How to teach a child to divide numbers. How to learn column division: examples and solutions. How to column divide four-digit, multi-digit large numbers, polynomials into polynomials: examples, explanation

16.04.2019

Unfortunately modern educational program does not always involve explaining every topic to students, especially as complex as long division. In such cases, the parents themselves have to work with the students at home.

Step-by-step instruction for learning long division

First, you need to determine the basis of the child: repeat with him the names of the division elements (dividend, divisor, quotient, remainder), number digits and the multiplication table. Without this knowledge, the child will not be able to master division. First, you need to show the operation using simple examples from the multiplication table, that is, 56: 7 = 8. Next, show an example of division three-digit number without a remainder, when the first digit of the dividend is greater than the divisor, for example, 422: 2. It is necessary to divide each digit in order by the divisor as follows: 4 divided by 2 will be 2, we write, 2 by 2 is 1, we write, 2 by 2 - again one, we write it down. The result is 211. The result must be double-checked by back multiplying.

Learning long division requires practice and repetition of each step. Pick up a few more of the same simple operations, for example, 936 divided by 3, 488 divided by 4, etc. Comment on your actions each time in the same way, so that they are imprinted in the child's head, and he himself repeated them to himself when dividing:

We take the first digit of the number, divide it by the divisor. How many times can a divisor be contained in a dividend?
If the first digit is less than the divisor, we take the number from the first two digits, divide, write the result.
We multiply the divisor by the quotient and subtract from the dividend, sign the result of the subtraction.
We demolish the next digit of the dividend: can it be divided by the divisor? If not, then we demolish one more figure and divide, write down the result.
We multiply the last digit of the quotient by the divisor and subtract from the remaining dividend. We get the remainder.

For example, it looks like this: we divide 563 by 11. 5 cannot be divided by 11, we take 56. 11 can fit 5 times into 56, we write it in the quotient. 5 multiplied by 11 is 55. 56 minus 55 will be 1. 1 cannot be divided by 11, demolish 3. 13 11 will fit only 1 time, write down. 1 multiplied by 11 is 11, subtract from 13, it turns out 2. Answer: quotient 51, remainder 2.

It is very important that the child correctly signs the result of the subtraction and reads the numbers, and each figure of the quotient is always determined only by the selection of numbers. Work with your child regularly, but not for very long: gradually he will fill his hand and will click such tasks as nuts.

Division of numbers with or without remainder is the most difficult of the four arithmetic operations. The child gets acquainted with the basics of this process even in the very early childhood sometimes the baby has to share the candy equally between teddy bear and a doll. It is usually not difficult for a child to correctly divide the treat into several piles.

However, problems may arise later. School tasks does not always imply dividing several objects by the number of people. These can be, for example, speed assignments - and they often put the child into a stupor.

In this case, parents are obliged to teach the principles of dividing a number. Math does not tolerate emptiness - if a child missed something or simply did not absorb the information, this can greatly complicate the study further topics as well as other disciplines in later grades.

Initial training in division

How before parents explain to the child the principles of division with or without a remainder - the better he will learn them. And to make the process easy, you need to do it in the form of a game. For example, give six candies and ask them to split equally between doll, pussy and dad. And now - between mom and grandmother. Naturally, the child will have different results. It is important to explain why this happened.
It should be noted that for learning it is better to use household items familiar to the baby: games with counting sticks or paper squares are unlikely to be of interest to him.
The next step is to try to explain division with remainder - the principle is the same: play. Let the little one try to treat Misha and Sveta with five nuts. He will give each of 2 nuts, and the rest can eat himself.
Now the child will be able to understand the very principle of division: a larger number is divided by a smaller one. Of course, adults know that this is not always the case, but for a child aged 5 to 8 this information will be enough.

Teaching division of elementary schoolchildren

If the child has perfectly mastered everything in game form, then at school he will have to apply his knowledge and skills in practice. It is at this time that moving away from the usual categories - candy, dolls, and others - can cause serious difficulties.

At this age, a schoolchild should already know the first three arithmetic operations and be able to operate with them. He must understand and know the multiplication table. Here it is, by the way, in some cases it will help explain to the student that division is multiplication in reverse. The parent should sit next to the child and, studying the multiplication table printed on the cover of the notebook, explain how it works in practice. For example, 4x7 = 28. And if you go the other way around? To clarify, at the intersection of which number with the number 7 is 28. From 4. So we divided it.
Now the child must make a digital recording of this process: this helps to consolidate the information in memory.

Long division

Only after the student has mastered and well remembered the previous methods, you can proceed to long division, with or without a remainder.

First, it is necessary for the child to understand and memorize the name of the components of the division process:

dividend - the number that is divided;
divisor - what is divided into;
the quotient is the final result.

first, the dividend is written - let it be 98;
to the right of it, a corner is drawn, like an inverted letter "T", a divider is written in it - in our case, 7;
now determine the smallest number in the dividend, which is divisible by 7 - this is 9;
the number 7 in the number 9 can fit 1 time - which means that in the private we write 1;
now you need to multiply the divisor 7 by the first digit of the quotient 1 - you get 7. It must be written under 9;
subtract 7 from 9 - you get 2.

Please note: the resulting difference can never be equal to or greater than the divisor. If this happened, it means that the number 7 in 9 was incorrectly determined.

since 2 is not divisible by 7, the next digit from the two-digit dividend is demolished downwards - 8. We got 28. It can be divided by 7 - we get 4;
this figure must be written next to 1 - it will turn out to be 14. This will be private in this example;
But you still need to correctly formulate the solution, so 7 is multiplied by 4 - you get the result 28, which is written under 28. Subtract 28 from 28 - get 0. It is written under the line that summarizes the solution.
if the remainder is not zero, then it is division with the remainder.

Not only the baby goes to the first grade - the parents start and finish school with him. The teacher does not always have the opportunity to explain a particular topic to each student. And then parents should teach their child what multiplication is, division with the remainder of a two-digit number by a single-digit number. When you move to the third grade, the task will become more complicated - you will need to teach division with a remainder and a three-digit number by a two-digit number. The main thing is to be patient and not scold the child because of the slightest oversight. Then everything will work out, and math may become a favorite school subject.

The first years at school and the knowledge gained at this time are one of the most important and most exciting adventures in a child's life. Parents can help their child overcome this difficult path by laying a certain knowledge base and preparing in advance for what awaits him at school. Most often, children without special problems master the basic knowledge of mathematics, especially since it is pleasant for the child to be a little more prepared than required and to have the basics of knowledge that will be taught to him. Among them, it will not be superfluous to learn how to teach a child mathematics, in particular division.

How to teach a child to divide numbers?

Many parents wonder how to teach their child mathematics, that is, to give him certain knowledge and skills related to elementary arithmetic operations. The easiest way is to use objects. You can explain to the kid the essence of such a mathematical action as division with the help of an illustrative game, then there will be no problems with how to teach a child to divide numbers.

To do this, you need to take 4 objects, it can be fruits, cubes or balls, the main thing is that they are the same, and perform 3 arithmetic operations with them (addition, subtraction and multiplication). For example, you can add one to two, then subtract two from four, and finally take two twice to get four. Now divide 4 objects in two - this is the essence of the division. Then do the same manipulations with division by 3. In how to teach a child to divide, it is important to patiently and clearly explain to him that division is the opposite of multiplication.

How to teach a child to divide by a column?

Many parents are faced with the problem of how to teach their child mathematics, since, unfortunately, not all teachers can clearly convey information to children. For correct arithmetic calculations, the baby needs to understand the process that is happening and which must be completed. Of all actions with numbers, division is perhaps the most difficult, and the ability to divide with a column can help in mastering it. Therefore, when teaching a kid mathematics, the question of how to teach a child to divide by a column is very important.

The advantage of this arithmetic operation is that it is schematic. When the time comes to master it, the child already has a little experience in mathematics, he is familiar with abstract concepts and knows how to operate with numbers and numbers, so he can learn well the column division scheme. It is important in this case that addition, subtraction and multiplication in a column for the child no longer cause any difficulties. And the main thing is how to teach a child to long division - patience. You need to slowly and in great detail disassemble several simple examples as many times as necessary until you are sure he has mastered the information well.

Doman's technique

Modern parents are becoming more and more interested in different techniques early development children. The question of how to teach a child mathematics quickly and efficiently is also relevant. Adherents of Glenn Doman's methodology argue that it is possible to teach at all in 5-6 months little child, starting from 4-6 months of age, arithmetic in the volume of the program of grades 1 and 2 primary school... At the same time, the kid will be able to quickly perform all mathematical actions in his mind and even learn to solve equations.

Training according to the Doman methodology is carried out using a special teaching material- mathematical cards that you can make yourself from white cardboard... They take into account the immaturity of the visual apparatus of children and contribute to its development, as well as the development of the brain as a whole. For classes, you need to prepare about 100 square cards with a side size of 27 cm. On them you need to randomly apply points with a red felt-tip pen with a thick rod - from 1 to 100. If possible, you can use a printer. WITH back side for each card, you need to write down a number that corresponds to the number of dots on the card. Leave small margins around the edges to hold the card while learning.

In a certain order, showing the child the cards and voicing what he sees in the picture, you can quickly, during the game, teach him how to count and teach him how to perform basic arithmetic operations. At the same time, very little time is spent on classes, starting with a few minutes a day, the duration of the lesson can be gradually increased to half an hour. The amazing speed with which the child learns the material will be your reward for the effort spent.

Do not be discouraged if your child did not understand in the lesson how the process of dividing numbers works. A teacher in a school cannot always pay attention to every student. Be patient and become a home teacher for your student. First, explain the mathematical process in a playful way. Gradually move on to more difficult tasks. The child will understand everything and mathematics will become his favorite subject.

Explaining division in the form of a game to the child

Put boring textbooks aside. Turn learning into fun:

take apples or candy. Ask your kid to share four candies or apples between two or three dolls or bears. Gradually increase the number of fruits to eight and ten. At first, the child will lay things out slowly. Don't yell at him, be patient. If you are mistaken, correct it calmly. After the toys “receive” the candies, have the child count how many each doll has got them. Summarize. If there were 6 candies and they were distributed to three dolls, each got two. Explain that “share” means that everyone should be given out equally;
another game example. Explaining the division by numbers. Tell your child that the numbers are the same apples or candy. Explain to him that the number of candies to be divided is called the dividend. And the number of people into whom sweets are divided is a divisor;
give the baby 6 apples. Ask him to distribute them equally to Grandma, Cat, and Dad. Then let him divide the same number of items between the cat and the grandmother. Explain why the results are different;
explain division with remainder. Give the kid 5 nuts, and let him treat dad and grandmother with them in the same amount. The kid takes the remaining nut for himself. Explain with this example that one nut is the remainder.

The above methods in a playful way will help the child understand the process of division and the fact that a larger number is divided by a smaller one. The first number is the number of apples or sweets, and the second number is the participants between whom the items are divided. For a child aged 5 to 8 years, this information is enough. Teach toddler division even before school, it will be easier for him to learn math lessons in the future.

Explaining division to a child using the example of a multiplication table

This way of teaching is suitable for students primary grades if they know multiplication. Tell that division is the same multiplication table, but the opposite of multiplication takes place in it. Illustrative example for a child:

multiply the number 5 by 4. You get 20;
remind the student that the number 20 is the result of multiplying the above two numbers;
divide 20 by 5. Get 4. This will clearly show that division is the opposite of multiplication.

Consider examples with different numbers. If the student has mastered the multiplication table well and understands the connection between the two mathematical actions, division will be easy to master.

Explaining division to a child - definition of concepts

Explain to your child the names of the numbers involved in division:

dividend. The number to be divided;
divider. The number by which the dividend is divided;
private. The total obtained after the division.

For clarity, use the same examples with sweets and people or toys that the child should treat with sweets.

Explaining column division to a child

Proceed to this training only after the child has mastered the above methods. He also needs to know how numbers are multiplied in a column. Let's take a simple example: divide 110 by 5. Explaining process:

write these numbers on a blank piece of paper;
divide them with perpendicular lines as you will divide them in a column;
Explain which number is divisible and which is divisible;
work out with your child which number can first be used for division. The first digit, 1 by 5, cannot be divided. So, you need to take the next digit to it and you get the number 11. The digit 5 can fit in 11 twice;
write down the number 2 in the column below the five. Ask the child to multiply 5 by 2. It will turn out to be 10. Write this number under the number 11;
subtract the number 10 from 11 with the child. It will turn out 1. Write the remaining zero in the column near the unit. It turns out 10;
Divide 10 by 5 with your child. You get 2. You write this number under the five, and the final total is 22.

Start learning with two-digit or even single-digit numbers that can be divided without a remainder. Gradually complicate the task.

For easy assimilation of math by the child, arouse his interest in this lesson. Now there are division tables. But does a child need to memorize it if he knows the multiplication table and understands that division is the opposite process? It all depends not only on school teacher, but also from your activities with the student.

One of the most important milestones teaching your child math operations is learning how to divide prime numbers. To teach division of a child, it is necessary that by the time of learning he has already mastered and well understood such mathematical operations as subtraction, addition.

In addition, it is important to have a clear understanding of the very nature of actions such as division and multiplication. Thus, he must understand that in action with division is the method of dividing something into equal parts. In conclusion, you must also learn the multiplication operations and know the multiplication table well.

Learning the operation of division into parts

On this stage it is better to form an understanding that the main thing in the division process is the division of something into equal parts. The most in a simple way to learn this for the child, it will invite him to share several items between him and family members or friends.

For example, take 6 identical objects and have your child divide them into two equal parts. You can complicate the task a little by proposing to divide not into two, but into three equal parts.

An important point here is considered to be to carry out operations to divide even numbers of objects. Such an action will be useful at a later stage, when the child needs to understand that division is the opposite of multiplication.

Divide and multiply using the multiplication table

Here it is worth explaining to the child that the action inverse to multiplication is called "division". Using the multiplication table, show the student this relationship between division and multiplication using an example.

For example: 2 times 4 is eight. Here, focus on the fact that the result of the multiplication will be the product of two numbers. It will then be better to illustrate the division operation by pointing out the operation of the inverse multiplication operation.

Divide the resulting answer "8" by any factor - "4" or "2", the result will always be the factor that was not used in the operation.

It is also worth teaching to recognize categories that describe division operations, such as "divisor", "dividend", "quotient". It is important to consolidate this knowledge, they are most necessary for the further learning process!

We divide by a column - easily and quickly

Before starting training, you should remember with the child what name each number has in the process of the separation operation. The main thing is to learn how to quickly and accurately identify these categories.

An illustrative example:

Let's try to divide 938 by 7. In this given example, the number 938 will be divisible, and the number 7 will be the divisor. As a result of the action, the answer will be called the quotient.

It is necessary to write down the numbers, dividing them with a "corner".
Ask the student to choose from the smallest number of divisors that is greater than the divisor. Of the numbers 9, 3, 8, the largest will be the number 9. Offer to analyze how many sevens can be contained in the number 9. There will be only one correct answer here. The first result is 1.
We design the division into a column.

Multiply the divisor 7 by 1, the answer will be 7. We enter the result under the first number of our dividend, then subtract it in a column. Thus, from 9 we subtract 7 and in the answer we get 2. We also write this down.

We see the number that is less than the divisor, so we increase it. To do this, combine it together with the unused number of the dividend, that is, with the number 3. Add 3 to the resulting 2.
Then we analyze how many times the divisor 7 will be in the number 23. The answer is 3 times and fix it in the quotient. The result of the product of 7 by 3 (21) is entered from the bottom into the column under the number 23.
It remains only to find the last quotient. Applying the same algorithm, it continues the calculations in the column. Subtracts in column 23-21 gets the difference, equal to the number 2. Of all the dividend, we have only the unused number 8. We combine it with the resulting result 2, we get 28 in the answer.
In conclusion, we analyze how much, the divisor 7 is contained in the number we received. The correct answer is 4 times. We put it in the result. As a result, our answer obtained during the division process is 134.

The most important thing in teaching a child the method of division will be assimilation and a clear understanding of the algorithm of actions, because in fact it is extremely simple.

If your child is good at using the multiplication table, then he shouldn't have any difficulties with the "reverse" division. Therefore, it is very important to train the acquired skills all the time. You shouldn't be satisfied with what has already been achieved.

For easy teaching of a young student the method of division follows:

at the age of three, correctly understand the terms "whole" and "part". An understanding of the concept of the whole, as an indivisible category, should be formed, as well as perception separate parts whole in the concept of an independent object.
correctly understand and understand the methods of division and multiplication.

In order for the child to enjoy the classes, it is necessary to arouse interest in mathematics in situations in everyday life, and not only in the process of study.

Therefore, train the child's observation skills, come up with analogies mathematical actions during games, in the process of construction, or in simple observations of nature.