One of his representatives, guy Jim, should get a mask. But before that, you need to cope with various tests - fishing, drumming and target shooting. The child must help the little savage to cope with obstacles. This can only be done by solving examples.
- "Multiplication Table: Skateboard Racing". A fun ride and memorization of examples will make learning seamless. A skateboarder rushes along the road, who constantly has to overcome obstacles. To help him, you should quickly solve examples. In the game, you can select the mode not only for multiplication, but also for other arithmetic operations.
- "Snake". A small worm crawls on a green meadow. Numbers are scattered everywhere - answers to examples that should be guessed. The snake is allowed to eat only the balls with the correct answer. The more eaten, the longer it is. The game has the ability to select the mode - the numbers by which the multiplication will be performed.
Many games are aimed not at learning, but at recall, that is, it is assumed that the child has already memorized the material, and during the game he simply tests himself. Therefore, you can allow to use this method after study - as a hitch.
sea battle
The multiplication table (a game to learn faster, it can be used in the form of a sea battle) is easier to remember in a playful way. According to the rules, a pair of players participate. Everyone draws two fields on a sheet in a cage: one for their own ships, and the second for the opponent's fleet. To memorize the table, instead of letters, numbers are written on one side - the field resembles a Pythagorean table.
Having drawn the ships, the battle begins. It’s worth playing like this: the multiplication action is called, for example, 2 x 7. The child sees that the answer is 14 at the intersection, looks to see if there are ships there. This is how all moves are made.
Another option - the answer is called, say, 32. And the child watches that this number is obtained by multiplying 4 by 8. The clarity of this method will simplify memorization.
How to learn the multiplication table by playing sea battle:
Real life examples
Learning will be easier and more enjoyable if you build the process on things that are close to the child. You can give examples from everyday life. Instead of the standard question: how much is 2 x 3, you can ask “how many cars are in the garage if 3 cars drove 2 times?”. For explanations, any objects are used: matches, coins, cubes and felt-tip pens.
You can play shop. Invite the child to buy 4 sweets for 3 rubles. Let him calculate how much money he will need.
Multiplication by 1 and 10
Solving examples with these numbers is very easy. When multiplying any number by 1, this number remains: 1 x 4 \u003d 4 (that is, they took the unit 4 times or the four 1 time). So it is with all other cases: 1 x 6 = 6; 1 x 8 = 8 and so on. When the number is increased by 10 times, 0 is simply attributed at the end: 5 x 10 \u003d 50; 10 x 28 = 280 and so on with any number.
Multiply by 2
The product of numbers by 2 shows the doubling of the digit, that is, it is taken 2 times: 2 x 12 \u003d 12 + 12; 5 x 2 = 5 + 5 and so on each. Therefore, all examples with doubling can be considered easy, because children already know addition.
Multiply by 3
It’s worth starting the explanation of the table for the number 3 with a simple one: 1 x 2 - this means that the number 1 is taken 2 times, that is, 1 + 1. If you take one more unit, it will come out 1 + 1 + 1. This example is replaced by multiplication: 1 x 3 or 3 x 1 (the result will not change from changing the places of the multipliers). 
Then it turns out that all other examples of multiplication by 3 are built according to the same principle: the number is doubled and added. For example, 6 x 3 means that 6 is multiplied by 2 and another 6 is added. It looks like this: 6 x 2 + 6 = 18, that is, 6 x 3 = 18.
Thus, it is worth doing multiplication with all numbers. It can also be noted that even results of multiplication by 3 in the table alternate with odd ones.
Multiply by 4
It is assumed that some number is taken 4 times, for example, 3 x 4 can be written as follows: 3 + 3 + 3 + 3 = 12, that is, the three was taken 4 times. If you swap places, you get 4 x 3 \u003d 4 + 4 + 4 - the four was taken 3 times. An example with the legs of an animal is used to explain. The child is asked the question: how many legs does a cat have? He answers that 4 (it is better to use a picture for clarity with the image of an animal).
If one cat has so many legs, then you get an example: 4 (legs) x 1 (cat) \u003d 4. Next, the number of legs of two cats is asked. The child will say that 8. An example is compiled again: 2 (cats) x 4 (legs) \u003d 8. In this way, you can write down all examples of multiplication by 4.
Multiply by 5
Memorizing the multiplication table for 5 is easy enough, but if you need to multiply large numbers, difficulties arise. To multiply a number by 5, you need to divide it in half (by 2), then 0 is simply attributed to the answer. If the result of dividing by 2 is not an integer, then 5 is simply put at the end (ignoring the comma).
Example: 3258 x 5 \u003d (3258 / 2) and a zero \u003d 16290 is attributed.
Multiply by 6,7,8
There is an easy way to count on your fingers. Until the child has memorized the entire multiplication table for large numbers, it will be useful for him to learn such a simple multiplication variant. So, the hands turn their palms towards themselves. Each finger on the hands is assigned numbers from 6 to 10 (you need to start with the little finger). 
For example:
- calculate the product of 6 by 7. You should connect the finger under the sixth number of the left hand and the seventh on the right.
