Addition of multivalued numbers. Oral addition of multivalued numbers addition of multivalued numbers
Topic: the sum of three and more components.
Purpose: - Passing by students by the method of addition of multivalued numbers, relying on previous knowledge of the laws of mathematics.
Tasks:
- Formation of computing skills.
- The development of logical thinking, speech, the ability to express their opinion, to prove its point of view, subordinate to the general rules.
Education of morality and.
Equipment:
- Textbook:, "Mathematics. »Part 1, Ventana Graph, 2013;
workbook: "Mathematics. Grade 3 "№1, Ventana Count, 2013;
- signs with examples;
- cards with task schemes and with additional tasks;
- Presentation.
During the classes
1. Organizing: Preparation of students for work
Teacher: - What mood came to lesson? (Children's answer options)
- What do you want yourself in this lesson? (Children's answer options)
I wish you to actively participated in the lesson, learned the new material and managed to apply it in the future.
(Recover notebooks. Record the number and "cool work".)
2. Actualization of reference knowledge:
On the board, examples:
49+203+301+17
40+29+125+231
99+85+105+201
Teacher: - We hold the game "Best Counter".
(From each row, it goes to one student and become back to the board. The teacher shows for example. Students sitting at the desk, verbally decide it. According to the student's sign, the choir say the answer. Students standing at the board at the same time turn to the examples and find that example, whose answer was named. Wins the one who first pointed out the correct example.)
Well done!
3. Definition of the lesson theme. Setting educational tasks.
Teacher: - What is the feature of these examples?
Pupils: - All examples for addition.
Teacher: - Did any of them have any difficulties?
Teacher: - Try to define theme lesson.
(Response options: addition. Addition in more difficult cases. New addition.)
Teacher: - Theme of the lesson "Amount of three and more components".
Teacher: - Suppose we will learn?
(Options for answers.)
Teacher: (on the screen)
Purpose:
a) find out the way of addition of three and more allegations
b) learn to perform the addition of numbers in a convenient way
4. Work on the subject of the lesson:
1) Preparatory
Open the working notebooks on with. 37, Perform № 000.
What should be done?
What conclusion can be done? (from the permutation of the terms value does not change)
On the board, the Move Property Property (Card)
Teacher: - Perform № 000.
What should be done?
Read what you have happened.
What conclusion can be done? (Conditions can be grouped)
On the board, the combinated property of the addition (card)
Teacher: - Perform № 000.
What should be done?
Read what you have happened.
What conclusion can be done? (expressions with brackets can be written without brackets, but provided that this expression is the amount)
On the board of expressions with brackets (sum) (card)
Teacher: - Close the workbooks, open textbooks on page 84 and tell me what properties of the addition were the wolf and hare, performing the records?
Teacher: - Now work in pairs, perform the same entries for expression
(8 + 3) +2 (on the screen) as a wolf and hare
On the screen - check if everyone turned out such records:
What properties of addition did you apply? (Move. And combine.)
Why do we need it? (To faster and correctly solve examples, 8 + 2 \u003d 10, and to 10 it is more convenient to add any numbers, you will not be mistaken).
Teacher: - When performing any task, we must look for rational, i.e., a convenient solution.
Teacher: - Let's return to our examples (a card with examples are displayed again).
- Relying on the conclusions that we have done, offer solutions.
2) "Opening" of a new knowledge
Children work at the board with an explanation (which properties of addition are used) (Ost. In Tetder)
49+203+301+17
40+29+125+231
99+85+105+201
Conclusion: Movement and combinated properties of addition make it possible to record expressions containing only addition, without brackets and perform calculations in any order.
3) specifying a new method of action; Primary fixing
Teacher: - What else needs to be done to learn how to make the addition of several terms?
Pupils: - try to solve an example almost.
Teacher: - And where can I take more examples for training?
Pupils: - in the textbook.
Teacher: - We work on the textbook.
Pupils open textbooks, find page (p.84) №3. Work at the board
They pronounce which embodiment properties are used and conclude: Movement and combinated addition properties make it possible to write expressions containing only addition, without brackets and perform calculations in any order.
4) independent
- Who believes that learned to perform examples of this type, raise your hand? Why do you think so?
(Options for answers.)
Teacher: - How could you check if you really know how to solve such examples?
Pupils: - Perform yourself to work yourself.
Teacher: - Check how well you learned. We carry out № 5 on page 85 itself
Teacher: - Do not forget to check your work.
Teacher: - Now change notebooks and check the work of the neighbor (on the screen 149 + 301 + 203 \u003d (149 + 301) + 203 \u003d 450 + 203 \u003d 653
340+129+231= 340+(129+231)=340+360=700
199+185+201=(199+201)+185=400+185=585
125+392+75=(125+75)+392=200+392=592
What conclusion can be done?
Movement and combinated addition properties make it possible to record expressions containing only addition, without brackets and perform calculations in any order.
We will use our knowledge gained in the lesson? When?
Fizminutka
5. Repetition passed: problem solving
Teacher: - Read № 13 on page 86
Read the task. - Who speaks about it? What do you know about boys?
Read the task. Can we answer it right away? Why?
Work in pairs. - Before you lies the table - a short condition for this task that will help you when solving. What should be in a brief condition? (All data and question). Fill in the table together.
Check. (ON THE SCREEN)
Teacher: - write down the problem in the notebook.
Teacher: - Compare your work with the work of the comrade. (Mutual test.)
Record at the board with one student.
Work in the working notebook № 000,131
6. The result of the lesson. Reflection.
Teacher: - What topic was studying in this lesson?
Pupils: - Amount of three and more components.
Teacher: - What was the particularly possible? (Options for answers.)
Teacher: - At what stage did the difficulty experience? Why was it difficult? (Options for answers.)
Teacher: - Try to evaluate your work; class work. (Answer options)
Teacher: - What would I want to still work on? (Options for answers.)
Teacher: - I thank everyone for the active work in the lesson. Today, inquisitiveness and seducker came to the rescue. Always remember "Learn - always come in handy" (the proverb is hanging on the board.)
7. Homework
Teacher: - I advise at home to consolidate the material studied, for this, in the working notebooks, comply with № 000,135. (Write down the task in the diary.) Additionally, who wishes a tutorial - №8, p. 85.
Unambiguous numbers fold using the folding table. The folding table, or rather the results of the addition of unambiguous numbers, you need to remember by heart.
Example. Mix the unambiguous numbers 4 and 9:
Addition of multivalued numbers
Multivissal numbers are folded by discharge, using a transitional and combat laws of addition.
Example. Mix two-digit numbers 26 and 48:
26 + 48 = (20 + 6) + (40 + 8) = 20 + 6 + 40 + 8 = (20 + 40) + (6 + 8) = 60 + 14 = 60 + (10 + 4) = 60 + 10 + 4 = (60 + 10) + 4 = 70 + 4 = 74
At first we laid down the components on the categories, then they were grouped into one group of dozens, to another - units and performed additions on discharges, i.e. there were dozens of dozens and units with units, then one dozen, resulting from the addition of units, added to dozens, Which we had 6 from the addition of tens, and at the end there are dozens with units.
The form of the addition form that we used is too long and therefore inconvenient, so when the multi-valued numbers are usually used, another, more convenient form of a recording, which is called the addition of a column.
Addition of the Stage
The addition of multivalued natural numbers is more convenient to perform in the column.
Addition of the Stage - This is a form of recording and a method of addition used by the addition of multivalued numbers. Adding a column otherwise called adding to the column.
Consider the addition of the column on the example of the addition of numbers 7056 and 483.
The addition in the column is written as follows: one term is recorded under another so that the numbers of the same discharges stood in each other (units under units, tens are ten or so on.). For convenience, it is usually a smaller number written under great. On the left between the terms sign plus, and under the bottom, a horizontal trait is carried out:
The resulting entry can be mentally divided into the columns as shown in the picture:
All further actions are reduced to the addition of unambiguous numbers that are in one column. The calculation is performed on the right left, starting from the discharge of units.
If, as a result of the addition, the number is less than 10, then it is recorded under the line in the same discharge.
We begin the calculation from the discharge of units: we fold the numbers 6 and 3. As a result, we have a number 9. Since 9< 10, то записываем это число под чертой, в том же разряде:
If, as a result of the addition, a number equal to 10 or more is obtained, then the value of the discharge of the obtained number is recorded under the line in the same discharge, and the discharge value of the tens of the received number is remembered (it is used in the next step).
Go to the addition of numbers in the next category, that is, the addition of the values \u200b\u200bof the discharge of dozens. We fold the numbers 5 and 8, we obtain the number 13. Since 13\u003e 10, then below the line, in the same discharge, write the number 3 (this is the value of the discharge of the numbers 13), and the number 1 remember (this is the value of the discharge of tens of number 13), At the same time they say three write, and one in mind . In order not to forget about the memorized number, it is usually written on top above the following (left) discharge:
The memorized number is added to the sum of the numbers of the next discharge.
We turn to the next discharge and fold the number 0 and 4. As a result, we have 4. To the resulting number add a memorized number 1, we get 5. Since 5< 10, то под чертой, в том же разряде, записываем число 5:
After that, the transition to one digit left and the actions are repeated. This process continues until the numbers are terminated.
If there is only one number in the column, and we have no memorized number (from previous addition), in this case we simply write this number under the feature, in the same discharge.
Since the next page there is only one number - 7, and in memory we do not have a memorized number, then we simply write 7 below the feature, in the same discharge:
There is no further numbers in memory, too, no numbers. On this process of addition can be considered completed. The natural number obtained under the feature is the result of the addition of these numbers. Now you can record the amount of these numbers in the usual form:
7056 + 483 = 7539
Consider a couple of examples of grades addition to deal with the remaining nuances.
Example. Moving the number 29 and 6 by the column.
We fold 9 and 6, as a result we obtain number 15. Since 15\u003e 10, then the number 5 is written, and the number 1 remember:
If the column contains only one number, and we have a memorized number (from previous addition), the memorized number is simply added to this one.
In the next column there is only one number - 2. Since we have a number 1 in memory, it must be added to 2. As a result, we obtain a number 3:
Example. Moving the column of numbers 43 and 94.
We fold 3 and 4. As a result, we have a number 7. Since 7< 10, то записываем это число под чертой, в том же разряде:
If in the last discharge as a result of the addition, a number of 10 or more 10 is obtained, then the value of the discharge of the obtained number is recorded under the line in the same discharge, and the discharge value of the tens of the received number is recorded below the line in the next discharge.
In the following discharge, we add numbers 4 and 9, we obtain number 13. Since 13\u003e 10, then below the line, in the same discharge, write the number 3, and the number 1 is written below the line in the next discharge:
The convenience of addition in the column lies in the fact that the addition of multivalued natural numbers is actually reduced to the addition of unambiguous numbers and the recording of the addition process takes less space.
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"Mathematics tasks for grade 3" - Mathematics 3 class. Consider triangles. Two neighbor came. Types of triangles. Triangle. Bring into the table number triangles. Signs of a triangle. Choose a stick. Isosceles triangle. What an excess figure. Crossword. Logical task.
"Check multiplication" - fun tasks. Objectives lesson. Fizkultminutka. Dividend. The design of the board. Verbal counting. Fastening a new material. Stages lesson. Multiplying two numbers check the division. Type of lesson. Check multiplication. Goal. Factor. Collective work. Studying a new material. Organizing time.
"Test for multiplication and division" - Finish the approval. Multiplication and division. Distribute the values \u200b\u200bof expressions in ascending order. Consider the drawing and answer the question. Decide the task. The sum of the numbers 20 and 16 is divided into the difference between numbers 80 and 76. Private of which two numbers is 8. How many pages in the second book. The area of \u200b\u200bwhich figure is 16 cm. Transferred objects. Increase 5 times. Choose a sure continuation.
"The division of numbers with the residue" is to fake with a picture of the drawing. 21: 5 76: 9. What is the intended number? Reduce 36 to 9 times. Is it always convenient to perform division using a picture? A task. I'll succeed today! Find a private: 20: 5 \u003d 4 Find the residue: 21 - 20 \u003d 1 21: 5 \u003d 4 (OST. 1). 3 less than the intended number 5 times. 36 Reduce 9 times. 13 athletes were prepared for jumping competitions. How many times are 24 more 6?
"Square decimeter" - 1 dm2 \u003d 100 cm2. Think. Square decimeter. The task. Theme lesson. Perimeter. 20 meters of fabric are needed for 10 suits. How it is associated with a square centimeter. Measure the side of the rectangle. Spectator gymnastics.
Compiled by: Oquessenova K.Zh.
Your attention is offered a system of cards for the correction of knowledge at the rate of mathematics 5-6 classes.
Cards cover key courses. Each is dedicated to one separate question and consists of three parts: Instructions (rule formulation), sample application of this instruction and fifteen tasks for students.
Cards are designed for additional classes with learning (in class or at home). If the student at such a lesson correctly completed the first five tasks out of fifteen, this is enough. If he could not do this, the teacher must explain to him the material and give the following five tasks. If these tasks cannot be performed, the explanation continues, and the remaining five tasks are solved.
Card number 1. Addition and subtraction of multivalued numbers (repetition)
| Find amounts and differences: |
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Card number 2. Multiplication of the Stage (Repetition)
| Perform the specimens on the samples | ₓ707 2) ₓ104 216 205 707 208___ 1414___ 21320 301____ | Find works: |
Card number 3.Corner (repetition)
| Make a sample task | 19034│_62 __ 186_ 307 | Find private: |
Card number 4.Comparison of decimal fractions
| Are parts equal? More that fraction that she is more Figures of the tenths are equal Figures of hundredths are equal | 1) 12.86 and 18.06 2) 6,453 and 6,2883 42→6,4536,2883 3) 120,3586 and 120,36 4) 2,112 and 2,1100 20→2,1122,1100 | Compare fractions: |
| 49,1803 and 49,18 |
Card number 5. Addition and subtraction of decimal fractions (repetition)
| Fold and deduct the numbers on the categories of the same name |
| Calculate: |
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Card number 6. Multiplying decimal fractions
| Experienced commas. Modify the resulting natural numbers. Separate in the work of so many decimal signs, how many of them in all the factors together. | 0,14 1,3 2=0,364 Short record: 0,14 1,3 2=0,364 | Find works: |
Card number 7.Decimal decimal fraction on a natural number.
| Delhi fraction as an integer. Immediately after demoling the figure of the tenths put the comma in private and continue the division. | 2452,800│75 225 32,704 | Find private: |
Card number 8.Calculate the values \u200b\u200bof alphabetic expressions.
| Fold the numerical values \u200b\u200bof variables instead of letters. Find the value of the resulting numerical expression. | Find the value of the expression: if a \u003d 25, b \u003d 13 a + 7- (b + 6) \u003d 25 + 7- (13 + 6) \u003d 32-19 \u003d 13 | Find expressions: |
| a + 3, if A \u003d 7 50-x, if x \u003d 23 4Y if Y \u003d 15 a + b if a \u003d 8, b \u003d 5 m: n, if m \u003d 12, n \u003d 4 |
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| 3 + B if b \u003d 14 k-37, if k \u003d 88 11a, if a \u003d 6 n-M, if m \u003d 7, n \u003d 43 aC if a \u003d 12, c \u003d 4 |
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| f-39, if f \u003d 77 t + 13, if t \u003d 28 16D if D \u003d 3 p-Q, if p \u003d 4, q \u003d 9 y: x, if x \u003d 5, y \u003d 25 |
Card number 9.The solution of the simplest equations.
| Find a similar sample and perform tasks. | x + 13 \u003d 19 2) x-3 \u003d 9 3) 29-x \u003d 18 4) x 7 \u003d 35 x \u003d 29-18 x \u003d 35: 7 5) x: 4 \u003d 9 6) 66: x \u003d 6 | |
Card number 10.Being percent of the number.
| Write that 100% is a. Find 1% of A. Find x% of a. | Find 2% of 2000m. 100% - it is 2000m 1% - It is 2000: 100 Answer: 40m. Short record: (2000:100) 2=20 00 2 =40 | Find 2% of 600. Find 15% of 6. Find 6% of 3 kg. The device worth 4000 TNG fell by 20%. How long did the device fell? What is more, 40% of 20 or 30% of 40? |
| Find 4% of 1600. Find 13% of 5. Find 8% from 7 km. The city had 3 million inhabitants. For 10 years, the population has grown by 17%. How many people are now in the city? What is more than 41% of 57 or 57% of 41? |
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| Find 5% of 2100. Find 18% of 2. Find 8% of 1 h. The contribution of $ 2000 per year increased by 5%. What is the contribution now? What is more than 50% of 47 or 52% of 49? |
Card number 11.Finding a percentage.
| Write that 100% is b. Find 1% of b. Find how many times 1% of B is placed in a. | Find the percentage ratio of the number 7 to the number 2.5. 100% is 2.5 1% is 2.5 100 1% is 0.025 0.025 is placed among 7. 7: 0.025 \u003d 280 times. Answer: 280. Short record: 7:(2,5:100)=7 100 =280 | Find a percentage: a) 2 to 100 b) 13 to 6.5 How many percent is: a) 17 from 50? b) 2.8 from 350? If in your class 25 students, how many percent of the class do you make? |
| Find a percentage: a) 12 to 50 b) 19 to 9.5 How many percent is: a) 23 from 200 b) 3.8 from 5.7 Frals of tea fastened with milk 6% fat. What is the percentage of fat in tea? |
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| Find a percentage: a) 29 to 25 b) 14 to 9.1 How many percent is: a) 17 from 50 b) 2.8 from 5.6 In class 12 girls and 16 boys. Find the percentage of these numbers. |
Card number 12. Finding a number by its percentage.
| Write that N% of numbers are equal to a. Find 1% of the number. Find 100% (number number). | Find the number of 3% of which is 960. 1% is 960: 3 100% - it is 320 100 100% is 32000 Answer: 32000. Short record: (960:3) 100=960 100 = 32000 | 6% What number are 180? 16% What number is equal to 36? Find the cost of goods, 14% of which is equal to 3500 TNGs. Find the distance, 73% of which is 2.6 km. |
| 5% of which number is equal to 30. 15% of which number is equal to 21. Find the cost of goods, 13% of which is equal to 6500 TNGs. Find area, 26% of which are 5.2 cm. 20% of the contribution to Sberbank is 8000 TNGs. What is the whole contribution? |
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| 10% of which number are equal to 240. 13% of which number is equal to 39. Find the cost of goods, 15% of which is 2250 TNG. Find the distance, 87% of which are equal to 17.4 km. 30% of the contribution to Sberbank is 45,000 TNGs. What is the whole contribution? |
Card number 13.Comparison, addition and subtraction of fractions with the same denominators.
| Compare, fold or deduct the numerators. | 4
2
Since 42. 4 2 4+2 6 4 2 4-2 2 | Compare fractions, find them amounts and differences: 11 and 9 ; 7 and 9 ; 17 and 15 20 20 15 15 19 19 3 and 5 ; 14 and 4 |
| 15 and 11 ; 8 and 29 ; 4 and 17 63 63 33 33 25 25 17 and 15 ; 64 and 13 |
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| 27 and 29 ; 105 and 215 ; 13 and 27 102 102 156 156 144 144 11 and 7 ; 14 and 26 |
Card number 14.The main property of the fraction.
| Give a fraction to a new denominator: multiply (or stripped) the denomoter of the fraction for a number. multiply (or stripped) the fluster numerator on the same number. | 1) lead fraction 2 to denominator 18. Answer: 12 2) lead fraction 8 to denominator 7. Answer: 4 | Lead fractions: but) 1 to denominator 22; b) 3 to denominator 7. on 2; multiply the numerator and denomoter 1 on 4. Split 26 on 2. |
| Lead fractions: but) 3 to denominator 28; b) 12 to denominator 7. 36 on 2. Multiply the numerator and denominator 3 by 5. Split 42 at 7. |
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| Lead fractions: but) 4 to denominator 36; b) 33 to the denominator 11. Split the numerator and denominator 28 at 7. Multiply the numerator and denomoter 3 on 4. Divide 55 at 11. |
Card number 15. Multiplication of fractions.
| Multiply the numerator to the numerator, and the denominator to the denominator: a. . c. = aC | 1) 3 4 = 3 4 = 12 2) 3 4 = 3 4 = 12 3) 5 13 = 5 13 = 13 | Find works: 1 4 ; 4 5 ; 4 5 ; 4 3 ; 3 11 3 5 7 9 1 11 3 4 2 5 |
| 7 1 ; 8 3 ; 4 3 ; 7 2 ; 7 4 9 2 9 7 13 1 3 5 2 3 |
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| 4 2 ; 7 6 ; 7 2 ; 6 16 ; 11 10 7 5 8 5 9 1 11 3 4 9 |
Card number 16. Division fractions.
| Multiply the numerator to the denominator, and the denominator on the numerator: a. : c. = aD | 1) 2 : 3 = 2 7 = 14 2) 3 : 21 = 3 1 = 1 3) 55 : 11 = 55 7 = 35 4) 5 : 55 = 5 6 = 2 5) 9 : 101 = 9 1 = 9 | Find private: 4 : 3 ; 2 : 7 ; 5 : 9 ; 4 : 1 ; 15 : 19 9 5 3 1 1 1 1 8 2 2 |
| 16 : 31 ; 2 : 7 ; 1 : 3 ; 14 : 2 ; 13 : 10 1 1 7 1 5 7 1 7 3 3 |
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| 17 : 37 ; 15 : 5 ; 2 : 11 ; 7 : 14 ; 19 : 38 1 1 1 3 11 1 9 81 7 21 |
Card number 17. The main property of proportion.
| The work of extreme members of the proportion is equal to the product of its average members. An unknown extreme member of the proportion is equal to the product of its average members shared on the famous extreme. An unknown medium member of the proportion is equal to the product of its extreme members shared on the famous average. | 1) Check the proportion: 2) Solve equation: a) x \u003d 7 18: 14 \u003d 9 b) x \u003d 75 2: 25 \u003d 6 3) Solve equation: a) x \u003d 24 13: 8 \u003d 39 b) x \u003d 6 70: 2 \u003d 210 | Check the proportion: Solve equations: x: 6 \u003d 8: 4 5: 2 \u003d T: 4 1: 5 \u003d x: 25 6: 3 \u003d 18: Y |
| Check the proportion: Solve equations: 2: A \u003d 5 : 5 ; x: 12 \u003d 75:15 12.4: x \u003d 5,58: 0.9 2 : 5 = h. : 1 |
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| Check the proportion: 9 : 3 = 12 : 8 Solve equations: 12.4: x \u003d 5,58: 0.9 4.5: x \u003d 12,5: 4 3 = 18 |
Card number 18. The addition of rational numbers using the coordinate direct.
| To add to the number but Positive b., enough to move from but Right to b. units. To add to the number but a negative number b., enough to move from butleft on ( - b.) Units. | 1) (-6)+4=? Answer: (-6) + 4 \u003d -2 Answer: (-7) + (- 3) \u003d - 10 | Find amounts: |
Card №19. The addition of rational numbers without the help of the coordinate direct.
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Numbers but and in one sign? |a + in | \u003d | a | + | in | Sign the same |a + in | \u003d | a | - | in | Sign of Number a. |a || in| not | Numbers (-6) and (-2) of one sign, which means: │-6+(-2)│=│-6│+│-2│=8 The sign is the same - minus. Answer: (-6) + (- 2) \u003d - 8 Numbers 4 and (-9) different characters, │-9││4│, So: │4+(-9)│=│-9│-│4│=5 So numbers (-9) - minus. Answer: 4 + (- 9) \u003d - 5 | Find amounts: |
Card number 20. Subtraction of rational numbers.
| a - b \u003d a + (-b) | 1) (-6) - (-2) = (-6) + 2 = -4 2) 5 – 13 = 5 + (-13) = -8 | Find differences: |
Card №21. Multiplying rational numbers.
| │a b│ \u003d │a│ │b│ If a and b is one sign, then the mark of the work is plus, and if different is minus. | │(-5) (-2)│=│-5│ │-2│=5 2=10, (-5) and (-2) one sign, so the sign of the work plus. Answer: (-5) (-2) \u003d 10 │5 (-2)│=│5│ │-2│=5 2=10, 5 and (-2) different signs, therefore the sign of the work minus. Answer: 5 (-2) \u003d - 10. | Find works: |
Card number 22. Division of rational numbers.
| │a: b│ \u003d │a│: │b│ If a and b is one sign, then the sign of the private plus, and if different is minus. | │(-21):(-7)│=│-21│:│-7│=21:7=3, (-21) and (-7) have the same signs, so a private plus sign. Answer: (-21): (- 7) \u003d 3 │21:(-7)│=│21│:│-7│=21:7=3, 21 and (-7) have different signs, so a sign of a private minus. Answer: 21: (- 7) \u003d - 3 | Find private: |
Mm «Merseys Orta Mecteb_»
GU "Pereleuskinskaya High School"
Mathematics 5-6 classes
Cards for knowledge correction.
34. Addition and subtraction of multivalued numbers.
On first:
Addition and subtraction of multivalued numbers are performed by receptions for written computing. The basis of the algorithms for addition and subtraction of the numbers of any class is the bonnetic addition and subtraction.
When selecting examples, such an order must be observed:
1. At the first stage, the actions of addition and subtracting without transition through the category are performed;
2. At the second stage, operations are performed with the transition through a discharge in one, then in two or more discharges;
3. In the third stage, the deduction actions are performed, in which the reduced contains one or more zeros or zeros in a decrease alternate with units.
When adding and subtracting, the pillars and biddly record numbers in the column are observed. Addition and subtraction are prepared on the first class, starting from the first class units.
In the first lessons, it is necessary to require students to explain the disconnection and subtraction, that is, the explanations of how the discharge units are folded or subtracted. Then the explanation is coagulated.
Before solving examples of addition and subtraction with the transition through a category, preparatory exercises must be carried out, which will make it easier for written computing. For example:
7 units. + 8 units. \u003d 15 units.
10 units. - This is 1 dec.
10 units. thousand - this is 1 dec. thousand
15 units. - It is 5 units. and 1 dec.
13 dec. - It is 3 units. and 1 dec.
15 hundred. - It is 5 hundred. and 1 thousand
10 dec. - This is 1 hundred.
10 dec. thousand - this is 1 hundred. thousand
The implementation of the action of addition and subtraction with the two components is accompanied by test actions, besides this, the addition is checked by the permutation of the terms, and subtraction is not only addition, but also by subtraction. Verification of actions is performed on accounts.
By destiny:
For the addition of multivalued numbers The basis of the actions of students is the algorithm of addition, the essence of which comes down to the following:
1. Record the second term under the first so that the corresponding discharges are in each other.
2. The figures are folded (this term is used for brevity, in general here we are talking about an unique number indicated by a digit) of the discharge of units. If the sum is less than 10, it is recorded in the discharge of the response units and go to the next discharge.
3. If the amount of numbers of units is greater than or equal to 10, then represent it in the form: 10 + C0, where C0 is a unique number; Record C0 in the discharge of the response units and add 1 to the digit of the top of the first term, after which they are moving to the discharge of dozens.
4. Repeat the same actions with dozens, then with hundreds, etc. The addition process ends when the digits of senior discharges are made.
The algorithm for subtracting multivalued numbers can be represented in this form.:
1. Record subtractable BN BN-I ... BI B0 under the reduced An APN ... A-I A0 so that the corresponding discharges are in each other.
2. If the digit in the discharge of the units of the subtracted does not exceed the corresponding figure of the dimension, then it is subtracted from the corresponding figure of the decreased, after which they go to the next discharge.
3. If the digit of the units subtracted larger numbers of units of reduced, i.e.
4. If the digit of the units subtracted longer numbers of the dimensions are reduced, and the numbers standing in the discharge of dozens, hundreds, etc. reduced, are zero, then they take the first, different from zero, the figure in a decrease (after the discharge of units), reduce it on 1, all the numbers in junior discharges to discharge dozens inclusively increase by 9, and the figure in the discharge of units - by 10 is subtracting BO from 10 + A0, write the result in the discharge of difference units and move to the next discharge.
5. In the next discharge, the process is repeated.
6. The subtraction process ends when subtraction from the older discharge is reduced.
The above describing algorithms are given by students of primary classes in a simplified form, where only the highlights are recorded:
1) the second term (subtracted) must be recorded under the first (under reduced) so that the corresponding discharges are found in each other;
2) Addition (subtraction) should be started with a lowest discharge, i.e. To fold (deduct) first units.
Methods of oral calculations
Oral techniques of addition and subtraction of multivalued numbers are studied in 4th grade of a four-year-old elementary school in the following order:
1. Numbering cases
a) cases of the form:
99 999 + 1 345 000 - 1 560 999 + 1
560 000 - 1 399 999 + 1 40 000 - 1
When performing the calculations of this species refer to the principle of constructing a natural range of numbers: adding to the number of units gives the number next to the account; The subtraction of the unit gives the number preceding in a row.
For example: 399 999 + 1 - adding to the number 1, we obtain the number the following. The following is 399 999 Number 400,000, which means 399 999 + 1 \u003d 400,000.
b) cases of the form:
30 000 + 1 000 650 999 - 900 600 000 + 5
60 345 - 5 345 000 - 45 000 800 700 + 1 000
When performing the calculations of this species, the child must know well the principle of the bonnetic structure of numbers in a decimal number system.
650 999 - 900 - 650 099
2. Addition and subtraction of whole thousand
Addition and subtraction of the type of 32,000 + 2,000, 690,000 - 50 000 is the first computing reception from which the formation of oral calculations in the amount of multivalued numbers begins.
To master this reception, the child must be good to represent the discharge composition of the multi-valued number. Considering 32,000 as 32 thousand and 2,000 as 2 thousand, receiving 32,000 + 2,000 is calculated as 32 thousand + 2 thousand. Answer 34 thousand is then considered as 34,000 and the result of calculations is recorded. Thus, the actions are considered by the total thousands as actions of the discharge units, the calculations in this case are reduced to the table computing within 10, 20 PL 100.
3. Addition and subtraction of whole thousand based on arithmetic rules
The textbook of mathematics for grade 4 practically does not offer computations of the corresponding species, but teachers often use them at an oral account.
These cases include calculations of the form: 70 200 + 400, 600 100 - 99, 3 008 + 351,425 100 - 24 100, etc.
When calculations, knowledge of the decimal composition of multivalued numbers is used and an understanding that in all cases the actions affect only part of the first number (the first number can be considered as the amount). Thus, actions can be performed only with part of the first number.
For example:
Calculating the amount of 70,200 + 400, you can separately fold 400 and 200, and then the amount to add to the number of 70,000. Actually uses the reduction rule to the amount.
When performing calculations in the case of 425 100 - 24 100, the subtraction rule is used from the amount. 425 100 is considered as the sum of 400,000 and 25 100. 24,100 (25 100 - 24 100 \u003d 1,000) are subtracted from one of the terms, and the resulting result is folded with the first term: 400,000 + 1 000 \u003d 401,000.
At the heart of all these cases lies a good knowledge of the discharge composition of multi-valued numbers and the ability to perform oral calculations with entire discharges.
Methods of written computing (in the column)
Written techniques of addition and subtraction are the main computational actions when calculating in the volume of multi-valued numbers, since the calculations in the mind with multi-valued numbers are too complicated for all children. The use of written algorithms for calculations under these conditions is psychologically and methodically justified.
The assimilation of the numbering of four-digit and multivalued numbers allows them to carry out the transfer of skills to fold and deduct the number "Stage" from the area of \u200b\u200bthree-digit numbers to the area of \u200b\u200bmultivalued numbers.
When finding out written techniques for addition and subtraction in the volume of multivalued numbers, an analogy with a written algorithm and subtraction within 1000 is carried out within 1000:
1) Written addition and subtraction of any multivalued numbers is performed in the same way as the addition and subtraction of three-digit numbers.
2) When recording a column, as well as when the three-digit numbers are addition, it is necessary to record a discharge under the appropriate discharge, and the units first fold, then dozens, and then hundreds, then thousands, etc. (right to left).
It is believed that children are well taught to perform the actions of addition and subtraction in the column, therefore, in the 4th textbook, it is not provided for the distribution of cases of addition and subtraction over difficulty levels.
The first are considered various cases with transitions through a discharge as in addition and at subtraction: 3 126 + 4 232; 25 346 - 13 407.
Then consider cases of subtraction with zeros in a decrease:
600 - 25; 1 000 - 124; 30 007 - 648.
These cases are the most difficult, since they require "loan" of discharge units not from neighboring, but from far distant discharges. These cases are useful at first accompany the detailed explanatory record on the board so that the children understand and see from where nine appear in "empty" discharges.
For example:
30 007 I submit a unit. From 7 it is impossible to subtract 8. 648 I trial to take a unit in a neighboring discharge.
In the category of dozens, hundreds and thousands there are no discharge units, so the "loan" can only be made from the discharge of tens of thousands: 30 thousand - 1 thousand \u003d 29 thousand. We subscribe 29 over 30.
"The occupied" one is present in the form of 1 thousand \u003d 1000 \u003d 990 + 10.
We subscribe over the discharges of hundreds and tens of nines, and from 10 units subtract 8, we get 2 units. But in the category of units there were 7 units. We add them to the 2 units received and write in the discharge of units 9.
We subtract: 9 sons. - 4 dec. \u003d 5 dec. We write 5 in the discharge of dozens. 9 hundred. - 6 hundred. \u003d 3 hundred. We write 3 in the discharge of hundreds.
From tens of thousands there are 29 thousand. We write 9 in the discharge of thousands, 2 - in the discharge of tens of thousands.
When studying the addition and subtraction of multivalued numbers, it is recommended to repeat and fix the names of the components and the results of actions; properties of finding unknown components of actions when checking the results of calculations; Consider the patterns of changes in sum and difference when one of the components of actions.
Many children use calculators both when performing computations with multi-valued numbers and when checking results. In high school, it is not for the use of calculators if necessary, perform bulky calculations (in the lessons of physics, chemistry, geometry).
To encourage the child to use the skill to be independently calculated in the column, you should offer assignments that do not allow the mechanical use of the calculator to calculate the result. These are various tasks to find an error in records or figures of calculations, to the attachment of rounded results of calculations, to restore the missed numbers in the components of actions, to choose from the right answers from the proposed, etc. The teacher should be remembered that the mechanical nature of computational actions in computing with multi-valued Numbers quickly leads to the fatigue of children, which provokes the appearance of errors. Therefore, you should not specify in a row more than three examples on calculations with multi-valued numbers.
Lecture 10. Multiplication
1. The meaning of the multiplication action.
2. Table multiplication.
3. Meetings to memorize the multiplication table.
The meaning of the action of multiplication
The action of multiplication is considered as the summation of the same terms.
By definition, multiplying as many non-negative numbers (natural) is the action performed according to the following rules:
a B \u003d A + A + A + A + A ... + A, with B\u003e 1
b Companies
a 1 \u003d A, with B \u003d 1
a 0 \u003d 0, at b \u003d 0
The use of multiplication symbols allows you to reduce the recording of the addition of the same terms.
Recording of the form 2-4 \u003d 8 implies a reduction in recording of the form 2 + 2 + 2 + 2 \u003d 8. It is read like this: "On 2 to take 4 times, it will turn out 8"; Or: "2 Multiply to 4 will be 8".
The action of multiplication in all textbooks of mathematics for primary classes is considering previously the actions of division.
From the multiple point of view, such subject actions with aggregates (sets, groups of objects) are corresponding to multiplication (sets, groups of objects) as an association of equal (equitable) aggregates. Therefore, before meeting the symbolism of the recording of actions and the calculations of the results of actions, the child must learn how to model all these situations on subject aggregates, to understand (i.e., to correctly submit them from the words of the teacher, to be able to show hands both the process and the result of the subject Actions and then characterize them verbally.
Types of assignments that are offered to children before exploring the symbolism of multiplication (in 1 and 2 grade):
1. Count the twins (three, five).
2. Draw a picture: "On three plates of 2 orange." Catch up how much oranges.
3. Find an extra entry:
Find the value of each expression most convenient way.
4. Make an expression record:
Types of tasks used to assimilate the meaning of multiplying when meeting this action:
a) on the correlation of drawing and mathematical recording:
Consider drawing and explain the records:
2 + 2 + 2 + 2 + 2 \u003d 10i2.5 \u003d 10 5 + 5 \u003d 10I5-2 \u003d 10
4 + 4 + 4 = 12 4-3=12
b) to find the amount of the same terms: consider the drawings and finish the record:
c) for replacing addition by multiplication:
Replace where it is possible to add multiplication and calculated the results:
5+5+5+5 1+1+1+1+1 5+6+3
42 + 42 0 + 0+0 + 0 + 0 4 + 6 + 8
d) to understand the meaning of determining the action of multiplication:
Consider the record and explain what number is taken by the term and how many times the term is taken. These are: 6-4 \u003d 24 9-3 \u003d ...
6 + 6 + 6 + 6 = 24 9 + 9 + 9 =...
The expression of the form 3 5 is called the work. Numbers 3 and 5 in this record are called the factors (multipliers).
Recording of the form 3 5 \u003d 15 is called equality. The number 15 is called the expression value. Since the number 15 in this case is obtained as a result of multiplication, it is also often called the work.
For example:
Find the product of numbers 4 and 6. (The product of numbers 4 and 6 is 24.)
Since the names of the multiplication action components are entered by agreement (children communicate these names and need to be remembered), the teacher actively uses tasks that require recognition of the components of actions and the use of their names in speech.
For example:
1. Among these expressions, find those in which the first factor is 3 (the second factor is 2, etc.):
2-2 7-3 6-2 1.6 3-5 3-2 7-3 3-4 3-1
2. Make a product in which the second factor is 5. Find its value.
3. Select Examples in which the work is 6. Emphasize them in red. Choose examples in which the work is 12. Emphasize them in blue.
7-3 6-1 2-2 2-3 6-2 3-2 2-6
4. How do they call the number 4 in expression 5 4? What is the number 5? Find a work. Make an example in which the product is equal to the same number, and the multipliers are others.
5. Multiplers 8 and 2. Find a work.
In the third grade, children get acquainted with the rule of interconnection of multiplication components, which is the basis for learning to find unknown multiplication components when solving equations:
If the work is divided into one multiplier, then another multiplier will be.
For example:
Decide equation 6 * x \u003d 24. (The multiplier is unknown in the equation. To find an unknown multiplier, a product should be divided into a known multiplier. X \u003d 24: 6, x \u003d 4.)
However, this rule in the 3 class mathematics textbook is not a generalization of the child's presentations about the methods of verifying the multiplication action. The rule of checking the results of multiplication is considered in the textbook much later - after acquaintance with off--table multiplication and division (acquaintance with multiplication and division of double-digit numbers on unambiguous, not included in the multiplication and division table). This is explained by the fact that the rule of interconnection of multiplication components is the basis for the preparation of the division table. Since it is assumed that table cases of multiplication of a child by this time knows by heart, then there is no need to check the results. There is only a need to quickly restore (remember) the necessary third number in two data.
For example:
9-2 = ... 5-4 = ... 1*7 = ...
18:2 = ... 20:4 = ... 7:7 = ...
When performing oral outdoor multiplication, requiring a sufficiently complex algorithm requires a test, since many children are often mistaken in these cases.
Multiplication verification rule:
1) The work is divided into a multiplier.
2) Compare the result with another multiplier. If these numbers are equal, the multiplication is done correctly.
For example: 18 4 \u003d 72. Check: 1) 72: 4 \u003d 18; 2) 18 \u003d 18.
Table multiplication
The study of the multiplication table is the central task of learning mathematics in 2 and 3 class.
Table multiplication includes cases of multiplication of unambiguous natural numbers per unambiguous natural numbers, the results of which are found on the basis of a specific meaning of the action of multiplication (they find the amount of the same terms).
The results of table multiplication in accordance with the software requirements for knowledge, skills and skills, children should know by heart. Multiplication with a number of zero, multiplication with numbers 1 and 10 refer to special cases.
The first methods of compiling multiplication tables are associated with the meaning of the multiplication action (see the previous item). The results of these tables are obtained by consistent addition of the same components.
For example:
Located next to the drawing helps the child get the result with the recalculation of the figures. With small values \u200b\u200bof the factors, the receipt reception is quite acceptable to obtain a table value, and the teacher often uses the results of the multiplication of numbers of numbers 2, 3, 4. The example shows that this reception is convenient only with small values \u200b\u200bof the second multiplier.
With the value of the second multiplier, more than 5, it is more convenient to use another reception to get the results of table values: receiving added to the previous result. For example:
Calculated and remember: 2-6 \u003d 2.5 + 2 \u003d ... 2-7 \u003d 2.6 + 2 \u003d ... 2-8 \u003d 2.7 + 2 2.9 \u003d 2-8 + 2 \u003d ...
In a textbook of mathematics for grade 2, this reception is more extensively, and therefore is not always correctly understood from the point of view of the implementation technique:
2 + 2 + 2 + 2 + 2 + 2 + 2 2-7IT.
Similarly, a table of multiplying values \u200b\u200bof the number 3 is drawn up.
The next reception, on the basis of which the tables of multiplication of numbers are drawn up, is the reception of rearrangement of multipliers.
This technique is actually the first mathematical law relative to the action of multiplication in elementary school:
From the permutation of multipliers, the work does not change.
The method of dating children with this rule (law) was due to the previously entered meaning of multiplication. Using subject models of sets, children pass the results of grouping their elements in different ways, making sure that the results do not change from changing the methods of grouping.
For example:
The count of the elements of the pattern (set) pairs horizontally coincides with the score of the elements three vertical. Consideration of several options for such cases gives the teacher the foundation to produce inductive generalization (i.e., a generalization of several special cases in a generalized rule) that the rearrangement of multipliers does not change the value of the work.
Based on this rule used as an invoice, a multiplication table is compiled by 2.
For example:
Using the multiplication table of Numbers 2, calculated and remember the multiplication table by 2:
2 = 2 = 2 = 2 = 2 = 2 = 2 =
Based on the same reception, a 3D multiplication table is drawn up:
3-4 = 12 3-7 = 21 4-3 = ... 7-3=...
3-5= 15 3-8 = 24 5-3 = ... 8-3 = ...
3-6 = 18 3-9 = 27 6-3=... 9-3 = ...
The preparation of the two first tables is distributed into two lessons, which, accordingly, increases the time allotted by their memorization. Each of the last two tables is drawn up in one lesson, since children, knowing the source table, should not separately memorize the results of the tables obtained by rearrangement of multipliers. In fact, many children teach each table separately, since the insufficient level of development of thinking flexibility does not allow them to easily rebuild the model of the scarce scheme of the tabular case in the reverse order. When calculating cases of the form 9 2 or 8 3, children are again returned to the reception of consistent addition, which naturally requires time to obtain the result. Such a situation is likely to be generated by the fact that for a significant number of children, such separation of interconnected cases of multiplication (those that are linked to the rules for rearrangement of multipliers) does not allow the associative chain oriented to the relationship. The same situation was traced in a number of children when applying the program of rearrangement of the terms for the preparation of the folding tables: remembering the case 3 + 5, such a child teaches a case 5 + 3 separately, since the requirement to learn this case comes from the teacher through 16 lessons after the requirement to memorize the first and In the interval, the table of the species □ + 4, □ - 4. In other words, delay in the formation of an associative connection, focused on the relationship of these cases, was too big for a child, which prevented such a relationship. Therefore, each case from the actual interconnected couple is studying the child by heart separately.
In compiling the multiplication table of the number 5 in grade 3, only the first product is obtained by adding the same terms: 5-5 \u003d 5 + 5 + 5 + 5 + 5 \u003d 25. The remaining cases receive the addition of grades five to the previous result:
5-6 = 5- 5 + 5 = 30 5-7 = 5-6 + 5 = 35 5-8 = 5-7 + 5 = 40 5-9 = 5- 8 + 5 = 45
Simultaneously with this table, the interconnected multiplication table by 5: 6 5 is also compiled; 7 5; 8 5; 9 5.
The multiplication table of the number 6 contains four cases: 6 6; 6 7; 6-8; 6-9.
The multiplication table on 6 contains three cases: 7 6; 8 6; 9 6.
The multiplication table of the number 7 contains three cases: 7 7; 7 8; 7 9.
The multiplication table on 7 contains two cases: 8 7; 9 7.
The multiplication table of the number 8 contains two cases: 8 8; 8 9.
The multiplication table on 8 contains one case: 9 8.
The multiplication table of the number 9 contains, only one case: 9 9.
A theoretical approach to such a construction of the study system of table multiplication assumes that it is in such a correspondence that the child will remember the cases of table multiplication.
The greatest number of cases contains the easiest to memorize the multiplication table of the number 2, and the most difficult to memorize the multiplication table of the number 9 contains only one case. Really, considering every new "portion" of multiplication tables, the teacher usually restores the entire volume of each table (all cases). Even if the teacher draws the attention of children to the fact that a new case in this lesson is, for example, only the case 9 9, and 9 8, 9 7, etc. studied on previous lessons, most of the children perceives the entire proposed volume As a material for a new learning. Thus, in fact, for many children, the multiplication table of the number 9 is the largest and complex (and this is true, referring to the list of all cases that relates to it).
A large volume of material requiring learning by heart, the complexity in the formation of associative connections when memorizing interrelated cases, the need to achieve all the children of durable memorization of all table cases by heart in the timeline established by the program - all of this makes the topic of studying table multiplication in elementary classes of one of the most methodically complex. In this regard, issues related to memorization of multiplication tables are important.
Plan-abstract lesson
Thing : mathematics.
Theme lesson: "The addition of multivalued numbers. Oral and written techniques of addition of multivalued numbers. Oral addition algorithms. "
Type of lesson: An educational lesson with new material.
The purpose of the lesson: To teach the application algorithm for the written addition of multivalued numbers, to transfer the skills to add numbers within 1000 to the area of \u200b\u200bmeaningful numbers within a billion.
Wood:
1. Personal: take and master the social role of the study, develop the motives of educational activities and form the personal meaning of the teaching;
2. Regulatory : Control your activities: Check the correctness of the computation by the studied methods;
3. Cognitive : simulate the situation illustrating the effect of addition;
4. Communicative : Mutual control in joint activities.
Equipment lesson: Board, chalk, textbook on mathematics grade 4, workbook on mathematics grade 4, notebook for entries.
1-2 min.5-10 min.
10-15 min.
5-10 min.
3 min.
I. . Organizing time
Hello! Sit down! Look at your jobs, do you on the table. On the place of whether your workbook, tutorial.
We open the notebook, write the number, "cool job".
II. . Actualization of knowledge
Verbal counting:
Reading and record of multivalued numbers.
Read the number of numbers, solve the rule by which a number of numbers are compiled. Continue the series by the same rule, write another five numbers.
What are these numbers called? How many numbers are required for their record?
Increase the last number per 1,000. What number did you get?
How many numbers are required to record it? What is the name of this number?
What kind of discharge appeared in five digits?
III . Message Topics lesson
Open the workbook on with. 13 and execute the task under No. 43. Record the results of the addition.
320 + 70 =
260 + 40 =
300 + 90 =
500 + 200 =
120 + 120 =
605 + 5 =
400 + 250 =
715 + 20 =
Perform the task under No. 44 and recall the method of writing three-digit numbers. Fold three digits.
436 + 251 =
308 + 167 =
732 + 196 =
296 + 487 =
Look at the picture in the textbook on with. 31. Explain how each of the students figured out the amount of multivalued numbers
What do you think we will learn today in the lesson?
IV. . Work on new material
We perform in the textbook to the task under No. 3 on with. 31. Find the sum of the numbers.
458207 + 207954 =
1480 + 260387 =
673 + 12869 =
306250 + 18998 =
18000 + 6375 =
68305 + 9286 =
Well done boys!
Perform the task number 5 in the textbook. Calculate the value of the expression.
3685 + A, if a \u003d 0;
a + 5001, if A \u003d 0.
What did you notice here?
Is the statement true: "If one of the data is zero is zero, then the amount is equal to another term"?
Give your examples.
In the textbook, perform the task under No. 6. Perform an action.
70616 + 19796 + 217 × 3 \u003d
56380 + 325478 + 130 × 6 + 714: 7 \u003d
Well done!
Now in the working notebook, we will perform the task under №45. Fill the table.
The next task under No. 46. Perform addition.
48356 + 12974 =
209366 + 1793 =
687 + 29630 =
2974 + 19057 =
V. . Total lesson
What did we do with you today in the lesson?
Did you know anything new today?
Did you like the lesson?
What did you like most?
Students welcome teachers.
Open notebooks, write the number, "cool work".
…, 5398, 6398, 7398, 8398, 9398.
These are multivalued numbers; Recording requires 4 digits.
10398 is a five-digit number.
To record it, this numbers require 5 digits; multivalued number.
D. eat thousand three hundred ninety eight.
320 + 70 = 390,
260 + 40 = 300,
300 + 90 = 390,
500 + 200 = 700,
120 + 120 = 240,
605 + 5 = 610,
400 + 250 = 650,
715 + 20 = 735.
436 + 251 \u003d 687, 308 + 167 \u003d 475, 732 + 196 \u003d 928, 296 + 487 \u003d 783; With written addition, each term is signed by each other: units under units, dozens are under dozens, etc. - and folded numbers is bone off.
1. Signing one term under another so that the units are under units, dozens are under dozens, etc.; 2. Conduct the line under the second term and I put the "+" sign. The amount will be below the bottom; 3. Fold starting from units. If I get a number of more than 9, then I write a unit at the bottom, and dozens of tens when adding tens. We will learn to add multivalued numbers.
68305 + 9286 = 77591,
18000 + 6375 = 24375,
306250 + 18998 = 325248,
673 + 12869 = 13642,
1480 + 260387 = 261867,
458207 + 207954 = 666161.
3685 + 0 = 3685;
0 + 5001 = 5001.
70616 + 19796 + 217 × 3 \u003d 91063
1) 217 \u200b\u200b× 3 \u003d 651;
2) 70616 + 19796 = 90412;
3) 90412 + 651 = 91063.
56380 + 325478 + 130 × 6 + 714: 7 \u003d 383010
1) 130 × 6 \u003d 780;
2) 714: 7 = 102;
3) 56380 + 325478 = 382128;
4) 382128 + 780 = 382908;
5) 382908 + 102 = 383010.
9008 + 16837 = 25845;
296375 + 38007 = 334382;
613084 + 2875305 = 3488389.
48356 + 12974 = 61330; 209366 + 1793 = 211159; 2974 + 19057 = 23031; 687 + 29630 = 30317;
Record on blackboard: 1398, 2398, 3398, 4398, ...
In mathematics, this property of addition in generalized form is written so. With any meaning, the equality is true: a + 0 \u003d a and 0 + a \u003d a .
Movement law.
Task at home
from. 33 № 16, 17, 18.
