One of the main problems for the parents of a younger student is to learn the multiplication table. After all, she is asked to teach after the first grade. By itself, this table is boring and difficult for a child to remember. But if you make a little effort, then you can easily manage it easily and playfully cope with it.
First of all, before you start teaching, try to explain to your child in an accessible way what it is and why it needs to be learned. Because for the first time when faced with this table, the child sees it as an incomprehensible set of numbers.
Take a piece of paper and show the child with an example how multiplication helps to shorten the example. That if you use only addition, then you have to write a long example. And if this example is replaced by multiplication, it turns out much easier and more convenient. Show a few different examples to make it easier for him to understand what it is.
Understanding the need for a table will help the child to begin to realize it in a different way. He will no longer consider it just a set of symbols that are so hard to learn.
Knowing this table will greatly help the child in the future, both during training and in adulthood. Therefore, it is very important to learn it well.
How to clearly explain multiplication to a child
Many children find it much easier to learn the multiplication table if they have visual examples that they can sort through and add themselves. Because it’s not enough just to know the essence of the table, you need to see and feel it. In order to link illustrative examples to the study of the table, you can use pencils, counting sticks, or whatever is convenient for you.
Take two sticks and place them in front of the child. Explain to him that if we want to double the number of sticks, we need to add sticks to them. After that, add more sticks and tell the baby to write down the actions that he performs in a notebook.
At the same time, in the learning process, let the child work with sticks on his own and you will see that after a while he can easily remember the entire table.
Multiplication table simulator
If you want to learn new knowledge with your child, suitable posters help a lot. Therefore, to help the child, you can use such a poster. If you hang such a poster in a conspicuous place at home, then it will be much easier for the child to remember it.
In addition, such a poster can be made independently and even involve a child in this process, so that learning is even easier.
Game how to learn the multiplication table
At the moment, a huge number of online games have appeared on the Internet that will help a child quickly and easily master the multiplication table.
One of these services: http://multoigri.ru/igri-tablica-umnozheniya
By clicking on it, you will see several options for games that a child can play and thereby develop their multiplication skills. And the fact that all this is provided in the form of a game will only help to interest the child.
Multiply by two game
In order to explain this column to the child, explain to him first that in order to calculate the correct answer, he only needs a number that we multiply and add to each other.
2*1=2 for this you can either add 1+1 or explain how 2 is repeated only 1 time
2*2=4 put two sticks in front of the child and ask him to add two more to them.
2*3=6 ask the child to make three stacks of two sticks and let them count how many they get in the end.
2*4=8 add two more sticks in the same way. Have your child write examples in a notebook.
2*5=10 show that you can make either two piles of 5 sticks or two sticks of 5 piles.
2*6=12 follow the same pattern, continue explaining and showing the child other examples. But do not forget to ask him to immediately write everything down in a notebook.
2*7=14 add 7 more sticks to seven sticks
2*8=16 put one more stick in each pile.
2*9=18 continue to explain further in the same way.
Multiply by three game
It is much easier to start studying the table if there are illustrative examples in front of the child. Take the same counting sticks for starters. Lay them out in front of the child and show him how the multiplication takes place. And then you yourself will notice how easy it is for a child to remember the entire column
Multiply by four game
Multiplication by 4 is also better to start learning with a good example in front of you. In addition, ask the child to write down the example itself with the answer in a separate notebook. So you can turn on several types of memory at once, which will speed up learning.
Multiply by five game
Multiplying by 5 is much easier for many children than with other numbers. To do this, tell the child that when we multiply this figure by an even number, then at the end it will be 0. And if, on the contrary, multiply by an odd number, it will be 5. But also do not forget about a good example. If the child already knows the division well by the time the table is studied, then you can learn the table as the second number multiplied by 10 and divided by 2.
Multiply by six game
From the moment of studying the 6th column, it becomes more and more difficult to learn the table. However, there is one trick that can be used. Tell the child that he no longer needs to memorize the first part, because he can find out the answer by rearranging the previous columns and he has to remember the last four lines. In addition, do not forget about illustrative examples. You can also independently show the child that if the numbers are reversed, then the result will remain the same.
multiplication by seven game
In this column, the child will also only have to learn the last 3 multiplications, and he has already learned the rest before and will only have to rearrange them.
multiplication by eight game
The penultimate column is also very difficult to remember. But the good news here is that if the child has learned all the other columns well, then all that remains for him is to learn only the last two lines.
Multiply by nine game
There is also one little trick to learning the last column that makes it easier to remember. To do this, simply multiply the second number by 10 and subtract the same number.
9*1=9
9*2=18 or 20-2
9*3=27 or 30-3
9*4=36 or 40-4
9*5=45 or 50-5
9*6=54 or 60-6
9*7=63 or 70-7
9*8=72 or 80-8
9*9=81 or 90-9
Board game multiplication, description
To help a child master such a complex science as mathematics, there are now a huge variety of different games, thanks to which the learning process itself is much easier and simpler. After all, even to lure a child to the beginning of education is much easier if he is interested in it.
In addition to the fact that now there are a lot of different games on store shelves that help in learning, you can easily make such games yourself using just improvised means.
with dice
For this game you will need:
1. Blank paper
2. Handle
3. Two cut-out and glued dice.
For this game, print out or redraw the block diagram in advance and glue it out by cutting it out. You will need 2 of these cubes.
When starting to play, the first player takes the dice in his hand and rolls them. He writes the dropped numbers to himself on a piece of paper in the form of an example and solves it. Then it is the turn of the second player.
At the end of the game, players exchange sheets of paper with each other and whoever gets the most correct answers wins.
cards
Cards are just a universal assistant during the development and learning of a child. A lot of classes are based on cards. In addition, cards can always be made independently.
For this game, cut out cards of different colors. It is important that each column of the multiplication table has its own color of the card.
After you have done this, fill in the cards on one side of the problem, write examples without answers. On the other side of the card, write your answers.
To start learning, take only one column with the number 2. At the beginning, let the child pick up the cards and answer on their own. If he answered correctly, he puts the card in one direction, and if not correctly, then in the other. After the cards are over, he picks up the cards that he answered incorrectly and answers them again.
After that, you can play this game together, putting the cards in the middle of the table. Take turns taking cards and answering. If you answer correctly, take your card. Whoever has more cards wins.
After studying the first column, add the second and so on in turn.
wand - counter
It is much more interesting to play such a game with a company, well, or at least together. In order to make such a game, take an ordinary glass and a lot of ice cream sticks. On each stick at the end, write an example without an answer and insert them into the cup with examples down. In addition, add a few sticks, on which, instead of an example, write three exclamation points.
The essence of the game is that each player takes out one stick and calls the answer. If he answered correctly, he takes the wand to himself. In this case, the one who pulled out a card with exclamation marks must put all his sticks in place. At the end, the player with the most sticks wins.
Multiplication table in verse
Two pairs of boots stood at the threshold
Two times two makes four - that's good!
Three cats are sitting at home
Three cats went for a walk
Twice three is always six
We can count!
four good friends
They invited us to walk
four times two eight
You should know it!
Brought by the hostess
We have two pies
We stuck a fork
Each of them has five
Twice five we get ten
Everyone has known for a long time!
A rooster sits on a branch and sings:
- Double six, double six
Double six twelve!
Seven doves sit on the roof
Seven doves - on wires
Double seven fourteen
It's easy for us to count!
We met at sea once
Two octopuses near corals
Eight legs and eight legs
Get sixteen!
Two flocks of ducks flew by
We counted nine
Counted twice nine
Eighteen received!
Three apples per branch
And in total we have three branches
Three times three we get nine
Let's eat those apples!
Four seasons a year
Three months each
Three times four we get twelve
twelve months of the year
Mom cooks breakfast for everyone
Five pancakes for everyone
Dad, me and mom
Five three - only fifteen
The parrot screams from the cage:
- We get eighteen
Three times six we are multiplying!
Three friends are going to school
Seven years each
Three times seven is twenty one
I took a hot pancake with me
three times eight twenty four
We'll get by folding the holes in the cheese
Three times nine is easy
Subtract three from thirty
Twenty-seven is easy to get
And we'll tell everyone the answer!
Kittens have four paws
four times four
Only sixteen paws in a row
Run in the apartment!
High five my friends shouted to me
Four times five is twenty!
four times six twenty four
Crows were crying under our window!
Autumn has suddenly come to us
Four times seven is twenty-eight!
Baba Yaga fell out of the stupa
four times eight
Broke thirty-two teeth!
Everyone should take this into account
Four times nine equals thirty-six!
The puppies went out for a walk
Five five makes twenty five!
Go hiking with the boys
Five six makes thirty
We have traveled so many roads!
They took down the hens
We have a lot of eggs
five seven thirty five
Let's go sell eggs!
The centipede decided
Get rid of boots
five eight forty
It's hard to find so many legs!
five nine forty five
We all need to know this!
six six thirty six
It's so easy for us to count!
There's a buzz in the city
Six seven forty two!
6*8=48
Let's go ask the magpie
six eight forty eight
Mother baked pies
Mouth open wider
By six nine we'll get
Fifty four
It's very hard to explain
Multiplying seven seven
We'll get forty nine
Not forty-five!
How can we solve the example
It's hard to get
We multiply seven by eight
Fifty six we'll get
One day a bear came to us
Eat our berries
seven nine sixty three
And there are no berries on the bush!
Video multiplication table on fingers easy
Easy Ways to Memorize the Multiplication Table
Multiplication by 1 and 10
It’s worth starting with this to calm the child: multiplication by one is the number itself, and multiplication by 10, the number and zero after it. So he already knows the answers to the first and last examples in all columns.
Multiply by 2
Multiplying a number by two means adding two identical numbers.
3x2 = 3+3
6x2 = 6+6
This column is the easiest to remember or calculate.
Multiply by 3
To memorize this column, mnemonic techniques are suitable, for example, short rhymes. You can invent them with your child or look for "ready-made" ones on the net:
Well, my friend, look
What is three times three?
Nothing to do!
Well, of course, nine!
Or
All the kids need to know
What is three times five
And don't be mistaken!
Three times five is fifteen!
If you are not strong in poetry, come up with prose stories, the heroes of which will be a two - a swan, a three - a snake, a four - an inverted chair, an eight - glasses, and so on - the children themselves will tell you who, in their opinion, the numbers look like .
Stories and rhymes can be invented not only for the triple, but also for any column of the Pythagorean table.
Multiply by 4
Multiplication by 4 can be represented as a multiplication by 2 and again by 2. This column for students who have mastered multiplication by two will not cause difficulties.
Multiply by 5
This is the easiest column to remember. All values in this column are located 5 units apart. Moreover, if an even number is multiplied by 5, the product will end with 0, and if it is odd - with 5.
Multiply by 6, 7, 8
These columns, as well as the multiplication by 9 column, traditionally cause difficulties for schoolchildren. You can reassure the students by explaining that they have already learned most of the examples from these columns and the awesome 83 is the same as the already studied 38. By swapping the factors, you can remember what the product is equal to.
This means that children will only have to remember 6 “unfamiliar” examples:
6x7=42
6x8=48
6x9=54
7x8=56
7x9=63
8x9=72
These examples can be written on cards, hung on the wall and memorized.
And you can learn to count on your fingers:
Put your hands on the table as shown in the picture;
Mentally number your fingers: 
Let the little fingers stand for fives, ring fingers for sixes, middle fingers for sevens, index fingers for eights, and thumbs for nines.
