Schoolchildren find the table boring and useless. Often children get angry, upset, trying to figure out a set of numbers they do not understand. Parents can make learning easy and fun by preparing ahead of time.
The basic rule in learning the multiplication table is to interest the child. Like adults, they perceive information differently. Some children like to learn poems and songs. Others can sit quietly at the table with their parents and look at the Pythagorean table.
How to teach a child the multiplication table (picture)
Easy to remember the multiplication table for a child help:
- Cards;
- Counting figures, sticks;
- Special programs for tablet and phone;
- Educational videos and cartoons;
- Poems and songs;
- Pictures;
- Child's fingers.
Game methods are captivating and give quick results. It is better to start classes in a good mood when the child is in school.
Learning the multiplication table: life hacks and videos
It is important to understand how it is more comfortable for a child to perceive information so that the process does not turn into “cramming”. Everything is very simple:
Auditory children it is better to learn new things in conversation. They like to memorize numbers by repeating examples out loud. A good option to remember the multiplication table is to learn poems, songs or watch educational videos.
Learning the multiplication table (video)
visual child learns more easily when vision and imagery are involved. They absorb information through bright drawings, coloring games that have large colored fonts and numbers.
Multiplication table coloring game (picture)
Also, with a visual child, you can watch educational cartoons in which your favorite characters act as a teacher.
9 times table with Fixies (video)
Kinesthetic children learn through the sensations and feelings that they have when they come into contact with a new object and information. In this case, you can try the card method.
Learning the multiplication table with cards (video)
It is important to consider how your child learns best so that the process of memorizing the multiplication table will be fun and easy.
How to learn the multiplication table in 5 minutes a day
Kukina Ekaterina Georgievna
mathematics teacher
You have probably heard the opinion more than once that the level of mathematical education is falling.
So, when my children were in the second grade, I clearly understood why the level of mathematical education at school was falling. It is in the second grade, when laying the very foundation of mathematical education, that such a gigantic irreparable hole arises that you can’t support with any crutches in the form of calculators.
Namely, the main problem is in the multiplication table. Look at the checkered notebooks that your schoolchildren have.
I went shopping for a long, long time looking for notebooks. And anyway, for everyone - here is such a picture.
Multiplication table (picture)
There are even worse notebooks (for high school students), where there are no multiplication tables, but there are a bunch of meaningless formulas.
So what's wrong with this notebook? The unsuspecting parent sees that the multiplication table is on the notebook. It seems that all your life there was a multiplication table on notebooks? What's wrong?
And the problem is just that the multiplication table is NOT on the notebook.
The multiplication table, my dear readers, is this:
Sometimes the same table is even called beautiful word"table of Pythagoras". The top and left columns can be omitted, only the main rectangle.
First, it's a table. Second, it's interesting!
No child in their right mind will consider the examples written out in columns.
Not a single child, no matter how brilliant he may be, will not be able to find interesting tricks and patterns in the written examples.
Well, in general, when a teacher says: “learn the multiplication table,” and the child doesn’t even see the table in front of him, he immediately understands that mathematics is such a science where ordinary things are named somehow differently and you need a lot, a lot cramming, but it is impossible to understand anything. And in general, it is necessary to do "as it is said", and not "as it makes sense".
Why is the Pythagorean table better?
Firstly, it does not contain garbage and informational noise in the form of the left side of the examples.
Secondly, you can think about it. It's not even written anywhere that this multiplication is just a table.
Thirdly, if she is constantly at hand and the child constantly stumbles upon her, he willy-nilly begins to memorize these numbers. In particular, he will never answer the question "seven of eight" with 55 - after all, the number 55 is not and never was in the table at all!
Only children with abnormal memory can memorize columns of examples. In the "table" you need to remember much less.
In addition, the child automatically looks for patterns. And he finds them himself. Even such patterns are found by children who do not yet know how to multiply.
For example: numbers that are symmetrical about the diagonal are equal. You see, the human brain is just set to look for symmetry, and if it finds and notices, it is very happy. And what does it mean? This means that the product does not change from permutation of the places of the factors (or that the multiplication is commutative, to put it simply).
Pythagorean table: multiplication (picture)
You see, the child notices it himself! And what a person invented himself, he will remember forever, in contrast to what he memorized or was told.
Remember your high school math exam? You forgot all the theorems of the course, except for the one that you got, and you had to prove it to the evil teacher! Well, that's if you didn't cheat, of course. (I exaggerate, but almost always it is close to the truth).
And then the child sees that you can not learn the whole table, but only half. If we already know the line of multiplication by 3, then we do not need to memorize "eight by three", but just remember "three by eight". Half the work already.
And besides, it is very important that your brain does not accept dry information in the form of some incomprehensible columns of examples, but thinks and analyzes. Those. trains.
In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you poke at any number and draw a rectangle from the beginning of the table to this number, then the number of cells in the rectangle is your number.
Pythagorean table: multiplication (picture)
And here the multiplication already gets a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of \u200b\u200ba rectangle is equal to the product of its sides)
And you have no idea how much easier it is to divide with such a table!
In short, if your child is in the second grade, print out such a correct multiplication table for him. Hang a large one on the wall so that he looks at it when he does his homework or sits at the computer.
And print and laminate a small one for him (or write on cardboard). Let him carry it to school with him, and just keep it conveniently at hand. (it does not hurt to highlight the squares diagonally on such a table so that you can see it better)
My kids have this one. And it really helped them in the second grade and still helps a lot in math classes.
Pythagorean table: multiplication (picture)
Here's my word of honor, immediately the average score in mathematics will increase, and the child will stop whining that mathematics is stupid. And in addition, in the future, your child will also be easier. He will understand that he needs to use his brains, and not cramming. And little that he understands, he also learns to do it.
And I repeat: there is nothing wrong with examples with columns. And the amount of information they contain is the same as in the "table". But there is nothing good in such examples either. This is informational garbage, from which you will not immediately find what you need.
Praise more often
Think of ways to reward your child. It could be the little things that make him happy.
Find an approach if the child is not in the mood
Forced to study, scream or completely deprive of entertainment - such methods beat off any desire to study. It makes sense to calmly explain the importance of classes and motivate the child.
Learn the multiplication table step by step
When a child first sees how many numbers he needs to remember, a protest arises. It is better to practice at a comfortable pace with rest breaks.
Remember that every child is an individual
As soon as children are compared with friends or classmates, they lose the desire to do anything. It must be remembered that each child has his own pace of learning and the careful attitude of parents is of great importance.
Talk about making mistakes
At the first failures, children lose interest, do not want to continue classes. It is important to explain that there are no mistakes good results. Everything will surely work out.
Now you know everything about how to teach a child the multiplication table in different ways so that the stammering process is a joy.
If my memory serves me right, the multiplication table up to and including 5 was easy enough. But with multiplication by 6, 7, 8 and 9, certain difficulties arose. If only I knew this trick before homework would run at least twice as fast ;)
Multiplication by 6, 7 and 8
Turn your hands with your palms facing you and assign the numbers 6 to 10 to each finger, starting with the little finger.
Now let's try to multiply, for example, 7x8. To do this, connect the number 7 finger on the left hand with the number 8 finger on the right.
And now we count the fingers: the number of fingers under the connected ones is tens.
(image is clickable)
And the fingers of the left hand, remaining on top, are multiplied by the fingers of the right - these will be our units (3x2 = 6). The total is 56.
Sometimes it happens that when multiplying “units”, the result is more than 9. In such cases, you need to add both results in a column.
For example, 7x6. In this case, it turns out that the "units" are equal to 12 (3x4). Tens equals 3.
3 (tens)
+
12 (units)
________
42
Multiply by 9
Again turn the palms towards you, but now the numbering of the fingers will go in order from left to right, that is, from 1 to 10.
Now we multiply, for example, 2x9. Everything that goes up to finger number 2 is tens (that is, 1 in this case). And all that remains after finger number 2 is units (that is, 8). As a result, we get 18.
When a student is faced with the task of learning the multiplication table, then, of course, parents want to help him and are looking for the best fast way learn the multiplication table. There are a lot of techniques, but everything needs an individual approach to your little one. We will tell you about how you can easily explain the principles of multiplying numbers to your child and help him remember it in the shortest possible time.
Most likely, it will be easiest for a student to multiply by 1 and 10. This account is given very easily to kids, since there is nothing terrible and difficult. Try drawing some examples in front of the baby, such as 1*2=2, 1*5=5, 8*1=8. In any case, the number will remain unchanged.
With the 10th it will be a little more complicated, but if you explain everything to a child of 8-9 years old, that multiplying by 10 is similar to the principle by 1, but you need to add 0 to the result, then the kid will remember it very easily. Be sure to tell your student that, having learned multiplication by 1 and 10, he will already know the first and last line in all other columns.
Multiply by 2
With a deuce, it will also be easy, since you will tell the baby that the correct result can be obtained by adding the two proposed numbers. For example, if a child has an example of 2 * 6, then he just needs to add 6 + 6 together and get 12. After each lesson, be sure to take a break for at least an hour, and it is best to continue classes every other day.
Multiply by 3
With multiplication by three, you can try the same method as with two. You just need to explain to the child that 3 * 4 and 4 + 4 + 4 will equally equal 12. If this method is absolutely not suitable for your child, then try playing with associations. First, ask the baby to dream up and draw his associations to the numbers from 1 to 9.
After that, start making up a story for each example, and so the student will remember the 3 sign much faster. Let your child play with these drawings and make up stories for them. You can draw your own story for each example, so it will be much easier to remember.
Multiply by 4
To make it easy for your baby to remember multiplying by 4, remind him of the principle that was used when he studied columns with a deuce. But only now we will need to double the desired number and double the result. For example, 4*4= 4*2=8*2=16.
Multiplication table 4
Multiply by 5
When studying the action by 5, you should immediately draw the attention of your 8-9 year old child to the fact that on the result of multiplication in this column, all results will end either in 5 or in zero. Also note that 5 is half a dozen. Therefore, the answers will be easier to multiply the number not by 5, but by 10 and then divide the result in half. For example, we need to find the answer to the example 7*5. Try 7 * 10, it will be 70. Now divide 70 by 2 - it will be 35.
Multiply by 6
For the six, there is also a way to make memorization easy for children of 8 years old, and this column of the plate was learned in an hour. Try to remind the kid how he learned the tablet for 3 and invite him to add the same number to the result. For example, 3*5=15 means 6*5=3*5+15=30.
Multiplication table 6
Multiply by 7
If multiplying to 6 is no longer a big deal for a child of 8 years old, then understanding how to multiply by 7 will be easy for him. If you need 7 * 2, then you just need to add 7 and 7, you get 14. An example of 7 * 4 will mean that the number needs to be doubled twice and so on. Separately, you will need to write down and learn only the multiplication by 7, 8 and 9.
Multiply by 8
By analogy with the previous methods, multiplying by 8 can be compared to four, only the result will need to be doubled three times. If in our example it is written that 4 * 8, then we multiply 2 by 4, the resulting eight by two more, we get 16 and then we multiply this result by another 2 and get 32.
Multiplication table 8
Multiply by 9
There is a simple and very easy method for multiplying by 9 on your fingers. It will definitely appeal to children 8-9 years old, since you can learn it in just a few minutes, and not in an hour or two.
Ask the student to place their pens on the table, palms down. Count your fingers from left to right. So, for example, we have an example of 7*9. We count 7 fingers on the right. We bend the finger on which we stopped the count. How many fingers are not bent to the left of the seventh - six.
So, we will have six tens in the answer. How many fingers to the right of the bent one - three. This will be the number of units in the answer. So we realized that the answer is 63. Such a study of the multiplication tablet on the fingers will be useful. Do not scold the baby that he uses this method for too long. It is this method that will allow the baby to firmly and firmly remember the multiplication by 9.
Multiplication table 9
How to multiply numbers by a column
Of course, after a child of 9 years old has learned the multiplication table well, he will need to be taught to multiply two-digit numbers in a column, and then three-digit numbers. Numbers that are multiplied by each other are called multipliers. They are called the first multiplier, the second multiplier, and so on. The result of multiplication will be called "product".
To multiply two numbers, you will need to arrange them in a column on top of each other so that units are above ones, tens over tens, and so on. The next step is that the top number will need to be multiplied by the digit of the bottom number. First, one is multiplied, then tens, hundreds, and so on. The result must be written below the line.
If, as a result of multiplication, you get a number that is greater than ten, that only the last digit of the result goes under the line, and ten, if any, is written on top. Then this ten must be added to the result of multiplying ten by one. Multiplying the top number by tens and hundreds of the bottom number follows the same rules.
If you give your child the opportunity to calmly learn this or that method of memorizing the multiplication table, then he will quickly begin to count. Do not insist if the baby does not want to engage. You may well follow the lead of the child, allowing him not to repeat the table.
Show him specific examples in life where the table can be useful to him. For example, ask your daughter to count how many sweets you need to buy so that her girlfriends all get three. It will be easy and interesting for a girl to find the answer, since this directly concerns practice and life.
Multiplication table or the Pythagorean table is a well-known mathematical structure that helps schoolchildren learn multiplication, as well as simply solve specific examples.
Below you can see it in its classic form. Pay attention to the numbers from 1 to 20, which head the lines on the left and the columns on top. These are multipliers.
How to use the Pythagorean table?
1. So, in the first column we find the number that needs to be multiplied. Then in the top line we look for the number by which we will multiply the first. Now we look at where the line and column we need intersect. The number at this intersection is the product of these factors. In other words, it is the result of their multiplication.
As you can see, everything is quite simple. You can view this table on our website at any time, and if necessary, you can save it to your computer as a picture so that you can access it without connecting to the Internet.
2. And again, pay attention, below there is the same table, but in a more familiar form - in the form mathematical examples. For many, this form will seem easier and more comfortable to use. It is also available for download on any medium in the form of a convenient picture.
And finally, you can use our calculator, which is present on this page, at the very bottom. Just enter the numbers you need for multiplication into the empty cells, click on the Calculate button, and right there in the Result window a new number will appear, which will be their product.
We hope this section will be useful to you, and our pythagorean table in one form or another it will help you more than once in solving examples with multiplication and just for memorizing this topic.
Pythagorean table from 1 to 20
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 | 51 | 54 | 57 | 60 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 | 64 | 68 | 72 | 76 | 80 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 | 95 | 100 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 | 96 | 102 | 108 | 114 | 120 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 | 112 | 119 | 126 | 133 | 140 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 | 128 | 136 | 144 | 152 | 160 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 | 144 | 153 | 162 | 171 | 180 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 | 176 | 187 | 198 | 209 | 220 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 | 192 | 204 | 216 | 228 | 240 |
| 13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 | 208 | 221 | 234 | 247 | 260 |
| 14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 | 154 | 168 | 182 | 196 | 210 | 224 | 238 | 252 | 266 | 280 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 | 240 | 255 | 270 | 285 | 300 |
| 16 | 16 | 32 | 48 | 64 | 80 | 96 | 112 | 128 | 144 | 160 | 176 | 192 | 208 | 224 | 240 | 256 | 272 | 288 | 304 | 320 |
| 17 | 17 | 34 | 51 | 68 | 85 | 102 | 119 | 136 | 153 | 170 | 187 | 204 | 221 | 238 | 255 | 272 | 289 | 306 | 323 | 340 |
| 18 | 18 | 36 | 54 | 72 | 90 | 108 | 126 | 144 | 162 | 180 | 198 | 216 | 234 | 252 | 270 | 288 | 306 | 324 | 342 | 360 |
| 19 | 19 | 38 | 57 | 76 | 95 | 114 | 133 | 152 | 171 | 190 | 209 | 228 | 247 | 266 | 285 | 304 | 323 | 342 | 361 | 380 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 | 260 | 280 | 300 | 320 | 340 | 360 | 380 | 400 |
Multiplication table in standard form from 1 to 10
| 1 x 1 = 1 1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 10 |
2 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20 |
3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30 |
4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40 |
5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50 |
| 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60 |
7 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70 |
8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48 8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80 |
9 x 1 = 9 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90 |
10 x 1 = 10 10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 10 x 6 = 60 10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x 10 = 100 |
Multiplication table in standard form from 10 to 20
| 11 x 1 = 11 11 x 2 = 22 11 x 3 = 33 11 x 4 = 44 11 x 5 = 55 11 x 6 = 66 11 x 7 = 77 11 x 8 = 88 11 x 9 = 99 11 x 10 = 110 |
12 x 1 = 12 12 x 2 = 24 12 x 3 = 36 12 x 4 = 48 12 x 5 = 60 12 x 6 = 72 12 x 7 = 84 12 x 8 = 96 12 x 9 = 108 12 x 10 = 120 |
13 x 1 = 13 13 x 2 = 26 13 x 3 = 39 13 x 4 = 52 13 x 5 = 65 13 x 6 = 78 13 x 7 = 91 13 x 8 = 104 13 x 9 = 117 13 x 10 = 130 |
14 x 1 = 14 14 x 2 = 28 14 x 3 = 42 14 x 4 = 56 14 x 5 = 70 14 x 6 = 84 14 x 7 = 98 14 x 8 = 112 14 x 9 = 126 14 x 10 = 140 |
15 x 1 = 15 15 x 2 = 30 15 x 3 = 45 15 x 4 = 60 15 x 5 = 70 15 x 6 = 90 15 x 7 = 105 15 x 8 = 120 15 x 9 = 135 15 x 10 = 150 |
| 16 x 1 = 16 16 x 2 = 32 16 x 3 = 48 16 x 4 = 64 16 x 5 = 80 16 x 6 = 96 16 x 7 = 112 16 x 8 = 128 16 x 9 = 144 16 x 10 = 160 |
17 x 1 = 17 17 x 2 = 34 17 x 3 = 51 17 x 4 = 68 17 x 5 = 85 17 x 6 = 102 17 x 7 = 119 17 x 8 = 136 17 x 9 = 153 17 x 10 = 170 |
18 x 1 = 18 18 x 2 = 36 18 x 3 = 54 18 x 4 = 72 18 x 5 = 90 18 x 6 = 108 18 x 7 = 126 18 x 8 = 144 18 x 9 = 162 18 x 10 = 180 |
19 x 1 = 19 19 x 2 = 38 19 x 3 = 57 19 x 4 = 76 19 x 5 = 95 19 x 6 = 114 19 x 7 = 133 19 x 8 = 152 19 x 9 = 171 19 x 10 = 190 |
20 x 1 = 20 20 x 2 = 40 20 x 3 = 60 20 x 4 = 80 20 x 5 = 100 20 x 6 = 120 20 x 7 = 140 20 x 8 = 160 20 x 9 = 180 20 x 10 = 200 |