This is an operation on two numbers, the result of which is a new natural number obtained by increasing the value of one number by the value of another number.

Add two natural numbers- means to add as many units to the first number as there are in the second number.

Example 1 Mom brought home some apples in two bags. There were 3 apples in one package, and 2 in the second. How many apples did mom bring home in total?

To answer this question, when taking apples out of packages, simultaneously count them, for example, laying out apples from the first package, say: one, two, three, and then, taking apples out of the second package, continue: four, five. So there are 5 apples in total.

Listing apples, we added the number of apples from the second package to the number of apples from the first package and got the total number of all apples, i.e. 5.

Example 2 Add two numbers: 4 and 2.

Solution:

We add to the first number all the units of the second: add one more to four units, you get five units, add one to five, you get six. Thus, from two given numbers 4 and 2, we received a new number 6, containing four units of the first number and two units of the second, that is, as many units as there were in both numbers.

The numbers to be added are called terms, and the result of addition, i.e., the number resulting from addition, is called sum.

The + (plus) sign is used to write addition. It is placed between the terms. For example, the entry 2 + 5 means that the numbers 2 and 5 are added. To the right of the addition entry, put the sign = (equal), after which the sum is written:

Addition is an action that is always feasible, that is, no matter what natural numbers we take as terms, we can always find their sum.

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Addition- an arithmetic operation that is performed on two numbers and consists in finding a number that means a quantity that corresponds to these two original numbers, when taken together. The number resulting from the operation of adding two numbers is called the sum of these numbers.

Addition is indicated by a "+" (plus) sign between the two operands. For example, the notation "A+B" means "enclose A and B" or "sum of A and B". The notation "A+B=C" means: the number C is the sum of the numbers A and B.

Addition is simply illustrated at the level of everyday life. For example, you can imagine that two numbers correspond to the number of inhabitants of a two-story house. Then the sum of these numbers indicates the number of inhabitants of the whole house.

Formally, the operation of addition of natural numbers can be defined as follows:

• x + 1 = S(x)
• x + S(y) = S(x + y)

where S(x) is the number following x.

In accordance with this, the result of addition (sum) of two single-digit numbers is determined as follows:

	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

Based on the addition of 2 natural numbers. Adding 3 or more numbers looks like consecutive addition of 2 numbers. In addition, due to displacement and , the numbers that add up can be interchanged and any 2 of the added numbers can be replaced by their sum.

Associative property of addition proves that the result of adding 3 numbers a, b and c does not depend on the location of the brackets. Thus, the amounts a+(b+c) and (a+b)+c can be written as a+b+c. This expression is called sum, and the numbers a, b and c - terms.

Likewise, due to associative property of addition, are equal to the sums (a+b)+(c+d), (a+(b+c))+d, ((a+b)+c)+d, a+(b+(c+d)) and a+((b+c)+d). That is, the result of adding 4 natural numbers a, b, c and d does not depend on the location of the brackets. In which case the sum is written as: a+b+c+d.

If the expression does not contain brackets, but it consists of more than two terms, you yourself can arrange the brackets as you like and add 2 numbers sequentially to get the answer. That is, the process of adding 3 or more numbers is reduced to the successive replacement of 2 adjacent terms by their sum.

For example, let's calculate the sum 1+3+2+1+5 . Consider 2 ways out of a large number of existing ones.

First way. At each step, we replace the first 2 terms with the sum.

Because sum of numbers 1 and 3 is equal to 4 , means:

1+3+2+1+5=4+2+1+5 (we have replaced the sum 1+3 with the number 4).

Because the sum of 4 + 2 is 6, then:

4+2+1+5=6+1+5.

Because the sum of the numbers 6 and 1 is 7, then:

6+1+5=7+5

And the last step 7+5=12 . That.:

1+3+2+1+5=12

We did the addition by placing the parentheses as follows: (((1+3)+2)+1)+5.

The second way. Let's put the brackets like this: ((1+3)+(2+1))+5 .

Because 1+3=4 , a 2+1=3 , then:

((1+3)+(2+1))+5=(4+3)+5

The sum of 4 and 3 is 7, so:

(4+3)+5=7+5.

And the last step: 7+5=12.

On the result of adding 2, 3, 4, etc. numbers are not affected not only by the placement of brackets, but also by the order in which the terms are written. Thus, when summing natural numbers, you can change the places of the terms. Sometimes this gives a more rational decision process.

Properties of addition of natural numbers.

• To get a number following the natural, you need to add one to it.

For example: 3 + 1 = 4; 39 + 1 = 40.

