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Ways of fast oral multiplication of numbers. Multiplication - Knowledge Hypermarket Chinese, or Japanese, multiplication




>>Math: Multiplication

35. Multiplication

Task 1. The factory produces 200 men's suits a day. When suits of a new style began to be produced, the consumption of fabric for one suit changed by 0.4 m 2. How much did the cost of fabric for suits change per day?

Decision. Fabric consumption for each suit increased by 0.4 m 2 . Therefore, in order to solve the problem, we need to multiply 0.4 by 200. We get 0.4 200 = 80. This means that the consumption of fabric for costumes per day increased by 80 m2, in other words, it changed by 80 m2

Task 2. The factory produces 200 men's suits a day. When suits of a new style began to be produced, the consumption of fabric for one suit changed by -0.4 m 2. How much did the cost of fabric for suits change per day?

Decision. Fabric consumption for each suit decreased by 0.4 m 2 . Therefore, the consumption of fabric for costumes per day decreased by 80 m 2 (0.4 200 \u003d 80). This means that the consumption of fabric for suits per day has changed by -80 m 2.
Thus, the product of -0.4 and 200 is -80, i.e. -0.4 200 = - (0.4 200) = - 80.
It is believed that 200 (-0.4) \u003d - (200 0.4) \u003d -80.

To multiply two numbers with different signs, you need to multiply modules these numbers and put a "-" sign in front of the resulting number

For example, (-1.2) 0.3= -(1.2 0.3)= -0.36; 1.2 (- 0.3)= -(1.2 0.3)= -0.36.

Comparing these two products with the product 1.2 0.3 = 0.36, you can see that when the sign of any factor changes, the sign of the product changes, but its modulus remains the same.

If the signs of both factors change, then the product changes sign twice and as a result the sign of the product does not change: 8 1.1 = 8.8; (- 8) 1.1 = - 8.8; (- 8) (-1.1)=-(-8.8) = 8.8. We see that the product of negative numbers is number positive.

To multiply two negative numbers, you need to multiply their modulus.

For example, (-3,2) (-9)= | -3.2| I-9| \u003d 3.2 9 \u003d 28.8. Usually they write shorter: (- 3.2) (- 9) \u003d 3.2 9 \u003d 28.8.
Since (- 3) 2 \u003d - (3 2), then you can write the first factor without brackets, i.e. (- 3) 2 \u003d - 3 2.
Formulate a rule for multiplying two numbers with different signs. How do you multiply two negative numbers?
1102. The water level in the river changes every day by a dm. How will the water level in the river change in 3 days if a = 4; -3?

1103. With an increase in air temperature by 1 ° C, the mercury column in the thermometer rises by 3 mm. By how much will the height of the mercury column change if the air temperature changes: a) by 15 °C; b) at -12°C?

1104. A tourist moves along the highway at a speed v km/h Now he is at point 0 (Fig. 89). If it moves in a positive direction, then its speed is considered positive, and in a negative direction - negative. The value t= -4 means "4 hours ago".

Where will the tourist be after t h? Solve the problem with the following meanings of the letters:


a) -5 6; g) 0.7 (- 8); m) 1.2 (-14);
b) 9 (-3); h) -0.5 6; o) -20.5 (-46);
c) - 8 (- 7); i) 12 (-0.2); n) -8.8 302;
d) -10 11; j) -0.6 (-0.9); p) -9.8 (-50.6);
e) 11 (12); l) -2.5 0.4; c) -17.5 (-17.4);
f) -1.45 0; m) 0 (-1.1); t) 3.08 (-4.05).

a) x + x + x + x + x + x c) - 2y - 2y - 2y;
b) -a -a -a -a; d) 5x + 5x + 5x + 5x + 5x.

1111. Find the value of the expression:

a) x + 4 + x + 4 + x + 4 if x = 9.1;
b) a - 1 + a - 1 + a - 1 + a - 1, if a \u003d -2.1.

1112. Guess what the root is equal to equations, and check:

a) -8 x = 72; b) - 4x=- 40; c) 6 y \u003d -54; d) -6 y = 66.

1113. Find the value of the expression:

a) 3 (- 2) + (- 3) (- 4) - (- 5) 7;
b) (-18 + 23-16-1+9) (-18);
c) (- 4.5 + 3.8) (2.01 -3.81);
d) (2.8-3.9) (-4.3-2.6);
e) - 4.5 0.1 + (- 3.7) (- 2.1) - (- 5.4) (- 0.2);
f) (2.3 (-1.8) -1.4 (-0.8)) (-1.5);
g) - 3.8 (-1.5) - (-1.2) 0.5 - 6.5;
h) - 2.321 (- 3.2 + 2.3 - 4.8 + 6.7) - 1.579.

1114. Do the following:

1115. Find the value:

1116. Perform the action:

1117. Compare:

a) |-3.5 + 2.9| and |-3.5| + |2,9|;
b) |-8.7-0.7| and |-8.7| + |-0.7|.

1118. Calculate orally:

1119. Present the number -12 as a difference: a) two positive numbers; b) two negative numbers; c) negative and positive numbers.

1120. Can the equality a-b = b-a be true? Give examples. Find a condition under which this equality is true.

1121. Can the difference of two numbers be greater than their sum?

1122. Choose such negative values ​​x and yy so that the value of the expression x - y is equal to:

1123. Do the following:

a) 3.78-(2.56-2.97); b) -6.19 + (-1.5 + 5.19).

1124. Solve the equation:

a) x + 3.2 = 1.8; c) 3.7 - x = -2.3;
b) 4.8 - x = 5.6; d) x - 3.9 = - 2.7.

1125. The album is more expensive than the book by 1.2 rubles. How much does a book cost and how much does an album cost if it is known that:
a) the album is 1.5 times more expensive than the book;
b) the book is 1.6 times cheaper than the album;
c) the price of the book is the price of the album;
d) the price of the book is 0.4 of the price of the album;
e) the price of the book is 80% of the price of the album?

1126. Find the value of the expression:


1127. Find the meaning of the work:
a) -24 36; e) -4.3 5.1; i) -1 (-1);
b) -48 (-15); f) -2.7 (-6.4); j) (-3) 2;
c) 33 (-11); g) - 1 (- 3.84); l) (-2.5) 2;
d) 1.6 (-2.5); h) -7.2 0; m) (-0.2) 3 .

1128. Multiply:

1129. Find the value of the expression:


1130. On Wednesday they brought 4.8 tons more hay than on Tuesday. How many tons of hay were brought over these two days, if on Tuesday they brought 1.4 times less than on Wednesday?

1131. The first number is 60. The second number is 80% of the first, and the third number is 50% of the sum of the first and second. Find average these numbers.

1132. The arithmetic mean of two numbers is 12.32. One of them is a third of the other. Find each number.

N.Ya.Vilenkin, A.S. Chesnokov, S.I. Schwarzburd, V.I. Zhokhov, Mathematics for grade 6, Textbook for high school

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Learn multiplication table - game

Try our educational e-game. Using it, tomorrow you will be able to solve math problems in the classroom at the blackboard without answers, without resorting to a tablet to multiply numbers. One has only to start playing, and after 40 minutes there will be an excellent result. And to consolidate the result, train several times, not forgetting the breaks. Ideally, every day (save the page so you don't lose it). The game form of the simulator is suitable for both boys and girls.

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Multiplication directly on the site (online)

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Multiplication table (numbers 1 to 20)
× 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120
7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160
9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180
10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220
12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260
14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280
15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320
17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340
18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360
19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380
20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

How to multiply numbers by a column (mathematics video)

To practice and learn quickly, you can also try to multiply numbers by a column.

And multiplication. Just about the operation of multiplication and will be discussed in this article.

Number multiplication

Multiplication of numbers is mastered by children in the second grade, and there is nothing complicated about it. Now we will look at multiplication by examples.

Example 2*5. This means either 2+2+2+2+2 or 5+5. We take 5 two times or 2 five times. The answer is 10 respectively.

Example 4*3. Similarly, 4+4+4 or 3+3+3+3. Three times 4 or four times 3. Answer 12.

Example 5*3. We do the same as the previous examples. 5+5+5 or 3+3+3+3+3. Answer 15.

Multiplication formulas

Multiplication is the sum of identical numbers, for example, 2 * 5 = 2 + 2 + 2 + 2 + 2 or 2 * 5 = 5 + 5. The multiplication formula is:

Where, a is any number, n is the number of terms a. Let's say a=2, then 2+2+2=6, then n=3 multiplying 3 by 2, we get 6. Consider in reverse order. For example, given: 3 * 3, that is. 3 multiplied by 3 - this means that the three must be taken 3 times: 3 + 3 + 3 \u003d 9. 3 * 3 \u003d 9.

Abbreviated multiplication

Abbreviated multiplication is an abbreviation of the multiplication operation in certain cases, and formulas for abbreviated multiplication have been developed specifically for this. Which will help to make the calculations the most rational and fast:

Abbreviated multiplication formulas

Let a, b belong to R, then:

    The square of the sum of two expressions is the square of the first expression plus twice the product of the first expression and the second plus the square of the second expression. Formula: (a+b)^2 = a^2 + 2ab + b^2

    The square of the difference of two expressions is the square of the first expression minus twice the product of the first expression and the second plus the square of the second expression. Formula: (a-b)^2 = a^2 - 2ab + b^2

    Difference of squares two expressions is equal to the product of the difference of these expressions and their sum. Formula: a^2 - b^2 = (a - b)(a + b)

    sum cube of two expressions is equal to the cube of the first expression plus three times the square of the first expression times the second plus three times the product of the first expression times the square of the second plus the cube of the second expression. Formula: (a + b)^3 = a^3 + 3a(^2)b + 3ab^2 + b^3

    difference cube of two expressions is equal to the cube of the first expression minus three times the product of the square of the first expression and the second plus three times the product of the first expression and the square of the second minus the cube of the second expression. Formula: (a-b)^3 = a^3 - 3a(^2)b + 3ab^2 - b^3

    Sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2)

    Difference of cubes two expressions is equal to the product of the sum of the first and second expressions by the incomplete square of the difference of these expressions. Formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Sign up for the course "Speed ​​up mental counting, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. In 30 days, you will learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Multiplication of fractions

Considering the addition and subtraction of fractions, the rule was voiced, bringing fractions to a common denominator in order to perform the calculation. When multiplying this do no need! When multiplying two fractions, the denominator is multiplied by the denominator and the numerator by the numerator.

For example, (2/5) * (3 * 4). Multiply two thirds by one quarter. We multiply the denominator by the denominator, and the numerator by the numerator: (2 * 3) / (5 * 4), then 6/20, we make a reduction, we get 3/10.

Multiplication Grade 2

The second grade is just the beginning of learning multiplication, so second graders solve the simplest tasks to replace addition with multiplication, multiply numbers, learn the multiplication table. Let's look at multiplication tasks at the second grade level:

    Oleg lives in a five-story building, on the top floor. The height of one floor is 2 meters. What is the height of the house?

    The box contains 10 packs of biscuits. Each pack contains 7 pieces. How many cookies are in the box?

    Misha arranged his toy cars in a row. There are 7 of them in each row, and there are only 8 rows. How many cars does Misha have?

    There are 6 tables in the dining room, and 5 chairs are pushed behind each table. How many chairs are in the dining room?

    Mom brought 3 bags of oranges from the store. The packages contain 22 oranges. How many oranges did mom bring?

    There are 9 strawberry bushes growing in the garden, and 11 berries grow on each bush. How many berries grow on all the bushes?

    Roma put 8 pipe parts one after the other, the same size of 2 meters. What is the length of the full pipe?

    Parents brought their children to school on the first of September. 12 cars arrived, each with 2 children. How many children did their parents bring in these cars?

Multiplication Grade 3

In the third grade, more serious tasks are given. In addition to multiplication, division will also be passed.

Among the tasks for multiplication will be: multiplication of two-digit numbers, multiplication by a column, replacement of addition by multiplication and vice versa.

Column multiplication:

Column multiplication is the easiest way to multiply large numbers. Consider this method using the example of two numbers 427 * 36.

1 step. Let's write the numbers one under the other, so that 427 is at the top and 36 is at the bottom, that is, 6 under 7, 3 under 2.

2 step. We start multiplication with the rightmost digit of the bottom number. That is, the order of multiplication is: 6 * 7, 6 * 2, 6 * 4, then the same with the triple: 3 * 7, 3 * 2, 3 * 4.

So, first multiply 6 by 7, the answer is: 42. We write it down like this: since it turned out 42, then 4 are tens, and 2 are ones, the recording is similar to addition, which means we write 2 under the six, and 4 is added to the two of the number 427.

3 step. Then we do the same with 6 * 2. Answer: 12. The first ten, which is added to the four of the number 427, and the second - units. We add the resulting two with the four from the previous multiplication.

4 step. Multiply 6 by 4. The answer is 24 and add 1 from the previous multiplication. We get 25.

So, multiplying 427 by 6, the answer is 2562

REMEMBER! The result of the second multiplication should be written down under SECOND number of the first result!

5 step. We perform similar actions with the number 3. We get the multiplication answer 427 * 3 = 1281

6 step. Then we add the received answers when multiplying and get the final answer of the multiplication 427 * 36. Answer: 15372.

Multiplication Grade 4

The fourth class is the multiplication of only large numbers. The calculation is performed by the multiplication method in a column. The method is described above in an accessible language.

For example, find the product of the following pairs of numbers:

  1. 988 * 98 =
  2. 99 * 114 =
  3. 17 * 174 =
  4. 164 * 19 =

Multiplication Presentation

Download a presentation on multiplication with the simplest tasks for second graders. The presentation will help children navigate this operation better, because it is presented in a colorful and playful way - in the best way for a child to learn!

Multiplication table

The multiplication table is studied by every student in the second grade. Everyone must know it!

Sign up for the course "Speed ​​up mental counting, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. In 30 days, you will learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Multiplication Examples

Multiplication by unambiguous

  1. 9 * 5 =
  2. 9 * 8 =
  3. 8 * 4 =
  4. 3 * 9 =
  5. 7 * 4 =
  6. 9 * 5 =
  7. 8 * 8 =
  8. 6 * 9 =
  9. 6 * 7 =
  10. 9 * 2 =
  11. 8 * 5 =
  12. 3 * 6 =

Multiplication by two digits

  1. 4 * 16 =
  2. 11 * 6 =
  3. 24 * 3 =
  4. 9 * 19 =
  5. 16 * 8 =
  6. 27 * 5 =
  7. 4 * 31 =
  8. 17 * 5 =
  9. 28 * 2 =
  10. 12 * 9 =

Two-digit multiplication by two-digit

  1. 24 * 16 =
  2. 14 * 17 =
  3. 19 * 31 =
  4. 18 * 18 =
  5. 10 * 15 =
  6. 15 * 40 =
  7. 31 * 27 =
  8. 23 * 25 =
  9. 17 * 13 =

Multiplication of three-digit numbers

  1. 630 * 50 =
  2. 123 * 8 =
  3. 201 * 18 =
  4. 282 * 72 =
  5. 96 * 660 =
  6. 910 * 7 =
  7. 428 * 37 =
  8. 920 * 14 =

Games for the development of mental counting

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

Game "Quick Score"

The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer "yes" or "no" to the question "are there 5 identical fruits?". Follow your goal, and this game will help you with this.

Game "Mathematical matrices"

"Mathematical Matrices" great brain exercise for kids, which will help you develop his mental work, mental counting, quick search for the right components, attentiveness. The essence of the game is that the player has to find a pair from the proposed 16 numbers that will give a given number in total, for example, in the picture below, this number is “29”, and the desired pair is “5” and “24”.

Game "Numerical coverage"

The game "number coverage" will load your memory while practicing with this exercise.

The essence of the game is to remember the number, which takes about three seconds to memorize. Then you need to play it. As you progress through the stages of the game, the number of numbers grows, start with two and go on.

Game "Guess the operation"

The game "Guess the operation" develops thinking and memory. The main essence of the game is to choose a mathematical sign so that the equality is true. Examples are given on the screen, look carefully and put the desired “+” or “-” sign so that the equality is true. The sign "+" and "-" are located at the bottom of the picture, select the desired sign and click on the desired button. If you answer correctly, you score points and continue playing.

Game "Simplify"

The game "Simplify" develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.

Game "Fast Addition"

The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers, the sum of which is equal to a given number. This game is given a matrix from one to sixteen. A given number is written above the matrix, you must select the numbers in the matrix so that the sum of these numbers is equal to the given number. If you answer correctly, you score points and continue playing.

Game "Visual Geometry"

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

Game "Mathematical Comparisons"

The game "Mathematical Comparisons" develops thinking and memory. The main essence of the game is to compare numbers and mathematical operations. In this game, you have to compare two numbers. At the top, a question is written, read it and answer correctly to the question posed. You can answer using the buttons below. There are three buttons "left", "equal" and "right". If you answer correctly, you score points and continue playing.

Development of phenomenal mental arithmetic

We have considered only the tip of the iceberg, in order to understand mathematics better - sign up for our course: Speeding up mental counting.

From the course, you will not only learn dozens of tricks for simplified and fast multiplication, addition, multiplication, division, calculating percentages, but also work them out in special tasks and educational games! Mental counting also requires a lot of attention and concentration, which are actively trained in solving interesting problems.

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Some quick ways verbal multiplication we have already sorted it out with you, now let's take a closer look at how to quickly multiply numbers in your mind using various auxiliary methods. You may already know, and some of them are quite exotic, such as the ancient Chinese way of multiplying numbers.

Ranking by category

It is the simplest way to quickly multiply two-digit numbers. Both factors must be divided into tens and ones, and then all these new numbers should be multiplied by each other.

This method requires the ability to keep up to four numbers in memory at the same time, and to do calculations with these numbers.

For example, you need to multiply the numbers 38 and 56 . We do it like this:

38 * 56 = (30 + 8) * (50 + 6) = 30 * 50 + 8 * 50 + 30 * 6 + 8 * 6 = 1500 + 400 + 180 + 48 = 2128 It will be even easier to do mental multiplication of two-digit numbers in three steps. First you need to multiply the tens, then add two products of ones by tens, and then add the product of ones by ones. It looks like this: 38 * 56 = (30 + 8) * (50 + 6) = 30 * 50 + (8 * 50 + 30 * 6) + 8 * 6 = 1500 + 580 + 48 = 2128 In order to successfully use this method, you need to know the multiplication table well, be able to quickly add two-digit and three-digit numbers, and switch between mathematical operations, not forgetting intermediate results. The last skill is achieved with help and visualization.

This method is not the fastest and most efficient, so it is worth exploring other ways of verbal multiplication.

Number Fitting

You can try to bring the arithmetic calculation to a more convenient form. For example, the product of numbers 35 and 49 can be imagined like this: 35 * 49 = (35 * 100) / 2 — 35 = 1715
This method may be more effective than the previous one, but it is not universal and is not suitable for all cases. It is not always possible to find a suitable algorithm to simplify the task.

On this topic, I recalled an anecdote about how a mathematician sailed along the river past a farm, and told his interlocutors that he managed to quickly count the number of sheep in the corral, 1358 sheep. When asked how he did it, he said that everything is simple - you need to count the number of legs, and divide by 4.

Visualization of multiplication in a column

This is one of the most versatile ways of mental multiplication of numbers, which develops spatial imagination and memory. First you need to learn how to multiply two-digit numbers by one-digit numbers in a column in your mind. After that, you can easily multiply two-digit numbers in three steps. First, a two-digit number must be multiplied by tens of another number, then multiplied by units of another number, and then sum the resulting numbers.

It looks like this: 38 * 56 = (38 * 5) * 10 + 38 * 6 = 1900 + 228 = 2128

Visualization with the arrangement of numbers

A very interesting way to multiply two-digit numbers is as follows. It is necessary to multiply the numbers in numbers sequentially to get hundreds, ones and tens.

Let's say you want to multiply 35 on 49 .

Multiply first 3 on 4 , you get 12 , then 5 and 9 , you get 45 . Write down 12 and 5 , with a space between them, and 4 remember.

You get: 12 __ 5 (remember 4 ).

Now multiply 3 on 9 , and 5 on 4 , and sum up: 3 * 9 + 5 * 4 = 27 + 20 = 47 .

Now you need to 47 add 4 which we remember. We get 51 .

We write 1 in the middle and 5 add to 12 , we get 17 .

So, the number we were looking for 1715 , it is the answer:

35 * 49 = 1715
Try mentally multiplying in the same way: 18 * 34, 45 * 91, 31 * 52 .

Chinese or Japanese multiplication

In Asian countries, it is customary to multiply numbers not in a column, but by drawing lines. For Eastern cultures, the desire for contemplation and visualization is important, which is probably why they came up with such a beautiful method that allows you to multiply any numbers. This method is complicated only at first glance. In fact, greater visibility allows you to use this method much more efficiently than multiplication in a column.

In addition, knowledge of this ancient oriental method increases your erudition. Agree, not everyone can boast of knowing the ancient multiplication system that the Chinese used 3000 years ago.

Video on how the Chinese multiply numbers

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Mathematics Date "___" _______ ____ d Grade 3- "B" (1st quarter) Lesson 35 Lesson topic: Multiplication and division table by 4 Lesson objectives: 1. to develop the ability to solve problems that reveal the meaning of multiplication and division, their relationship; tasks related to four arithmetic operations. 2. To consolidate thinking, speech, attention. 3. To cultivate cognitive activity, the ability to work in a team, the ability to evaluate oneself and classmates Type of lesson: a lesson in consolidating knowledge; Equipment, visibility, TSO: ________________________________________________________________________________________________________________________________________________ Stages and structure of the lesson. 1. Organizational moment. Emotional mood. Motivation. Psychological mood. Children sit with their eyes closed and listen carefully to the teacher, the last word of each of his phrases is spoken in unison. - In the lesson, our eyes carefully look and everything ... (see). Ears listen attentively and that's it... (hear). Head well... (thinks). (Calligraphy) 2. Actualization of knowledge 1. Game "Yes. No". Examples are given on the board: 4x6, 8x3, 4x5, 7x3, 9x4, 5x6. Show cards with numbers. If the number is the answer, the students say "Yes" in unison, then say the example 4x6=24. if the number is not the answer, say "No". 2. Game "In order". Examples are given: 8x3 4x2 3x6 7x3 5x3 4x9 Name the values ​​of the expressions in ascending (or descending) order. Mathematical dictation. Purpose: to test knowledge of the multiplication table and division by 2-4. 1). The first factor is 7, the second is 3. Find the product. 2). 20 to reduce by 5 times. 3). What is the dividend if the quotient is 2 and the divisor is 7? four). Dividend 28, divisor 4. Find the quotient. five). Take the number 8 3 times. 6). 6 increase by 4 times. 7). Find the product of the numbers 4 and 7. No. 1, No. 2 3. Repetition of the material covered. No. 3 a) In the entrance of an eight-story building, 4 apartments on each floor. How many apartments are in the block? 4 8 \u003d 32 (sq.) Inverse: There are 32 apartments in the house. There are 4 apartments on each floor. How many floors are in the house? The 32 apartment building has 8 floors. How many apartments are on each floor. It is convenient to make a table and move the question to compose inverse problems. Apartments per floor Number of floors in the building Total apartments in the building 4 sq. 8 ? 4 sq. ? 32 sq. ? 8 32 sq. b) The electrician screwed in 32 light bulbs, 4 in each chandelier. How many chandeliers were there? Bulbs in one chandelier Number of chandeliers Total bulbs 4 bulbs. ? 32 lamps. 4 lamps. 8 ? ? 8 32 lamps c) To congratulate the veterans, the children bought 4 bouquets of 3 carnations each. How many carnations did the children buy in total? Carnations in one bouquet Number of bouquets Carnations in total 3 4 ? 3? 12 ? 4 12 4. Repetition of the multiplication table and calculation rules for actions No. 7 14 + 18: 2 (5 + 7) : 4 (15 + 3): 2 1) 18: 2 = 9 1) 5 + 7 = □ 1) 15 + 3 = 2) 14 + 9 = 23 2) 12: 4 = □ 2) 18: 2 = 5. Primary consolidation Dynamic pause We worked together, A little tired. Quickly, everyone at once stood behind their desks. Let's raise our hands, then spread them apart And inhale very deeply with our whole chest. 6. Independent work. No. 4, No. 5 Self-examination No. 4 With games - 5 d With films - ? 4 times more 5 4 = 20 (e) Dynamic pause. 7. Repetition Work in a notebook on a printed basis can be done independently. 8. Reflection To summarize, you can involve several students who play the role of an "observer". They are invited to analyze the work of the class as a whole and the work of individual students. Homework. Multiplication table by 4. Theme of the lesson: Multiplication and division table by 4 Lesson objectives: 1. to develop the ability to solve problems that reveal the meaning of the operations of multiplication and division, their relationship; tasks related to four arithmetic operations. 2. To consolidate thinking, speech, attention. 3. To cultivate cognitive activity, the ability to work in a team, the ability to evaluate oneself and classmates

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