« Oral techniques of multiplication and division of three-digit numbers. "

Objectives:

1. To multiply and divide multivalued numbers;

2. Repeat the multiplication property and the multiplication property of the amount by the number;

3. Repeat units of measurement.

4. Fasten knowledge of multiplication table.

5. Form computing skills and develop logical thinking.

6. Develop the cognitive activity of students in the study of mathematics.

Tasks:forming the ability to search for information and operate it;

develop the ability to reasonably justify and defend the judgment expressed;

develop the motivation of learning activities and interest in acquiring knowledge and ways of action;

rail interest in the subject, activity.

Org. moment

Children, today a wonderful day. Look, I smile you and you smile to me. Turn to each other and smile. Well done, sitting per desk. Feel how warmth and light has become in our class from smiles.

Grach offers you a game called "Tangram". Take envelopes with geometric shapes and make up the silhouette pattern of the ridge. (work in pairs).

- Look, what rhk turned out with me. Compare.

- Tell me, what figures used?

- How many triangles?

- What other geometric shapes do you know?

Grac ashes to remember what you studied at last lessons, as this knowledge will come to us today?

1. Read the numbers: 540, 700, 210, 900, 650, 380,400, 820

- Specify the amount of hundreds and tens in each of them.

2. Name the number in which: 87дs., 5cot., 64дs., 3Sot., 25 degrees, 49Des.,

7 hundred., 11des.

3. Increase by 10 times: 42, 27, 91, 65, 73, 58.

2. Blitz survey

1. Waterhouse has two weeks and 4 more days. How many days stayed by Volodya at her grandmother? (18 days)

2. I walked 26 meters. He sailed 4 meters less than Seryozha. How many meters sailed seryozha? (30 meters)

3. In the garden 38 old apple trees and 19 young. How many less young apple trees than old? (for 19 apple trees)

- Well done! Well worked. Let `s have some rest.

3. Fizminutka

4. Summing up to the topic.

Which groups can be divided by the following expressions:

15 ∙ 4 200 ∙ 4

320 ∙ 2 25 ∙ 3

Record them in 2 columns, find a value.

- What groups did you share these expressions?

- What tasks are you more difficult to cope? (What do you think, why?)

- What was the difficulty?

(In that one column - with three-digits)

- Try to put the learning task for today's lesson.

(Learn to multiply and divide three-digit numbers in oral way)

5. Message of the lesson theme. Setting educational tasks.

Theme of today's lesson: "Receptions of oral calculations within 1000"

- What should we do for this to make it easier to solve such examples? ( Listen to the explanation of the teacher, read information in the textbook, listen to classmates, remember the multiplication and division table, to practice solve such examples, etc.)

6. Acquaintance with the new material.

Let's try to solve the expression: 120 * 4. To verbally multiply the number on the unambiguous multiplier performs the action, starting multiplication from units, as with written multiplication, and otherwise: first hundreds, 100 * 4 \u003d 400 are multiplied, then dozens of 20 * 4 \u003d 80, after a unit, but we will learn later As a result, we fold the numbers 400 + 80 \u003d 480

Let's try to solve the expression with the division: 820: 2. To verbally divide the number on a unambiguous multiplier, perform the action as with a multiplication method. First we divide hundreds of 800: 2 \u003d 400, then tens of 20: 2 \u003d 10, then we perform the addition of the results obtained 400 + 10 \u003d 410 let's try to perform together:

230 * 4 = 200 * 4 + 30 * 4=920; 360: 4 =300:4(75)+60:4(15)=90

150 * 4 =100*4+50*4=600; 680: 4 =600:4(150)+80:4(20)=170

A TASK. One rhose, following the tractor plow, is able to destroy 420 worms - pests of plants per day. How many worms will eat grace for 2 days?

- What is said in terms of the task?

- What question must be answered?

- How many actions need to do to do this?

- How to find out how many worms will eat grace in two days?

- Record the solution to the task in the notebook.

