How to divide a four-digit number in a column. How to explain to a child the division in a column

The first years of school life in elementary grades are not easy for a child. Often after a math lesson, they do not understand the topic very well. To help the child in the assimilation of the material covered, you will need to explain to the student himself what he does not understand. Parents come to the rescue, in which the question immediately arises: “How to explain the division to the child?”. This can be done in several ways, but initially it is worth making sure that the child has mastered mathematical operations such as addition, subtraction and multiplication.(You can read about ways to teach children addition and multiplication and ).

Teaching your child the basics of division

It is important that the child understands the essence of such a mathematical action as division. To do this, it is necessary for him to explain that division is the division of something into equal parts. It is recommended to turn the learning process into an interesting game so that the child is concentrated.

Division in a playful way

TIP: The division table is just as important to learn as the multiplication table. Better to do it on vacation!

Help your child understand that division is the opposite of multiplication.

The easiest way to explain the division is to make a visual demonstration of the division of objects into equal shares. Anything can be used as divisible items, but something interesting for the child is desirable. Examples include candy and toys.

How to explain division to a child with toys?

Initially, you need to take 2 sweets and ask the child to divide them between 2 plush toys. Thanks to such a simple example, the child will understand the essence of mathematical division. After that, you can move on to more complex examples of division.

How division occurs is shown in detail and in a playful way in the following video:

You can also take a box of colored pencils, which will act as one, and invite the baby to divide them equally between you and yourself. After, ask the child to count how many pencils were in the box at the beginning and how many he was able to distribute.

As the child understands, the parent can increase the number of items and the number of participants in the task. Then you need to tell that it is not always possible to divide something equally and some items sometimes remain “no man's”. For example, you can offer to share 9 apples between grandma, grandpa, dad and mom. The child must understand that everyone will receive only 2 apples, and one will be in the balance.

Division in a playful way

In this way, you will explain the basics of division and prepare the child for more complex school tasks.

TIP: Try to engage with your child in a playful way. Then it will be interesting for him to study, which means that the classes will be fun and effortless.

It will also be interesting and useful for you to print the division table as a picture.

Dividing single digits by single digits is easiest using . To do this, it is enough to explain to the child that division is the reverse action of multiplication. This can be done on any correct example of dividing natural numbers.

For example: 2 multiplied by 3 is 6. Based on this example, demonstrate to the child the division process. You should proceed as follows: divide 6 by any factor, for example, by the number 2. The answer will be 3, that is, the factor not used in division.

In this way, you can divide multi-digit (two-digit) numbers by single-digit ones.

Long division algorithm

Before starting the explanation of division into a column, you need to tell the child about the meaning of the dividend, divisor and quotient. In the example 20:4=5, 20 is divisible, 4 is a divisor, and 5 is quotient. Each individual digit in the example has one name.

Multi-digit numbers (three-digit and two-digit) are easiest to divide into a column. To do this, you need to write multi-digit numbers in a corner.

For example, you need to divide the three-digit number 369 by the single-digit number 3.

The divisor is a three-digit number 369, and as a divisor a single-digit number 3. First of all, it is important to explain to the child that division into a column occurs in several stages:

• Determination of the part of the dividend suitable for primary division. In this case, the number is 3. 3:3=1. The number 1 must be written in the quotient column.
• "Lower" the next divisible number. In this case, it's number 6. 6:3=2 . The resulting number 2 must be written in private.
• Next, you need to "lower" the next divisible number 9. 9 is divisible without a remainder by 3, the result must be written in a quotient. The result of dividing the three-digit number 369 by 3 is 123.

Dividing a decimal number by two digits works in much the same way. In the case of a decimal number, it is necessary to explain to the child that the comma in the divisor is transferred to as many characters as it was transferred in the dividend. This is followed by the usual division into a column.

It is necessary to warn the child about the occurring cases of division with a remainder. As an example, you can divide the two-digit number 26 by 5 by a column. The result is a remainder of 1.

After the explanation, it is important to allow the child to independently solve several examples so that all the studied material remains in the child’s memory for a long time.

You can also watch a video where everything is explained in an understandable language.

And finally, do not teach yourself and your child to use an online calculator to learn how to divide 145 by 9, 34 by 40, 100 by 4, 30 by 80, 416 by 52 and other examples. It won't benefit you or him.

Not only the child goes to the 1st grade - the parents start and finish the educational institution together with him. The teacher at school does not always have time to explain this or that discipline to each individual student. Therefore, it has its own advantages. You can explain to the child, individually and slowly, what he did not understand. In this difficult period, the main thing is to be patient and not scold the student because of the wrong decisions. Then everything will work out for you.

Instruction

Before teaching how to divide two-digit numbers, it is necessary to explain to the child that a number is the sum of tens and units. This will save him from a future rather common mistake that many children make. They begin to divide the first and second digits of the dividend and divisor into each other.

First, work from numbers to single digits. This technique is best practiced using the knowledge of the multiplication table. The more such practice, the better. The skills of such division should be brought to automaticity, then it will be easier for the child to move on to the more complex topic of the two-digit divisor, which, like the dividend, is the sum of tens and ones.

The most common way of dividing two-digit numbers is the selection method, which involves dividing successively by numbers from 2 to 9 so that the final product equals the dividend. Example: Divide 87 by 29. Reason as follows:

29 times 2 equals 54 - not enough;
29 x 3 = 87 is correct.

Pay the student's attention to the second digits (units) of the dividend and divisor, which are convenient to navigate when using the multiplication table. For example, in the example above, the second digit of the divisor is 9. Think about how much you need to multiply the number 9 so that the number of units of the product is 7? The answer in this case is only one - by 3. This greatly simplifies the task of two-digit division. Test your guess by multiplying the whole number 29.

If the task is performed in writing, then it is advisable to use the method of dividing into a column. This approach is similar to the previous one, except that the student does not need to keep the numbers in his head and do mental calculations. It is better to arm yourself with a pencil or a draft sheet for written work.

Sources:

• multiplication of two-digit numbers by two-digit tables

The topic of dividing numbers is one of the most important in the 5th grade math program. Without mastering this knowledge, further study of mathematics is impossible. Divide numbers come into life every day. And don't always rely on a calculator. To separate two numbers, you need to remember a certain sequence of actions.

You will need

• Checkered sheet of paper
• pen or pencil

Instruction

Write the dividend and on one line. Separate them with a vertical bar two lines high. Draw a horizontal line under the divisor and dividend perpendicular to the previous line. To the right, under this line, the quotient will be written. Below and to the left of the dividend, under the horizontal line, write zero.

Move one leftmost, but not yet transferred, digit of the dividend down under the last horizontal line. Mark the transferred digit of the dividend with a dot.

Compare the number under the last horizontal bar with the divisor. If the number is less than the divisor, then continue with step 4, otherwise go to step 5.

Column division is an integral part of the school curriculum and necessary knowledge for the child. To avoid problems in the lessons and with their implementation, it is necessary to give the child basic knowledge from a young age.

It is much easier to explain certain things and processes to a child in a playful way, and not in the format of a standard lesson (although today there are quite a variety of teaching methods in different forms).

From this article you will learn

The principle of division for kids

Children constantly come across different mathematical terms, without even suspecting where they come from. Indeed, many mothers, in the form of a game, explain to the child that dads are more of a plate, go further to the kindergarten than to the store and other simple examples. All this gives the child an initial impression of mathematics, even before the child goes to first grade.

To teach a child to divide without a remainder, and later with a remainder, it is necessary to directly invite the child to play division games. Divide, for example, sweets among themselves, and then add the following participants in turn.

First, the child will share candy, giving each participant one. And at the end, draw a conclusion together. It should be clarified that "sharing" means the same number of candies for everyone.

If you need to explain this process using numbers, then you can give an example in the form of a game. We can say that the number is candy. It should be explained that the number of sweets to be divided between the participants is divisible. And the number of people into whom these sweets are divided is a divisor.

Then you should show it all clearly, give “live” examples in order to quickly teach the crumbs to divide. Playing, he will understand and learn everything much faster. While the algorithm will be difficult to explain, and now it is not necessary.

How to teach your baby to divide in a column

Explaining math to a little bit is a good preparation for going to class, especially math class. If you decide to move on to teaching your child to divide by a column, then he has already learned such actions as addition, subtraction, and what the multiplication table is.

If this still causes some difficulties for him, then all this knowledge needs to be tightened up. It is worth recalling the algorithm of actions of previous processes, teaching how to freely use your knowledge. Otherwise, the baby will simply get confused in all processes, and will cease to understand anything.

To make this easier to understand, there is now a division table for toddlers. The principle is the same as for multiplication tables. But is such a table already needed if the baby knows the multiplication table? It depends on the school and the teacher.

When forming the concept of "division", it is necessary to do everything in a playful way, give all examples on things and objects familiar to the child.

It is very important that all items be of an even number, so that it is clear to the baby that the result is equal parts. This will be correct, because it will allow the baby to realize that division is the reverse process of multiplication. If the items are an odd number, then the result will come out with the remainder and the baby will get confused.

Multiply and divide using a spreadsheet

When explaining to the baby the relationship between multiplication and division, it is necessary to clearly show all this using some example. For example: 5 x 3 = 15. Remember that the result of multiplication is the product of two numbers.

And only after that, explain that this is the reverse process to multiplication and demonstrate this clearly using a table.

Say that you need to divide the result “15” by one of the factors (“5” / “3”), and the result will be a constantly different factor that did not take part in the division.

It is also necessary to explain to the baby how the categories that perform division are correctly called: dividend, divisor, quotient. Again, use an example to show which of these is a particular category.

Dividing by a column is not a very complicated thing, it has its own easy algorithm that the baby needs to be taught. After fixing all these concepts and knowledge, you can proceed to further training.

In principle, parents should learn the multiplication table in reverse order with their beloved child, and remember it by heart, as this will be necessary when teaching division by a column.

This must be done before going to the first grade, so that it would be much easier for the child to get used to school and keep up with the school curriculum, and so that the class does not start teasing the child due to small failures. The multiplication table is both at school and in notebooks, so you don’t have to carry a separate table to school.

Divide with a column

Before starting the lesson, you need to remember the names of the numbers when dividing. What is a divisor, dividend and quotient. The child must divide these numbers into the correct categories without errors.

The most important thing when learning division by a column is to learn the algorithm, which, in general, is quite simple. But first, explain to the child the meaning of the word "algorithm" if he has forgotten it or has not studied it before.

In the event that the baby is well versed in the multiplication table and inverse division, he will not have any difficulties.

However, it is impossible to linger on the result obtained for a long time; it is necessary to regularly train the acquired skills and abilities. Move on as soon as it becomes clear that the baby understood the principle of the method.

It is necessary to teach the baby to divide in a column without a remainder and with a remainder, so that the child is not afraid that he failed to divide something correctly.

To make it easier to teach the baby the process of division, you must:

• in 2-3 years, understanding the whole-part relationship.
• at 6-7 years old, the baby should be able to freely perform addition, subtraction and be aware of the essence of multiplication and division.

It is necessary to encourage the child’s interest in mathematical processes so that this lesson at school brings him pleasure and a desire to learn, and not motivate him only in the classroom, but also in life.

The child should carry different tools for math lessons, learn how to use them. However, if it is difficult for a child to carry everything, then do not overload it.

It is easy to teach a child to divide by a column. It is necessary to explain the algorithm of this action and consolidate the material covered.

• According to the school curriculum, children begin to explain division by a column already in the third grade. Students who grasp everything “on the fly” quickly understand this topic
• But, if the child fell ill and missed the lessons of mathematics, or he did not understand the topic, then the parents must explain the material to the child on their own. It is necessary to convey information to him as clearly as possible.
• Moms and dads during the educational process of the child must be patient, showing tact in relation to their child. In no case should you yell at a child if something does not work out for him, because this way you can discourage him from all the desire to study

Important: In order for a child to understand the division of numbers, he must thoroughly know the multiplication table. If the kid does not know multiplication well, he will not understand division.

