Corner division online. The secret of an experienced teacher: how to explain long division to a child
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 division, it is necessary that by the time of teaching he has already mastered such mathematical operations as addition, subtraction, and also has a clear understanding 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 have already written about this. This article may be useful to 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 an understanding that division is the division of something into equal parts. The easiest way to teach a child this is to invite him to share a certain number of items among his friends or family members.
Let's say you take 8 identical cubes and ask your child to divide them into two equal parts - for him and for another person. Vary and complicate the task, invite the child to divide 8 cubes not between two, but into four people. Analyze the result with him. Change the components, try with a different number of objects and people into whom 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 at the next stage, when the child needs to understand that division is the inverse operation 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 the relationship between multiplication and division using any example.
Example: 4x2=8. Remind your child that the result of multiplication is the product of two numbers. After this, 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 a different factor that was not used in the operation.
You also need to teach the young student the names of the categories that describe the operation of division - “dividend”, “divisor” and “quotient”. Using an example, show which numbers are the dividend, divisor and quotient. Consolidate this knowledge, it is necessary for further training!
Essentially, you need to teach your child the multiplication table in reverse, and it is necessary to memorize it just as well as the multiplication table itself, because this will be necessary when you start learning long division.
Divide by column - let's give an example
Before starting the lesson, remember with your child what the numbers are called during the division operation. What is a “divisor”, “divisible”, “quotient”? Teach how to accurately and quickly identify these categories. This will be very useful when teaching your child how 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 that is what needs to be calculated.
Step 1. We write down the numbers, separating them with a “corner”.
Step 2. Show the student the numbers of the dividend 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 your 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 recorded will be 1.
Step 3. Let's move on to the design of division by column:
We multiply the divisor 7x1 and get 7. We write the resulting result under the first number of our dividend 938 and subtract it, as usual, in a column. That is, from 9 we subtract 7 and get 2.
We write down the result.
Step 4. The number 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 assign 3 to the resulting number 2.
Step 5. Next we proceed 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 all that remains is to find the last number of our quotient. Using the already familiar algorithm, we continue to do calculations in the column. By subtracting in column (23-21) we get the difference. It equals 2.
From 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 number into the result. So, we get the quotient obtained by dividing by a column = 134.
How to teach a child division - reinforcing the skill
The main reason why many schoolchildren have problems with mathematics is the inability to quickly do simple arithmetic calculations. And all mathematics in elementary school is built on this basis. 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 his head, the correct teaching methods and consolidation of the skill are necessary. To do this, we advise you to use today’s popular textbooks on learning division skills. Some are designed for children to study with their parents, others for independent work.
- "Division. Level 3. Workbook" from the largest international center for additional education Kumon
- "Division. Level 4. Workbook" from Kumon
- “Not Mental Arithmetic. A system for teaching a child fast multiplication and division. In 21 days. Notepad-simulator." from Sh. Akhmadulin - author of best-selling educational books
The most important thing when you teach a child long division is to master the algorithm, which, in general, is quite simple.
If a child is good at using the multiplication table and “reverse” division, he will not have any difficulties. However, it is very important to constantly practice the acquired skill. Don't stop there once you realize that your child has grasped the essence of the method.
In order to easily teach your child division operations you need:
- So that at the age of two or three years he masters the whole-part relationship. He must 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 can freely operate with addition and subtraction of numbers and understand the essence of the processes of multiplication and division.
In order for a child to enjoy mathematics, it is necessary to arouse his interest in mathematics and mathematical operations, not only during learning, but also in everyday situations.
Therefore, encourage and develop your child’s observation skills, draw analogies with mathematical operations (counting and division operations, analysis of “part-whole” relationships, etc.) during construction, games and observations of nature.
Teacher, child development center specialist
Druzhinina Elena
website specifically for the project
Video story for parents on how to correctly explain long division to a child:
The division of natural numbers, especially multi-digit ones, is conveniently carried out by a special method, which is called division by a column (in a column). You can also find the name corner division. Let us immediately note that the column can be used to both divide natural numbers without a remainder and divide natural numbers with a remainder.
In this article we will look at how long division is performed. Here we will talk about recording rules and all intermediate calculations. First, let's focus on dividing a multi-digit natural number by a single-digit number with a column. After this, we will focus on cases when both the dividend and the divisor are multi-valued natural numbers. The entire theory of this article is provided with typical examples of division by a column of natural numbers with detailed explanations of the solution process and illustrations.
Page navigation.
Rules for recording when dividing by a column
Let's start by studying the rules for writing the dividend, divisor, all intermediate calculations and results when dividing natural numbers by a column. Let's say right away that it is most convenient to do column division in writing on paper with a checkered line - this way there is less chance of straying from the desired row and column.
First, the dividend and divisor are written in one line from left to right, after which a symbol of the form is displayed between the written numbers. For example, if the dividend is the number 6 105 and the divisor is 5 5, then their correct notation when dividing into a column will be as follows:
Look at the following diagram to illustrate where to write the dividend, divisor, quotient, remainder, and intermediate calculations in long division.
From the above diagram it is clear that the desired quotient (or incomplete quotient when dividing with a remainder) will be written below the divisor under the horizontal line. And intermediate calculations will be carried out below the dividend, and you need to take care in advance about the availability of space on the page. In this case, you should be guided by the rule: the greater the difference in the number of characters in the entries of the dividend and divisor, the more space will be required. For example, when dividing by a column the natural number 614,808 by 51,234 (614,808 is a six-digit number, 51,234 is a five-digit number, the difference in the number of characters in the records is 6−5 = 1), intermediate calculations will require less space than when dividing the numbers 8 058 and 4 (here the difference in the number of characters is 4−1=3). To confirm our words, we present complete records of division by a column of these natural numbers:
Now you can proceed directly to the process of dividing natural numbers by a column.
Column division of a natural number by a single-digit natural number, column division algorithm
It is clear that dividing one single-digit natural number by another is quite simple, and there is no reason to divide these numbers into a column. However, it will be helpful to practice your initial long division skills with these simple examples.
Example.
Let us need to divide with a column of 8 by 2.
Solution.
Of course, we can perform division using the multiplication table, and immediately write down the answer 8:2=4.
But we are interested in how to divide these numbers with a column.
First, we write down the dividend 8 and the divisor 2 as required by the method:
Now we begin to find out how many times the divisor is contained in the dividend. To do this, we sequentially multiply the divisor by the numbers 0, 1, 2, 3, ... until the result is a number equal to the dividend (or a number greater than the dividend, if there is a division with a remainder). If we get a number equal to the dividend, then we immediately write it under the dividend, and in place of the quotient we write the number by which we multiplied the divisor. If we get a number greater than the dividend, then under the divisor we write the number calculated at the penultimate step, and in place of the incomplete quotient we write the number by which the divisor was multiplied at the penultimate step.
Let's go: 2·0=0 ; 2·1=2 ; 2·2=4 ; 2·3=6 ; 2·4=8. We have received a number equal to the dividend, so we write it under the dividend, and in place of the quotient we write the number 4. In this case, the record will take the following form:
The final stage of dividing single-digit natural numbers with a column remains. Under the number written under the dividend, you need to draw a horizontal line, and subtract the numbers above this line in the same way as is done when subtracting natural numbers in a column. The number resulting from the subtraction will be the remainder of the division. If it is equal to zero, then the original numbers are divided without a remainder.
In our example we get
Now we have before us a completed recording of the column division of the number 8 by 2. We see that the quotient of 8:2 is 4 (and the remainder is 0).
Answer:
8:2=4 .
Now let's look at how a column divides single-digit natural numbers with a remainder.
Example.
Divide 7 by 3 using a column.
Solution.
At the initial stage, the entry looks like this:
We begin to find out how many times the dividend contains the divisor. We will multiply 3 by 0, 1, 2, 3, etc. until we get a number equal to or greater than the dividend 7. We get 3·0=0<7
; 3·1=3<7
; 3·2=6<7
; 3·3=9>7 (if necessary, refer to the article comparing natural numbers). Under the dividend we write the number 6 (it was obtained at the penultimate step), and in place of the incomplete quotient we write the number 2 (the multiplication was carried out by it at the penultimate step).
It remains to carry out the subtraction, and the division by a column of single-digit natural numbers 7 and 3 will be completed.
Thus, the partial quotient is 2 and the remainder is 1.
Answer:
7:3=2 (rest. 1) .
Now you can move on to dividing multi-digit natural numbers by columns into single-digit natural numbers.
Now we'll figure it out long division algorithm. At each stage, we will present the results obtained by dividing the multi-digit natural number 140,288 by the single-digit natural number 4. This example was not chosen by chance, since when solving it we will encounter all possible nuances and will be able to analyze them in detail.
First we look at the first digit on the left in the dividend notation. If the number defined by this figure is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add to the consideration the next digit on the left in the record of the dividend, and continue to work with the number determined by the two digits under consideration. For convenience, we highlight in our notation the number with which we will work.
The first digit from the left in the dividend 140288 is the digit 1. The number 1 is less than the divisor 4, so we also look at the next digit on the left in the notation of the dividend. At the same time, we see the number 14, with which we have to work further. We highlight this number in the dividend notation.
The following points from the second to the fourth are repeated cyclically until the division of natural numbers by a column is completed.
Now we need to determine how many times the divisor is contained in the number we are working with (for convenience, let's denote this number as x). To do this, we sequentially multiply the divisor by 0, 1, 2, 3, ... until we get the number x or a number greater than x. When the number x is obtained, we write it under the highlighted number according to the recording rules used when subtracting natural numbers in a column. The number by which the multiplication was carried out is written in place of the quotient during the first pass of the algorithm (in subsequent passes of 2-4 points of the algorithm, this number is written to the right of the numbers already there). When we get a number that is greater than the number x, then under the highlighted number we write the number obtained at the penultimate step, and in place of the quotient (or to the right of the numbers already there) we write the number by which the multiplication was carried out at the penultimate step. (We carried out similar actions in the two examples discussed above).
Multiply the divisor 4 by the numbers 0, 1, 2, ... until we get a number that is equal to 14 or greater than 14. We have 4·0=0<14
, 4·1=4<14
, 4·2=8<14
, 4·3=12<14
, 4·4=16>14. Since at the last step we received the number 16, which is greater than 14, then under the highlighted number we write the number 12, which was obtained at the penultimate step, and in place of the quotient we write the number 3, since in the penultimate point the multiplication was carried out precisely by it.
At this stage, from the selected number, subtract the number located under it using a column. The result of the subtraction is written under the horizontal line. However, if the result of the subtraction is zero, then it does not need to be written down (unless the subtraction at that point is the very last action that completely completes the long division process). Here, for your own control, it would not be amiss to compare the result of the subtraction with the divisor and make sure that it is less than the divisor. Otherwise, a mistake was made somewhere.
We need to subtract the number 12 from the number 14 with a column (for the correctness of the recording, we must remember to put a minus sign to the left of the numbers being subtracted). After completing this action, the number 2 appeared under the horizontal line. Now we check our calculations by comparing the resulting number with the divisor. Since the number 2 is less than the divisor 4, you can safely move on to the next point.
Now, under the horizontal line to the right of the numbers located there (or to the right of the place where we did not write down the zero), we write down the number located in the same column in the notation of the dividend. If there are no numbers in the record of the dividend in this column, then the division by column ends there. After this, we select the number formed under the horizontal line, accept it as a working number, and repeat points 2 to 4 of the algorithm with it.
Under the horizontal line to the right of the number 2 already there, we write down the number 0, since it is the number 0 that is in the record of the dividend 140,288 in this column. Thus, the number 20 is formed under the horizontal line.
We select this number 20, take it as a working number, and repeat with it the actions of the second, third and fourth points of the algorithm.
Multiply the divisor 4 by 0, 1, 2, ... until we get the number 20 or a number that is greater than 20. We have 4·0=0<20
, 4·1=4<20
, 4·2=8<20
, 4·3=12<20
, 4·4=16<20
, 4·5=20
. Так как мы получили число, равное числу 20
, то записываем его под отмеченным числом, а на месте частного, справа от уже имеющегося там числа 3
записываем число 5
(на него производилось умножение).
We carry out the subtraction in a column. Since we are subtracting equal natural numbers, then by virtue of the property of subtracting equal natural numbers, the result is zero. We do not write down the zero (since this is not the final stage of division by a column), but we remember the place where we could write it (for convenience, we will mark this place with a black rectangle).
Under the horizontal line to the right of the remembered place we write down the number 2, since it is precisely it that is in the record of the dividend 140,288 in this column. Thus, under the horizontal line we have the number 2.
We take the number 2 as the working number, mark it, and we will once again have to perform the actions of 2-4 points of the algorithm.
We multiply the divisor by 0, 1, 2 and so on, and compare the resulting numbers with the marked number 2. We have 4·0=0<2
, 4·1=4>2. Therefore, under the marked number we write the number 0 (it was obtained at the penultimate step), and in the place of the quotient to the right of the number already there we write the number 0 (we multiplied by 0 at the penultimate step).
We perform the subtraction in a column, we get the number 2 under the horizontal line. We check ourselves by comparing the resulting number with the divisor 4. Since 2<4
, то можно спокойно двигаться дальше.
Under the horizontal line to the right of the number 2, add the number 8 (since it is in this column in the entry for the dividend 140 288). Thus, the number 28 appears under the horizontal line.
We take this number as a working number, mark it, and repeat steps 2-4.
There shouldn't be any problems here if you have been careful up to now. Having completed all the necessary steps, the following result is obtained.
All that remains is to carry out the steps from points 2, 3, 4 one last time (we leave this to you), after which you will get a complete picture of dividing the natural numbers 140,288 and 4 into a column:
Please note that the number 0 is written in the very bottom line. If this were not the last step of division by a column (that is, if in the record of the dividend there were numbers left in the columns on the right), then we would not write this zero.
Thus, looking at the completed record of dividing the multi-digit natural number 140,288 by the single-digit natural number 4, we see that the quotient is the number 35,072 (and the remainder of the division is zero, it is in the very bottom line).
Of course, when dividing natural numbers by a column, you will not describe all your actions in such detail. Your solutions will look something like the following examples.
Example.
Perform long division if the dividend is 7 136 and the divisor is a single-digit natural number 9.
Solution.
At the first step of the algorithm for dividing natural numbers by columns, we get a record of the form
After performing the actions from the second, third and fourth points of the algorithm, the column division record will take the form
Repeating the cycle, we will have
One more pass will give us a complete picture of the column division of the natural numbers 7,136 and 9
Thus, the partial quotient is 792, and the remainder is 8.
Answer:
7 136:9=792 (rest. 8) .
And this example demonstrates what long division should look like.
Example.
Divide the natural number 7,042,035 by the single-digit natural number 7.
Solution.
The most convenient way to do division is by column.
Answer:
7 042 035:7=1 006 005 .
Column division of multi-digit natural numbers
We hasten to please you: if you have thoroughly mastered the column division algorithm from the previous paragraph of this article, then you almost already know how to perform column division of multi-digit natural numbers. This is true, since stages 2 to 4 of the algorithm remain unchanged, and only minor changes appear in the first point.
At the first stage of dividing multi-digit natural numbers into a column, you need to look not at the first digit on the left in the notation of the dividend, but at the number of them equal to the number of digits contained in the notation of the divisor. If the number defined by these numbers is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add to the consideration the next digit on the left in the notation of the dividend. After this, the actions specified in paragraphs 2, 3 and 4 of the algorithm are performed until the final result is obtained.
All that remains is to see the application of the column division algorithm for multi-valued natural numbers in practice when solving examples.
Example.
Let's perform column division of multi-digit natural numbers 5,562 and 206.
Solution.
Since the divisor 206 contains 3 digits, we look at the first 3 digits on the left in the dividend 5,562. These numbers correspond to the number 556. Since 556 is greater than the divisor 206, we take the number 556 as a working number, select it, and move on to the next stage of the algorithm.
Now we multiply the divisor 206 by the numbers 0, 1, 2, 3, ... until we get a number that is either equal to 556 or greater than 556. We have (if multiplication is difficult, then it is better to multiply natural numbers in a column): 206 0 = 0<556
, 206·1=206<556
, 206·2=412<556
, 206·3=618>556. Since we received a number that is greater than the number 556, then under the highlighted number we write the number 412 (it was obtained at the penultimate step), and in place of the quotient we write the number 2 (since we multiplied by it at the penultimate step). The column division entry takes the following form:
We perform column subtraction. We get the difference 144, this number is less than the divisor, so you can safely continue performing the required actions.
Under the horizontal line to the right of the number there we write the number 2, since it is in the record of the dividend 5562 in this column:
Now we work with the number 1,442, select it, and go through steps two through four again.
Multiply the divisor 206 by 0, 1, 2, 3, ... until you get the number 1442 or a number that is greater than 1442. Let's go: 206·0=0<1 442
, 206·1=206<1 442
, 206·2=412<1 332
, 206·3=618<1 442
, 206·4=824<1 442
, 206·5=1 030<1 442
, 206·6=1 236<1 442
, 206·7=1 442
. Таким образом, под отмеченным числом записываем 1 442
, а на месте частного правее уже имеющегося там числа записываем 7
:
We carry out the subtraction in a column, we get zero, but we don’t write it down right away, we just remember its position, because we don’t know whether the division ends here, or whether we’ll have to repeat the steps of the algorithm again:
Now we see that we cannot write any number under the horizontal line to the right of the remembered position, since there are no digits in the record of the dividend in this column. Therefore, this completes the division by column, and we complete the entry:
- Mathematics. Any textbooks for 1st, 2nd, 3rd, 4th grades of general education institutions.
- Mathematics. Any textbooks for 5th grade of general education institutions.
Teaching your child long division is easy. It is necessary to explain the algorithm of this action and consolidate the material covered.
- According to the school curriculum, division by columns begins to be explained to children in the third grade. Students who grasp everything on the fly quickly understand this topic
- But, if the child got sick and missed math lessons, or he did not understand the topic, then the parents must explain the material to the child themselves. It is necessary to convey information to him as clearly as possible
- Moms and dads must be patient during the child’s educational process, showing tact towards their child. Under no circumstances should you yell at your child if he doesn’t succeed in something, because this can discourage him from doing anything.
Important: In order for a child to understand the division of numbers, he must thoroughly know the multiplication table. If your baby doesn't know multiplication well, he won't understand division.
During extracurricular activities at home, you can use cheat sheets, but the child must learn the multiplication table before starting the topic “Division.”
So, how to explain to a child division by column:
- Try to explain in small numbers first. Take counting sticks, for example 8 pieces
- Ask your child how many pairs are there in this row of sticks? Correct - 4. So, if you divide 8 by 2, you get 4, and when you divide 8 by 4, you get 2
- Let the child divide another number himself, for example, a more complex one: 24:4
- When the baby has mastered dividing prime numbers, then you can move on to dividing three-digit numbers into single-digit numbers.
Division is always a little more difficult for children than multiplication. But diligent additional studies at home will help the child understand the algorithm of this action and keep up with his peers at school.
Start with something simple—dividing by a single digit number:
Important: Calculate in your head so that the division comes out without a remainder, otherwise the child may get confused.
For example, 256 divided by 4:
- Draw a vertical line on a piece of paper and divide it in half from the right side. Write the first number on the left and the second number on the right above the line.
- Ask your child how many fours fit in a two - not at all
- Then we take 25. For clarity, separate this number from above with a corner. Ask the child again 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 to get the correct answer.
- Write down the number 24 under 25, and underline it to write down the answer - 1
- Ask again: how many fours can fit in a unit - not at all. Then we bring down the number “6” to one
- It turned out 16 - how many fours fit in this number? Correct - 4. Write “4” next to “6” in the answer
- Under 16 we write 16, underline it 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 division by a single digit number, you can move on. Written division by a two-digit number is a little more difficult, but if the child 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 select numbers correctly and it will be easy for him to divide complex numbers.
Do this simple action together: 184:23 - how to explain:
- Let's first divide 184 by 20, it turns out to be approximately 8. But we do not write the number 8 in the answer, since this is a test number
- Let's check if 8 is suitable or not. We multiply 8 by 23, we get 184 - this is exactly the number that is in our divisor. The answer will be 8
Important: For your child to understand, try taking 9 instead of 8, let him multiply 9 by 23, it turns out 207 - this is more than what we have in the divisor. The number 9 does not suit us.
So gradually the baby will understand division, and it will be easy for him to divide more complex numbers:
- Divide 768 by 24. Determine the first digit of the quotient - divide 76 not by 24, but by 20, we get 3. Write 3 in the answer under the line on the right
- Under 76 we write 72 and draw a line, write down the difference - it turns out 4. Is this number divisible by 24? No - we take down 8, it turns out 48
- Is 48 divisible by 24? That's right - yes. It turns out 2, write this number as the answer
- The result is 32. Now we can check whether we performed the division operation correctly. Do the multiplication 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 it is necessary 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:
- Let's divide 146064 by 716. Take 146 first - ask your child whether this number is divisible by 716 or not. That's right - no, then we take 1460
- How many times can the number 716 fit in the number 1460? Correct - 2, so we write this number in the answer
- We multiply 2 by 716, we get 1432. We write this figure under 1460. The difference is 28, we write it under the line
- Let's take down 6. Ask a child - is 286 divisible by 716? That's right - no, so we write 0 in the answer next to 2. We also remove the number 4
- Divide 2864 by 716. Take 3 - a little, 5 - a lot, which means you get 4. Multiply 4 by 716, you get 2864
- Write 2864 under 2864, the difference is 0. Answer 204
Important: To check that the division is performed correctly, multiply together with your child in a column - 204x716 = 146064. The division is done correctly.
The time has come to explain to the child 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 using a simple example: 35:8=4 (remainder 3):
- How many eights fit in 35? Correct - 4. 3 left
- Is this number divisible by 8? That's right - no. It turns out the remainder is 3
After this, the child should learn that division can be continued by adding 0 to the number 3:
- The answer contains the number 4. After it we write a comma, since adding a zero indicates that the number will be a fraction
- It turns out 30. Divide 30 by 8, it turns out 3. Write it down, and under 30 we write 24, underline it and write 6
- We add the number 0 to number 6. Divide 60 by 8. Take 7 each, it turns out 56. Write under 60 and write down the difference 4
- To the number 4 we add 0 and divide by 8, we get 5 - write it down as the answer
- Subtract 40 from 40, we get 0. So, the answer is: 35:8 = 4.375
Advice: If your child doesn’t understand something, don’t get angry. Let a couple of days pass and try again to explain the material.
Mathematics lessons at school will also reinforce knowledge. Time will pass and the child will quickly and easily solve any division problems.
The algorithm for dividing numbers is as follows:
- Make an estimate of the number that will appear in the answer
- Find the first incomplete dividend
- Determine the number of digits in the quotient
- Find the numbers in each digit of the quotient
- Find the remainder (if there is one)
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 working with your child, often give him examples of how to perform the estimate. He must quickly calculate the answer in his head. 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 must have the correct answer.
Condition for the child: Among several examples, only one was solved correctly. Find him in a minute.
Video: Arithmetic game for children addition, subtraction, division, multiplication
Video: Educational cartoon Mathematics Learning by heart multiplication tables and division by 2
Long division is an integral part of the school curriculum and necessary knowledge for a child. To avoid problems in lessons and with their implementation, you should give your child basic knowledge from a young age.
It is much easier to explain certain things and processes to a child in a playful way, rather than 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 are constantly exposed to different mathematical terms without even knowing where they come from. After all, many mothers, in the form of a game, explain to the child that dads are bigger than a plate, it’s farther to go to kindergarten than to the store, and other simple examples. All this gives the child an initial impression of mathematics, even before the child enters first grade.
To teach a child to divide without a remainder, and later with a remainder, you need to directly invite the child to play games with division. Divide, for example, candy among yourself, and then add the next participants in turn.
First, the child will divide the candies, giving one to each participant. And at the end you will come to a conclusion together. It should be clarified that “sharing” means everyone has the same number of candies.
If you need to explain this process using numbers, you can give an example in the form of a game. We can say that a number is candy. It should be explained that the number of candies that must be divided between the participants is divisible. And the number of people these candies are divided into is the divisor.
Then you should show all this clearly, give “live” examples in order to quickly teach the baby to divide. By playing, he will understand and learn everything much faster. For now, it will be difficult to explain the algorithm, and now it is not necessary.
How to teach your child long division
Explaining different mathematical operations to your child is good preparation for going to class, especially math class. If you decide to move on to teaching your child long division, then he has already learned such operations as addition, subtraction, and what the multiplication table is.
If this still causes some difficulties for him, then he needs to improve all this knowledge. It is worth recalling the algorithm of actions of the previous processes and teaching them to freely use their knowledge. Otherwise, the baby will simply get confused in all the processes and stop understanding anything.
To make this easier to understand, there is now a division table for kids. Its principle is the same as that of multiplication tables. But is such a table necessary if the child knows the multiplication table? It depends on the school and teacher.
When forming the concept of “division”, it is necessary to do everything in a playful way, to give all examples on things and objects familiar to the child.
It is very important that all items are of an even number, so that the baby can understand that the total is equal parts. This will be correct, because it will allow the baby to realize that division is the reverse process of multiplication. If there are an odd number of items, the result will come out with a remainder and the baby will get confused.
Multiply and divide using a table
When explaining to a child the relationship between multiplication and division, it is necessary to clearly demonstrate all this with 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 always be a different factor that did not take part in the division.
It is also necessary to explain to the child the correct names of the categories that perform division: dividend, divisor, quotient. Again, use an example to show which is a specific category.
Column division is not a very complicated thing; it has its own easy algorithm that the baby needs to be taught. After consolidating all these concepts and knowledge, you can move on to further training.
In principle, parents should learn the multiplication table in reverse order with their beloved child and memorize it by heart, as this will be necessary when learning long division.
This must be done before going to first grade, so that it is 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 available both at school and in notebooks, so you don’t have to bring a separate table to school.
Divide using 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 be able to divide these numbers into the correct categories without errors.
The most important thing when learning long division is to master the algorithm, which, in general, is quite simple. But first, explain to your child the meaning of the word “algorithm” if he has forgotten it or has not studied it before.
If the baby is well versed in the multiplication and inverse division tables, he will not have any difficulties.
However, you cannot dwell on the results obtained for long; you need to regularly train the acquired skills and abilities. Move on as soon as it becomes clear that the baby understands the principle of the method.
It is necessary to teach the child 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 your baby the division process, you need to:
- at 2-3 years old understanding of the whole-part relationship.
- at 6-7 years old, the child should be able to fluently perform addition, subtraction and understand the essence of multiplication and division.
It is necessary to stimulate the child’s interest in mathematical processes so that this lesson at school brings him pleasure and a desire to learn, and not only to motivate him in the classroom, but also in life.
The child must carry different instruments for math lessons and learn to use them. However, if it is difficult for a child to carry everything, then you should not overload him.