- What answer did you get?

- Who agrees with ... Show.

- How did you think?

- Guys, you coped very well with the tasks that birds offered to you.

The outcome of the lesson. Reflection.

- Guys, did we handle the tasks?

The division is one of the four main mathematical operations (addition, subtraction, multiplication). The division, as well as other operations, is important not only in mathematics, but also in everyday life. For example, you are a whole class (person 25) Share money and buy a gift to the teacher, but not everyone will pass. So I will need to share at all. A division operation comes to work that will help you solve this task.

Delivery is an interesting operation, which we will make sure with you in this article!

Division of numbers

So, a little theory, and then practice! What is division? Delivery is a breaking on equal parts of something. That is, it can be a package of candies to be divided into equal parts. For example, in a bag of 9 sweets, and the person who wants to get them - three. Then you need to divide these 9 candies for three people.

This is written as follows: 9: 3, the answer will be the number 3. That is, the division of the number 9 to the number 3 shows the number of numbers three of the number 9. The reverse action, verification, will multiply. 3 * 3 \u003d 9. Right? Absolutely.

So, consider an example 12: 6. To begin with, we denote the names to each component of the example. 12 - Delimi, that is. The number that is divided into parts. 6 - divider, this is the number of parts to which divide is divided. And the result will be the number that is called "Private".

We divide 12 to 6, the answer will be the number 2. Check the solution can be multiplying: 2 * 6 \u003d 12. It turns out that the number 6 is contained 2 times among 12.

Division with the rest

What is the division with the residue? This is the same division, only as a result is not a flat number, as shown above.

For example, we divide 17 to 5. Since, the largest number divided by 5 to 17 is 15, then the answer will be 3 and the residue 2, and it is written as follows: 17: 5 \u003d 3 (2).

For example, 22: 7. In the same way, the maximum number divided by 7 to 22 is determined. This is a number 21. The answer will then be: 3 and the residue 1. A recorded: 22: 7 \u003d 3 (1).

Division at 3 and 9

A special case of division will be divided into number 3 and number 9. If you want to know whether to share a number by 3 or 9 without a balance, then you will need:

Find the amount of Delimo numbers.

Share at 3 or 9 (depending on what you need).

If the answer is happening without a balance, then the number will share without a residue.

For example, the number 18. The sum of numbers 1 + 8 \u003d 9. The amount of numbers is divided into 3 and 9. Number 18: 9 \u003d 2, 18: 3 \u003d 6. Divided without residue.

For example, the number 63. The sum of numbers 6 + 3 \u003d 9. It is divided both at 9 and by 3. 63: 9 \u003d 7, and 63: 3 \u003d 21.Tell operations are carried out with any number to find out if it is divided with the residue 3 or 9, or not.

Multiplication and division

Multiplication and division are opposite to each other operations. Multiplication can be used as a division check, and division is like a multiplication check. Read more about multiplication and master the operation can in our article about multiplication. In which the multiplication is described in detail and how to perform. There you will find a multiplication table and examples for training.

Let us give an example of verification of division and multiplication. Suppose this is example 6 * 4. Answer: 24. Then check the answer in the division: 24: 4 \u003d 6, 24: 6 \u003d 4. Solved right. In this case, the check is made by dividing the response to one of the multipliers.

Or given an example for division 56: 8. Answer: 7. Then the check will be 8 * 7 \u003d 56. Right? Yes. In this case, the check is made by multiplying the response to the divider.

Division grade 3.

In the third grade only begin to take division. Therefore, third graders decide the simplest tasks:

Task 1.. An employee in the factory gave a task to decompose 56 cupcakes in 8 packs. How many cupcakes need to put in each package so that it is equal to the amount in each?

Task 2.. On the eve of the New Year at school, children on the class in which 15 people study 75 candies. How many candies should every child get?

Task 3.. Roma, Sasha and Misha collected with apple 27 apples. How much will everyone get apples if you need to divide them equally?