During home extra classes, cheat sheets can be used, but the child must learn the multiplication table before proceeding to the topic “Division”.

So how do you explain to a child column division:

• Try to explain in small numbers first. Take counting sticks, for example, 8 pieces
• Ask the child how many pairs are in this row of sticks? Correct - 4. So, if you divide 8 by 2, you get 4, and if you divide 8 by 4, you get 2
• Let the child divide by himself another number, for example, a more complex one: 24:4
• When the baby has mastered the division of prime numbers, then you can proceed to the division of three-digit numbers into single-digit

Division is always given to children a little more difficult than multiplication. But diligent additional classes at home will help the baby understand the algorithm of this action and keep up with their peers at school.

Start simple - division by a single digit:

Important: Calculate in your mind so that the division turns out without a remainder, otherwise the child may get confused.

For example, 256 divided by 4:

• Draw a vertical line on a sheet of paper and divide it in half on the right side. Write the first number on the left, and the second on the right above the line.
• Ask the baby how many fours fit in a two - not at all
• Then we take 25. For clarity, separate this number from above with a corner. Again ask the child how many fours fit in twenty-five? That's right, six. We write the number "6" in the lower right corner under the line. The child must use the multiplication table for the correct answer.
• Write down the number 24 under 25, and underline to write down the answer - 1
• Ask again: how many fours can fit in a unit - not at all. Then we demolish the number "6" to one
• It turned out 16 - how many fours fit in this number? Correct - 4. We write down "4" next to "6" in the answer
• Under 16 we write 16, underline and it turns out “0”, which means we divided correctly and the answer turned out to be “64”

Written division by two digits

When the child has mastered the division by a single number, you can move on. Written division by a two-digit number is a little more complicated, but if the baby understands how this action is performed, then it will not be difficult for him to solve such examples.

Important: Again, start explaining with simple steps. The child will learn to correctly select numbers and it will be easy for him to divide complex numbers.

Perform together this simple action: 184:23 - how to explain:

• First we divide 184 by 20, it turns out approximately 8. But we do not write the number 8 in the answer, since this is a trial number
• Check if 8 fits or not. We multiply 8 by 23, it turns out 184 - this is exactly the number that we have in the divisor. The answer will be 8

Important: For the child to understand, try to take 9 instead of the eight, let him multiply 9 by 23, it turns out 207 - this is more than we have in the divisor. The number 9 does not suit us.

So gradually the baby will understand the division, and it will be easy for him to divide more complex numbers:

• Divide 768 by 24. Determine the first digit of the private - we divide 76 not by 24, but by 20, it turns out 3. We write 3 in response under the line to the right
• Under 76 we write down 72 and draw a line, write down the difference - it turned out 4. Is this figure divisible by 24? No - we demolish 8, it turns out 48
• Is 48 divisible by 24? That's right - yes. It turns out 2, we write this figure in response
• It turned out 32. Now you can check whether we performed the division action correctly. Multiply in a column: 24x32, it turns out 768, then everything is correct

If the child has learned to divide by a two-digit number, then you need to move on to the next topic. The algorithm for dividing by a three-digit number is the same as the algorithm for dividing by a two-digit number.

For example:

• Divide 146064 by 716. First we take 146 - ask the child if this number is divisible by 716 or not. That's right - no, then we take 1460
• How many times will the number 716 fit in the number 1460? Correct - 2, so we write this figure in the answer
• We multiply 2 by 716, it turns out 1432. We write this figure under 1460. It turns out the difference is 28, we write under the line
• Demolition 6. Ask the child - 286 is divisible by 716? That's right - no, so we write 0 in the answer next to 2. We demolish another number 4
• We divide 2864 by 716. We take 3 each - a little, 5 each - a lot, which means we get 4. We multiply 4 by 716, we get 2864
• Write 2864 under 2864 for a difference of 0. Answer 204

Important: To check the correctness of the division, multiply together with the child in a column - 204x716 = 146064. The division is correct.

