How to create equalities and inequalities using. What is equality? The first sign and principles of equality

In this lesson, you and the frog will become familiar with mathematical concepts: “equality” and “inequality,” as well as comparison signs. With fun and interesting examples, learn to compare groups of shapes using pairing and compare numbers using the number line.

Subject:Introduction to basic concepts in mathematics

Lesson: Equality and Inequality

In this lesson we will introduce mathematical concepts: "equality" And "inequality".

Try answering the question:

There are tubs against the wall,

Each one contains exactly a frog.

If there were five tubs,

How many frogs would there be in them? (Fig. 1)

Rice. 1

The poem says that there were 5 tubs, each tub contained 1 frog, no one was left without a pair, which means the number of frogs is equal to the number of tubs.

Let's denote the tubs with the letter K, and the frogs with the letter L.

Let's write the equality: K = L. (Fig. 2)

Rice. 2

Compare the number of two groups of figures. There are many figures, they are of different sizes, arranged in no order. (Fig. 3)

Rice. 3

Let's make pairs of these figures. Let's connect each square to a triangle. (Fig. 4)

Rice. 4

Two squares were left without a pair. This means that the number of squares is not equal to the number of triangles. Let's denote the squares with the letter K, and the triangles with the letter T.

Let's write the inequality: K ≠ T. (Fig. 5)

Rice. 5

Conclusion: You can compare the number of elements in two groups by making pairs. If all elements have enough pairs, then the corresponding numbers equal, in this case we put it between numbers or letters =. This entry is called equality. (Fig. 6)

Rice. 6

If there are not enough pairs, that is, there are extra items left, then these numbers not equal. Place between numbers or letters unequal sign. This entry is called inequality.(Fig. 7)

Rice. 7

The elements remaining without a pair show which of the two numbers is greater and by how much. (Fig. 8)

Rice. 8

The method of comparing groups of figures using pairing is not always convenient and takes a lot of time. You can compare numbers using number beam. (Fig. 9)

Rice. 9

Compare these numbers using a number line and put a comparison sign.

We need to compare the numbers 2 and 5. Let's look at the number ray. The number 2 is closer to 0 than the number 5, or they say the number 2 on the number line is further to the left than the number 5. This means that 2 is not equal to 5. This is an inequality.

The sign “≠” (not equal) only fixes the inequality of numbers, but does not indicate which of them is greater and which is less.

Of the two numbers on the number line, the smaller one is located to the left, and the larger one is located to the right. (Fig. 10)

Rice. 10

This inequality can be written differently using less sign "< » or greater than sign ">" :

On the number line, the number 7 is further to the right than the number 4, therefore:

7 ≠ 4 and 7 > 4

The numbers 9 and 9 are equal, so we put the = sign, this is an equality:

Compare the number of dots and the number and put the appropriate sign. (Fig. 11)

Rice. eleven

In the first picture we need to put the = or ≠ sign.

Compare two points and the number 2, put an = sign between them. This is equality.

We compare one point and the number 3, on the number line the number 1 is to the left than the number 3, put the ≠ sign.

We compare four points and 4. We put an = sign between them. This is equality.

We compare three points and the number 4. Three points are the number 3. On the number line it is to the left, we put the ≠ sign. This is inequality. (Fig. 12)

Rice. 12

In the second figure, you need to put = signs between the dots and numbers,<, >.

Let's compare five dots and the number 5. We put an = sign between them. This is equality.

Let's compare three dots and the number 3. Here you can also put the = sign.

Let's compare five points and the number 6. On the number line, the number 5 is to the left than the number 6. We put a sign<. Это неравенство.

Let's compare two points and one, the number 2 is further to the right on the number line than the number 1. We put the > sign. This is inequality. (Fig. 13)

Rice. 13

Insert a number into the box to make the resulting equality and inequality true.

This is inequality. Let's look at the number line. Since we are looking for a number less than the number 7, then it must be to the left of the number 7 on the number line. (Fig. 14)

Rice. 14

You can insert several numbers into the window. The numbers 0, 1, 2, 3, 4, 5, 6 are suitable here. Any of them can be substituted in the window and you will get several true inequalities. For example, 5< 7 или 2 < 7

On the number line we will find numbers that will be less than 5. (Fig. 15)

Rice. 15

These numbers are 4, 3, 2, 1, 0. Therefore, any of these numbers can be substituted in the window, we will get several true inequalities. For example, 5 >4, 5 >3

You can only substitute one number 8.

In this lesson, we got acquainted with the mathematical concepts: “equality” and “inequality”, learned how to correctly place comparison signs, practiced comparing groups of figures using pairing and comparing numbers using a number line, which will help in the further study of mathematics.

Bibliography

1. Alexandrova L.A., Mordkovich A.G. Mathematics 1st grade. - M: Mnemosyne, 2012.
2. Bashmakov M.I., Nefedova M.G. Mathematics. 1 class. - M: Astrel, 2012.
3. Bedenko M.V. Mathematics. 1 class. - M7: Russian Word, 2012.

1. Game.pro().
2. Slideshare.net().
3. Iqsha.ru ().

Homework

1. What comparison signs do you know, in what cases are they used? Write down the comparison signs for numbers.

2. Compare the number of objects in the picture and put a sign “<», «>" or "=".

3. Compare the numbers by putting the sign “<», «>" or "=".

1. The concept of equality and inequality

2. Properties of equalities and inequalities. Examples of solving equalities and inequalities

Numerical equalities and inequalities

Let f And g- two numeric expressions. Let's connect them with an equal sign. We will receive an offer f= g which is called numerical equality.

Take, for example, the numerical expressions 3 + 2 and 6 - 1 and connect them with the equal sign 3 + 2 = 6-1. It is true. If we connect the equal sign 3 + 2 and 7 - 3, we get the false numerical equality 3 + 2 = 7-3. Thus, from a logical point of view, a numerical equality is a statement, true or false.

A numerical equality is true if the values ​​of the numerical expressions on the left and right sides of the equality coincide.

Properties of equalities and inequalities

Let us recall some properties of true numerical equalities.

1. If we add the same numerical expression that makes sense to both sides of a true numerical equality, we also obtain a true numerical equality.

2. If both sides of a true numerical equality are multiplied by the same numerical expression that makes sense, then we also obtain a true numerical equality.

Let f And g- two numeric expressions. Let's connect them with the sign ">" (or "<»). Получим предложение f > g(or f < g), which is called numerical inequality.

For example, if we connect the expression 6 + 2 and 13-7 with the “>” sign, we get the true numerical inequality 6 + 2 > 13-7. If we connect the same expressions with the sign “<», получим ложное числовое неравен­ство 6 + 2 < 13-7. Таким образом, с логической точки зрения число­вое неравенство - это высказывание, истинное или ложное.

Numerical inequalities have a number of properties. Let's look at some.

1. If we add the same numerical expression that makes sense to both sides of a true numerical inequality, we also obtain a true numerical inequality.

2. If both sides of a true numerical inequality are multiplied by the same numerical expression that has meaning and a positive value, then we also obtain a true numerical inequality.

3. If we multiply both parts of a true numerical inequality by the same numerical expression, which has a meaningful and negative value, and also change the sign of the inequality to the opposite, then we also obtain a true numerical inequality.

Exercises

1. Determine which of the following numerical equalities and inequalities are true:

a) (5.05: 1/40 - 2.8 ·5/6) ·3 +16·0.1875 = 602;

b) (1/14 – 2/7) : (-3) – 6 1/13: (-6 1/13)> (7- 8 4/5) 2 7/9 – 15: (1/8 – 3/4);

c) 1.0905:0.025 - 6.84·3.07 + 2.38:100< 4,8:(0,04·0,006).

2. Check whether the numerical equalities are true: 13 93 = 31 39, 14 82 = 41 28, 23 64 = 32 46. Is it possible to say that the product of any two natural numbers will not change if the digits in each factor are rearranged?

3. It is known that x > y - true inequality. Will the following inequalities be true:

a )2x > 2y; V ) 2x-7< 2у-7;

b)- x/3<-y/3; G )-2x-7<-2у-7?

4. It is known that A< b- true inequality. Replace * with a ">" or "<» так, чтобы получилось истинное неравенство:

a) -3.7 a * -3,7b; G) - a/3 * -b/3 ;

b) 0.12 A * 0,12b; d) -2(a + 5) * -2(b + 5);

V) a/7 * b/7; e) 2/7 ( a-1) * 2/7 (b-1).

5. Given the inequality 5 > 3. Multiply both sides by 7; 0.1; 2.6; 3/4. Based on the results obtained, is it possible to say that for any positive number A inequality 5a> 3A true?

6. Complete tasks intended for primary school students and draw a conclusion about how the concepts of numerical equality and numerical inequality are interpreted in the initial mathematics course.

The other side of equality is inequality. In this article we will introduce the concept of inequalities, and give some basic information about them in the context of mathematics.

First, let's look at what inequality is and introduce the concepts of not equal, greater than, less. Next we’ll talk about writing inequalities using the signs not equal, less than, greater than, less than or equal to, greater than or equal to. After this, we will touch on the main types of inequalities, give definitions of strict and non-strict, true and false inequalities. Next, let us briefly list the main properties of inequalities. Finally, let's look at doubles, triples, etc. inequalities, and let’s look at the meaning they carry.

Page navigation.

What is inequality?

Concept of inequality, like , is associated with the comparison of two objects. And if equality is characterized by the word “identical,” then inequality, on the contrary, speaks of the difference between the objects being compared. For example, the objects and are the same; we can say about them that they are equal. But the two objects are different, that is, they not equal or unequal.

The inequality of compared objects is recognized along with the meaning of words such as higher, lower (inequality in height), thicker, thinner (inequality in thickness), further, closer (inequality in distance from something), longer, shorter (inequality in length) , heavier, lighter (weight inequality), brighter, dimmer (brightness inequality), warmer, colder, etc.

As we already noted when getting acquainted with equalities, we can talk both about the equality of two objects as a whole, and about the equality of some of their characteristics. The same applies to inequalities. As an example, we give two objects and . Obviously, they are not the same, that is, in general they are unequal. They are not equal in size, nor are they equal in color, however, we can talk about the equality of their shapes - they are both circles.

In mathematics, the general meaning of inequality remains the same. But in its context we are talking about the inequality of mathematical objects: numbers, values ​​of expressions, values ​​of any quantities (lengths, weights, areas, temperatures, etc.), figures, vectors, etc.

Not equal, greater, less

Sometimes it is the very fact that two objects are unequal that is of value. And when the values ​​of any quantities are compared, then, having found out their inequality, they usually go further and find out what quantity more, and which one – less.

We learn the meaning of the words “more” and “less” almost from the first days of our lives. On an intuitive level, we perceive the concept of more and less in terms of size, quantity, etc. And then we gradually begin to realize that in fact we are talking about comparison of numbers, corresponding to the number of certain objects or the values ​​of certain quantities. That is, in these cases we find out which number is greater and which is less.

Let's give an example. Consider two segments AB and CD, and compare their lengths . Obviously, they are not equal, and it is also obvious that the segment AB is longer than the segment CD. Thus, according to the meaning of the word “longer”, the length of the segment AB is greater than the length of the segment CD, and at the same time the length of the segment CD is less than the length of the segment AB.

Another example. In the morning the air temperature was recorded at 11 degrees Celsius, and in the afternoon – 24 degrees. According to 11 is less than 24, therefore, the temperature value in the morning was less than its value at lunchtime (the temperature at lunchtime became higher than the temperature in the morning).

Writing inequalities using signs

The letter has several symbols for recording inequalities. The first one is not equal sign, it represents a crossed out equal sign: ≠. The unequal sign is placed between unequal objects. For example, the entry |AB|≠|CD| means that the length of the segment AB is not equal to the length of the segment CD. Likewise, 3≠5 – three does not equal five.

The greater than sign > and the less than sign ≤ are used similarly. The greater sign is written between larger and smaller objects, and the less sign is written between smaller and larger objects. Let us give examples of the use of these signs. The entry 7>1 is read as seven over one, and you can write that the area of ​​triangle ABC is less than the area of ​​triangle DEF using the ≤ sign as SABC≤SDEF.

Also widely used is the greater than or equal to sign of the form ≥, as well as the less than or equal to ≤ sign. We'll talk more about their meaning and purpose in the next paragraph.

Let us also note that algebraic notations with the signs not equal to, less than, greater than, less than or equal to, greater than or equal to, similar to those discussed above, are called inequalities. Moreover, there is a definition of inequalities in the sense of the way they are written:

Definition.

Inequalities are meaningful algebraic expressions composed using the signs ≠,<, >, ≤, ≥.

Strict and non-strict inequalities

Definition.

Signs are called less signs of strict inequalities, and the inequalities written with their help are strict inequalities.

In its turn

Definition.

The signs less than or equal to ≤ and greater than or equal to ≥ are called signs of weak inequalities, and the inequalities compiled using them are non-strict inequalities.

The scope of application of strict inequalities is clear from the information above. Why are weak inequalities needed? In practice, with their help it is convenient to model situations that can be described by the phrases “no more” and “no less.” The phrase “no more” essentially means less or the same; it is answered by a less than or equal sign of the form ≤. Likewise, “not less” means the same or more, and is associated with the greater than or equal sign ≥.

From here it becomes clear why the signs< и >are called signs of strict inequalities, and ≤ and ≥ - non-strict. The former exclude the possibility of equality of objects, while the latter allow it.

To conclude this section, we will show a couple of examples of using non-strict inequalities. For example, using the greater than or equal sign, you can write the fact that a is a non-negative number as |a|≥0. Another example: it is known that the geometric mean of two positive numbers a and b is less than or equal to their arithmetic mean, that is, .

True and false inequalities

Inequalities can be true or false.

Definition.

Inequality is faithful, if it corresponds to the meaning of the inequality introduced above, otherwise it is unfaithful.

Let us give examples of true and false inequalities. For example, 3≠3 is an incorrect inequality, since the numbers 3 and 3 are equal. Another example: let S be the area of ​​some figure, then S<−7 – неверное неравенство, так как известно, что площадь фигуры по определению выражается неотрицательным числом. И еще пример неверного неравенства: |AB|>|AB| . But the inequalities are −3<12 , |AB|≤|AC|+|BC| и |−4|≥0 – верные. Первое из них отвечает , второе – выражает triangle inequality, and the third is consistent with the definition of the modulus of a number.

Note that along with the phrase “true inequality” the following phrases are used: “fair inequality”, “there is inequality”, etc., meaning the same thing.

Properties of inequalities

According to the way we introduced the concept of inequality, we can describe the main properties of inequalities. It is clear that an object cannot be equal to itself. This is the first property of inequalities. The second property is no less obvious: if the first object is not equal to the second, then the second is not equal to the first.

The concepts “less” and “more” introduced on a certain set define the so-called “less” and “more” relations on the original set. The same applies to the relations “less than or equal to” and “greater than or equal to.” They also have characteristic properties.

Let's start with the properties of the relations to which the signs correspond< и >. Let us list them, after which we will give the necessary comments for clarification:

• anti-reflexivity;
• antisymmetry;
• transitivity.

The anti-reflexivity property can be written using letters as follows: for any object a the inequalities a>a and a b , then b a. Finally, the transitivity property is that from a b and b>c it follows that a>c . This property is also perceived quite naturally: if the first object is smaller (larger) than the second, and the second is smaller (larger) than the third, then it is clear that the first object is even smaller (larger) than the third.

In turn, the relations “less than or equal to” and “greater than or equal to” have the following properties:

• reflexivity: the inequalities a≤a and a≥a hold (since they include the case a=a);
• antisymmetry: if a≤b, then b≥a, and if a≥b, then b≤a;
• transitivity: from a≤b and b≤c it follows that a≤c, and from a≥b and b≥c it follows that a≥c.

Double, triple inequalities, etc.

The property of transitivity, which we touched upon in the previous paragraph, allows us to compose so-called double, triple, etc. inequalities that are chains of inequalities. As an example, let us give the double inequality a

Now let's look at how to understand such records. They should be interpreted in accordance with the meaning of the signs they contain. For example, double inequality a

In conclusion, we note that sometimes it is convenient to use notations in the form of chains containing both equal and not equal signs, as well as strict and non-strict inequalities. For example, x=2

Bibliography.

• Moro M.I.. Mathematics. Textbook for 1 class. beginning school In 2 hours. Part 1. (First half of the year) / M. I. Moro, S. I. Volkova, S. V. Stepanova. - 6th ed. - M.: Education, 2006. - 112 p.: ill.+Add. (2 separate l. ill.). - ISBN 5-09-014951-8.
• Mathematics: textbook for 5th grade. general education institutions / N. Ya. Vilenkin, V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd. - 21st ed., erased. - M.: Mnemosyne, 2007. - 280 pp.: ill. ISBN 5-346-00699-0.

In this lesson, you and the frog will become familiar with mathematical concepts: “equality” and “inequality,” as well as comparison signs. With fun and interesting examples, learn to compare groups of shapes using pairing and compare numbers using the number line.

Subject:Introduction to basic concepts in mathematics

Lesson: Equality and Inequality

In this lesson we will introduce mathematical concepts: "equality" And "inequality".

Try answering the question:

There are tubs against the wall,

Each one contains exactly a frog.

If there were five tubs,

How many frogs would there be in them? (Fig. 1)

Rice. 1

The poem says that there were 5 tubs, each tub contained 1 frog, no one was left without a pair, which means the number of frogs is equal to the number of tubs.

Let's denote the tubs with the letter K, and the frogs with the letter L.

Let's write the equality: K = L. (Fig. 2)

Rice. 2

Compare the number of two groups of figures. There are many figures, they are of different sizes, arranged in no order. (Fig. 3)

Rice. 3

Let's make pairs of these figures. Let's connect each square to a triangle. (Fig. 4)

Rice. 4

Two squares were left without a pair. This means that the number of squares is not equal to the number of triangles. Let's denote the squares with the letter K, and the triangles with the letter T.

Let's write the inequality: K ≠ T. (Fig. 5)

Rice. 5

Conclusion: You can compare the number of elements in two groups by making pairs. If all elements have enough pairs, then the corresponding numbers equal, in this case we put it between numbers or letters =. This entry is called equality. (Fig. 6)

Rice. 6

If there are not enough pairs, that is, there are extra items left, then these numbers not equal. Place between numbers or letters unequal sign. This entry is called inequality.(Fig. 7)

Rice. 7

The elements remaining without a pair show which of the two numbers is greater and by how much. (Fig. 8)

Rice. 8

The method of comparing groups of figures using pairing is not always convenient and takes a lot of time. You can compare numbers using number beam. (Fig. 9)

Rice. 9

Compare these numbers using a number line and put a comparison sign.

We need to compare the numbers 2 and 5. Let's look at the number ray. The number 2 is closer to 0 than the number 5, or they say the number 2 on the number line is further to the left than the number 5. This means that 2 is not equal to 5. This is an inequality.

The sign “≠” (not equal) only fixes the inequality of numbers, but does not indicate which of them is greater and which is less.

Of the two numbers on the number line, the smaller one is located to the left, and the larger one is located to the right. (Fig. 10)

Rice. 10

This inequality can be written differently using less sign "< » or greater than sign ">" :

On the number line, the number 7 is further to the right than the number 4, therefore:

7 ≠ 4 and 7 > 4

The numbers 9 and 9 are equal, so we put the = sign, this is an equality:

Compare the number of dots and the number and put the appropriate sign. (Fig. 11)

Rice. eleven

In the first picture we need to put the = or ≠ sign.

Compare two points and the number 2, put an = sign between them. This is equality.

We compare one point and the number 3, on the number line the number 1 is to the left than the number 3, put the ≠ sign.

We compare four points and 4. We put an = sign between them. This is equality.

We compare three points and the number 4. Three points are the number 3. On the number line it is to the left, we put the ≠ sign. This is inequality. (Fig. 12)

Rice. 12

In the second figure, you need to put = signs between the dots and numbers,<, >.

Let's compare five dots and the number 5. We put an = sign between them. This is equality.

Let's compare three dots and the number 3. Here you can also put the = sign.

Let's compare five points and the number 6. On the number line, the number 5 is to the left than the number 6. We put a sign<. Это неравенство.

Let's compare two points and one, the number 2 is further to the right on the number line than the number 1. We put the > sign. This is inequality. (Fig. 13)

Rice. 13

Insert a number into the box to make the resulting equality and inequality true.

This is inequality. Let's look at the number line. Since we are looking for a number less than the number 7, then it must be to the left of the number 7 on the number line. (Fig. 14)

Rice. 14

You can insert several numbers into the window. The numbers 0, 1, 2, 3, 4, 5, 6 are suitable here. Any of them can be substituted in the window and you will get several true inequalities. For example, 5< 7 или 2 < 7

On the number line we will find numbers that will be less than 5. (Fig. 15)

Rice. 15

These numbers are 4, 3, 2, 1, 0. Therefore, any of these numbers can be substituted in the window, we will get several true inequalities. For example, 5 >4, 5 >3

You can only substitute one number 8.

In this lesson, we got acquainted with the mathematical concepts: “equality” and “inequality”, learned how to correctly place comparison signs, practiced comparing groups of figures using pairing and comparing numbers using a number line, which will help in the further study of mathematics.

Bibliography

1. Alexandrova L.A., Mordkovich A.G. Mathematics 1st grade. - M: Mnemosyne, 2012.
2. Bashmakov M.I., Nefedova M.G. Mathematics. 1 class. - M: Astrel, 2012.
3. Bedenko M.V. Mathematics. 1 class. - M7: Russian Word, 2012.

1. Game.pro().
2. Slideshare.net().
3. Iqsha.ru ().

Homework

1. What comparison signs do you know, in what cases are they used? Write down the comparison signs for numbers.

2. Compare the number of objects in the picture and put a sign “<», «>" or "=".

3. Compare the numbers by putting the sign “<», «>" or "=".

Class: 3

Presentation for the lesson

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Lesson type: discovery of new knowledge.

Technology: technology for developing critical thinking through reading and writing, gaming technology.

Goals: To expand students' knowledge about equalities and inequalities, to introduce the concept of true and false equalities and inequalities.

Didactic task: Organize joint, independent activities of students to study new material.

Lesson objectives:

1. Subject:
   • introduce the signs of equality and inequality; expand students' understanding of equalities and inequalities;
   • introduce the concept of true and false equality and inequality;
   • developing skills in finding the value of an expression containing a variable;
   • formation of computing skills.
2. Metasubject:
   1. Cognitive:
      • promote the development of attention, memory, thinking;
      • developing the ability to extract information, navigate one’s knowledge system and recognize the need for new knowledge;
      • mastering the techniques of selecting and systematizing material, the ability to collate and compare, and converting information (into a diagram, table).
   2. Regulatory:
      • development of visual perception;
      • continue work on the formation of self-control and self-esteem among students;
   3. Communicative:
      • observe the interaction of children in pairs and make the necessary adjustments;
      • foster mutual assistance.
3. Personal:
   • increasing students' learning motivation by using the Star Board interactive school board in the classroom;
   • improving skills in working with the Star Board.

Equipment:

• Textbook “Mathematics” 3rd grade, part 2 (L.G. Peterson);
• individual handout sheet ;
• cards for working in pairs;
• presentation for the lesson displayed on the Star Board panel;
• computer, projector, Star Board.

During the classes

I. Organizational moment.

And so, friends, attention.
After all, the bell rang
Sit back comfortably
Let's start the lesson soon!

II. Verbal counting.

– Today we will go with you to visit. After listening to the poem, you will be able to name the hostess. (Reading a poem by a student)

For centuries, mathematics has been covered in glory,
The luminary of all earthly luminaries.
Her majestic queen
No wonder Gauss christened it.
We praise the human mind,
The works of his magical hands,
The hope of this century,
Queen of all earthly sciences.

– And so, Mathematics awaits us. There are many principalities in her kingdom, but today we will visit one of them (slide 4)

– You will find out the name of the principality by solving the examples and arranging the answers in ascending order. ( Statement)

7200: 90 = 80	WITH		280: 70 = 4	AND
5400: 9 = 600	Y		3500: 70 = 50	Z
2700: 300 = 9	IN		4900: 700 = 7	A
4800: 80 = 60	A		1600: 40 = 40	Y
560: 8 = 70	TO		1800: 600 = 3	E
4200: 6 = 700	IN		350: 70 = 5	N

- Let's remember what a statement is? ( Statement)

– What could the statement be? (True or False)

– Today we will work with mathematical statements. What does this mean? (expression, equalities, inequalities, equations)

III. Stage 1. CHALLENGE. Preparing to learn new things.

(slide 5 see note)

– Princess Saying offers you the first test.

- There are cards in front of you. Find an extra card and show it (a + 6 – 45 * 2).

- Why is she superfluous? (Expression)

– Is the expression a complete statement? (No, it is not, because it has not been brought to its logical conclusion)

– What are equality and inequality? Can they be called statements?

– Name the correct equalities.

– What is another name for true equalities? ( true)

– What about the infidels? (false)

– What equations cannot be said to be true? ( with variable)

– Mathematics constantly teaches us to prove the truth or falsity of our statements.

IV. Communicate the purpose of the lesson.

– And today we must learn what equality and inequality are and learn to determine their truth and falsity.

- Here are statements before you. Read them carefully. If you think it is correct, then put “+” in the first column; if not, put “–”.

	Before reading	After reading
Equalities are two expressions connected by the sign “=”
Expressions can be numeric or alphabetic.
If two expressions are numeric, then equality is a proposition.
Numerical equalities can be true or false.
6 * 3 = 18 – correct numerical equality
16: 3 = 8 – incorrect numerical equality
Two expressions connected by a ">" or "<» - неравенство.
Numerical inequalities are propositions.

Collective verification with justification for your assumption.

V. Stage 2. REFLECTION. Learning new things.

– How can we check if our assumptions are correct?

(textbook p. 74.)

– What is equality?

– What is inequality?

– We have completed the task of Princess Saying, and as a reward she invites us to a holiday.

VI. Physical education minute.

VII. Stage 3. REFLECTION-REFLECTION

1. p. 75.5 (displayed) (slide 8)

– Read the task, what needs to be done?

8 + 12 = 20		a > b
8 + 12 + 20		a – b
8 + 12 > 20		a + b = c
20 = 8 + 12		a + b * c

– How many equalities did you emphasize? Let's check.

– How many inequalities?

– What helped you complete the task? (signs “=”, “>”, “<»)

– Why were there ununderlined entries? (expressions)

2. Game “Silence” (slide 9)

(Students write down equalities on narrow strips and show them to the teacher, then check themselves).

Write the statement as an equality:

• 5 is more than 3 by 2 (5 – 3 = 2)
• 12 is 6 times greater than 2 (12: 2 = 6)
• x is less than y by 3 (y – x = 3)

3. Solving equations (slide 10)

– What is in front of us? (equations, equalities)

– Can we tell whether they are true or false? (no, there is a variable)

– How to find at what value of a variable the equalities are true? (decide)

• 1 column – 1 column
• Column 2 – Column 2
• 3 column – 3 column

Exchange notebooks and check your friend's work. Rate it.

VIII. Lesson summary.

– What concepts did we work with today?

– What kind of equality can there be? (false or true)

– Do you think it’s only in mathematics lessons that we need to be able to distinguish false statements from true ones? (A person encounters a lot of different information in his life, and one must be able to separate the true from the false).

IX. Assessing student work and assigning grades.

– What can Queen Mathematics thank us for?

Note. If the teacher is using the Star Board, this slide is replaced with cards typed on the board. When checking, students work on the board.