Task 4.. Four friends bought 58 cookies. But then they realized that they would not divide them equally. How many guys do you need to buy cookies to get every 15 pieces?

Division grade 4.

The division in the fourth grade is more serious than in the third. All calculations are carried out by dividing in a column, and the numbers that participate in division are not small. What is division in the column? You can see the answer below:

Division in column

What is division in the column? This method allows you to find a reply to division of large numbers. If simple numbers like 16 and 4 can be divided, and the answer is clear - 4. then 512: 8 in the mind for a child is not easy. And to tell about the technique of solving such examples - our task.

Consider an example, 512: 8.

1 step. We write a divide and divider as follows:

Private will be recorded in the end under the divider, and the calculations under divisible.

2 step. The division starts from left to right. First we take the number 5:

3 Step. Figure 5 less than 8 figures, which means to divide will not succeed. Therefore, we take another divide figure:

Now 51 more 8. This is incomplete private.

4 Step. We put the point under the divider.

5 step. After 51, there is still a digit 2, which means there will be another number in the answer, that is. Private - two-digit number. Standing the point:

6 step. We begin the division operation. The largest number, divided without a residue, 8 to 51 - 48. Uach 48 to 8, we get 6. Record number 6 instead of the first point under the divider:

7 step. Then write the number of exactly under Number 51 and put the sign "-":

8 step. Then, out of 51, we subtract 48 and get the answer 3.

* 9 Step* We demote the figure 2 and write next to the number 3:

10 Step The resulting number 32 divide on 8 and we get a second digit of the answer - 4.

So, the answer is 64, without a residue. If the number 513 were divided, then the rest would be a unit.

Three-digit division

The division of three-digit numbers is performed by dividing in the column, which was explained by the example above. An example is as a three-digit number.

Division of fractions

The division of fractions is not as difficult, as it seems at first glance. For example, (2/3) :( 1/4). The method of this division is quite simple. 2/3 - Delimi, 1/4 - divider. You can replace the division sign (:) to multiplication ( ), But for this you need to swap the numerator and denominator of the divider. That is, we get: (2/3)(4/1), (2/3) * 4, this is equal to 8/3 or 2 and 2 / 3. Another example, with an illustration for the best understanding. Consider the fractions (4/7) :( 2/5):

As in the previous example, we turn the 2/5 divider and get 5/2, replacing the division into multiplication. We get then (4/7) * (5/2). We produce abbreviation and answer: 10/7, then we take a whole part: 1 whole and 3/7.

Classes

Imagine the number 148951784296, and divide it three digits: 148 951 784 296. So, right to left: 296 - class of units, 784 - class thousand, 951 - class of millions, 148 - class billion. In turn, in each class 3 digits have their discharge. Right left: The first digit is units, the second digit is dozens, the third is hundreds. For example, class units - 296, 6 - units, 9 - tens, 2 - hundreds.

Division of natural numbers

The division of natural numbers is the simplest division described in this article. It can be, both with the residue and without a residue. Deliel and divisible can be any non-fractional, integers.

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Decision presentation

Presentation - another way to visually show the topic of divisions. Below we will find a link to an excellent presentation, which is well explained how to share what division is what is divisible, divider and private. I will not spend time in vain, and fasten your knowledge!

Examples for division

Easy level

Average level

Complex level

Games for the development of oral account

Special educational games designed with the participation of Russian scientists from Skolkovo will help improve the skills of the oral account in an interesting game form.

Game "Guess the operation"

Game "Guess Operation" develops thinking and memory. Main essence of the game It is necessary to choose a mathematical sign so that equality is correct. Examples are given on the screen, look carefully and put the desired "+" or "-" sign, so that the equality is correct. The "+" and "-" sign are located down in the picture, select the desired sign and click on the desired button. If you answered correctly, you type glasses and continue playing further.

Game "Simplification"

The game "Simplification" develops thinking and memory. The main essence of the game must quickly perform a mathematical operation. A student is drawn on the screen, and a mathematical action is given, the disciple must consider this example and write an answer. Below is given three answers, count and click the number you need with the mouse. If you answered correctly, you type glasses and continue playing further.

Fast Addition game

The game "Quick Addition" develops thinking and memory. The main essence of the game to choose the numbers whose amount is equal to the specified digit. In this game, the matrix is \u200b\u200bgiven from one to sixteen. A specified number is written above the matrix, you need to select the numbers in the matrix so that the sum of these numbers is equal to the specified digit. If you answered correctly, you type glasses and continue playing further.

Game "Visual Geometry"

The "Visual Geometry" game develops thinking and memory. The main essence of the game is quickly counting the number of painted objects and select it from the answer list. In this game, the blue squares are shown on the screen for a few seconds, they must be counted quickly, then they close. Four numbers are written below the table, you need to select one correct number and click on it using the mouse. If you answered correctly, you type glasses and continue playing further.

Game "Piggy Bank"

The game "Piggy" develops thinking and memory. The main essence of the game to choose, in which piggy bank more money. In this game, four piggy banks are given, it is necessary to calculate in which piggy bank more money and show this piggy bank with the mouse. If you answered correctly, then you dial the glasses and continue playing further.

"Fast addition to reboot" game

The game "Fast addition reboot" develops thinking, memory and attention. The main essence of the game to choose the right terms, the sum of which will be equal to the specified number. In this game, there are three digits on the screen and task is given, fold the number, it is specified in the screen what figure should be folded. You choose from three digits the desired numbers and press them. If you answered correctly, then you dial the glasses and continue playing further.

The development of a phenomenal oral account

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From the course you will not just recognize dozens of techniques for simplified and fast multiplication, addition, multiplication, divisions, calculating interest, but also work them in special tasks and educational games! The oral account also requires a lot of attention and concentrations that are actively trained in solving interesting tasks.

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The summary of the lesson of mathematics in grade 3. The program "School 2100".

Technology "Problem Dialogue"

Topic: multiplication and division of round three-digit numbers (lesson transfer of existing knowledge to a new numerical concentration).

Purpose: Open a method of oral multiplication techniques and division of round-digit numbers, similar to the same techniques when multiplying and dividing two-digit numbers.

Tasks:

repeat oral techniques of multiplication and division of double-digit numbers;

create an algorithm of oral methods of multiplication and division of round three-digit numbers, similar to the same techniques when multiplying and dividing two-digit numbers;

solve on a new numerical concentrate textual tasks of the studied type;

During the classes:

Orgmoment.

Before the lesson to start,

I want to wish you:

Be attentive to learning

And learn with passionate.

Success situation. Actualization of knowledge.

Mathematical dictation.

How does a mathematics lesson usually begins?

And why do we write mathematical dictations?

Let's draw in computing.

Find a number that is 3 times more than 20.

Find a number that is 6 times less than 78.

Find the work 23 and 4.

Find a private 90 and 5.

Check.

Record all three-digit numbers that can be made from numbers of 2.6.0.

Name how much dozens in these numbers. How many hundreds of hundreds in these numbers?

Check. Self-holding workbook works.

Gap situation. Introduction to the subject of the lesson.

Here is our next task. What do you think, what is the purpose of the task?

On the chalkboard 2 column of examples. The first option solves examplesI. Stumpka, second option - examplesII. Point. (Examples are solved at the time).

16*6 840:4

84:7 130*5

13*5 360:6

72:4 840:7

84:4 160*6

36:6 720:4

Perform a check.

What option coped with the task better, faster?

Why? What are the sample columns? (INI.stage Examples for multiplication and division of double-digit numbers to unambiguous).

Do we know how well?

What differs are examplesII.point? (More complicated. Here are examples for multiplication and division of three-digit numbers to unambiguous).

We can, we know? What do we do not know how? (I do not know how to multiply and share three-digit numbers).

And what are all three-digit numbers of 2 columns? (They end 0, round)

Setting the purpose of the lesson.

What is the purpose of our current lesson? (Learn to multiply and share round three-digit numbers for unambiguous). What is the subject of the lesson?

Fizkultminutka.

Opening a new knowledge. (Group work)

I think you yourself will handle this task. Today I give you different examples. Try to open the method of multiplying and dividing three-digit numbers to unambiguous.

Children work in the group.

Examples: 1 row - 840: 40 2 row - 130 * 5 3 Row - 400 * 2

Select the desired method of action.

Groups put their solutions on the board. Solutions are compared. The more rational solution is selected.

Question to 3rd row:

Is it possible to divide 400 to 2 in this way?

Formulation of the rule.

How can you multiply or share round three-digit numbers on unambiguous? (Three-digit numbers can be expressed in dozens and hundreds and perform multiplication and division as double-digit; turn into easier examples within 100, expressing three-digit numbers in dozens and hundreds)

Comparison of your conclusions with conclusions data in the textbook on P.74.

Does our conclusion coincide with the conclusions given in the textbook?

Guys, we reached the purpose of the lesson?

Did you understand a new topic? (Self-examination of the understanding of the topic - on the fields in the notebook guys paint self-esteem (reception of self-standard - smiley)

Application of new knowledge.

Explanation of the solution of examples No. 4 at S.74 textbook.

Solving Tasks No. 2.3 on S.74 textbook.

Fastening passed.

Solving Tasks No. 6 on the S.75 of the Tutorial. (Solution on a new numerical concentration of text objectives of the studied type).

Total lesson:

Generalization:

What was the subject of the lesson? What was our goal? What is the method of multiplication and division of round three digits? (Converting them to dozens and hundreds and to perform multiplication and division as with double-digit numbers).

2) Reflection:

What did you particularly like it in the lesson? What was hard? Did you understand the topic of the lesson? Rate your work at the lesson.

3) Homework: №5.7 on a C.29 textbook.

At school, these actions are studied from simple to complex. Therefore, it will certainly assume good to assimilate the algorithm for the execution of these operations on simple examples. So that there are no difficulties with the division of decimal fractions in the column. After all, this is the most difficult version of such tasks.

This subject requires a consistent study. Spaces in knowledge are unacceptable here. Such a principle must learn every student in the first grade. Therefore, with a pass of several lessons in a row, the material will have to master on its own. Otherwise, the problems will arise not only with mathematics, but also other objects associated with it.

The second prerequisite for the successful study of mathematics is to move to examples to divide into a column only after the addition, subtraction and multiplication are mastered.

It will be difficult for a child if he did not learn the multiplication table. By the way, it is better to learn it on the Tipagora table. There is nothing superfluous, and it is absorbed by multiplication in this case.

How are natural numbers multiply in the column?

If there is a difficulty in solving examples in a division and multiplication column, then start changing the problem relying from multiplication. Since division is a reverse operation of multiplication:

1. Before multiplying two numbers, they need to carefully look at. Choose the one in which more discharges (longer), write it first. Under it to place the second. Moreover, the figures of the corresponding discharge should be under the same discharge. That is, the right figure of the first number should be above the right second.
2. Multiply the extreme right digit of the lower number for each digit of the top, starting on the right. Write down the answer below the line so that its last digit is under that which is multiplied.
3. The same repeat on another digital lower number. But the result from multiplication should be shifted to one digit to the left. At the same time, its last digit will be under the one that is multiplied.

Continue this multiplication in the column until the figures are run out in the second multiplier. Now they need to be folded. This will be the desired answer.

Algorithm multiplication in the columns of decimal fractions

First, it is supposed to imagine that there are not decimal fractions, but natural. That is, to remove commas from them and then act as described in the previous case.

The difference begins when the answer is recorded. At this point, you must count all the numbers that are standing after commas in both fractions. It is so much that they need to be counted from the end of the answer and put a comma there.

It is convenient to illustrate this algorithm for example: 0.25 x 0.33:

How to start learning a division?

Before deciding for dividing in a column, it is supposed to remember the names of the numbers that are in the example for division. The first of them (then that is divided) is divisible. The second (divided into it) is a divider. The answer is private.

After that, on a simple everyday example, explain the essence of this mathematical operation. For example, if you take 10 candies, then divide them equally between mom and dad easily. And what if you need to distribute them to parents and brother?

After that, you can get acquainted with the rules of division and master them on specific examples. First, simple, and then go to everything more complex.

Algorithm for dividing numbers in the column

Initially, imagine the procedure for natural numbers that are divided into an unambiguous number. They will be the basis for multivalued dividers or decimal fractions. Only then it is supposed to make minor changes, but this is later:

• Before making division into a column, you need to find out where the divider and divider.
• Write a divide. To the right of it - the divider.
• Dig up to the left and below near the last corner.
• Determine incomplete divisible, that is, the number that will be minimal for division. It usually consists of one digit, a maximum of two.
• Choose a number that will be the first to be recorded in response. It should be how many times the divider is placed in division.
• Record the result from multiplying this number per divider.
• Write it under incomplete division. Perform subtraction.
• To demolish the first digit to the residue after that part that is already divided.
• To recall the number to answer again.
• Repeat multiplication and subtraction. If the residue is zero and the divisible ended, the example is made. Otherwise, repeat the steps: to demolish the number, pick up the number, multiply, subtract.

How to solve division in a column if in the divider more than one number?

The algorithm itself fully coincides with what was described above. The difference will be the number of numbers in incomplete division. Their minimum should now be two, but if they are less than a divider, it should work with the first three numbers.

There is another nuance in this division. The fact is that the residue and the number demolished to it are sometimes not divided into a divider. Then it is supposed to attribute another digit in order. But at the same time, it is necessary to put zero in response. If the division of three-digit numbers in the column is carried out, then it may be necessary to carry more than two digits. Then the rule is introduced: noise in response should be one less than the number of demolished digits.

Consider such a division by example - 12082: 863.

• An incomplete divisible in it is the number 1208. The number 863 is placed only once. Therefore, in response, it is necessary to put 1, and under 1208 record 863.
• After subtraction, the residue is obtained 345.
• It is necessary to demolish the number 2.
• Among 3452, 863 fits four times.
• Four need to write in response. Moreover, when multiplying on 4 it turns out exactly this number.
• The residue after subtraction is zero. That is, the division is completed.

The answer in the example will be the number 14.

How to be if divisible ends on zero?

Or a few nobles? In this case, the zero residue is obtained, and in Delim, there are still zeros. It is not necessary to despair, everything is easier than it may seem. It is enough just to attribute to the answer all zeros, which remained not divided.

For example, you need to divide 400 to 5. Incomplete divisible 40. The top 8 placed in it. So, in response, it is necessary to write 8. When subtracting the residue does not remain. That is, the division is completed, but a zero remained in Delim. He will have to attribute to the answer. Thus, when dividing 400 per 5 is obtained 80.

What if you need to share a decimal fraction?

Again, this number is similar to the natural, if it were not for a comma separating the whole part of the fractional. This suggests that the division of decimal fractions in the column is similar to that described above.

The only difference will be a semicolon. It is supposed to put in response immediately as soon as the first digit of the fractional part is demolished. In a different way, this can be said like this: the division of the whole part is over - put the comma and continue the decision on.

During the solution of examples of dividing in a column with decimal fractions, it is necessary to remember that in part after the comma it is possible to attribute any number of nonols. Sometimes it is necessary in order to let the numbers to the end.

Division of two decimal fractions

It may seem complex. But only at the beginning. After all, how to make division in the column fractions on a natural number, it is already clear. So you need to reduce this example to the already familiar mind.

Make it easy. You need to multiply both fractions by 10, 100, 1,000 or 10,000, and maybe a million, if this requires a task. The multiplier should be chosen based on how many zoli is in the decimal part of the divider. That is, as a result, it turns out that it will have to divide on a natural number.

And it will be in the worst case. After all, it may turn out that dividable from this operation will become an integer. Then the solution of an example with division in a column fraction will be reduced to the simplest option: operations with natural numbers.

As an example: 28.4 divide by 3.2:

• First, they must be multiplied by 10, since in the second number after the comma, there is only one digit. Multiplication will give 284 and 32.
• They should be divided. And immediately all the number 284 to 32.
• The first selected number for the answer is 8. From its multiplication it turns out 256. The residue will be 28.
• The division of the whole part is over, and in response it is necessary to put a comma.
• Demolish to the residue 0.
• Take 8 again.
• Rest: 24. To him to attribute one more 0.
• Now you need to take 7.
• The result of multiplication is 224, the residue is 16.
• To demolish another 0. Take 5 and it turns out just 160. The residue is 0.

The division is completed. The result of an example 28.4: 3.2 is 8,875.

What if the divider is 10, 100, 0.1, or 0.01?

As well as with multiplication, the division in the column is not needed here. It is enough to simply transfer the comma in the desired side to a certain number of numbers. Moreover, according to this principle, examples can be solved with both integers and decimal fractions.

So, if you need to divide by 10, 100 or 1,000, the comma is transferred to the left of the number of numbers as zeros in the divider. That is, when the number is divided into 100, the comma should be shifted to the left into two digits. If divisible is a natural number, then it is understood that the comma stands at its end.

This action gives the same result as if the number was needed to multiply by 0.1, 0.01 or 0.001. In these examples, the comma is also transferred to the left of the number of numbers equal to the length of the fractional part.

When divided by 0.1 (, etc.) or multiplication by 10 (, etc.), the comma should move to one digit (or two, three, depending on the number of zeros or the length of the fractional part).

It is worth noting that the number of numbers, data in the division may be insufficient. Then on the left (in the whole part) or on the right (after the comma) you can attribute the missing zeros.

Division of periodic fractions

In this case, it will not be possible to obtain an accurate answer when dividing in the column. How to solve an example if you met a fraction with a period? Here it is necessary to move to ordinary fractions. And then perform their division according to the previously studied rules.

For example, it is necessary to divide 0, (3) by 0.6. The first fraction is periodic. It is converted into a fraction 3/9, which after the reduction will give 1/3. The second fraction is the ultimate decimal. It is even easier to burn it: 6/10, which is 3/5. The rule of division of ordinary fractions prescribes to replace the division by multiplication and the divider - inverse. That is, an example is reduced to a multiplication of 1/3 to 5/3. The answer will be 5/9.

If in the example, different fractions ...

Then there are several solution options. First, an ordinary fraction can be tried to translate into decimal. Then we already divide two decimal on the algorithm specified above.

Secondly, each finite decimal fraction can be written in the form of an ordinary. Only it is not always convenient. Most often, such fractions are huge. Yes, and the answers are cumbersome. Therefore, the first approach is considered more preferable.

Abstract open lesson in grade 3.

Volkov Love Andreevna, primary school teacher.

Type of lesson: combined.

Purpose: - consolidate the ability to share and multiply three-digit numbers per unambiguous number;

Form the ability to perform calculations of the type 800: 200; 630: 90 (division of three-digit numbers on round three-digit and double-digit);

Tasks:

Continue to develop an oral account skills;

Improve the ability to solve problems and examples;

Develop mental processes - memory, thinking, attention;

Bring up communicative relationships between students, a sense of collectivism;

Educate interest in the subject;

Rail interest in the child to the subject, knowledge of the world.

Equipment: Tutorial, workbook, colorful tasks for differentiated work, computer, presentation, poster (discharge of three-digit numbers), picture depicting a cat.

During the classes.

Organizing time.

(Slide 1)

In life a lot of interesting things

But for now we are unknown,

And to learn a lot.

Teacher: Guys, I see that you are all ready for a lesson. Sit down. We continue to study three-digit numbers, train to multiply and share them. Today, our lesson will begin unusual. Listen to the melody from the famous cartoon.

There is a passage from the song "There is nothing better in the world ..." (30 sec., Slide 1)

Teacher: Did you find out the melody? What cartoon?

Children: Bremen Musicians.

Teacher: True! Today, we will solve the tasks in the lesson and find the values \u200b\u200bof expressions along with the Troubadrome and the Bremen musicians.

(Slide 2)

Verbal counting.

a) And here is the first task! (Slide 3) Bremen musicians staged a presentation on the square of the city. The first number with a tablet 75:15. Who acts next?

Children find the values \u200b\u200bof expressions, arguing out loud. The answer to the previous example serves as the beginning of each next.

b)slide 4.

Teacher: Imagine that the cat from the Bremen musicians decided to show tricks with three-digit numbers. I will ask a question, and you call a number.(The work is carried out on the blackboard, under the table with the discharges of three-digit numbers and the image of the cat).

Now there will be a number in which 5 hundred 6 dozen and 2 units.

…… 30 dozen.

… 4 hundred.

The number that is more than 289 per 1

A number that is less than 658 to 1.

Fizminutka (game "Attention")

Actualization of knowledge. Setting a problematic issue.

Teacher: Check how we learned to multiply and share three-digit numbers. Rooster prepared examples.(Slide 5)

Look, we have already solved all kinds of examples? Rooster hid examples here with the receptions of which we have not met.

Teacher: We will argue and find a solution to the problem.

Open notebooks, write the number, cooling, number 1

Opening a new knowledge.

The board solves one student, the rest of the students in the notebook. When we reach the fourth column, we take the "new" reception of the division of a three-digit number. We divide the three-digit number on round double-digit and three-digit, arguing as follows (by analogy with the division of round two-digit numbers):

800: 200 \u003d 4, as 4 * 200 \u003d 800 (slide 6)

Confirm the justice of our withdrawal by rule in the textbook on page 55

Fixing

Tasks of the textbook page 56 No. 5 (1, 2 columns)

One student works at the board, argues out loud, the rest in the notebooks.

Task number 8 p. 56

The teacher is together with the children a brief record on the board, disassembles the stages of solving the problem. One student solves the task on the back of the board. At the end of the check: Schoolchildren check their entry with a record on the board. I drag the answer with the answer to the slide(Slide 8)

Fizminutka (Eye Charging)

Working with cards.

Solving the tasks of two levels of complexity. For successive students, the text of the task coincides with the text of the task number 9 from the textbook.

Card 1 Level (Green Card)

Bremen musicians gave a concert for residents of the city. Spectators heard 27 songs, which is 8 less than dance melodies. How many musical works sounded in a concert?

Card 2 Level (Red Card)

Bremen musicians gave a concert for residents of the city. Spectators heard 27 songs, which is 8 less than dance melodies. These musical works were performed in two branches of the concert, equally in each department. How many musical works sounded in each of the offices?

Drawing up a brief record to both tasks deal with the teacher.(slide 13-14)

Independent work guys.

The results of the lesson.

Teacher: Every lesson we try to learn more than knew. Raised to the step above. What new we learned today?

(Learned to share three-digit numbers on round double and three-digit)

Homework.

The task is offered by the guys multi-level. It is written with a multicolored chalk on the board.

Green (for all): s. 56 No. 5 (3.4 columns), №7.

Red chalk (for those who want more complicated): S.56 No. 6, No. 10.

Additional task (if time)

Slide 15.

Drink the names of all polygons containing the angle of ABC (№11 p.56)

Slide 16. Well done!

MUNICIPAL PERSONAL EDUCATIONAL EDUCATION OF LITERATE № 7

Abstract of the open lesson of mathematics.

Multiplication and division of three-digit numbers per unambiguous numbers.

Primary school teacher

Volkova Love Andreevna

solnechnogorsk

2013