It's time for the child to explain that division can be not only whole, but also with a remainder. The remainder is always less than or equal to the divisor.

Division with a remainder should be explained with a simple example: 35:8=4 (remainder 3):

• How many eights fit in 35? Correct - 4. Remains 3
• Is this number divisible by 8? That's right - no. So the remainder is 3.

After that, the child should learn that you can continue the division by adding 0 to the number 3:

• The answer is the number 4. After it, we write a comma, since adding zero indicates that the number will be with a fraction
• It turned out 30. Divide 30 by 8, it turns out 3. We write in response, and under 30 we write 24, underline and write 6
• We carry the number 0 to the number 6. Divide 60 by 8. Take 7 each, it turns out 56. Write under 60 and write down the difference 4
• We add 0 to the number 4 and divide by 8, it turns out 5 - we write it down in response
• We subtract 40 from 40, we get 0. So, the answer is: 35:8=4.375

Tip: If the child does not understand something, do not be angry. Let a couple of days go by and try to explain the material again.

Mathematics lessons at school will also reinforce knowledge. Time will pass and the kid will quickly and easily solve any division examples.

The algorithm for dividing numbers is as follows:

• Make an estimate of the number that will be in the answer
• Find the first incomplete dividend
• Determine the number of digits in a quotient
• Find the digits in each digit of the quotient
• Find the remainder (if any)

According to this algorithm, division is performed both by single-digit numbers and by any multi-digit number (two-digit, three-digit, four-digit, and so on).

When studying with a child, often ask him examples for making an estimate. He must quickly calculate the answer in his mind. For example:

• 1428:42
• 2924:68
• 30296:56
• 136576:64
• 16514:718

To consolidate the result, you can use the following division games:

• "Puzzle". Write five examples on a piece of paper. Only one of them should be with the correct answer.

Condition for the child: Among several examples, only one is solved correctly. Find him in a minute.

Video: Arithmetic game for kids addition subtraction division multiplication

Video: Educational cartoon Mathematics Learning by heart the multiplication and division tables by 2

One of the important stages in teaching a child mathematical operations is learning the operation of dividing prime numbers. How to explain division to a child, when can you start mastering this topic?

In order to teach a child to divide, it is necessary that by the time of learning he has already mastered such mathematical operations as addition, subtraction, and also has a clear idea of ​​the very essence of the operations of multiplication and division. That is, he must understand that division is the division of something into equal parts. It is also necessary to teach multiplication operations and learn the multiplication table.

I already wrote about how this article can be useful for you.

We master the operation of division (division) into parts in a playful way

At this stage, it is necessary to form in the child the understanding that division is the division of something into equal parts. The easiest way to teach a child to do this is to invite him to share a certain number of objects among his friends or family members.

For example, take 8 identical cubes and invite the child to divide into two equal parts - for him and another person. Vary and complicate the task, invite the child to divide 8 cubes not into two, but into four people. Analyze the result with him. Change the components, try with a different number of objects and people into which these objects need to be divided.

Important: Make sure that at first the child operates with an even number of objects, so that the result of division is the same number of parts. This will be useful in the next step, when the child needs to understand that division is the inverse of multiplication.

Multiply and divide using the multiplication table

Explain to your child that, in mathematics, the opposite of multiplication is called division. Using the multiplication table, demonstrate to the student, using any example, the relationship between multiplication and division.

Example: 4x2=8. Remind your child that the result of multiplication is the product of two numbers. Then explain that division is the inverse of multiplication and illustrate this clearly.

Divide the resulting product "8" from the example - by any of the factors - "2" or "4", and the result will always be another factor that was not used in the operation.

You also need to teach the young student how the categories that describe the operation of division are called - “divisible”, “divisor” and “quotient”. Use an example to show which numbers are divisible, divisor and quotient. Consolidate this knowledge, they are necessary for further learning!