Now you need to count: the number of fingers under the connected and those that are grappled. In this case, one finger is below and two are connected, 3 fingers came out. It will be 3 tens. The fingers remaining on top are multiplied: four on the left hand and three on the right - 3 x 4 = 12. Since the number is greater than 9, the tens and the resulting figure are added: 30 + 12 = 42. This will be the answer.
One more example:
- 8 x 7. The eighth finger of the left hand is connected by the seventh finger of the right. Together with the connected ones you get five fingers, that is, the number 50. If you multiply the rest, you get 6 (units). The result is 56.
Multiply by 9
Multiplying by nine with fingers was discussed above. In fact, here it is worth remembering only one example: 9 x 9 \u003d 81. All the rest refer to other numbers, because the product does not change from changing places. So, 9 x 8 = 8 x 9, and 9 x 5 = 5 x 9 and so on.
So that the child is not afraid of the huge number of examples on the spread of the math notebook, he should immediately tell that you can cross out the plate by more than half, because it is not necessary to learn all this. 
When multiplying by 1 and 10, you do not need to memorize the answers. Multiplying by 2 is simply doubling a number, children are taught to add before. By changing the factors in places, the product does not change, so not everything will have to be memorized.
| Secret | What does | Example |
| Product by 1 and 10 | Multiplying by 1 leaves the number as it is; by 10 - zero is assigned | 1 x 5 = 5 (the number has not changed); 2 x 10 \u003d 20 (zero was written to the deuce) |
| Multiply by 2 | The number is added to itself | 30 x 2 = 60 (since 30 + 30 = 60) |
| Swapping multipliers | If, when multiplying, the first number is put in place of the second, and the second in place of the first, then the answer will not change | 6 x 3 = 3 x 6 = 18 |
So, out of 80 examples located on the back of the notebook, you will need to learn only 36 (the rest are crossed out).
Among the presented methods for working with the Pythagorean table and memorization tricks, one can distinguish those that will help you quickly and efficiently learn the material, do not turn mathematics into a boring and uninteresting subject, but make it look like a game.
It is worth making a little effort, and the child will not have to peep anywhere even the most complex examples.
Article formatting: Svetlana Ovsyanikova
Video on the topic: activities with a child: how to quickly learn the multiplication table
How to quickly learn the multiplication table:
In real life, people who can calculate in their minds look like "super smarts", although there is nothing complicated about this. A calculator is a calculator, but counting in your mind is useful!
How to help your child learn the multiplication table
Below are some simple tricks
Multiply by 2 or doubling. Doubling is pretty easy, just add something to yourself. At first, I showed on my left and right hand at the same time one, two, three, four, five fingers - so we got 2, 4, 6, 8, 10. Together with the fingers of my student, we reached twenty, and then I pointed to different things in the room, and offered to count and double - the number of letters in the poster, the number of symbols on the clock face, count the number of spokes on one side of the bicycle wheel, and see if the total converges with doubled, and so on.
Multiply by 4 and 8, 3 and 6
When you know how to multiply by two, it's mere trifles. Multiplying by four is the same as doubling the answer for something that has already been doubled, for example, 7 × 4 is 7 × 2x2, and that 7 × 2 is 14 we already remembered well in the previous lesson about doubling, so turn 14 itself into 28 is not difficult. When you figured out the four, it's not so difficult to deal with the large numbers of the 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.
By multiplying by 3 and 6, we learned the old pirate method of "dividing by three". If you add the digits in a number multiplied by 3, 6, or any other that is divisible by three, then the result of adding the digits of the answer 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 you can add the numbers to 12, you get 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 would give a number, even a three or four digit number, and ask if it was divisible by 3. To answer, just add the numbers, which is quite simple. If the number was divisible by 3, then I asked - "what about 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 would happen with such a division by 3 or 6. It was a very fun activity.
Multiplication by 5 and 7, prime numbers
And now we have multiplication by five, seven, and nine. And this means that we learned how to multiply them by many other numbers - by 1, 2, 3, 4, 6, 8 and 10. We dealt with the five very quickly - it is easy to remember: at the end there is either a zero or five, just the same as a multiplying number: either even or odd. As a subject on which it is convenient to deal with fives, the watch face is great, you can come up with many tasks about traveling in time and space. At the same time, I told why there are sixty minutes in an hour, and we understood how convenient it is.
We saw that it is convenient to divide 60 by 1, 2, 3, 4, 5, 6, and it is inconvenient to divide by 7. So it was time to take a closer look at this number. Of the multiplication by the seven, it remained to remember only 7 × 7 and 7 × 9. Now we knew almost everything we needed. I explained that seven is just a very proud number - such numbers are called prime, they are divisible only by 1 and by themselves.
Math can be fun and easy. Check out this cute table.
If you study it thoughtfully, then there is not much to learn. There are 36 positions in total. The rest are either simple (1 x 10) or reversible (2 x 4 = 4 x 2). Minus 10 positions from the multiplication table by 9. It can be learned in 5 minutes. There is a focus:
So let's go.
To begin with, let's put our hands on the table and mentally number the fingers from left to right from 1 to 10. To perform the multiplication operation, let's say 9 x 3 = ?, bend the third finger from the left. Everything! The answer is ready: the fingers remaining not bent on the left form the number of tens in the answer, and not bent on the right - the number of units. We count and say the answer: 27!
This way you can get the answer for any number. Here, for example, an example 9 x 7 = 63
watch multiplication by 9 in the video:
This article is about how to learn the multiplication table without pain and cramming. In it, we tell you how to learn how to multiply numbers up to 10 by each other, memorizing 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.
Turning 100 examples into 36
The multiplication table on the back of most notebooks looks like this:
It could take a whole summer to learn it. It is clear that mechanically memorizing the correct answers to a hundred examples is the most time-consuming way to remember the results of multiplying numbers up to 10 with each other.
The process speeds up many times when we show how all these 100 combinations can be reduced to 36. In this case, the Pythagorean table is a much better 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 fit into a rectangle with sides of length 3 and 5 (count them together to make sure).
- 5 * 3 = 15 for the same reason (count together).
Here we clearly demonstrate the property of commutativity: the product does not change from the permutation of the places of the factors. Of course, it is better to keep the name of this property until Halloween, so as not to frighten anyone ahead of time :)
Because of this, the Pythagorean table is symmetrical about its diagonal, so out of 100 examples there are already 55 left to remember: the diagonal itself with the values 1, 4, 9, ..., 100 and everything that is above or below.
This discovery can be made independently by filling in the part of the empty Pythagorean table, in which only factors are initially marked:
The child can begin to fill it in, even if he does not yet know the rules of multiplication - 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 a row with threes , and so on.
Having filled in 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 entirely.
After that, 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 in any way. .
- If a number is multiplied by 10, it ends in a zero.
We subtract 19 more “automated” multiplication examples from the remaining 55 examples, and we get only 36 combinations that need to be remembered. Almost three times less than they offer us on the covers of notebooks!
It's easier now, isn't it?
We play and remember
It is difficult to remember what cannot be applied in life. That is why it is important to show that the multiplication table can be useful. This will help games and fun activities.
big snowfall
These puzzles will allow the child to be in a situation 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 - it is enough to multiply the length by the width!
Battle of the Rectangles
This is a simple game for two people to understand multiplication and the area of a rectangle.
You will need 2 felt-tip pens, a piece of squared paper and 2 cubes. Each player chooses the color of the pencil or felt-tip pen with which he will draw.
The players take turns. The first player rolls 2 dice. Then he must draw on a piece of paper on his side a rectangle or square, 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 space left on the sheet for new pieces. The winner is the one whose figures occupy more cells on a sheet of paper.
Multiplication fishing game
With this game, children will easily figure out the principle of multiplication: why two by four will be eight, or three by three will be 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 pick up the right cards.
Training
To play, print out a game board, at least 4 fish pages, and a net for each player. Prepare a dice, chips for each player, and paper with a pen.
How to play
Players take turns rolling the die and moving around the board. If a player stops on a cage with an animal, then he does not receive fish.
If the player stops on a cell with words, then he catches the indicated number of fish - he takes the cards and puts them in his net.
When all players have reached the end, we count the catch. Whoever has more fish in the nets wins.
Board game
There are many, many useful and entertaining things in this game. But most importantly, the main part of the multiplication table is 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 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 images 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 separate pleasure. The set also includes task cards, a game token, a cute waterproof storage pouch, and detailed instructions with original illustrations.
In "Many-Many" there are two variants of the game. 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 well.
Board game
Players will perform many interesting actions: plant flowers in the flower beds, uproot them if necessary, arrange surprises for their competitors - pleasant and not very pleasant. But the main thing for the participants is to fulfill orders with accuracy: you need to grow exactly as many flowers in your flowerbeds as the buyer wants. During the game, children in practice are convinced that in order to fulfill an order for 18 flowers, it is necessary to collect 3 flower beds of 6 flowers. 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 beds of cards with the same number of flowers in order to grow the required number of flowers for sale: three beds of seven flowers to get "21", six beds of nine flowers to get "54" and so on.
In the game, you can be harmful - throw moles and bugs to other players, or, on the contrary, give gifts. There are also cards with magic watering cans in the deck - they multiply the number of flowers in a flower bed by 2 or 3. And sometimes this is just an invaluable help!
Life hack: multiply by 9 with 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 palms towards 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 bent is tens, in our example it is “6”.
The number of fingers after the bent one is units, that is, "3".
As a result, we get 63!
colorful posters
To make the multiplication table easier, we have prepared for you bright posters that you can print and hang in a conspicuous place.
To make the process of studying the table more dynamic, you can paint over or stick with stickers the values \u200b\u200bthat are already well entrenched in memory.
And finally
It is not so important how exactly you will learn the multiplication table: the main thing is to do it with pleasure - because this way knowledge is absorbed much better, and the process becomes pleasant and interesting!
