Some elements can be included in such multipliers. Elements of the theory of multiples. The impersonal operation on them. Rakhunkov and indistinguishable multipliers

Understanding the multiplier is one of the main math understand. Tse not clear understanding, yoga can be described and explained on the butts. So, you can talk about the nameless letter in the Latin alphabet, the namelessness of all books in this library, the namelessness of students in this group, the namelessness of the points of this line. To install an impersonal, it’s enough to resurrect the elements or say characteristic the power of the elements, that is. such dominion that all the elements of this multiplicity and only stench can lead.

Appointment 1.1. Objects (objects) that make a deaku kіlkіst are called yoga elements.

The impersonal is accepted to be denoted by great Latin letters, and the elements of the multiplier - by small letters. Those who xє an element of a multiplication A, written like this: x A(x linger A). Record mind x A(x A) means that x not lie down A, then. not a multiplication element A.

Elements of multiplicity are accepted to be recorded at curly arches. For example, like A- impersonal, which is composed of the first three letters of the Latin alphabet, it is written as follows: A={a, b, c} .

Anonymity can avenge impersonal elements (multiple points straight, impersonal natural numbers), the final number of elements (anonymous schoolchildren in the class), or else do not take revenge on the same element (anonymous students in an empty auditorium).

Appointment 1.2. The impersonal, that does not avenge the same element, is called empty faceless, denoted by Ø.

Appointment 1.3. Bezlich A called multiplied faceless B, as a skin element multiple A lie down and faceless B. Tse signified A B(A- submultiple B).

An empty multiplicity is taken into account by a multiplicity, whether it be a multiplier. How impersonal A not a multiplier B, then write A B.

Appointment 1.4. Two multiples Aі B name equal yakscho є p_dzhinami one of one. signify A=B. Tse means what x A, then x B and navpak, tobto. if i , then .

Appointment 1.5.Peretin multiple Aі B name the impersonal M, elements of which є at the same time elements of both multiples Aі b. signify M=A b. Tobto. x A B, then x Aі xB.

Write down A B={x | x Aі x B). (Deputy of the split і – marks, &).

Appointment 1.6. Yakscho A B=Ø, then it seems that you multiply Aі B do not overthink.

Similarly, it is possible to designate the number of 3, 4 and even the last number of multipliers.

Appointment 1.7.United multiple Aі B name the impersonal M, the elements of which lie, wanting to use one of the tsikh multiplies. M=A b. That. A B={x | x A or x B). (Deputy of the split or - put a sign).

Similarly, it stands for impersonal A 1 A2 … An. It is made up of elements, skins of which to lay down, wanting to be one of many A 1,A2,…,A n(and maybe even dekilkom once) .

butt 1.8. 1) yakscho A=(1; 2; 3; 4; 5) i B=(1;3;5;7;9), then A B=(1;3;5) that A B={1;2;3;4;5;7;9}.

2) yakscho A=(2;4) that B=(3;7), then A B=Ø ta A B={2;3;4;7}.

3) yakscho A=(summer months) and B=(months, in any 30 days), then A B=(worm) that A B=(blotch; worm; lime; serpen; veresen; leaf fall).

Appointment 1.9.natural the numbers 1,2,3,4, ... are called, victorious for the subject matter.

The numberless natural numbers are denoted by N, N=(1;2;3;4;…;n;…). It is not limited, but the smallest element 1 does not have the largest element.

butt 1.10. A- impersonal natural dilnikіv number 40. Recalculate the elements of qiєї multiply. Chi true sho 5 A, 10 A, -8 A, 4 A, 0 A, 0 A.

A= (1,2,4,5,8,10,20,40). (V, V, N, N, N, V)

butt 1.11. List the elements of the plurality, given by the characteristic powers.

From the majestic rіznomanіttya vіlyakih multiple of particular interest to represent such a name number multiplier, tobto, multiply, by elements of which are numbers. I realized that for manual work with them it is necessary to record them. From the meaning of the principle to the recording of numerical multiplications, we need to clarify the article. And let's look further, as numerical multiplications are displayed on the coordinate line.

Navigation on the side.

Recording Numeric Multiplies

Let's take a look at the accepted designations. As you can see, for the recognition of many, great letters of the Latin alphabet are used. The number of multipliers, like the number of vipadok multiplies, are also indicated. For example, you can talk about the number multipliers A, H, W and so on. Particularly important are the impersonal natural, whole, rational, real, complex numbers and so on, for them they took their own designations:

N is the multiplier of all natural numbers;
Z - impersonal integers;
Q - impersonal rational numbers;
J - faceless irrational numbers;
R - faceless day numbers;
C is an impersonal complex number.

Zvіdsi zvіdsi zumіlo, scho varto designate impersonality, scho folded, for example, from two numbers 5 і −7 yak Q , tse designation is introduced into Oman, oscills with the letter Q sound to designate impersonality of all rational numbers. To understand the assigned numerical multiplier, it is better to vikoristovuvat as another "neutral" letter, for example, A.

As we have already started talking about recognition, then here we are guessing about the recognition of an empty multiplier, that is multiplied, so as not to avenge the elements. Yogo is denoted by the sign ∅.

So we guess about the meaning of belonging and non-ownership of the impersonal element. For which vicorist signs ∈ - lie down and ∉ - do not lie down. For example, the notation 5∈N means that the number 5 is a multiple of natural numbers, and 5.7∉Z is the decimal point 5,7 is not a multiple of whole numbers.

And I’ll guess more about the designations, accepted for inclusion one multiplier to another. It was understood that all elements of the multiplier N are included before the multiplier Z, so the numerical multiplier N is included in Z, so it is designated as NZ. You can also twist the notation Z⊃N , which means that the absence of all integers includes the absence of N . Vidnosini not included ta not included are indicated by signs ⊄ ta . Also, signs of non-strict inclusion are written in the form ⊆ and ⊇, which means that it is included, or it turns on, or it turns on.

For understanding, we talked, let's move on to the description of numerical multiplies. In case of torknemos less than the main vipadkіv, yakі most vykoristovuyutsya in practice.

Let's take a look at the number of multiplies, how to avenge Kіltsev and that small number of elements. Numerical multipliers that add up from the final number of elements, describe clearly, resurrecting all the elements. All elements-numbers are recorded through someone and are used by, which are useful from the headlines rules for describing plurals. For example, impersonal, which is composed of three numbers 0 −0.25 and 4/7 can be described as (0, −0.25, 4/7).

Sometimes, if the number of elements in the numerical multiplier is large, then the elements are subordered by a kind of regularity, for the description of the vicorist speck. For example, the absence of all unpaired numbers from 3 to 99 inclusive can be written as (3, 5, 7, ..., 99).

So we smoothly went to the description of the numerical multitudes, the number of elements of which is not limited. Some of them can be described, vicory, all the same bagatokrapka. For example, let's describe the impersonality of all natural numbers: N=(1, 2. 3, …) .

They are also written with a description of the numerical multitudes for the help of statements of the authorities of the yogo elements. Whom has a sign (x | power). For example, the notation (n| 8·n+3, n∈N) specifies the absence of such natural numbers, so when subdivided by 8, give an excess of 3 . Tse impersonal can be described as (11.19, 27, ...).

In okremy types, there are numbers of multipliers with an infinite number of elements, there are multipliers N, Z, R, then. chi numeric gaps. And in the main number, the multipliers are seen as association warehouse okremy numeric promizhkіv і numeric multiplies with the last number of elements (about yakі mi talked about three times more).

Let's show an example. Don't let the numberless set the numbers −10 , −9 , −8.56 , 0 , these numbers are in addition to [−5, −1.3] and the numbers of the open numerical exchange (7, +∞) . By virtue of the designation of the combination of multipliers, the indicated numerical multiplier can be written as {−10, −9, −8,56}∪[−5, −1,3]∪{0}∪(7, +∞) . Such a record actually means a multiplier, which means to take back all the elements of the multiplier (−10, −9, −8.56, 0) , [−5, −1.3] and (7, +∞) .

Similarly, one by one the difference between the numbers of numbers and the impersonal numbers, you can describe whether a numerical multiplier (what is added up from the actual numbers). Here it became clear why they introduced such a numerical interval as an interval, napіvіninterval, vіdrіzok, nіdkritiy nіvіnіnі і nоmerіnі promіn: all the stink in odnnnі z znannymi znіzhnnі znіzhkіn numbers allow to describe whether nоnіvіnі vіnіnі і

To pay attention that when recording the numerical multiplier of the warehouses of the th number and the number of intervals, they are ordered after the increase. It’s not obov’yazkova, but a bazhana umova, for that, in the order of numerically impersonal, it’s easier to show and depict on the coordinate line. It is also significant that in such records there are no numerical gaps with the main elements, the shards of such records can be replaced with the same number gaps without double elements. For example, the combination of numerical multipliers from the main elements [−10, 0] and (−5, 3) є nip_interval [−10, 3) . Why do we need to combine and combine numerical intervals with the same boundary numbers, for example, combine (3, 5] ∪ (5, 7] є impersonal (3, 7] ), on the basis of which we are okremo zupinimosya, if we learn to know the overlap i the union of numerical multiplies.

Image of numerical multiplies on the coordinate line

Really, it’s easy to flirt with geometric images of numerical multiplies - their images on. For example, when unraveling of inconsistencies, in which it is necessary to secure the ODZ, to be brought to the image of the numerical multiplier in order to know their limits and/or commonality. Also, it will be good to sort out the nuances of the image of numerical multiplies on the coordinate line.

Apparently, between the points of the coordinate line and the actual numbers, the validity is mutually unambiguous, which means that the coordinate line itself is a geometric model of the multiplier of all the actual numbers R. In such a way, in order to depict the impersonal real numbers, it is necessary to cross the coordinate line of the hatching on the її stretch:

And often do not show the cob for a single ear:

Now let's talk about the image of numerical multiplies, which is a kind of kіltsevoy kіlkіstyu okremіh numbers. For example, imagine the numerical multiplier (−2, −0.5, 1.2) . The geometric rank of this multiplier, which is added up from three numbers −2, −0.5 and 1.2, will be three points of the coordinate line with alternate coordinates:

Significantly, scho call the needs of practice, there is no need to pick up the chair for sure. Often draw a schematic armchair, which can be seen on a neobov'yazkove scale, with which it is important to take care of each other, the points are visible one by one: be it a point with a smaller coordinate is due to a point with a larger coordinate. The front of the chair is schematically seen as follows:

Okremo from different numerical multiplies, we see numerical intervals (intervals, napiveintervals, exchanges, etc.) that represent their geometric images, which we reportedly sorted out in divisions. We do not repeat here.

І zašaєєєєєєєєєєя stuples only on the image of numerical multiplies, which are combined for a number of numeric spaces and multipliers, which are added up from okremih numbers. There is nothing tricky here: for the purpose of combining in these directions on the coordinate line, it is necessary to depict all the warehouses of the numerical multiplier. As an example, the image of a numerical multiplier is shown (−∞, −15)∪{−10}∪[−3,1)∪ (log 2 5, 5)∪(17, +∞) :

І zupinimos more broaden the views, if the images are impersonal numbers and all impersonal real numbers, except for one few dots. Such multipliers are often set by minds like x≠5 or x≠−1 , x≠2 , x≠3.7 just. In these vipads, geometrically stench is the entire coordinate line, behind the grapevine there are points. In other words, from the coordinate line, it is necessary to “vicolate” the points. They are depicted as circles from an empty center. For accuracy, let's imagine a numerical multiplier, which confirms the minds (Tse impersonal as a matter of fact є):

Let's bring a bag. Ideally, the information in the front paragraphs is responsible for formulating such a look at the record and images of numerical multiplies, as well as a look at the other numerical spaces: recording a numerical multiplier can be given a second image on the coordinate line, and on the image on the coordinate line, it is easy to write impersonal through the union of okremih promizhkiv and the multitude that add up from okremih numbers.

List of literature.

Algebra: navch. for 8 cells. zahalnosvit. set/[Yu. N. Makarichev, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; for red. S. A. Telyakovsky. - 16th kind. - M.: Prosvitnitstvo, 2008. - 271 p. : il. - ISBN 978-5-09-019243-9.
Mordkovich A. G. Algebra. Grade 9 At 2 o'clock. - 13th species., erased. – K.: Mnemozina, 2011. – 222 p.: il. ISBN 978-5-346-01752-3.

Mathematical analysis is a branch of mathematics that deals with successive functions based on the idea of an infinitely small function.

The main concepts of mathematical analysis are value, multiplier, function, infinitely small function, boundary, poor, integral.

size everything is called that can be vimiryan and expressed by number.

Bezlich the collection of certain elements is called, united as a sacred sign. The elements of a multiplier can be numbers, figures, objects, understandable just.

The impersonal are denoted by great letters, and the impersonal elements by small letters. Elements of a plurality lie at the figurine bow.

Yakscho element x lie faceless X, then write down x∈X (∈ - lie down).
If the multiplier A is a partial multiplier B, then write down A ⊂ B (⊂ - Utrimuєtsya).

Anonymity can be given in one of two ways: by resurrecting it for the help of the original power.

For example, reworking the tasks with the following multipliers:

A \u003d (1,2,3,5,7) - numberless numbers
X \u003d (x 1,x 2,...,x n) - impersonal elements x 1,x 2,...,x n
N = (1,2, ..., n) - numberless natural numbers
Z=(0,±1,±2,...,±n) — numberless integers

Faceless (-∞;+∞) is called number line and be a number - a point on a straight line. Let a - enough point of the number line i - date. The interval (a-δ; a+δ) is called δ-neighborhood of point a.

Rich X is surrounded by the beast (bottom), which means that the number c is such that for any x ∈ X, the unevenness x≤с (x≥c) is calculated. The number is called for the first time upper (lower) face multiplied X. Multiplied, surrounded by the beast and below, called let's get cold. The smallest (largest) of the upper (lower) faces of the multiplier is called exact upper (lower) facet multiply.

Basic Numerical Multipliers

N	(1,2,3,...,n) The impersonal of all
Z	(0, ±1, ±2, ±3,...) whole numbers. The numberless integers include the numberless natural numbers.
Q	Bezlich rational numbers. Krіm qіlih numbers є th fraction. Fraction - tse viraz mind, de p- whole number, q- Naturally. Decimals can also be written as . For example: 0.25 = 25/100 = 1/4. The number of numbers can also be written as . For example, like a shot with a banner "one": 2 = 2/1. Be like this rational number you can write decimal fraction- extremely chicane periodical.
R	Faceless of all day numbers. Irrational numbers - not infinitely non-periodic fractions. Before them one can see: At the same time, two multiplies (rational and irrational numbers) - establish impersonal real (or speech) numbers.

How impersonal does not take revenge on the element, it is called empty faceless that sign up Ø .

Elements of logical symbols

Write ∀x: |x|<2 → x 2 < 4 означает: для каждого x такого, что |x|<2, выполняется неравенство x 2 < 4.

quantifier

When writing mathematical expressions, quantifiers are often used.

quantifier a logical symbol is called, which characterizes such elements in a kolkish language.

∀- quantifier vikoristovuetsya zamіst sіv "for vsіh", "for whatever".
∃- quantifier isnuvannia vikoristovuetsya zamіst sliv "іsnuє", "є". Vikoristovuetsya podnannya symbols ∃!

Operations on multiplies

Two multiplies A and B are equal(A = B), as if the stench is formed from the quiet elements themselves.
For example, if A=(1,2,3,4), B=(3,1,4,2), then A=B.

United (sum) the plurals A and B are called impersonal A ∪, the elements of which would lie in one of these plurals.
For example, if A=(1,2,4), B=(3,4,5,6), then A ∪ B = (1,2,3,4,5,6)

Peretin (creative) the plurals A and B are called the impersonal A ∩ B, the elements of which lie like the plurality A, so the plurality B.
For example, if A=(1,2,4), B=(3,4,5,2), then A ∩ B = (2,4)

Retail multiples A and B are called impersonal AB, the elements of which are multiples of A, but not multiples of B.
For example, if A = (1,2,3,4), B = (3,4,5), then AB = (1,2)

Symmetrical retail multiples A і B are called impersonal A Δ B, which means that the difference between multiples AB and BA is called, so A Δ B \u003d (AB) ∪ (BA).
For example, if A=(1,2,3,4), B=(3,4,5,6), then A Δ B = (1,2) ∪ (5,6) = (1,2,5 ) ,6)

Power of operations over multiples

Powerful permutability

A ∪ B = B ∪ A
A ∩ B = B ∩ A

Happy power

(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)

Rakhunkov and indistinguishable multipliers

In order to equalize the two, whether it be multiplies A and B, between them, establish consistency with the elements.

Since the validity is one-to-one, then the multipliers are called equivalent or equally strong, AB or BA.

butt 1

The leg point BC is rich and the hypotension AC of the tricot ABC is equally strong.

side 1

9-10 class

Module 1: Fundamentals of the theory of multiples

. . .
Task 1.

A) Explain how many elements add up N, Z, Q, R.

B) Name the sprat of numbers, which are the elements of the skin multiplier.

C) Name the numbers that are the elements of one of the plurals, and the elements of the other three.

D) Paint a diagram that shows the interrelationship between them.

Vidpovid.

C) Such elements are less for the impersonal R. For example,  R , ale  N,  Z,  Q. Elements be-as-a-multiple N, Z, Q obov'yazkovo enter and into the faceless R.

G

N – impersonality of natural numbers;
Z – impersonal whole numbers;
Q – impersonal rational numbers;

R – impersonal real numbers.
Teacher. Looking at the material, we cannot see for the impersonal real numbers.
Task 2. Set anonymity:

A) mathematics teachers of your school;

B) unpaired numbers;

B) root rіvnyanya X 2 + 5 = 0;

D) rozvyazkіv nerіvnostі X > 4;

Suggestion: B) ( X X = 2n - 1; n  Z };

D) (4; + ).

Teacher. If necessary, it is possible to repeat the recording of numerical multiplications for solving irregularities of a different type (addition "Table").
Equal multipliers. The impersonality, which is composed of the quiet elements themselves, is respected by equals.

For example, A = ( 1, 2, 3 ); Y = ( X (X- 1)(X- 2)(X- 3) = 0). A = B.

Ratio of equality for multiplies, like the introduction of equality for numbers, may have the power of reflexivity, symmetry and transitivity.

A = A (reflexivity);
If A \u003d B, then B \u003d A (symmetry);
If A = B and B = C, then A = C (transitivity).

The pressure of the multiplier. For the multiplicity, which is the last number of elements, the number of elements is called the number of elements.

BUT = {a;b; c; d). Yoga tightness:  BUT= 4.

As if two multiplies may have the same tightness, it seems that the stench is equally strong. Bezlich BUT equally impersonal to fate.

Cіkavo, sho pochatka people have learned to prіvnjuvat multiplicity for the number of elements, and pіznіshe - to rahuvat objects. You can equalize two multiplies for the number of elements as follows: put one multiplier on the skin element for the other element. If all the elements “stand up” in pairs, then multiply them equally. Well, when the elements are set, one of the many elements will be lost without a bet, there will be more elements to avenge.

You can sort out all the last multiples of ideas, just like in the same class all the multiples with the same number of elements. Put the І skin class in vіdpovіdnіst as a characteristic of tsієї multiplier deake number. Thus, the natural number 1 is the main characteristic of all multiplies, which can be one element, the natural number 5 is the main characteristic of all multiplies, which can be five elements.

One-to-one validity can be set for non-reduced multiplies. For example, let's write down to one row all natural numbers, and the next - all guys, element under element.

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

2 4 6 8 10 12 14 16 18 20 22 24 . . .
Bachimo, that all the numbers of the first multiplier can unambiguously sing a couple in the other multiplier and at the same time. Tobto impersonality of natural numbers can be style and elements, scali and impersonality of natural numbers. Tobto stink є equally strong.

Non-lich, equal non-lich natural numbers N, are called rachunk. Tsіkavo, scho lіchilnym є, for example, impersonal positive rational numbers.

The intensity of the multiplier of all real numbers is called the intensity of the continuum. The tension of the continuum may also be all multipliers that are equal to the interval (0.1). In this order, without any number of actual numbers, it is equal to the interval (0,1).
Influence of equal potency also has the power of reflexivity, symmetry and transitivity.

So for any multiplies A and B it is true:

A = A
If A = B, then B = A;
If A = B and B = C, then A = C.

Manager 3. Find the tightness of multiples:

A) T - impersonal three-digit natural numbers;

B) Before - faceless faces of the cube;

U) R - impersonal natural numbers multiple of 7.

D) Give multiple applications that are equal to the skin z n. A-B.

Suggestion: A) Т= 900; B) K= 6; B) impersonal K - lіchlne.
to the teacher. Speak with the students about the wisdom to understand the equality of the multitudes and the equality of the multitudes.

Task 4. A - anonymous letter of the word "KILTS", B - anonymous letter of the word "KILTSYA", C -

anonymous letter of the word "VULITSYA". Indicate equal and equal multiples.

Suggestion: A \u003d (K, O, L, L, C), B \u003d (C, O, K, L, L), C \u003d (Y, L, I, C, A). The exhaustion of all three is good 5, then, the stench is equally strong.

Materials provided by the methodologists of the Novosibirsk Center for Productive Education

side 1

Class: 2

Presentation before the lesson

Back forward

Respect! The forward review of the slides is scored solely for the purpose of learning and may not give notice about all the possibilities of the presentation. Like you got hooked by this robot, be kind, zavantazhte povnu version.

Qile:

Enter the concept "bezlich".
Introduce the concept of "multiplier elements."
Learn to assign the belonging of an element to impersonality.

Early preparation:

Bring the ball.
Bring pictures, depicting objects from a common name (you can win cards of a child's loto).

Hid lesson

Lads, today in the classroom we know with you what such a “multiplier” is and what is called “multiple elements”!

I have a bear painted on my doshtsi. While wine is empty. We take in a new animal, which you know.

Gra:

The teacher walks around the class with the ball and throws the ball, and the student can quickly name the animal.

And now let's take all the names of animals to our bear.

The children guess, and the teacher writes on the doshtsі all the names of the grіzvіrіv (a.k.a win cards with a magnet).

Chi rich in a bear veyshlo zvіrіv?

In mathematics, such a group of subjects (or living things) is called by the common name and chosen at once "Bagata". "Bagato" as in the word BAGATO. (Slide 3.4)

Try to name the impersonal.

"Name the impersonal":

The teacher shows an image of the same objects. The children are guilty of giving the name of the multitude, for example - ribs, birds, roslins, books.

Tse faceless rib. (slide 5)

Tse faceless birds. (Slide 6)

Let's take a look at task number 1 in zoshity.

Zavdannya No. 1. (Slide 7)

Learn to name and sign the name of proponated multitudes.

Bezlich: utensils, creatures, vzuttya, toys, laser accessories, objects for painting.

Now let's play.

Gra "Name the impersonal" (Slide 8,9,10)

The teacher overhauls a number of subjects, and the students guess the names of the plurality.

Cloth, pants, fur coat, back, jacket, jacket ... - clothes.

(- Shafa, stіlets, stіl, sofa, bedside table ... - furniture.)

Birch, pine, yalina, poplar, oak, willow ... - tree.

(- Moscow, Odessa, London, Paris, St. Petersburg ... - place.)

Grandmother, horse, blizzard, fly, bjola ... - komakhi.

If there is one more bear on the doshtsi, in which case name the objects, but there are no other names. Yogo children can invent themselves. For example, chobots, felt boots, sneakers, laces, capts.

Tse faceless vzuttya.

Name all objects with multiples elements. (Slide 11,12)

Vikonaemo task number 2.

Manager No. 2 . (Slide 13)

Under the hour of squeezing the task of the skin picture, the next is to review the skin word.

Can you tell me what to graze on the meadow with the cows?

And riy koriv?

And the bouquet of cows?

So, for cows that graze in the meadow, the word “herd” is more appropriate.

Similarly to other pictures, possible options are sorted out, and the appropriate word is selected.

Also, for certain groups of objects, sing words, yak call these groups, for example, a herd of cows. Ale say "riy koriv" is no longer possible. Then, be it a group of objects, chosen at once, can be called a “multiple”: faceless cows, faceless ribs, faceless flowers.

I’ll call you again at once. We need your palms for the grill.

Gra "Find the bunny" (Slide 14,15,16)

The teacher calls the name impersonal and begins to resurrect yoga elements. Learn to blame in the valley, as if the names of the subject are not an element of a given multiplier.

Mi demo park i bachimo tree : birch, oak, troyanda (bavovna), poplar, pine, chamomile (bavovna), yalina, buzok (bavovna)…

We go to the store and buy vegetable : tomatoes, potatoes, oranges (bavovna), carrot, cowbass (bavovna), ogirki, beetroot, apple (bavovna) ...

At the gym mi bachimo sports equipment : ball, lie, dumbbells, armchair (bavovna), tennis rackets, comb (bavovna), forging, stіlets (bavovna) ...

Vikonuemo zavdannya at zoshity.

Manager No. 3 . (Slide 17)

Learn to name the subject that you need to name a lot of other subjects.

The klitz have impersonal birds, and the rabbit in the middle of them is zayvim.

Manager No. 4 . (Slide 18)

Similarly to the front.

Why is Neznayko vikresliv kolo?

That's why the reshta of all objects with kutas.

And if you lose the ear of the cob multiplier, then how can another figure be zayvoi and why?

Let's take a straight cut, like a sir figure.

Manager No. 5 . (Slide 19)

From the given multiplier, children are guilty of seeing the elements of the names of the multiplies: vegetables and fruits. Dolіdzhuєtsya kozhen subject: as tse ovoch - nagoloshuvat one rice, as fruit - two rice. The subject, which is not included in the names of the multitudes until the end, is not required to be added.

After that, slid all the omitted multiplies out of your voice.

Anonymous vegetables: potatoes, beetroot, carrots, ogirok, tomato, watermelon.

Infinite fruits: pear, apple, orange, lemon, pineapple.

Chi not pіdkreslenі: olіya, bread, cowbass, sir, ball.

Manager No. 6 . (Slide 20)

Golovne at the head, so that the student could immediately name a lot of things he saw and resurrect yogo elements.

Anonymous musical instruments: trumpet, violin, guitar, harmonica, drum.

Anonymous sports equipment: dumbbells, ball, forging, racket.

Anonymous everyday tools: saw, pliers, twist.

I call again. Here you need your knowledge.

Gra "Continue the row":

The teacher overhauls a number of subjects, and the scholars, guessing about the name of the impersonal objects, continue with their own elements.

Obov'yazkovo naprikіntsi dermal stage pіdbiti pіdbags: scho bulo rehabilitated, tobto. give the name of the impersonal.

honeymoon, fly agaric, opinok ... (birch, boletus, chanterelle) - tse ... impersonal mushrooms
fox, witch, elephant, hippopotamus ... (vovk, hare, tiger, rhinoceros) - tse ... faceless animals
grandma, blizzard, konik ... (beetle, mosquito, bjola, fly) - tse ... bezlich komakh
beret, capelyukh, panama ... (hustka, cap, hat) - tse ... faceless headwear
pike, perch, catfish, roach ... (shark, crucian carp, lyash) - tse ... impersonal rib

Manager No. 7 . (Slide 21)

Children win independently. You can ask 1-2 students to voice their opinions.

Domalyuvav tulip, because. tse impersonal colors.

Children, name the place for you (children, name the place).

Can you name the Volga as a place?

No, little church.

Can you call Russia mist?

No, tse country.

Manager No. 8 . (Slide 22)

Win independently.

Manager No. 9 . (Slide 23)

Learn how to name the skin tissue from trioma with objects (clothing, ribi, wood). After what oak May buti inscriptions at the stovpets under the name of "tree", because that tree.

Other subjects are similarly followed: perch, lyash- "Ribi" back- "clothes".





Spidnytsia	Perch

Sub-bag for the lesson:

Ozhe, today in the lesson we have become acquainted with you with such concepts, like “multiplier” and “multiple elements”. Learned to signify the impersonal, as well as the reliability of the element of the given multiplicity.

Cards from tasks (Slide 24-30)

Let's learn how to lunate cards from the tasks of looking at tests for two options. The steps of mastering the new material are being reconsidered.

1 option:

2 option:

Home tasks:(Slide 31)

Children are guilty of painting whether a number of objects from the sacred name and signing the name under the picture.

Literature:

Methodological recommendations for the teacher, grade 2, A.V. Goryachov, K.I. Gorina, N.I. Suvorova.
Informatics in games and tasks, grade 2, part 2. A.V. Goryachev, K.I. Gorina, N.I. Suvorova.
Informatics test, 2nd grade, O.M. Krilova.