• When rearranging the places of the terms, the sum does not change:

3 + 4 = 4 + 3 = 7 .

This addition property is called displacement law.

• The sum of 3 or more terms will not change from changing the order of adding numbers.

For example: 3 + (7 + 2) = (3 + 7) + 2 = 12 ;

means: a + (b + c) = (a + b) + c .

Therefore, instead of 3 + (7 + 2) write 3 + 7 + 2 and add up the numbers in order, from left to right.

This addition property is called associative law of addition.

• When adding 0 to a number, the sum is equal to the number itself.

3 + 0 = 3 .

Conversely, when a number is added to zero, the sum equals the number.

0 + 3 = 3;

means: a + 0 = a ; 0 + a = a .

• If point C separates the segment AB, then the sum of the lengths of the segments AC and CB equal to the length of the segment AB.

AB=AC+CB.

If a AC=2cm a CB=3cm,

then AB=2+3=5cm.

Test. Addition and subtraction of natural numbers. coordinate beam. 1 option 1 . What is the result of adding two numbers called? a) difference; b) private; c) term; d) amount. 2 .Determine which of the properties of addition is formulated: "The sum does not change from changing the arrangement of brackets." a) transferable; b) combination; c) distributive; d) property of zero. 3. Add 69538 + 25347. a) 91 345; b) 94885; c) 93875; d) 83 885. 4 . Subtract 40002 - 8975 . a) 30127; b) 29027; c) 31027; d) 30037. 5. Find the difference between two numbers knowing that the subtrahend is 569 and the minuend is 659. a) 80; b) 70; c) 90; d) 100. 6. Fill in the missing word: “To find the unknown. . . , we must add the subtrahend and the difference. c) term; d) divisible. 7. a) 3x + 4; b) 5 \u003d x + 1; c) 5 7 - 3 = 32; G) a+ b= d. 8 . Solve the equation: X - 341 = 418 a) 77; b) 759; c) 87; d) 779. 9. Find the coordinates of the points shown in coordinate beam. a) M (2), N (3), C (6), P (7); b) N(4), C(5), M(2), P(6); c) P(8), C(7), N(5), M(3); d) M(2), N(4), C(6), P(7).

Test. Addition and subtraction of natural numbers. coordinate beam. Option 2 1. What is the result of subtracting two numbers called? a) difference; b) reduced; c) deductible; d) amount. 2 .Determine which of the properties of addition is formulated: "The sum does not change from a rearrangement of the terms." a) transferable; b) combination; c) distributive; d) property of zero. 3. Add 42,175 + 58,619. a) 99 794; b) 101684; c) 100794; d) 100 974. 4. Subtract 50070 - 3506 . a) 45654; b) 36454; c) 46554; d) 46564. 5 . Find the difference between two numbers knowing that the subtracted equals 331, and the minuend is 411. a) 80; b) 70; c) 90; d) 100. 6. Fill in the missing word: “To find the unknown. ., it is necessary to subtract the difference from the reduced. a) reduced; b) deductible; c) term; d) divisible. 7. Which of the following is an equation: a) 10+ 4 a; b) 5 = d – 51 ; c) 15 2+ 3 = 33; G) a+ b= d. 8 . Solve the equation: 341 - x = 118 a) 459; b) 223; c) 233; d) 437. 9 . Find the coordinates of the points shown in coordinate beam. a) D (4), T (9), K (11), E (2); b) E (2), D (5), T (9), K (12); c) T (8), K (12), E (2), D (4); d) K (12), T (9), E (2), D (4)

Test solution.

1 option
Option 2

TEST "EQUATIONS"1 option “The value of the letter at which the equation turns into the correct numerical equality is called ...” following equation: a – 8 = 15 ? a) term; b) difference; 3. If at– 39 = 128, then at can be found by the expression: a) 128 + 39; c) 128:39; b) 128 - 39; d) 128 * 39. a) 7 X– 6; b) 5 X = X +1; c) 5 7 - 3 = 0; G) a +2 b= d 5. What is the root of the equation 19 – X = 13 a) 3; b) 15; at 6; d) 8. 6. Find the product of the roots of the equations X+ 12 = 25 and 7. Find the root of the equation 68 + X = 95. 8. Solve equation 647 - at = 258. 9. Solve the equation ( X + 458) – 156 = 348.