Now let's multiply! For example, we need to multiply 6 by 7. We are looking for the first multiplier on the left hand - this is the six, that is, the ring finger.
We are looking for the second multiplier on the right hand, this is the seven, that is, the middle finger.
We connect these fingers (six and seven, the ring finger of the left hand and the middle finger of the right hand), move the connected fingers to the edge of the table and place them strictly on its edge.
We look at how many fingers hung from the table - this is the little finger of the left hand and the little finger and ring finger of the right hand, that is, only 3 fingers. They represent tens. Three fingers = three tens = 30. Remember this number.
Now we look at how many fingers are left on the table (together with the connected ones) - these are four fingers of the left hand and three fingers of the right. Multiply the fingers of one hand by the fingers of the other hand: 43 = 12.
We add to the previously memorized number 30 the number 12: 30+12=42. This is the product of 6 and 7.
Similarly, you can multiply 7 by 8 or 8 by 9.
Multiply by 9
To begin with, you can remember that in the multiplication table for nine, the sum of tens and units in the answer is always equal to 9. Namely: 92=18 (add the numbers of the answer: 1+8=9), the same in other examples: 96=54 (5+4=9).
In this case, the ten digit in the answer is always one less than the second factor in the example. In practice: 97 = 63 (the second factor is 7, which means tens in the answer 6. If we now recall the first pattern that the sum of tens and ones in the answer should be 9, we get the answer 63).
And one more “secret”: if you have paper and a pencil at hand, it’s fashionable to quickly write numbers from 0 to 9 in a column (these will be tens), and next to the second column from 9 to 0, you will get the answers of the multiplication table by 9.
09
18
27
36
45
54
63
72
81
90
You can quickly check multiplication by 9 on your fingers:
Place your hands on the table with your palms;
Mentally number the fingers from the little finger of the left hand to the little finger of the right (the little finger of the left hand is 1, the ring finger of the left hand is 2, and so on to the little finger of the right hand, which, accordingly, will be 10): 
Name the number by which you want to multiply nine. Let's say it's number 3: 
Bend the finger that was assigned the serial number 3 (this will be the middle finger of the left hand);
The fingers that remain to the left of the bent one indicate tens (we have the little finger and the ring finger - two fingers, that is, 2 tens, the number 20);
The fingers that remained to the right of the bent one are units. We have 2 fingers of the left hand on the right + all 5 fingers of the right hand - a total of 7 fingers, 7 units;
2 tens (20) + 7 ones (7) = 27. This is the product of 9 and 3.
Similarly, you can multiply 9 by 7 or 9 by 10.
Learning the multiplication table from any student will require perseverance and patience, but counting on the fingers, rhymes, cards with examples will help make memorization easier and make it interesting and fast.
At some point, parents will definitely face the question: how to quickly learn the multiplication table for a child? He will not be able to do this on his own, he needs the help of adults. And also - correctly chosen methods of memorization.
Basics of learning
To help your child quickly learn the multiplication table, it is best to first explain to him the essence of this action. He already has the concept of addition and subtraction. We explain that 2 multiplied by 2 means adding two deuces, that is, 2 + 2.
You can give more complex examples: 3 times 4 means to add three 4 times - 3+3+3+3.
It is good to support your explanations with real, understandable examples for the child: “Grandfather brought 2 sets of felt-tip pens to you and Ksyusha. Each has 5 pieces. And just how many felt-tip pens will it make? How do we count: 5 plus 5 or 2 times 5? And so, and so we get 10.
Game tricks
How to quickly learn the multiplication table for a child? Of course, use game visual techniques. We take a box and balls. I put them in a box in pairs. Then the next two balls, then another and another. It turned out like this:
Methods for studying the multiplication table
Different methods will help a child quickly learn the multiplication table. The fact is that some of the children memorize numbers well simply mechanically (at this age, this type of memory is quite well developed in them).
Some will need visual reinforcement: videos, drawings, emotional nourishment, games work well, and tools such as online games and poetry.
Multiplication table - where to start?
The child needs to explain how the Pythagorean table is arranged: there are numbers in columns and in rows, and where they intersect, we look for the answer - the product of numbers, for example, six by eight will be forty-eight (6x8 = 48).
You can start studying the table with its usual version. Immediately explain to the child - do not be afraid that it is so big at first glance. Many examples there are already known and do not require memorization.
For example, multiplying by 1 and by 10. What does it mean to multiply a number by 1 - take it 1 time. Two will remain a deuce, four will remain a four, and so on. That is, the number will not change. And multiplying by 10 is also easy - just add a zero to the number: 5x10=50.
Multiply by 2, by 5 and learn the squares of numbers
How to quickly learn the multiplication table for a child - remember at first simpler options. Multiplying by 2 is usually not difficult for children. It's like adding another one to a number.
After that, you can learn how to multiply by 5. Answers will end in either 0 (even numbers) or 5 (odd numbers).
The next step is memorizing the squares of numbers. Repetition and consolidation is indispensable here. The child will just have to remember that 8 by 8 is 64, and 9 by 9 is 81.
Usually the first difficulties begin with multiplying by 3. Here it is time to introduce additional memorization methods - visual techniques, for example, playing cards or associations using poems. About them - a little lower.
How to multiply by 6, 7, 8 and 9
This stage is the most difficult, and some examples just need to be remembered. You will have to repeat these few of the most difficult works with your child constantly until the numbers reach automatism.
The main thing is to show the child that he already knows almost the entire table, and there are mere trifles left. Here are those tricky values that are so hard to remember:
6x7=42
6x8=48
6x9=54
7x8=56
7x9=63
8x9=72
On the change of factors
Adults understand that 4x3 = 3x4. But the child needs to be explained that if you swap the factors, the result will not change.
Then it will be much easier for your student to remember how much it will be, for example, 7 by 4. If you forgot, let him remember the multiplication of 4 by 7. This is an important point in learning the multiplication table.
Different methods of studying the multiplication table
A variety of ways to study the multiplication table helps you find the right one for your child.
Memory cards
All kinds of online games on the Internet also contribute to memorization, but the most reliable and proven method remains a visual method that uses memory cards.
Make cards with examples: for example, on one side write 7x8, and on the other - the answer. How we play - the child takes a card, answers the question and turns it over to see the answer. He answered correctly - he keeps the card for himself, if not - he takes another card. The one with the most cards wins. During the game there is repetition and memorization, but in a fun way.
One such option is digital lotto. Enter the answers from the table into the cards, make cards with example tasks. The gameplay stimulates memorization.
Multiply with fingers
There is such a way of counting - on the fingers. Suitable for multiplying by 9. You need to put your hands down with your palms and straighten your fingers. We need to multiply 7 by 9. We bend the 7th finger in a row and look - the number of fingers before it will be equal to tens in the answer - 6, and after the 7th finger - units, that is, three. We get 63.
There is another interesting method for multiplying by 9. It is necessary to multiply a given number, for example 6, by 10 (6 by 10 \u003d 60). And now we subtract 6, we get 54.
Repetition is the key to memory
To make it easier for your child to remember, make visual aids for him. He must constantly see examples before his eyes and repeat them. You can brightly and colorfully decorate the table and hang it in the children's room and in the kitchen. This will make the information easier to remember.
Teaching verses
For many children, especially humanists, it is much easier to memorize the table using a poetic form. The most famous similar poems were written by Marina Kazarina and Alexander Usachev:
Multiply five by six
As a result, we get THIRTY.
And five seven - easy to count -
Short answer: THIRTY-FIVE!
Once the deer asked the elk:
How old is seven eight? —
The moose did not climb into the textbook:
- Fifty, of course, six!
Cartoons to remember
If you set a goal, you can find a lot of interesting cartoons to help those who study the basics of multiplication. Children always perceive this form of presentation well, so we advise you to actively use it. An example is in this video:
Take it, tell your friends!
Read also on our website:
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Do you think it is difficult to depict people on paper, and this art is only available to the gifted? Nothing like this! We will tell you how to draw a person, breaking down the process into stages and simplifying it as much as possible. Following our instructions, even a child can portray homo sapiens.
In modern elementary school, the multiplication table begins to be taught in the second grade and ends in the third, and it is often given to learn the multiplication table in the summer. If you didn’t study in the summer, and the child is still “floating” in multiplication examples, we’ll tell you how to learn the multiplication table quickly and fun - with the help of drawings, games and even fingers.
Problems that often arise in children in connection with the multiplication table:
- Children don't know what 7 × 8 is.
- They do not see that the problem must be solved by multiplication (because it does not say directly: "What is 8 times 4?")
- They do not understand that if you know that 4 × 9 = 36, then you also know what 9 × 4, 36: 4 and 36: 9 is equal to.
- They do not know how to use their knowledge and restore a forgotten piece of the table from it.
How to quickly learn the multiplication table: the language of multiplication
Before you start learning the multiplication table with your child, it’s worth stepping back a little and realizing that a simple multiplication example can be described in a surprising number of different ways. Take the 3 × 4 example. You can read it as:
- three times four (or four times three);
- three times four;
- three times four;
- the product of three and four.
At first, it is far from obvious to the child that all these phrases mean multiplication. You can help your son or daughter if, instead of repeating yourself, you casually use different language when talking about multiplication. For example: "So how much is three times four? What happens if you take three times four?"
How to learn the multiplication table
The most natural way for children to learn the multiplication table is to start with the easiest and work your way up to the hardest. A reasonable sequence is:
Multiply by ten (10, 20, 30...), which children learn naturally in the process of learning to count.
Multiply by five (after all, we all have five fingers and toes).
Multiplication by two. Pairs, even numbers and doubling are familiar even to young children.
Multiplying by four (after all, this is just doubling the multiplication by two) and eight (doubling the multiplication by four).
Multiplication by nine (for this there are quite convenient tricks, about them below).
Multiply by three and six.
Why 3x7 equals 7x3
When helping a child memorize the multiplication table, it is very important to explain to him that the order of the numbers does not matter: 3 × 7 gives the same answer as 7 × 3. One of the best ways to visualize this is - use an array. This is a special mathematical word denoting a set of numbers or shapes enclosed in a rectangle. Here, for example, is an array of three rows and seven columns.
*******
*******
*******
An array is a simple and visual tool to help a child understand how multiplication and fractions work. How many dots are there in a 3 by 7 rectangle? Three lines of seven elements each have 21 elements. In other words, arrays are an easy-to-understand way to visualize multiplication, in this case 3 × 7 = 21.
What if we draw the array in a different way?
***
***
***
***
***
***
***
Obviously, both arrays must have the same number of points (they do not have to be counted individually), because if the first array is rotated a quarter of a turn, it will look exactly like the second.
Look around, look nearby, in the house or on the street, for some arrays. Take a look at the cakes in the box, for example. Cakes are stacked in a 4 by 3 array. And if you rotate? Then 3 by 4.
Now take a look at the windows of the high-rise building. Wow, this is also an array, 5 by 4! Or maybe 4 by 5, how to look? As soon as you start paying attention to arrays, it turns out that they are everywhere.
If you have already taught your children the idea that 3 × 7 is the same as 7 × 3, then the number of multiplication facts that you need to remember decreases dramatically. It is worth memorizing 3 × 7 - and as a bonus, you get the answer to 7 × 3.
Knowing the commutative law of multiplication reduces the number of multiplication facts from 100 to 55 (not exactly by half due to cases of squaring, such as 3×3 or 7×7, which do not have a pair).
Each of the numbers above the dotted diagonal (for example, 5 × 8 = 40) is also present below it (8 × 5 = 40).
The table below contains another hint. Children usually begin to learn the multiplication table using counting algorithms. To figure out what 8 × 4 is, they count like this: 4, 8, 12, 16, 20, 24, 28, 32. But if you know that eight times four is the same as four times eight, then 8, 16 , 24, 32 will be faster. In Japan, children are specially taught to "put the lower number first." Seven times 3? Do not do this, count 3 times 7 better.
Learning the squares of numbers
The result of multiplying a number by itself (1×1, 2×2, 3×3, etc.) is known as square number. This is because graphically such a multiplication corresponds to a square array. If you go back to the multiplication table and look at its diagonal, you will see that it is all squares of numbers.
They have an interesting feature that you can explore with your child. When listing the squares of numbers, pay attention to how much they increase each time:
Squares of numbers 0 1 4 9 16 25 36 49...
Difference 1 3 5 7 9 11 13
This curious connection between square numbers and odd numbers is a perfect example of how different kinds of numbers are related in mathematics.
Multiplication table for 5 and 10
The first and easiest table to memorize is the 10 multiplication table: 10, 20, 30, 40...
In addition, children memorize the multiplication table for five with relative ease, and their hands and feet, visually representing four fives, help them in this.
It is also convenient that the numbers in the five times table always end in 5 or 0. (So, we know for sure that the number 3,451,254,947,815 is present in the five times table, although we cannot verify this with a calculator: on such a number simply does not fit on the screen of the device).
Children can easily double numbers. This is probably due to the fact that we have two hands with five fingers on each. However, children do not always associate doubling with multiplying by two. The child may know that if you double six, you get 12, but when you ask him what six is equal to two, he has to count: 2, 4, 6, 8, 10, 12. In this case, you should remind him that six is two - the same as twice six, and twice six - this is the doubled six.
Thus, if your child is good at doubling, then he essentially knows the multiplication table by two. At the same time, he is unlikely to immediately realize that with its help you can quickly imagine a multiplication table for four - for this you just need to double and double again.
Game: double walker
It is possible to adapt any game in which players roll a die so that all rolls count as doubles. This gives several advantages at once: on the one hand, children like the idea of going twice as far with each throw as the dice shows; on the other hand, they gradually master the multiplication table by two. In addition (which is important for parents busy with other things), the game ends twice as fast.
9 Times Table: Compensation Method
One way to master the nine times table is to take the result of ten times and subtract the excess.
What is nine times seven equal to? Ten times seven is 70, subtract seven, we get 63.
7 x 9 = (7 x 10) - 7 = 63
Perhaps a quick sketch of the appropriate array will help cement this idea in the child's mind.
If you memorized the multiplication table for nine only up to "nine ten", then nine 25 will confuse you. But ten times 25 is 250, subtract 25, we get 225. 9 × 25 = 225.
Test yourself
Can you solve the 9 × 78 example mentally using the compensation method (multiplying by 10 and subtracting 78)?
There is another convenient way to master the nine times table. It uses fingers and kids love it.
Hold your hands in front of you, palms down. Imagine that your fingers (including the thumb) are numbered from 1 to 10. 1 is the little finger on the left hand (the extreme finger on your left), 10 is the little finger on the right (the extreme finger on the right).
To multiply a number by nine, bend the finger with the corresponding number. Let's say you are interested in nine 7. Bend the finger that you mentally labeled as the seventh number.
Now look at your hands: the number of fingers to the left of the curled one will give you the number of tens in the answer; in this case it is 60. The number of fingers on the right will give the number of units: three. Total: 9 × 7 = 63. Give it a try: this method works with all single digit numbers.
Multiplication table for 3 and 6
For children, the multiplication table by three is one of the most difficult. In this case, there are practically no tricks, and the multiplication table by 3 will simply have to be memorized.
The six times table follows directly from the three times table; here, again, it all comes down to doubling. If you can multiply by three, just double the result and you get a multiplication by six. So 3 x 7 = 21, 6 x 7 = 42.
Multiplication table by 7 - dice game
So, all we have left is the multiplication table for seven. There is good news. If your child has successfully mastered the tables described above, there is no need to memorize anything at all: everything is already in the other tables.
But if your child wants to learn the multiplication table for 7 separately, we will introduce you to a game that will help speed up this process.
You will need as many dice as you can find. Ten, for example, is a great number. Tell your son or daughter that you want to see which of you can add the numbers on the dice the fastest. However, let the children decide for themselves how many dice to roll. And to increase the child's chances of winning, you can agree that he must add the numbers indicated on the upper faces of the cubes, and you - those on both the upper and lower ones.
Have each child choose at least two dice and place them in a glass or mug (they are great for shaking the dice for random rolls). You only need to know how many cubes the child took.
As soon as the dice are rolled, you can immediately calculate how much the numbers on the upper and lower faces will give! How? Very simple: multiply the number of dice by 7. Thus, if three dice were drawn, the sum of the top and bottom numbers would be 21. (The reason, of course, is that the numbers on opposite sides of the die always add up to seven.)
The kids will be so amazed at how fast you can calculate that they'll want to learn this method too so they can use it someday with their buddies.
In the era of the so-called British imperial system of measures and "non-decimal" money, everyone needed to own an account up to 12 × 12 (then there were 12 pence in a shilling, and 12 inches in a foot). But even today, 12 pops up every now and then in the calculations: many people still measure and count in inches (in America this is the standard), and eggs are sold by the dozen and half a dozen.
Little of. A child who freely multiplies numbers greater than ten begins to develop an understanding of how large numbers are multiplied. Knowing the multiplication tables for 11 and 12 helps to notice interesting patterns. Here is the complete multiplication table up to 12.
Note that the number eight, for example, occurs four times in the table, while 36 occurs five times. If you connect all the cells with the number eight, you get a smooth curve. The same can be said about the cells with the number 36. Indeed, if a certain number appears in the table more than twice, then all places of its occurrence can be connected by a smooth curve of approximately the same shape.
You can encourage your child to explore on their own, which will keep them busy for (maybe) half an hour or more. Print out several copies of the 12 times 12 multiplication table, and then ask him to do the following:
- colorize all cells with even numbers in red, and with odd numbers in blue;
- determine which numbers occur there most often;
- say how many different numbers are found in the table;
- answer the questions: "What is the smallest number not found in this table? What other numbers from 1 to 100 are missing in it?".
Focus with eleven
The multiplication table for 11 is the easiest to build.
1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
4 x 11 = 44
5 x 11 = 55
6 x 11 = 66
7 x 11 = 77
8 x 11 = 88
9 x 11 = 99
- Take any number from ten to 99 - let's say 26.
- Break it into two numbers and push them apart so that there is a gap in the middle: 2 _ 6.
- Add together the two digits of your number. 2 + 6 = 8 and paste what you got in the middle: 2 8 6
This is the answer! 26 x 11 = 286.
But be careful. What happens when you multiply 75 × 11?
- Splitting the number: 7 _ 5
- Add up: 7 + 5 = 12
- We insert the result in the middle and we get 7125, which is obviously wrong!
What's the matter? There is a little trick to this example that needs to be applied when the digits used to represent the number add up to ten or more (7 + 5 = 12). We add one to the first of our numbers. Therefore, 75 × 11 will not be 7125, but (7 + 1)25, or 825. So the trick is actually not as simple as it might seem.
Game: beat the calculator
The purpose of this game is to develop the skill of quickly using the multiplication table. You will need a deck of playing cards without pictures and a calculator. Decide which player will use the calculator first.
- The player with the calculator must multiply the two numbers drawn on the cards; however, he must use a calculator, even if he knows the answer (yes, this can be very difficult).
- Another player must multiply the same two numbers in their mind.
- The one who gets the answer first gets a point.
- After ten attempts, the players change places.
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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.