Column subtraction. Subtraction Rules

Theoretical principles underlying the subtraction of multi-digit numbers:

Representation of a number in decimal notation;

Rules for subtracting a number from a sum and a sum from a number;

Tabular cases of addition of single-digit numbers;

Distributive properties of multiplication with respect to subtraction.

1) We write the subtrahend under the reduced strictly discharge under the discharge.

2) We start subtracting from the unit digit. If the number of units in the unit digit of the minuend is greater than or equal to the number of units in the unit digit of the subtrahend, then we subtract and write the result in the difference unit digit and proceed to the subtraction in the trace. discharge.

3) If the number of units in the place of the unit being reduced is less than the number of units in the place of the unit being subtracted, then we reduce the number of units in the place of tens of the reduced (if the place of tens is not zero) by 1, simultaneously increasing the number of units in the discharge of the unit being reduced by 10, after which we perform the subtraction. We write down the received rez-at in the category of unit difference.

4) If the number of units in the tens place of the reduced is zero, then we find the first of the digits in the reduced, in the cat. the number of units is not equal to zero and we reduce the number of units in it by 1, while simultaneously increasing the number of units in those digits in the cat. zero is at 9, and the number of units in the discharge of units is reduced by 10. We subtract, write the answer in the corresponding bit of the difference and proceed to subtract in the next bit.

5) In the next discharge, No. 2, 3 or 4 is repeated.

6) We consider the subtraction process to be completed when the subtraction from the highest digit of the reduced one was made.

Methodology for studying the algorithm.

Of course, younger students cannot master written subtraction algorithms in general terms. But the teacher needs to know them.

This will allow him to:

When familiarizing students with the algorithm, it is correct to organize the preparatory work;

Manage the activities of schoolchildren aimed at mastering the algorithm;

In the exercises to reinforce the algorithm, take into account all the possibilities of its use.

Descriptions of algorithms are given to primary school students in a simplified form, where only the main points are fixed:

1) the subtracted must be written under the reduced so that the corresponding digits are one under the other;

2) subtraction should start from the lowest digit, i.e. subtract units first.

Other operations included in the algorithm are either explained to younger students using specific examples, or are realized by them in the process of performing special tasks. selected exercises.

Traditional program: familiarity with the methods of writing. addition / subtraction in the topic "Thousand"; addition / subtraction "in a column" of two-digit numbers according to the model of actions: Explain the solution of example 43 - 29 "in a column": I write units under units, tens - under tens. subtract units. I take 1 ten. 13-9=4. I write in units of 4.

Subtract tens. We took one dozen, so there are 3 dozens left in the reduced one. 3-2=1. I write 1 under tens. I read the answer: the difference is 14.

Various cases of subtracting three-digit numbers are successively considered.

Istomina's program: children get acquainted with the algorithms of written addition and subtraction after they learn the numbering of numbers within a million.

Starting to study the algorithms of written addition and subtraction, students perform the task:

By how much can 308282 be reduced so that the digits in the ones and tens digits change, while the digits of the other digits remain the same?

(Analysis of the method of action when subtracting in a column). Explain how numbers are subtracted. Can you guess why the subtraction of multi-digit numbers “in a column” must be started with the units digit? (Emphasis on the execution of the entry "in a column", a discussion of correct and incorrect entries).

§ 1 Algorithm for written subtraction of multi-digit numbers

Consider the written subtraction algorithm for multi-digit numbers. For example, we need to find the value of the difference between the numbers 397.539 and 25.128.

1. Let's read them. Decreased - 397.539, subtracted - 25.128.

2. Determine the number of digits in each number. These are six-digit and five-digit numbers.

3. We write the numbers one under the other so that the units of the same digits are in the same column.

We subtract bit units, starting from the very first bit - units, ending with the last bit - tens of thousands.

9 units minus 8, you get 1.

3 digit tens will decrease by 2 digit tens, it will also be 1.

Subtract the hundreds of digits. 5 minus 1 makes 4.

In the thousands class, from 7 units of thousands, subtract 5 units of thousands, we get 2.

Lastly, subtract tens of thousands. Nine minus two is seven.

The digit hundreds of thousands remain unchanged.

4. We read the answer. This six-digit number is 372.411.

§ 2 Algorithm for written subtraction of three-digit numbers

Consider the algorithm for subtracting from three-digit numbers. You need to remember the bit composition of the number. For example, we need to subtract 6 from 750. Let's represent the reduced as a sum of bit terms: 750=700+50

The rule must always be observed: actions are performed with units of the same digits, starting with the smallest. It is impossible to subtract 6 from zero, therefore, the reduced can be represented as the sum of bit terms as follows:

We take one ten out of 5 tens, then subtract 6 from this ten and get 4. The value of the difference is 700+40+4=744.

Let's try to record this subtraction action in a column. When subtracting bit units, we occupied one bit ten. In order not to forget about this, put a dot on the memory line above the number 5. When subtracting tens places, the dot will remind us that there are only 4 tens places left. Thus, a dot is placed on the memory line if it is impossible to perform a subtraction without units of a higher digit.

§ 3 Subtraction of multi-digit numbers with the transition to the next digit

Consider the subtraction of multi-digit numbers with the transition to the next digit.

Decreased - 290.380, subtracted - 37.161. These are six-digit and five-digit numbers.

We write the numbers one under the other so that the units of the same digits are in the same column.

We subtract the bit units, starting from the very first bit - units, ending with the last bit - tens of thousands.

It is impossible to subtract 1 from 0, we occupy one digit ten, and in order not to forget, we put a dot on the memory line above the tens digit. Subtract 1 from 10 to get 9 digits. The dot reminds us that there are 7 digit tens left. 7 minus 6, you get 1.

Subtract the hundreds of digits. 3 minus 1 is 2.

There is 0 in the decrement in the thousands place. This means that we need to take one tens of thousands. To remember, we put a dot on the memory line and subtract 7 from 10. We get 3 digit units of thousands.

In bit tens of thousands, taking into account the mark with a dot, it turns out 8. 8 minus 3 is 5. The hundreds of thousands of digits remain unchanged.

We read the answer: the value of the quotient is the six-digit number 253.219.

§ 4 Brief conclusions on the topic of the lesson

Thus, the written subtraction of multi-digit numbers is performed in a column according to certain rules:

First, it is necessary to write the numbers one under the other so that the units of the same digits are in the same column.

Thirdly, if it is impossible to subtract digit units without using units of a larger digit, a dot is put on the memory line.

Question 6.Algorithms for written addition and subtraction.

As practice shows, mastering written addition and subtraction algorithms is not an easy task. One of the reasons for the difficulties in the wrong organization of the educational process. There should be a focus on the personality of the student, his individual abilities.

When performing written calculations, fatigue quickly develops when working with numbers, since it is necessary to perform a large number of operations in order to find the result, spend more time and effort, greater concentration of attention is required, therefore, errors appear. Alternating various activities will help to avoid fatigue: oral with written, solving examples with solving problems, performing standard tasks less often, more tasks that require ingenuity, non-standard approaches.

Students do not get tired so quickly if they fully perceive new knowledge and receive a calculation sample written in sign form, as well as in verbal formulation (in the form of an explanation of the solution). The study of the topic should also be preceded by preparatory work, since understanding the material being studied is a huge internal incentive to study mathematics.

Children should be shown familiar material, as they often try to perceive all the material as new without highlighting what is known, and at the same time, studying large educational material may not be possible. The study of written calculations makes it possible to pose problematic questions, organize a joint search for answers to them, and teach self-control.

Written receptions include the following cases (see table above)

addition and subtraction without passing through ten;

rule for checking addition and subtraction;

written addition techniques with the transition through a dozen;

written subtraction techniques with the transition through a dozen.

At the preparatory stage, you can give a table of addition and subtraction within 20, the studied oral methods of addition and subtraction within 100. When familiarizing yourself, you need to show 2 types of recording techniques: in a line and in a column, paying attention that when adding and subtracting the units of the second number, they sign under the units of the first number, and tens under tens.

35 (give only entry, not requiring calculation). Condition 12 of the example is separated from the answer

a line that represents the equals sign.

An explanation of written addition and subtraction can be started by solving examples of adding and subtracting two-digit numbers without going through a dozen. Then independently record the example in a column, as more convenient. The teacher should show that in each of the digits the numbers add up as single digits. Addition and subtraction starts with units. To introduce jumping calculations, you can ask to observe the difference between the examples:

47 47 47 74 74 74

32 33 34 53 54 55

At the initial stage, you can allow the use of a point as a reference signal for self-control. The point (reference signal) is a purely psychological factor, therefore, it will increase attention. If the student is tired, feels that attention is weakened, then he can put an end to it. Clear algorithms that are presented in mathematics textbooks for elementary schools will help to learn new knowledge.

For example: 56+23. Students' reasoning: I write 56 below, I write in column 23 (I sign units under units, tens under tens), put a + sign, underline, calculate. I add ones, add tens, read the answer. Subtraction algorithm: subtract units, subtract tens, read the answer. They are based on the written addition and subtraction algorithms of the mathematics course.

The addition algorithm is based on the following algorithm:

Write the second term under the first so that the corresponding digits are one under the other.

Add up the units digits. If the sum is less than 10, it is written in the category of units of the answer and go to the next category.

If the sum of the digits is greater than 10 or equal, then they represent it in the form: 10+c 0, where c 0 is a single-digit number, write from 0 to the units of the answer and add 1 to the tens digit of the first term, after which they go to the tens category.

They repeat the same actions with tens, then with hundreds, etc. The addition process ends when the digits of the highest digits are added.

subtraction algorithm.

Write the subtracted b n , b n -1 ... b 1 , b 0 under the reduced one, so that the corresponding digits are one under the other.

If the digit in the units place of the subtrahend does not exceed the corresponding digit of the minuend, then it is subtracted from the corresponding digit of the minuend, after which they move on to the next digit.

3. If the digit of the units of the subtrahend is greater than the digit of the units of the minuend, i.e. a 0

4. If the digit of the unit of the subtrahend is greater than the digit of the units of the minuend, and the digits in the category of tens, hundreds, etc. reduced are equal to 0, then they take the first digit, different from 0, in the reduced (after the units digit), decrease it by 1, increase all the digits in the lower digits up to the tens digit inclusively by 9, and the digit in the units digit by 10, subtract b 0 out of 10+ a 0 , write the result in the difference units digit, and move on to the next digit.

The teacher needs to know the algorithms of addition and subtraction in general terms in order to:

a) when getting acquainted with the algorithm, organize the work correctly;

b) manage the activities of schoolchildren aimed at mastering the algorithm;

c) in the exercises to consolidate the algorithm, take into account all the possibilities of its use.

The activities of students aimed at developing the skills of written addition and subtraction can be organized in different ways.

Typical mistakes.

When using computational methods of addition and subtraction within 100, students may make the following mistakes.

They mix calculation methods based on the rules for subtracting a sum from a number and a number from a sum:

50-36=50-(30+6)=(50-30)+6=26

56-30=(50+6)-30=(50-30)-6=14

2. Do not distinguish discharges when adding:

54+2=74 (the number of tens is added to the number of units)

54-40=50 (the number of tens is subtracted from the number of units)

3. Make mistakes in tabular addition and subtraction:

4. Skip computational receive operations or include unnecessary:

76-20=50 (skip operation +6)

64+30=97 (+3 is an extra operation)

5. Mix addition and subtraction operations:

Methodical task:

How should the work of students be organized in order to prevent the occurrence of such errors.

To find the difference using the " column subtraction”(in other words, how to count in a column or a subtraction by a column), you must follow these steps:

• put the subtrahend under the minuend, write units under units, tens under tens, and so on.
• subtract bit by bit.
• if you need to take a ten from a larger category, then put a dot over the category in which you took it. Above the category for which they took, put 10.
• if the digit in which we occupied is 0, then we take the decreasing one from the next digit and put a dot over it. Above the category for which they took, put 9, because. one dozen are busy.

The examples below will show you how to subtract two-digit, three-digit and any multi-digit numbers in a column.

Subtraction of numbers in a column helps a lot when subtracting large numbers (as well as addition in a column). The best way to learn is by example.

It is necessary to write the numbers one under the other in such a way that the rightmost digit of the 1st number becomes under the rightmost digit of the 2nd number. The number that is greater (decreasing) is written on top. On the left between the numbers we put the action sign, here it is “-” (subtraction).

2 - 1 = 1 . What we get is written under the line:

10 + 3 = 13.

Subtract nine from 13.

13 - 9 = 4.

Since we took ten from four, it decreased by 1. In order not to forget about this, we have a point.

4 - 1 = 3.

Result:

Column subtraction from numbers containing zeros.

Again, let's look at an example:

We write the numbers in a column. Which is more - on top. We start subtracting from right to left, one digit at a time. 9 - 3 = 6.

Subtracting 2 from zero will not work, then again we borrow from the number on the left. This is zero. We put a point above zero. And again, you won’t be able to borrow from zero, then we move on to the next digit. We borrow from the unit. We put a dot on it.

Note: when there is a dot in the subtraction above 0, zero becomes nine.

There is a dot above our zero, which means it has become a nine. Subtract 4 from it. 9 - 4 = 5 . There is a point above the unit, that is, it decreases by 1. 1 - 1 = 0. The resulting zero does not need to be recorded.

1. We write units under units, tens under tens, hundreds under hundreds.

2. Subtract units.

3. Subtract tens.

4. Subtract hundreds.

5. We read the answer.

Formulate the objectives of the lesson. (Remember the algorithm for subtracting three-digit numbers in a column, learn how to use it when solving examples.)

IV. Work on the topic of the lesson

Repetition of the subtraction technique

Write down an example. 405 -136 (269)

Is it possible to subtract 6 units from 5 units? (It is forbidden.)

- What do we do? (Take 1 ten.)

There are no separate tens. What to do? (Take 1 hundred.)

What does it mean? (We will borrow 10 dozen.)

Take 1 ten out of 10 tens. How many tens are left? (9.)

Replace 1 ten with units. (10.)

And how many units are already in the number 405? (5.)

So how many units have become? (15.) Subtract. We get 9 units, 6 tens, 2 hundreds, i.e. 269.

Textbook work

Look at the examples in the boxes on p. nine.

Explain how you did column subtraction.

No. 29 (p. 9).(The first three examples are frontal, the last two are on their own. Two students work on a folding board. Mutual check, mutual assessment.)

V. Physical education

I go and you go - one, two, three. (Steps in place.)

I sing and you sing - one, two, three. (Clap hands.)

We go and we sing - one, two, three. (Jumping in place.)

We live very friendly - one, two, three. (Steps in place.)

VI. Consolidation of the studied material

Completing tasks in a workbook

No. 6 (p. 4).

- Read the task.

What do you need to know to answer the question? (How much water was poured into the watering can, bucket and barrel separately.)

How much water was poured into the watering can? (evil)

- How much water was poured in bucket? (4 times more than in a watering can.)

- How do you know how many liters it is? (3 . 4.)

How many liters of water were poured into the barrel? (28L more than a bucket.)

How do you know how many liters it is? (IN+ 28.)

Solve the problem step by step with explanation.

(One student works on a folding board. Check, self-assessment.)

Solution

1) 3 4 \u003d 12 (l) - water was poured into a bucket;

2) 12 + 28 = 40 (l) - water was poured into a barrel;

3) 3 + 12 + 40 = 55 (l).

Answer: only 55 liters of water were poured into a watering can, a bucket and a barrel.

No. 7 (p. 4).(Independent work. One student works on a folding board. Those who are having difficulty take an assistant card with a solution plan.)

1) How many meters of wire went into all the small cages?

2) How many meters of wire are left for 3 large cages?

3) How many meters of wire goes into one big cage? (Verification, self-assessment.)

Solution

1) 8 5 = 40 (m) - wire went to small cells;

2) 76 - 40 = 36 (m) - wire went to large cells;

3) 36: 3 = 12 (m).

Answer: 12 m of wire was used to make one large cage.

Textbook work

No. 30 (p. 9)- a basic level of.

No. 32 (p. 9) - the level of increased complexity.(Self-execution (optional). Self-examination according to the model, self-assessment.)

No. 33 (p. 9).(Oral execution in a chain.)

No. 35 (p. 9).(Independent implementation. Mutual verification.)

VII. Reflection

(Independent completion of the task “Check Yourself” (textbook, p. 9). Self-examination according to the model.) Answers: 214, 319.

VIII. Summing up the lesson

What task caused the problem?

Homework

Textbook: No. 31, 34, 36 (optional) (p. 9).

Topic: Techniques for written multiplication of a three-digit number by a one-digit number.

Goals: repeat the algorithm for written multiplication of a three-digit number by a one-digit number; develop logical thinking; improve oral and written computing skills, the ability to solve problems.

Planned results: students will learn how to multiply a three-digit number by a one-digit number; to solve problems; build a logical chain of reasoning; establish analogies.

During the classes

I. Organizational moment

II. Checking homework

No. 36 (p. 9).

III. Knowledge update

(39 + 140 - 19): 80 + 35: 5 8 (58)

(78:13 6): (153: 17) (4)

- Calculate by writing in a column.

303-157 801-476 707-559

Verbal counting

What action signs can be put instead of circles, and what numbers - instead of squares, so that the correct equalities are obtained?

39 O 16 = 5 (39 + 16 = 55)

9 04: = 6 (9- 4: 6 = 6)

4 5-60 = 0(4-15-60 = 0) (Checking individual work at the blackboard.)

IV. Self-determination to activity

Calculate in a column.

(One student works at the blackboard, explaining the algorithm solution in detail.)

Open your textbook on p. 10, look at the examples whose solution is explained. How do they differ from those that we solved? (Multiply not a two-digit number, but a three-digit one.)

- Formulate the objectives of the lesson. (Remember the algorithm for multiplying a three-digit number by a single-digit number, learn how to use it when solving examples.)

V. Work on the topic of the lesson

Textbook work

Explain the solution of examples according to the algorithm.

No. 38 (p. 10).

No. 39 (p. 10).

- Read the condition of the problem.

What trees are in the garden? (Apple and plum trees.)

What is known about apple trees? (We planted 4 rows of 12 apple trees.)

What number is repeated? How many times? How to write it down? (12-4.)

What is known about plums? (We planted 2 rows of 18 plums.)

How to write it down? (18-2.)

- How do you know how many trees have been planted? (Add up the number of apple trees and plums.)

- Write the solution to the problem as an expression. (12-4 + 18- 2 \u003d 84 (d.).)

Read task 2. How will you change the question of the task? (How much less plums were salted than apple trees 7)

Write down the solution to the new problem. (12- 4- 18- 2 = 12 (d.).)

VI. Physical education minute

I play the violin

Tili-tili-tili. (Show how the violin is played.)

Bunnies jump on the lawn

Tili-tili-tili. (Jumping in place.)

And now on the drum

Boom Boom Boom, (Clap hands.)

Tram-tram-tram! (Stomp.)

Bunnies fled in fear

Through the bushes, through the bushes. (Sit down.)

VII. Consolidation of the studied material

Textbook work No. 40 (p. 10).

Read the task.

How many mushrooms could brother find?

Solve the problem yourself. (One student works at the blackboard. Check.)

Solution

First way: (27 + □) - 3.

Who decided the same? Who else has a solution? (Students write down two more solutions.) Second way: (27 - 3) + P. Third way: 27 + (□ - 3).

No. 41 (p. 10).(Oral performance.)

Task Options

Grandfather is 64 years old, and grandson is 16. How many times older is grandfather than grandson? (How much less or more?)

Olya has 64 rubles, while Kolya has 16 times less. How much money y, If?

Olya has 64 rubles, while Kolya has 16 rubles less. How much money does Kolya have?

No. 42 (p. 10).

(Independent performance. Mutual verification, mutual evaluation.) No. 43 (p. 10).

(Self-execution. Self-examination according to the sample.)

VIII. Reflection

(Independent completion of the task “Check Yourself” (textbook, p. 10). Self-examination according to the model.) Answers: 748, 558.

(At this stage of the lesson, you can use a collection of independent and control work: independent work 3 (pp. 7-9).)

IX. Summing up the lesson

What did you learn in class today?

Which task seemed easy?

What task gave you difficulty?

Who would you like to thank for helping in class?

Homework

Workbook: No. 19 (p. 8)

Topic: Properties of multiplication

Goals: repeat the properties of multiplication; learn to use them in calculations; to consolidate the skills of written multiplication of a three-digit number by a single one; develop attention; cultivate accuracy.

Planned results: students will learn how to multiply a three-digit number by a one-digit number using the commutative property of multiplication; to solve problems; build a logical chain of reasoning; establish analogies.

During the classes

I. Organizational moment

II. Knowledge update

Logic task

On the On one side of the scale lies a large head of cabbage, and on the other - a 2 kg weight and a small head of cabbage. The scales are in balance. How many kilograms is the mass of the large head more than the mass of the small one? (For 2 kg.)

Individual card work

Calculate by writing in a column.

307-258 625-515 356-2 218-3

806-537 702-159 137-6 158-4

Individual work at the blackboard

Specify the order of actions, calculate.

Topic: MULTIPLICATION BY O AND 1

The goals of the teacher	To promote the development of skills to multiply a number by 1 and 0, analyze problems, draw up a plan and solve text problems of various types, perform oral mathematical calculations, solve equations based on the relationships between components and results of arithmetic operations; promote the development of logical thinking
Lesson type	Consolidation of knowledge and methods of action
Planned educational outcomes	subject(volume of development and level of competencies): they will learn to apply the rule of multiplying a number by 0, perform oral calculations, solve equations for addition, subtraction, multiplication and division, tasks of various types. Metasubject(components of cultural competence experience/acquired competence): they will master the ability to understand the learning task of the lesson, answer questions, generalize their own ideas; listen to the interlocutor and conduct a dialogue, evaluate their achievements in the lesson; able to engage in verbal communication, use the textbook. Personal: understand the universality of mathematical ways of knowing the world around
Methods and forms of education	Forms: frontal, individual. Methods: verbal, visual, practical
Educational Resources	1. Mathematics. Grades 3-4: lesson plans for the program "School of Russia". - Volgograd: Uchitel, 2012. - 1 electron, opt. disc (CD-ROM). 2. http://rusfolder.com/32474579
Equipment	Interactive whiteboard (screen), computer, projector
Basic concepts and terms	Rules for multiplying any number by 0 and 1
Lesson stages	Educational and developmental components, tasks and exercises	Teacher activity	Student activities	Forms of organizing interaction in the lesson	Formed skills (universal learning activities)	Intermediate control
I. Motivation (self-determination) for learning activities	Emotional, psychological and motivational preparation of students for the assimilation of the studied material	Greets students, checks the readiness of the class and equipment, emotionally sets them up for learning activities. Our rest ends, work begins. We will work hard to learn something	Listen to teachers. Demonstrate readiness for the lesson, prepare the workplace for the lesson		K - plan educational cooperation with the teacher and peers. L - understand and accept the meaning of knowledge for a person; have a desire to learn; showing interest in the subject being studied	Supervision of the teacher over the organization of the workplace by students
II. Topic message, lesson objectives		Voices the topic, the purpose of the lesson	Listen to teachers	Frontal, individual	R - accept and save learning tasks
III. Knowledge update	1. Checking homework. 2. Oral counting: 1) Working with tables. 3) Problem solving	Checks for homework in notebooks. No. 47, 48. - What quantities are mentioned in the problem? - What is known in the problem? - What do you need to find? - How to find the cost if the price and quantity are known? - How do we solve the problem? - Make two inverse problems to this problem	- About price, quantity and value. - Price and quantity. - Cost - It is necessary to multiply the price by the quantity. 10-4=40	Frontal, individual. Frontal. Frontal	P - establish mathematical relationships between objects; use mathematical knowledge in an extended field of application; own logical actions, ways of performing tasks of a search nature; use various ways to search for the necessary information, sign-symbolic means to solve educational and cognitive problems. R - accept and save learning tasks, plan their actions in accordance with the set learning task to solve it. K - exchange opinions; they know how to listen to each other, build speech statements that are understandable for the communication partner, ask questions in order to obtain the information necessary to solve the problem; can work in a team, respect the opinions of other participants in the educational process. L - are aware of their capabilities in learning; are able to adequately reason about the reasons for their success or failure in learning, linking success with efforts, diligence; show a cognitive interest in the study of the subject	Oral answers, teacher's observations, completed assignments. Solving a text arithmetic problem
IV. Learning new material	1. Repetition of the rules for multiplying by 0 and 1. 2. Solving multiplication examples.	Consider the notes in the margins of the textbook, formulate the rules. What property of multiplication do you know? What are numbers called when multiplied? What are numbers called when divided? - Open the textbook on page 11 and look at the task at the top of the page. Why do you think these equalities are true? - Right. Using this property of multiplication, we will now decide with commenting at the board No. 44. No. 46.	1. If you multiply a number by zero, you get zero. 2. If you multiply zero by a number, you get zero. 3. If you multiply one by a number, you get the same number. 4. If the number is multiplied by one, the same number will be obtained. - Commutative: permutation of factors does not change the product. They answer questions.- These equalities are true, since the product does not change from the permutation of factors Rearrange the factors and solve the examples in a column with comments.	Frontal, individual.		Work with educational article. Know the rules for multiplying by 0 and 1.
	Physical education minute	Offers to perform movements according to physical education	Perform physical education	Frontal	P - accept and save the learning task K - manifest. willingness to listen to L - have a healthy lifestyle	Performing movements according to instructions
V. Practical activities	1. Problem solving. 2. Solution of examples. 3. Tasks from the electronic application to the textbook	No. 50. - What is asked to do in the task? Can you draw a rectangle right away? - Can you find its length? How to find the area of ​​a rectangle? 2-6=12 (cm). #53	- They ask you to first draw a rectangle, and then indicate how many centimeters the length is greater than the width. - No, because we don't know the length. - Yes. Need 2-3 = 6. Draw a rectangle. - You need to multiply the length by the width. Decide on their own.- Perform tasks		P - spend ; analysis, synthesis, comparison, generalization; consciously and arbitrarily build a speech statement, a logical chain of reasoning, evidence P - exercise control, assessment of volitional self-regulation in a situation of difficulty.
VI. Lesson results. Reflection	Summarizing the information received in the lesson. Final conversation. Grading	- Guys, what did we repeat at the lesson today? - Where were the rules applied? - What remains unclear? What task would you like to start the next math lesson with?			P - are guided in their system of knowledge. R - evaluate their own activities in the lesson. L - show interest in the subject, strive to acquire new knowledge
VII. Homework	Homework instruction	S. 113, No. 49, 52	Ask clarifying questions	Front work	R- accept and save the learning task, search for means to complete it.