TEST "EQUATIONS"Option 2 1. Continue with the following sentence: « An equality containing a variable whose value is to be found is called. . ." a) an equation; c) an unknown component; b) the root of the equation; d) your answer. 2. What component is the unknown in the following equation: 13 - X = 15 ? a) term; b) difference; c) deductible; d) reduced. 3. If 127 - X= 35, then X can be found by the expression: a) 127 - 35; c) 127 + 35; b) 127: 35; d) 127 * 35. 4. Which of the expressions is an equation: a) 9 X+ 4; b) 15:3 +7 = 32; in 2 X= 5 – X; G) 3 a – b= d. 5. What is the root of the equation at – 8 = 17 a) 13; b) 25; c) 16; d) 8. 6. Find the sum of the roots of the equations = 96 and 630: at= 63 7. Find the root of the equation X + 43 = 92. 8. Solve the equation at – 584 = 425. 9. Solve equation 888 - ( X + 364) = 419.

Test solution.

1 option
Option 2								1009private . four. Which operation in the expression 200–1216+56:8 is performed last? a) addition; b) subtraction; c) multiply... The program for the formation of universal educational activities for students at the stage of primary general education 2 17 Program Comparisons natural numbers. Double digit representation numbers as amounts bit terms. Call any... private cases additions and subtraction two-digit numbers. Establishing a hierarchy of difficulty in these cases. Changing values amounts and differences ... Educational program of primary general education for the period 2011-2015 Educational program Head." This option how once and... oh natural number and zero, arithmetic operations ( addition, subtraction, ... addition and subtraction(24h) Addition two unambiguous numbers, sum ... Terms. Sum. Will learn: call components and result additions ... The program is an algorithm written in a programming language that serves to perform some action. Translator Program ... two any numbers, displays amount, difference, product and private from dividing these numbers ... - addition; "*" - multiplication; "-" - subtraction; "/" - division; ( result always... called nested loops. What kind... splits natural numbers on the terms, ...

So, I propose to find the result of the example in pairs using your rulers.

Whoever has the result will be ready to raise his hand.

How much did it turn out?

- Guys, what have we done now?

But what should I do if I find myself in a different class, and I don’t have so many rulers. How can I get out of this situation?

(Bring to the fact that this can be done with the help of number lines or rays).

Can I show this on the board how I will need to act?

Good. You taught me. Tell me, using rulers for one person, is it convenient to act?

So how to be? After all, our task was to learn how to quickly and correctly add long examples? ...

Which?

Fixation on the board, using the sign:

3. ???

I'll prompt. Can we do it in one line? What do you think?

This diagram clearly shows how you can perform these actions on one number line.

We will count the measurements (our steps) with you. When we add and count steps, we go, in what direction for our case?

What do you think, what word in mathematics is this method called?

Can you tell me how you did the addition?

Good. When we add up, we count the measurements and step to the right. What if I need to do a subtraction?

What do you think this method is called in mathematics?

You are real explorers and inventors! And everyone who discovers something new receives a reward for it. Your reward is also waiting for you. She's closer than you think. And if you carefully examine your workplace, you will find it. I wish you success!

Take a look at the board. What will you do now?

6+5+2+3=

What do I need to do?

Fixing on plan board:

1. Straight line or beam
2. Measure, direction, beginning.
3. Number 6
4. Count 5
5. Count 2
6. Counting 3
7. Let's find the result.

What is the name of what we recorded?

Those guys who can do it on their own work on their own, and those who find it difficult can work in pairs.

Independent work of students

What is the result of addition called in mathematics?

How much did it turn out?

Is it possible to calculate the result without a number line or a ray? How?

Gather in groups. Each group has a task card. The task is the same. Let's read it aloud.

What is this issue about?

What they were doing?

How?

How many sat on the first tree?

How do you understand the words as many?

- What is said about the second tree?

What is asked in the problem?

What scheme is suitable for solving this problem. Choose from those offered.

1) 2)

3) 4)

The diagram that suits this task should be cut out and pasted onto the control sheet.

Complete the diagram.

Below on this sheet should be drawn up and written down the formula for solving the problem.

Let's check how you coped with this task.

Approach representatives of each group to the document camera.(Demonstration of group work)

Guys, let's go to our seats.

Tell me, what is left for us to do in the work on the task?

Substitute the numbers, solve and write down the answer.

Write the solution and the answer in your notebook yourself.

How will you find the result of addition, what will help you? (What is the name of this tool)

- What was the task in the lesson?

Did you complete it completely?

What difficulties did you encounter and why?

What will you work on in the next lessons?

* I know and I can add myself.

*I can teach others.

Who feels like he grew up for a lesson?

What do you think we will do in the next lessons?

Choose a card of the level you can handle: