How to explain the principle of division to a child. How to divide a smaller number by a larger one? How to explain division to a child using toys

Counting in the mind, according to many of us, is no longer relevant in our time. There is a calculator in every smartphone, and even more so on a computer and laptop. However, constantly, before your every action, step or sneeze, you will not get into the calculator, but you need to count constantly and a lot. - a skill that is very necessary even in our high-tech age of gadgets and electronic computing systems. A simple example illustrating these theoretical calculations is the behavior of buyers and sellers in a store: you need to act quickly, because there is a long queue behind you, and if you cannot count in your head, the seller can cheat you - by mistake or deliberately. Children most often make their first independent "forays" to the store, so the oral bill is very useful to them.

- not an innate skill in humans, and very young children still have no idea about numbers, quantity, actions with groups of objects (adding one group to another, subtracting, etc.). The primitive peoples of Asia, Africa and America also have undeveloped ideas about numbers and arithmetic operations: most often their number system consists of the concepts "one", "two" and "many"; some tribes can count up to five, some up to seven, but then they all have the same “many”. From this we can conclude that counting in general is a rather complex function for human consciousness.

So how do you teach your child the first number manipulation? Before mastering the ability to operate with abstract numbers, children need to understand counting using visual examples. To begin with, the child needs to be told about the numbers, at least up to the first ten, and count with him the various objects that can be seen around: birds in trees, flowers in the garden, people on the street, cars in the parking lot, and so on. Gradually, the baby will understand the "appearance" of specific quantities - be it one, five or ten objects. With undeveloped abstract thinking, young children have a very developed visual memory, he quickly remembers shapes and colors. You can practice counting with him, showing vivid pictures.

The main thing is to understand that a small child perceives everything as a game. And learning to count must also be presented in a playful way to make it interesting. With the right approach, the baby will grasp information very quickly, because at this age his brain absorbs everything new very actively. You can't put him at the table and read a tedious "lecture" about arithmetic operations for a long time - the child will only lose interest in learning. You need to count with him in different places and situations, during a walk, games and other joint actions. You can offer to cook something tasty together, and the child can help determine, for example, how many eggs are needed to knead the dough.

After the idea of \u200b\u200bquantity is more or less formed, the game can be complicated. Teach your child the first arithmetic operations - addition and subtraction. For example, take a toy house (an ordinary large box can play its role) and figures of people or animals (you can use ordinary cubes, which we will call, for example, "gnomes"). Place one person in the house and ask the kid how many people live in the house. He must answer that he is alone. Then put another figure in the house and ask how many people there are. Let the child think and say the correct answer. At first, it will take him a few minutes, he will be wrong; do not rush or scold him. When he says the correct answer, he must open the house and make sure that there are exactly two people. The abstract model, which the child reproduced from memory, was confirmed by an illustrative example. Add and subtract little people from the total number of "inhabitants" of the house, than you will consolidate and develop the child's skill of oral counting.

How to teach a child to multiply and divide

If and are fairly easy procedures, then the child is much more difficult to understand. Division is even more difficult to master. Illustrative examples, toys and figures will also come to help parents.

You need to prepare the same boxes and sets of figures. In the simplest case, pebbles, cubes, plastic bottle caps will serve as figurines - you can find anything you like. Each box must contain an equal number of figures. Invite your baby to fill one box by folding the figures there. Have him count how many items are in the box. After that, let him fill the second box, make sure that there are the same number of items in it, and count the total number of figures in both boxes. At first, only a few items should be included in one box - two, three. In this way, you can bring the baby to the idea that two times three is six, two times two is four, and so on. There is no need to increase the boxes and figures to infinity: at this stage it is important that the child understands the concrete, material meaning of multiplication as the sum of several identical groups of objects. The next step is memorizing the multiplication table. You need to learn by heart, like a poem. More precisely, a group of poems. Examples are "lines" in them: twice three - six, twice four - eight ... You can learn only one "poem" at a time - multiplying by two, three, four, and so on. Multiplication by five resembles a poem outwardly - its "lines" rhyme with each other, so it is easiest to remember it.

- the most difficult action for a kid, even in elementary school they start to do it later than to other sections of arithmetic. Division is the inverse procedure of multiplication, therefore, to master it, the child must already know the multiplication table. However, at first, all the same illustrative examples will do, and in this sense, division is the action that is closest and most relevant to the baby. How to divide candies for everyone so that everyone has equal shares? After all, if someone has less than others, he will be offended. It is necessary to divide fairly, and at first this can be done by the selection method: first, distribute one candy at a time, then one more ... The total number of candies must be picked up by an adult so that it is really divided among all children without a remainder. Subsequently, you can explain to the child that not all numbers can be divided by each other. In this, division is more difficult than multiplication - after all, absolutely all numbers can be multiplied. If possible, the children are also introduced to the division with the remainder: the remaining candies, which cannot be distributed equally to everyone, are taken by an adult (or they will go to the most obedient of the children).

How you can help your child

Performing arithmetic operations for a child can be simplified if you tell him about the properties of numbers from 2 to 10. For example, 4 is two times two; 5 can be obtained in different ways - add 3 to 3 or 1 to 4. Particular attention should be paid to the number 0. To simplify the count, you need to figure out the round numbers: 30 is three times 10, and 5 is half 10.

Formulas for more complex procedures

When the child gets older and already masters basic arithmetic operations, you can introduce him to the formulas for quickly adding and multiplying large numbers. There are many such formulas, and here we will give only a few.

You just need to multiply two-digit numbers by 11. For example, 23 * 11. You just need to add the digits of the first factor and write down this factor in the answer, in the middle of which write the resulting sum: 2 + 3 \u003d 5, therefore, 23 * 11 \u003d 253. If, when adding the digits, a two-digit number is obtained, then the first digit of this number is added to the first digit of the multiplier. For example, 38 * 11. 3 + 8 \u003d 11; we add the first unit to the three, and the second we write in the middle of the answer: 38 * 11 \u003d 418.

The addition of large numbers can be simplified by increasing one term by some number, which is then subtracted from the answer. For example: 358 + 340 \u003d (358 + 2) + 340-2 \u003d 360 + 340-2 \u003d 700-2 \u003d 698.

Such formulas will certainly be of interest to many adults, because they will significantly simplify the workflow, counting money and other vital operations with numbers.

Children in grades 2-3 master a new mathematical action - division. It is not easy for a student to grasp the essence of this mathematical action, so he needs the help of his parents. Parents need to understand exactly how to present new information to their child. TOP 10 examples will tell parents how to teach children how to divide numbers with a column.

Learning long division in the form of a game

Children get tired at school, they get tired of textbooks. Therefore, parents need to give up textbooks. Present information in a fun game.

You can set tasks in this way:

1 Provide play-based learning space for your child. Place his toys in a circle, and give the child pears or candy. Have a student divide 4 candies between 2 or 3 dolls. To gain understanding on the part of the child, gradually add the number of candies to 8 and 10. Even if the baby will act for a long time, do not press or shout at him. You will need patience. If the child does something wrong, correct it calmly. Then, as he completes the first action of dividing the candies between the participants in the game, he will ask him to calculate how many candies each toy got. Now the conclusion. If there were 8 candies and 4 toys, then each got 2 candies. Let your child know that sharing means distributing an equal amount of candy to all toys.

2 You can teach mathematical action using numbers. Let the student know that numbers qualify as pears or candy. Tell them that the number of pears you want to divide is the dividend. And the number of toys containing candies is a divisor.

3 Give your child 6 pears. Give him a problem: divide the number of pears between grandfather, dog and dad. Then ask him to divide 6 pears between Grandpa and Dad. Explain to your child the reason why the division is not the same.

4 Tell your student about division with remainder. Give the child 5 candies and ask him to distribute them equally between the cat and the dad. The child will have 1 candy left. Tell your child why it turned out this way. This mathematical action should be considered separately, as it can be difficult.

Learning through play can help your child quickly understand the whole process of dividing numbers. He will be able to learn that the largest number is divisible by the smallest, or vice versa. That is, the largest number are candies and the smallest are participants. In column 1, the number will be the number of sweets, and 2 - the number of participants.

Don't overload your child with new knowledge. You need to teach gradually. You need to move on to a new material when the previous material is fixed.

Learning long division using the multiplication table

Pupils up to grade 5 will be able to figure out division more quickly, provided that they know multiplication well.

Parents need to be educated that division is similar to the multiplication table. Only the actions are opposite. For clarity, you need to give an example:

• Tell the student to arbitrarily multiply the values \u200b\u200b6 and 5. The answer is 30.
• Tell the student that the number 30 is the result of a mathematical operation with two numbers: 6 and 5. Namely, the result of multiplication.
• Divide 30 by 6. As a result of the mathematical action, you get 5. The student will be able to make sure that division is the same as multiplication, but vice versa.

You can use the multiplication table for clarity of division, if the child has mastered it well.

Learning long division in a notebook

You need to start learning when the student understands the material about division in practice, using the game and the multiplication table.

You need to start dividing in this way using simple examples. So, dividing 105 by 5.

Explain the mathematical operation in detail:

• Write an example in your notebook: 105 divided by 5.
• Write it down like long division.
• Tell us that 105 is the dividend and 5 is the divisor.
• With the student, identify 1 digit that allows division. The value of the dividend is 1, this figure is not divisible by 5. But the second number is 0. As a result, you get 10, this value is allowed to divide this example. The number 5 is twice included in the number 10.
• In the division column, under the number 5, write the number 2.
• Ask the child to multiply the number 5 by 2. The result of the multiplication will be 10. This value must be written under the number 10. Next, you need to write the subtraction sign in the column. From 10 you need to subtract 10. You get 0.
• Write down in a column the number obtained as a result of subtraction - 0. 105 has a number left that did not participate in the division - 5. This number must be written down.
• As a result, you get 5. This value must be divided by 5. The result is the number 1. This number must be written under 5. The result of the division is 21.

Parents need to explain that this division has no remainder.

You can start division with numbers 6,8,9, then go to 22, 44, 66 , and after k 232, 342, 345 , etc.

Learn division with remainder

When the child learns the material about division, the task can be complicated. Division with remainder is the next step in learning. You need to explain using the available examples:

• Invite your child to divide 35 by 8. Write the problem in the column.
• To make the child as clear as possible, you can show him the multiplication table. The table clearly shows that the number 35 includes 4 times the number 8.
• Write down the number 32 under the number 35.
• The child needs to subtract 32 from 35. It turns out 3. The number 3 is the remainder.

Simple examples for a child

Using the same example, you can continue:

• When dividing 35 by 8, the remainder is 3. Add 0 to the remainder. In this case, after the number 4 in the column, you need to put a comma. The result will now be fractional.
• When dividing 30 by 8, you get 3. This figure must be written after the decimal point.
• Now you need to write 24 under the value 30 (the result of multiplying 8 by 3). As a result, you get 6. Zero also needs to be added to the number 6. It turns out 60.
• Number 8 is placed in the number 8 is included 7 times. That is, you get 56.
• If you subtract 60 from 56, you get 4. This number also needs to be signed 0. It turns out 40. In the multiplication table, the child can see that 40 is the result of multiplying 8 by 5. That is, number 8 is included in the number 40 5 times. There is no remainder. The answer looks like this - 4.375.

This example may seem difficult to a child. Therefore, you need to divide the values \u200b\u200bmany times, which will have a remainder.

Learning division through games

Parents can use division games to teach students. You can give your child coloring pages in which you need to determine the color of the pencil by dividing. It is necessary to choose coloring pages with easy examples so that the child can solve the examples in his head.

The picture will be divided into parts, which will contain the results of the division. And the colors to be used are examples. For example, red is marked with an example: 15 divided by 3. It turns out 5. You need to find a part of the picture under this number and color it. Math coloring is fun for kids. Therefore, parents should try this teaching method.

Learning to divide the smallest number by the largest number

Division by this method assumes that the quotient will start at 0, followed by a comma.

In order for the student to correctly assimilate the information received, he needs to give an example of such a plan.

Instructions

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

First, work from numbers to single digits. This technique is best practiced using knowledge of the multiplication table. The more of this practice, the better. The skills of such a division should be brought to automatism, 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 units.

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

29 times 2 equals 54 - not enough;
29 x 3 \u003d 87 - 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 above example, the second digit of the divisor is 9. Think how much you need to multiply the number 9 so that the number of units of the product equals 7? The answer in this case is only one - by 3. This greatly facilitates the problem of two-digit division. Test your guess by multiplying the whole number 29.

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

Sources:

• multiplying two-digit numbers by two-digit tables

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

You will need

• A sheet of paper in a cage
• pen or pencil

Instructions

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

Move the left-most digit of the dividend, but not yet wrap, under the last horizontal bar. Mark the transferred digit of the dividend with a dot.

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

A column? How can you independently practice the skill of long division at home if your child has not learned something at school? Column sharing is taught in grade 2-3, for parents, of course, this is a passed stage, but if you wish, you can remember the correct entry and explain to your student what he needs in life.

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What should a 2-3 grade child know to learn long division?

How to correctly explain to a child of 2-3 grades division by a column so that in the future he does not have problems? First, let's check if there are any gaps in knowledge. Make sure that:

• the child freely performs addition and subtraction operations;
• knows the digits of numbers;
• knows by heart.

How to explain to the child the meaning of the action "division"?

• The child needs to explain everything with a visual example.

Ask family or friends to share something. For example, candy, cake pieces, etc. It is important that the child understands the essence - you need to divide equally, i.e. without a remainder. Practice with different examples.

Let's say 2 groups of athletes have to sit on the bus. It is known how many athletes are in each group and how many seats are on the bus. You need to find out how many tickets one and the second group need to buy. Or 24 notebooks need to be distributed to 12 students, how much each will get.

• When the child learns the essence of the principle of division, show the mathematical record of this operation, name the components.
• Explain that division is the opposite of multiplication, multiplication inside out.

It is convenient to show the relationship between division and multiplication on the example of a table.

For example, 3 times 4 is 12.
3 is the first factor;
4 is the second factor;
12 - product (result of multiplication).

If 12 (product) is divided by 3 (first factor), we get 4 (second factor).

Division Components are called differently:

12 - dividend;
3 - divider;
4 - quotient (result of division).

How to explain to a child dividing a two-digit number by a one-digit number not in a column?

It is easier for us, adults, to write down the “corner” in the old fashioned way - and that's the end of it. BUT! Children have not yet passed long division, what should I do? How to teach a child to divide a two-digit number by a one-digit number without using a column record?

Take 72: 3 for example.

It's that simple! We decompose 72 into numbers that can be easily divided orally by 3:
72=30+30+12.

Everything immediately became clear: we can divide 30 by 3, and the child can easily divide 12 by 3.
All that remains is to add up the results, i.e. 72: 3 \u003d 10 (obtained when 30 divided by 3) + 10 (30 divided by 3) + 4 (12 divided by 3).

72:3=24
We didn’t use long division, but the child understood the reasoning and performed the calculations without difficulty.

After simple examples, you can proceed to the study of long division, teach the child to correctly write down examples "in a corner". First, use only division examples without remainder.

How to explain long division to a child: an algorithm for solving

Large numbers are difficult to divide in your head, it's easier to use long division notation. To teach a child to perform calculations correctly, follow the algorithm:

• Determine where the dividend and divisor are in the example. Ask your child to name the numbers (what we will divide by).

213:3
213 - dividend
3 - divisor

• Write down the dividend - "corner" - divisor.

• Determine how much of the dividend we can use to divide by a given number.

We argue like this: 2 is not divisible by 3, so we take 21.

• Determine how many times the divider "fits" in the selected part.

21 divided by 3 - we take 7.

• Multiply the divisor by the selected number, write the result under the "corner".

7 times 3 - we get 21. We write down.

• Find the difference (remainder).

At this point in your reasoning, teach your child to test themselves. It is important that he understands that the result of the subtraction should ALWAYS be less than the divisor. If it didn't work out, you need to increase the selected number and perform the action again.

• Repeat the steps until the remainder is 0.

How to reason correctly to teach a 2-3 grade child to divide by a column

How to explain division to a child 204:12=?
1. We write it down in a column.
204 is the dividend, 12 is the divisor.

2. 2 is not divisible by 12, so we take 20.
3. To divide 20 by 12 we take 1. Write down 1 under the "corner".
4. 1 multiplied by 12 we get 12. Write under 20.
5. 20 minus 12 is 8.
Checking ourselves. 8 less than 12 (divisor)? Ok, that's right, let's move on.

6. Next to 8 we write 4. 84 divided by 12. How much should 12 be multiplied to get 84?
It's hard to say right away, let's try to use the selection method.
Let's take, for example, 8, but don't write it down yet. We count verbally: 8 times 12 we get 96. And we have 84! Doesn't fit.
Trying smaller ones ... For example, let's take 6. Check ourselves verbally: 6 times 12 equals 72. 84-72 \u003d 12. We got the same number as our divisor, but it should be either zero or less than 12. So the optimal number is 7!

7. We write 7 under the "corner" and perform the calculations. 7 times 12 gets 84.
8. We write down the result in a column: 84 minus 84 is zero. Hurrah! We decided correctly!

So, you taught the child to divide by a column, now it remains to work out this skill, bring it to automatism.

Why is it difficult for children to learn long division?

Remember that problems with math arise from the inability to quickly do simple arithmetic operations. In elementary school, you need to work out and bring the addition and subtraction to automatism, to learn the multiplication table "from cover to cover". All! The rest is a matter of technology, and it is developed with practice.

Be patient, do not be lazy to explain to the child once again what he did not learn in the lesson, it is tedious, but meticulous to understand the reasoning algorithm and say each intermediate operation before voicing the ready answer. Give additional examples to practice skills, play math games - this will bear fruit and you will see the results and rejoice at the success of the child very soon. Be sure to show where and how you can apply the knowledge gained in everyday life.

Dear Readers! Tell us how you teach your children to divide in a column, what difficulties you had to face and in what ways you overcame them.