In fact, you need to teach your child the multiplication table “in reverse”, and you need to memorize it as well as the multiplication table itself, because this will be necessary when you start learning to divide in a column.

Divide by a column - give an example

Before starting the lesson, remember with your child how the numbers are called during the division operation. What is a "divisor", "divisible", "quotient"? Learn to accurately and quickly identify these categories. This will be very useful while teaching the child to divide prime numbers.

We explain clearly

Let's divide 938 by 7. In this example, 938 is the dividend, 7 is the divisor. The result will be a quotient, and then you need to calculate it.

Step 1. We write down the numbers, dividing them with a "corner".

Step 2 Show the student the number of divisible and ask him to choose from them the smallest number that is greater than the divisor. Of the three numbers 9, 3 and 8, this number will be 9. Invite the child to analyze how many times the number 7 can be contained in the number 9? That's right, just once. Therefore, the first result we write down will be 1.

Step 3 Let's move on to the design of the division by a column:

We multiply the divisor 7x1 and get 7. We write the result under the first number of our dividend 938 and subtract, as usual, in a column. That is, we subtract 7 from 9 and get 2.

We write down the result.

Step 4 The number that we see is less than the divisor, so we need to increase it. To do this, we combine it with the next unused number of our dividend - it will be 3. We attribute 3 to the resulting number 2.

Step 5 Next, we act according to the already known algorithm. Let's analyze how many times our divisor 7 is contained in the resulting number 23? That's right, three times. We fix the number 3 in the quotient. And the result of the product - 21 (7 * 3) is written below under the number 23 in a column.

Step.6 Now it remains to find the last number of our quotient. Using the already familiar algorithm, we continue to do calculations in a column. By subtracting in the column (23-21) we get the difference. It equals 2.

Of the dividend, we have one number left unused - 8. We combine it with the number 2 obtained as a result of subtraction, we get - 28.

Step 7 Let's analyze how many times our divisor 7 is contained in the resulting number? That's right, 4 times. We write the resulting figure in the result. So, we have the quotient obtained as a result of division by a column = 134.

How to teach a child to divide - we consolidate the skill

The main reason why many students have a problem with mathematics is the inability to quickly do simple arithmetic calculations. And on this basis, all mathematics in elementary school is built. Especially often the problem is in multiplication and division.
In order for a child to learn how to quickly and efficiently carry out division calculations in the mind, the correct teaching methodology and consolidation of the skill are necessary. To do this, we advise you to use the currently popular aids in mastering the division skill. Some are designed for children to work with their parents, others for independent work.

1. "Division. Level 3. Workbook "from the largest international center for additional education Kumon
2. "Division. Level 4 Workbook by Kumon
3. “Not mental arithmetic. A system for teaching a child rapid multiplication and division. For 21 days. Notepad simulator.» from Sh. Akhmadulin - the author of best-selling educational books

The most important thing when you teach a child to divide in a column is to master the algorithm, which, in general, is quite simple.

If the child operates well with the multiplication table and "reverse" division, he will not have difficulties. Nevertheless, it is very important to constantly train the acquired skill. Don't stop there as soon as you realize that the child has grasped the essence of the method.

In order to easily teach a child the operation of division, you need:

• So that at the age of two or three years he mastered the relationship "whole - part". He should develop an understanding of the whole as an inseparable category and the perception of a separate part of the whole as an independent object. For example, a toy truck is a whole, and its body, wheels, doors are parts of this whole.
• So that at primary school age the child freely operates with actions for adding and subtracting numbers, understands the essence of the processes of multiplication and division.

In order for the child to enjoy mathematics, it is necessary to arouse his interest in mathematics and mathematical actions, not only during training, but also in everyday situations.

Therefore, encourage and develop observation in the child, draw analogies with mathematical operations (operations on counting and division, analysis of part-whole relationships, etc.) during construction, games and observations of nature.

Lecturer, child development center specialist
Druzhinina Elena
site specially for the project

Video plot for parents, how to correctly explain the division into a column to the child: