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How can a second grader learn the multiplication table? How to quickly learn to multiply two-digit numbers in your head? Why do it in your head when you can do it on a calculator or in a column? |
Familiar school mathematics can be very practical in everyday life, because it makes it possible to carry out serious arithmetic calculations in the mind. We'll tell you a few tricks to help you multiply two-digit numbers quickly without using a calculator or a piece of paper and pen. How to multiply two-digit numbers in your head?It may seem impossible to multiply such large numbers in your head, but this is not so. There is a method that will be understandable even to schoolchildren. So, for example, take the numbers 96 and 97. Calculate the difference between these numbers relative to 100. In our case, these are 3 and 4. Their product will be the second part of the solution to multiplying the numbers 97 and 96 (3*4=12). The first part will be the difference of the first number and the difference of 100 and the second number. In our example it is: 97-4=93. Thus, we get 97*96 = 93 12 How to quickly multiply in your head?The essence of this simple and familiar method is to decompose the factors into ones and tens. Then they are multiplied one by one. This is easy to do; you only have to keep no more than 3 numbers in your mind at a time. Here's the standard way to do this: 64*86 = (60+4)*(80+6) = 60*80 + 60*6 + 4*80 + 4*6 = 4800 + 360 + 320 + 24 = 5504 But here is a method designed for only 3 steps. 1
) Let's multiply the tens 60 and 80. The result is 4800, remember it. See how easy it is to multiply in your head! First you need to do two things: print out the multiplication table itself and explain the principle of multiplication. To work, we will need the Pythagorean table. Previously, it was published on the back of notebooks. She looks like this: You can also see the multiplication table in this format: Now, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make his job easier, find or print the actual chart. 2. Explain the working principle![]() When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike what he has memorized or what someone else told him. Therefore, try to turn studying the table into an interesting game. When starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.
Next you need to understand the structure of the table itself. Show that the numbers in the left column are multiplied by the numbers in the top row, and the correct answer is where they intersect. Finding the result is very simple: you just need to run your hand across the table. 3. Teach in small chunks![]() There is no need to try to learn everything in one sitting. Start with columns 1, 2 and 3. This way you will gradually prepare your child to learn more complex information. A good technique is to take a blank printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count. When he has figured it out and mastered the simplest columns well enough, move on to more complex numbers: first, multiplying by 4–7, and then by 8–10. 4. Explain the property of commutativity![]() The same well-known rule: rearranging the factors does not change the product. The child will understand that in fact he needs to learn not the whole, but only half of the table, and he already knows some examples. For example, 4×7 is the same as 7×4. 5. Find patterns in the table![]() As we said earlier, in the multiplication table you can find many patterns that will simplify its memorization. Here are some of them:
6. Repeat![]() Practice repetition often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Watch your pace too: give yourself more time to think at first, but gradually increase the pace. 7. Play![]() Don't just use standard methods. Learning should captivate and interest the child. Therefore, use visual aids, play, use different techniques. CardsThe game is simple: prepare cards with examples of multiplication without answers. Mix them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, if he gives the wrong answer, we return it to the pile. The game can be varied. For example, giving answers on time. And count the number of correct answers every day so that the child has a desire to break his yesterday’s record. You can play not only for a while, but also until the entire stack of examples runs out. Then for every wrong answer you can assign the child a task: recite a poem or tidy things up on the table. When all the cards have been solved, give them a small gift. From the reverseThe game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will result in 30 (for example, 3 × 10 and 6 × 5). Examples from lifeLearning becomes more interesting if you discuss with your child things that he likes. So, you can ask a boy how many wheels four cars need. You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass multiplied by the number of glasses. PoetryRhyme will help you remember even complex examples that are difficult for a child. Come up with simple poems on your own. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine is seventy two.” 8. Don't be nervousUsually, in the process, some parents forget themselves and make the same mistakes. Here is a list of things that you should never do:
First you need to do two things: print out the multiplication table itself and explain the principle of multiplication. To work, we will need the Pythagorean table. Previously, it was published on the back of notebooks. She looks like this: You can also see the multiplication table in this format: Now, this is not a table. These are just columns of examples in which it is impossible to find logical connections and patterns, so the child has to learn everything by heart. To make his job easier, find or print the actual chart. 2. Explain the working principle![]() When a child independently finds a pattern (for example, sees symmetry in the multiplication table), he remembers it forever, unlike what he has memorized or what someone else told him. Therefore, try to turn studying the table into an interesting game. When starting to learn multiplication, children are already familiar with simple mathematical operations: addition and multiplication. You can explain to your child the principle of multiplication using a simple example: 2 × 3 is the same as 2 + 2 + 2, that is, 3 times 2.
Next you need to understand the structure of the table itself. Show that the numbers in the left column are multiplied by the numbers in the top row, and the correct answer is where they intersect. Finding the result is very simple: you just need to run your hand across the table. 3. Teach in small chunks![]() There is no need to try to learn everything in one sitting. Start with columns 1, 2 and 3. This way you will gradually prepare your child to learn more complex information. A good technique is to take a blank printed or drawn table and fill it out yourself. At this stage, the child will not remember, but count. When he has figured it out and mastered the simplest columns well enough, move on to more complex numbers: first, multiplying by 4–7, and then by 8–10. 4. Explain the property of commutativity![]() The same well-known rule: rearranging the factors does not change the product. The child will understand that in fact he needs to learn not the whole, but only half of the table, and he already knows some examples. For example, 4×7 is the same as 7×4. 5. Find patterns in the table![]() As we said earlier, in the multiplication table you can find many patterns that will simplify its memorization. Here are some of them:
6. Repeat![]() Practice repetition often. Ask in order first. When you notice that the answers have become confident, start asking randomly. Watch your pace too: give yourself more time to think at first, but gradually increase the pace. 7. Play![]() Don't just use standard methods. Learning should captivate and interest the child. Therefore, use visual aids, play, use different techniques. CardsThe game is simple: prepare cards with examples of multiplication without answers. Mix them, and the child should pull out one at a time. If he gives the correct answer, we put the card aside, if he gives the wrong answer, we return it to the pile. The game can be varied. For example, giving answers on time. And count the number of correct answers every day so that the child has a desire to break his yesterday’s record. You can play not only for a while, but also until the entire stack of examples runs out. Then for every wrong answer you can assign the child a task: recite a poem or tidy things up on the table. When all the cards have been solved, give them a small gift. From the reverseThe game is similar to the previous one, only instead of cards with examples, you prepare cards with answers. For example, the number 30 is written on the card. The child must name several examples that will result in 30 (for example, 3 × 10 and 6 × 5). Examples from lifeLearning becomes more interesting if you discuss with your child things that he likes. So, you can ask a boy how many wheels four cars need. You can also use visual aids: counting sticks, pencils, cubes. For example, take two glasses, each containing four pencils. And clearly show that the number of pencils is equal to the number of pencils in one glass multiplied by the number of glasses. PoetryRhyme will help you remember even complex examples that are difficult for a child. Come up with simple poems on your own. Choose the simplest words, because your goal is to simplify the memorization process. For example: “Eight bears were chopping wood. Eight nine is seventy two.” 8. Don't be nervousUsually, in the process, some parents forget themselves and make the same mistakes. Here is a list of things that you should never do:
Reading time: 9 minutes. Nowadays, many parents believe that a child, even before entering first grade, should learn not only to write and count, but also to know the basic techniques of algebra: addition, subtraction, multiplication and division. That is why mothers and fathers are faced with a serious question: “how to teach a child to learn the multiplication table”? Basic rules for obtaining optimal results
Regardless of which method you choose, the following rules must be carefully observed:
Basic way to learn multiplication tablesA parent who is seriously thinking about how to learn the multiplication table with a child can, in a burst of inspiration, remember his own childhood: counting sticks, a blackboard, a strict teacher and a huge table completely filled with numbers. This is the table that is most often used in schools, so it is recommended to spend at least the first lesson with it. First, you should print (or draw) two versions of the tables: the first is completely filled out, and the second is only with numbers around the edges. It is advisable that the second table be large, since the child will enter the numbers independently. During the first lesson, try to explain to your child the basic meaning of multiplication: it is the same as addition, only multiple times. Use small numbers as an example to show how multiplication works. An example option might look like this: “Here are numbers two and three. In order to multiply three by two, we need to add three and three. How much will it be? That's right, six!” What should you do after the first “trial” lesson with the table? If everything went well, try working with the table again: explain to your child the peculiar “mirroring” of multiplication:
If a child cannot quickly perform the addition operation, there is no need to prompt him: he will definitely count on his own, he just needs more time than an adult. If it took a short amount of time to explain this rule, then you can start filling out the part of the multiplication table with the number 1 (usually children quickly understand the meaning of multiplication by 1). As soon as the child’s attention begins to wander, you should stop the lesson - the preschooler will not learn more material. When you click you will have a large printable table Subsequent classesMake a large number of multiplication table example cards. Before each lesson, be sure to let your child solve familiar examples, otherwise the knowledge will simply be forgotten. Multiplying by two, three and four. Usually these actions are not particularly difficult, since they can be easily counted on your fingers. How to teach a child to multiply by five? It’s very simple: any even number will end in 0, and any odd number will end in 5. Counting them is a matter of technique. I've practically learned the entire multiplication table. But how can you easily and quickly learn multiplication by the most difficult numbers: six, seven and eight? Most likely, you will simply have to memorize them: even adults often get confused when multiplying these numbers. Is there an alternative to the table?If during the first lessons you see that it is clearly difficult for your child to remember even the simplest examples, do not swear at him under any circumstances, but start trying alternative methods.
However, studying with the help of poems or fairy tales alone can be infinitely long without the use of such additional techniques as flashcards. Remember that the child’s brain needs tireless repetition - only then will the information be not only mechanically learned, but also understood. And this is a guarantee that the baby will not forget the multiplication table until old age. How can you understand in advance whether it is easier to learn the multiplication table through a simple table or by adding poetry games with your child? Remember the child’s character: if he is a strong humanist, then games will definitely appeal to him, thereby making the learning process more fun. Toys always help
The only criterion for toys is that any outsider should easily understand that they illustrate multiplication. For example, when you multiply three wheels from a car by two, you should get exactly six wheels, and not four wheels, a bumper and a headlight (in this case it will be extremely difficult to teach a child!). Also, if you choose to learn with toys, then don’t try to teach your child to count on their fingers instead – these are two completely different methods! One of the most interesting ideas was the idea of one father to use a huge number of LEGO parts, which were scattered in huge quantities throughout the apartment. Taking the smallest piece as one, the father began to show his son the basics of multiplying by two, three and four (after all, there was a lot of LEGO, so they did not experience a shortage of pieces). As a result, all the lessons were held in the form of a game, and the father could not even imagine that teaching his son multiplication would be so easy and quick! Many parents have helped using interactive sound posters in teaching. In this case, memorization occurs better than during a regular lesson or cramming. Fingers and multiplicationOddly enough, you can quickly learn the multiplication table even on your own fingers! Many parents do not approve of children's habit of checking all calculation results on their fingers, arguing that it is easy to count only small numbers on their fingers. In fact, this is not entirely true: you can easily learn the multiplication table (and quite quickly!), using only your own fingers and knowledge of interesting mathematical patterns (however, this will not save your child from solving examples to repeat the material). ![]() Of course, with the simplest examples everything is clear: ten fingers are enough for calculation. But what about multiplying by nine?
Of course, it is extremely difficult to learn a table in this way without repetition, so choosing this approach requires a large number of practical tasks. Change is necessaryRegardless of the child’s age, he needs a large number of breaks (preferably every 10-15 minutes), otherwise it will not be possible to easily learn the basic laws of multiplication: after 10 minutes of continuous classes, the child will be distracted every now and then by a cat, a ray of sun peeking through the window, a ringing sound heard on the street and so on. How to maximize the level of effectiveness of classes? Firstly, you should draw a table with a clear lesson plan (there should be short breaks in it) and follow it all the time. Secondly, you need to be imaginative: you can learn the material in a playful way. For example, you can create your own card game.
Thirdly, do not hesitate to divide into parts: learning one large table is more difficult than many small tablets. In addition
Schoolchildren find the table boring and useless. Children often get angry and upset when trying to figure out a set of numbers that is incomprehensible to them. Parents can make learning easier and fun by preparing ahead of time. The main rule in learning the multiplication tables is to interest the child. Like adults, they perceive information differently. Some children like to learn poems and songs. Others can sit quietly with their parents at the table and look at the Pythagorean table. How to teach a child the multiplication table (picture) Help your child remember the multiplication table easily:
Game methods are captivating and give quick results. It is better to start classes in a good mood, when the child is ready to study. Learning the multiplication tables: life hacks and videosIt is important to understand how a child can more comfortably perceive information so that the process does not turn into “cramming.” Everything is very simple: Auditory children They learn new things better through conversation. They enjoy learning numbers by repeating examples out loud. A good option to remember the multiplication tables is to learn poems, songs or watch educational videos. Learning the multiplication table (video)
Visual child learns more easily if vision and imagery are involved. They absorb information with the help of bright drawings, coloring games, which 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. Multiplication table by 9 with Fixies (video)
Kinesthetic children learn through the sensations and feelings they have when coming into contact with new objects and information. In this case, you can try the card method. Learning the multiplication table using cards (video)
It's important to consider how your child learns best so that learning times tables will be fun and easy. How to learn the multiplication tables in 5 minutes a dayKukina Ekaterina Georgievna mathematics teacher You've probably heard the opinion more than once that the level of mathematics education is falling. When my children were in second grade, I clearly understood why the level of mathematics 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 appears, which cannot be supported by 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 all the same, for everyone - this is the picture. Multiplication table (picture) There are even worse notebooks (for high school students), in which there are no multiplication tables, but there are a bunch of meaningless formulas. Well, why is this notebook bad? An unsuspecting parent sees that there is a multiplication table on the notebook. It seems like you’ve had multiplication tables on your notebooks all your life? What's wrong? But the problem is that the notebook does NOT contain the multiplication table. The multiplication table, my dear readers, is this:
Sometimes this same table is even called the beautiful word “Pythagorean table”. You don't have to take the top and left columns, just the main rectangle. Firstly, this is a table. Secondly, she is interesting! No child in his right mind would look at examples written out in columns. Not a single child, no matter how brilliant he is, will be able to find interesting features and patterns in the written examples. Well, in general, when the 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 a science where ordinary things are named somehow differently and you need a lot, a lot cram, but it’s impossible to understand anything. And in general, we must do it “as it is said,” and not “as it makes sense.” Why is the Pythagorean table better? Firstly, there is no garbage and information 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 it is always at hand and the child constantly bumps into it, he willy-nilly begins to remember these numbers. In particular, he will never answer the question “seven and eight” with 55 - after all, the number 55 is not and never was in the table! Only children with abnormal memory are able to remember 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 relative to the diagonal are equal. You see, the human brain is simply determined to look for symmetry, and if it finds and notices it, it is very happy. And what does it mean? This means that rearranging the places of the factors does not change the product (or that multiplication is commutative, to put it more simply). Pythagorean table: multiplication (picture) You see, the child notices this himself! And what a person came up with himself, he will remember forever, unlike what he memorized or was told. Remember your math exam at university? You forgot all the theorems of the course, except for the one you got, and you had to prove it to the evil teacher! Well, that is if you didn’t cheat, of course. (I'm exaggerating, but it's almost always close to the truth). And then the child sees that he 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 remember “eight by three,” but just remember “three by eight.” Already half the work. 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. is training. In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you point at any number and draw a rectangle from the beginning of the table to that number, then the number of cells in the rectangle is your number. Pythagorean table: multiplication (picture) And here multiplication already takes on a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of a rectangle is equal to the product of its sides) You have no idea how much easier it is to divide with such a table! In short, if your child is in second grade, print out this correct multiplication table for him. Hang a large one on the wall so he can look at it when he does his homework or sits at the computer. And print and laminate a small one for him (or write on cardstock). Let him carry it to school with him, and just keep it conveniently at hand. (it wouldn’t hurt to highlight the squares diagonally on such a table to make it easier to see) My kids have this one. And it really helped them in second grade and still helps them a lot in math lessons. Pythagorean table: multiplication (picture) Honestly, your average math score will immediately increase, and your child will stop whining that math is stupid. And in addition, it will be easier for your child in the future too. He will understand that he needs to use his brains and not cram. And not only will he understand, he will also learn to do it. And I repeat: there is nothing wrong with the examples in 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 oftenCome up with ways to encourage your child. These can be pleasant little things that make him happy. Find an approach if the child is not in the moodForcing people to study, shouting, or completely depriving them of entertainment - such methods discourage any desire to study. It makes sense to calmly explain the importance of activities and motivate the child. Learn the multiplication table graduallyWhen a child first sees how many numbers he needs to remember, a protest arises. It is better to study at a comfortable pace with rest breaks. Remember that every child is an individualAs 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 caring attitude of parents is of great importance. Saying that mistakes are normalAt the first failures, children lose interest and do not want to continue classes. It is important to explain that without mistakes there are no good results. Everything will definitely work out. Now you know everything about how to teach your child the multiplication tables in different ways to make the stuttering process a joy. |
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