The ancient Sumerians were the first to come up with the idea of ​​writing numbers. They only used two numbers. A vertical line meant one unit, and an angle of two lying lines meant ten. They made these lines in the form of wedges, because they wrote with a sharp stick on damp clay tablets, which were then dried and fired. This is what these planks looked like (Fig. 2).

Fig.2

Along with the usual logographic, compound, and alphabetic-compound signs, special written signs are used. These are numbers, algebraic, geometric, chemical, astronomical, meteorological, as well as dividing punctuation marks, diacritics, etc. Notes occupy a separate group.

Numbers

Even now, science cannot answer the question of when and how the first letter developed, just as it cannot say exactly when and how the first numbers arose, as well as the first signs to denote quantitative units. People became acquainted with natural numbers at the dawn of civilization. Almost all digital systems were built on the decimal principle. Almost the only exception is the Mayan and Aztec systems with their five-twenty principle. The dominant position of the decimal system is explained by the fact that the most ancient tool for calculating a person had two hands with ten fingers. Nevertheless, the Babylonians had in use the sexagesimal principle of calculation associated with their weight units. The fact that it was human fingers that were the first instrument of calculation can be seen, for example, from the following fact: in the Hamitic language in Africa, the words hand and five and the pronunciation of the words ten and two hands have a common root. Almost all digital systems had independent signs only for the simplest numbers; the number of such signs ranged from 4-5 to 30. The rest of the numbers were obtained by addition (for example, in the Roman system, the number 6 is the addition of the signs “five” and “one” (VI)). Large numbers were sometimes obtained by the principle of multiplication (for example, in the Greek Ionic system, the sign “three” was placed above the sign “ten thousand”, and this should have meant “thirty thousand”; less often the principle of subtraction was used (for example, Roman numerals IV, IX). A significant but late achievement in the history of numbers was the use of the “positional principle”, according to which the numerical value of digital signs depends not only on their shape, but also on their location (for example, 52, 25). what's the word number comes from Arabic emptiness, and at first this word meant zero. The sign 0 indicated the absence of a number.

The development of numbers is related to the general development of writing. At the early pictographic stage of writing, numbers did not yet exist. In case of need to indicate the number of things, these things and the image were drawn the required number of times. Later, a more complex method arose: they depicted the object in question, and placed dots or lines next to it, the number of which indicated the desired number. This method was used at the beginning of the 19th century on Russian coins. The dots placed next to the number determined the value of the coin. This principle was convenient for transmitting small numbers used at an early stage of the development of society; dots and dashes served as the prototype for the simplest digital signs - units.

We don’t know exactly how people counted and how they called numbers before the invention of writing. At the dawn of civilization, people made do with three numbers: “one”, “two”, “many”. It was probably more than a millennium before this calculation advanced further. In any case, by the time writing was invented, people were already able to count quite well.

As we noted, the Aztecs and Mayans used the five-twenty number system. Their special symbols for writing units were a dot, a five-dash, and a twenty-flag. The remaining numbers were obtained by repetition, adding the main characters, for example:

According to Yu.V. Knorozov, the Mayans also used a positional method of writing numbers (1). Using their number system, the Mayans achieved a high degree of mathematical and astronomical knowledge.

It is known that the cuneiform system of writing numbers was born almost 4000 years ago. This system was very common in the Middle East. Even in modern practice, the influence of the Babylonian culture of distant times is reflected. When at the end of the 3rd century BC. There was a merger of the two peoples of Sumerians and Akkadians (the northern part of Babylon at the beginning of the Hellenistic period of history was called Akkad), the unit of weight among the Sumerians was mina (approximately 0.5 kg), the monetary unit was mina of silver. Among the Akkadians, the basic unit, the shekel, was approximately sixty times smaller. After the merger of the mentioned peoples, both systems of units of measurement remained in use. Minas and shekels were used then as we now use kilograms and grams. In monetary use, minas and shekels played the role of our rubles and koppeks, but with the difference that the large unit of measurement was equal not to 100, but to 60 small units. Later, an even larger unit of measurement “talent” appeared here; one talent was equal to sixty mina. This system has been preserved to this day to measure angles and time. After all, a sixth of a circle is divided into 60 degrees, a degree into 60 minutes, a minute into 60 seconds. Minute means in Latin small.

As a test material for wedge-shaped writing, numbers were written with sticks, pressing them into soft clay. The peoples of Western Asia who used cuneiform writing (Babylonians, Assyrians, Hittites, Elamites) designated different numbers in the sexagesimal system using three basic meanings. The first sign was a wedge wrapped with a sharp ulg downwards, the second was a sign made up of two wedges placed diagonally and connected by their bases, and the third was a horizontally laid wedge with its tip turned to the right.

To write the number 1, the first sign was used, that is, a wedge placed vertically with the tip downwards; two such wedges were used to indicate the number 2, and so on. To write the number ten (10), the second sign was used, for the number 100, a combination of the first and third signs, that is, a vertically placed wedge and a horizontal one next to it (). When they wanted to write with these signs, for example, 200 or 300, they wrote as many vertically placed wedges as there were in the hundreds, and next to them one horizontally laid wedge, which played the role of a multiplier (multiplier).

A thousand was designated as follows: having written the number ten, a hundred sign was added to its right, and the number ten thousand was designated as follows: having written the number 10, a thousand was added to it to the right.

When a horizontally laid one was added to the vertical wedge on the left, it meant (60).

The Western Asian numeral system, like the cuneiform system, was very complex at that time; it turned out to be the most progressive among the ancient systems; in it, for the first time, the positional principle was used, which made it possible to write down very large numbers, and a special sign (the prototype of zero) was introduced to indicate that there is no digit digit.

For three thousand years in the eastern Mediterranean basin, the Phoenicians (Phoenicians (Ukr)), Cypriots and residents of Crete had a similar spelling of numbers: they had three main features: a vertical line, which served as a unit, a horizontal line, which indicated the number ten , circle - one hundred. Combinations of these signs could represent different numbers:

On the island of Cyprus, which lies on the same parallel as the island of Crete, 500 kilometers east of it, the number system was almost the same as on the island of Crete, but for ten there was a sign similar to the capital (versal) Latin L or small semicircle

Chinese numbers)

The Chinese numerals of that time are reminiscent of the ancient Chinese script "Pakwa".

The Chinese use three number systems, which are based on the number ten (10), and the signs (numbers) are built on the system of addition and multiplication. The main signs are:

Numbers, like text, are written in a vertical direction. When the column at the top contains units, that is, numbers from 1 to 10 (9 is excluded), then these units play the role of a multiplier, for example:

In commercial documents, the Chinese write numbers horizontally, with the highest digits on the left. They look like this:

The third Chinese number system is graphically constructed on the basis of vertical lines and a horizontal line - the basis; the numbers, as in the two previous systems, are positioned positionally.

Egyptian numeral system

The Egyptian number system was built on strict adherence to the decimal principle. To designate units, horizontal, less often vertical, lines were used, for ten - an arc, for hundreds - a bent rope, for a thousand - a lotus stem, for ten thousand - a bent finger, for hundreds of thousands - a tadpole (because tadpoles were hatched in large numbers). For a million there was a sign in the form of a man who raised his hands up in surprise in front of such a large number. In another interpretation, this is a deity who supports the sky.

The remaining numbers were obtained by the principle of adding the mentioned main numbers placed side by side; Thus, for the number twenty-five (25) they write two bows (bows) and five dashes; to designate 1852 they wrote one thousand sign, eight hundreds sign, five ten sign and two unit sign.

Digital signs began to be used in Egypt back in the predynastic period, during the transition from pictography to logography. Thus, in Narmer’s record on a slate table (end of the 4th millennium BC) there are such papyrus stems that are interpreted by Egyptologists as the designation of a thousand. Starting from the “Middle Kingdom,” the designation of large numbers was based not on the principle of addition, but on the principle of multiplication. As Egyptian writing developed, especially when the Egyptians began to write on papyrus, the numbers in hieratic and demonic writing were formed as follows:

The writing of numbers in the Egyptian script developed in the same way as text writing. Accordingly, we distinguish between hieroglyphic, hieratic and demonic numbers.

European number systems, Greek, Hebrew, Slavic, Etruscan, Roman and others

The Herodian system did not last long, and the Greeks later used individual letters of the alphabet to denote numbers up to 24:

Later, the Greeks introduced special notations for units, separate for tens and hundreds, namely:

The method of writing numbers using individual letters of the alphabet has long been used in Hebrew writing. Of the 22 letters of the alphabet, the first nine were used to write units, the next nine denoted tens, and the last four were used to write hundreds (up to 400). When it was necessary to write more hundreds, by combining the signs of the previous four hundreds, four more hundreds were obtained, and then auxiliary signs were introduced to indicate numbers:

Thousands of Jews wrote by placing two dots with the corresponding hundreds sign, which meant that the number (hundreds) was multiplied by ten.

This number system was in use by the ancient Syrians, and for some time it was used by the Arabs, until it was supplanted by numbers that were brought in from India.

Slavic number systems

In the old Church Slavonic Cyrillic alphabet, numbers were also designated by letters:

The Slavs, especially the Orthodox, used this code for writing numbers for quite a long time, namely until the beginning of the 19th century, until it was finally replaced by Arabic ones. Kulundzic informs, for example, that on many old Serbian church images from before the 19th century, you can read Old Slavonic numbers and letters, which serve to date historical landmarks (memoirs). Lubmir Stojanovic, in his work “Old Serbian Records and Inscriptions,” cites an inscription on a gravestone in the altar of the Decani Monastery, dated 1867.

In our Slavic-Cyrillic number system, as a rule, only letters borrowed from the Greek letter received a digital value. 27 characters - lowercase letters, above which there is also a special sign - titlo (), which is also used in ordinary Slavic writing to abbreviate words:

The numbers eleven, twelve were written respectively like this: twenty-one, twenty-two - and so on. The title was placed only above one of the numbers. The order of digits when writing a number was the same as in the oral name of this number. We say, for example, “fifteen” (in Slavic five by ten), that is, calling first one and then ten. .

The Slavs wrote like this: that is, first “five”, and then ten.

On the contrary, in the number “twenty-three” we first name tens, then ones. According to the condition of this number, it was written like this.

Large numbers were easily written using Cyrillic characters. The number 29,946 was defined, for example, like this: the sign meant thousands. By repeating it, very large numbers could be written down. Here's how, for example, the number 20,178,073 was written:

The form of Roman numerals comes from counting on fingers and from the verbal naming of numbers. The numbers are constructed according to the first principle: 1 (one finger), V (palm with thumb extended), X (crossed arms); according to a different principle, the numbers C (the first letter of the word centum - one hundred) and M (the first letter of the word mille - thousand); there is not enough information about the origin of the numbers L and D. In ancient Roman monuments (BC), the number D (500) was not found, and Western Greek letters were sometimes used for the numbers 50, 100, 1000.
Using the seven mentioned above Latin letters we can write any number.

Roman numerals were widely used in the Middle Ages, before the appearance of so-called Arabic numerals in Europe. Now Roman numerals are used to indicate historical dates, on watch dials, in cases of complex numbering, when the Arabic numeral system alone is not enough (for example, when a book is divided into sections, which in turn are divided into subsections).

Arabic counting system

Using nine characters - Arabic numerals (1,2,3,4,5,6,7,8,9) and zero (0) we can write any number. The first digits of this type appear in the 3rd century. BC. in the record of the Indian king Ashoka (273-232 BC), but in this record the numbers do not stick to certain places, there is no zero in everyday life. A perfect system of numbers was created in India only in the 5th century. based on the consistent use of principles proven throughout the history of the development of numbers - decimal, positional and addition principles, as well as on the basis of the use of the zero sign (approximately 500 AD)

It is believed that the Arabs became acquainted with Indian numerals when they came to Baghdad in 772/773 AD. An embassy arrived, bringing with them some astronomical books written in the Sanskrit language and script. Thanks to these books, the Arabs learned about Indian numbers, the decimal system and named them themselves first hindyan, arquam, which in translation means Indian numerals. The Arab Khuwarizmi wrote about this in his famous work, the first Arabic book on numbers "Chisab hindu".

In 1130 the mentioned work was translated into English language Englishman Abelard from Baza entitled "Liber Algoritmi de numero Indorum". So the Europeans found out new system calculus, which according to Arabic work was called algoritmus or algorismus. In Spain, the first cases of using Arabic numerals occurred in the 10th century, in other European countries in the 12th century.

Almost eighty years after Abelard’s translation, the book of the Italian mathematician Leonardo Fibonacci from Pisa “Liber abaci” (“Book of Accounts” 1208) appeared, and in 1494. Luca Pacioli's book "Summa Aritmetica" ("The Essence of Arithmetic") appeared. Since the 15th century, Arabic numerals have already become more widespread in Europe, moving ahead of Roman numerals.

In Rus', Arabic numerals appeared in the 14th-15th centuries, spread in the 17th century, and in the 18th century, after the introduction of the civil alphabet in Russia, they finally replaced Slavic-Cyrillic numerals in the public press.

The primitive forms of Arabic numerals were somewhat different (except for the signs 1,6,7,8,9,0) than their forms in Europe, where they finally developed to modern forms already at the end of the Middle Ages.

Nowadays, in a form close to the primitive style, Arabic numerals are common in those countries that use the Arabic writing system (Iraq, Afghanistan, Pakistan, etc.).

Decimal fractions, introduced in Europe by the Dutch scientist S. Stevin, were a significant improvement in the Arabic numeral system. After this, Arabic numerals became suitable for decimal positional notation of any small and large numbers.

Printing fonts for transmitting numbers in the assortment of domestic printing houses

The presence of medial numerals in the assortment of printed fonts allows the compiler to adhere to stylistic unity when combining digital materials with medial fonts in the text.

Dividing marks

In modern Ukrainian, Russian and Latin writing, 10 dividing marks are used, of which 6 are used to separate speech and separate its elements (period, comma, semicolon, two dots, dash, quotation marks) and 4 symbols are used to separate speech and emphasize emotional and semantic meaning. its characteristics (question mark, exclamation mark, quotation marks and periods). In addition to the listed characters, another special character is used - a hyphen (-) to connect words. Regarding the use of question marks and exclamation mark, in Spanish writing these signs are placed not only as usual, that is, at the end of the sentence, but also at the beginning inverted, so that the reader knows in advance with what intonation the previous sentence should be read. In poems, if necessary, instead of headings, a designation of three asterisks is used, and if the asterisks are placed in reverse, then they serve instead of the author’s signature.

Diacritics and other marks

Among the special printed signs that are widely used in foreign practice, there is a sign (English ampersand; German Et-Zeichen; French et-commercial, which abbreviated as And). Such a sign, for example, is always placed to connect the surnames of the owners of the merged company. The & sign comes from the combination of the words and per se and. To denote the English currency, pounds sterling, the sign is used. The sign is used to indicate the US currency - dollars. The abbreviation DM is used to denote German marks.

We noted above that special written signs also include: algebraic, geometric, chemical, astronomical, meteorological and others. Such signs are used in the works of certain branches of science and technology, where they are described.

(1) See: Knorozov Yu.V. Writing of the Mayan Indians. M.-L., 1963.

Website about art and creativity

Lesson plans for mathematics with UUD in 2nd grade for September

Publication date: 21.08.2016

Short description:

material preview

Mathematics 3.09.

Topic: Drawing numbers.

Objectives: Familiarity with the textbook. Repetition: number names, reading and writing; even and odd numbers; designation of numbers by digits; composition of single digit numbers.

1.Organizational moment

Checking readiness for the lesson.

Come on, check it out, my friend.

Are you ready to start the lesson?

Pen, book and notebook?

Is everyone sitting correctly?

Is everyone watching carefully?

2.Oral counting

We count in chorus from 1 to 10, and vice versa.

3.Updating lesson objectives

What's on your desk??? (textbook and notebook)

What do you think we will do with them?

Let's look at: the cover, look at the title, the designations on page 2, the drawing and listen to the author's message to you.

We also consider the notebook.

How will you handle these items?

4. Defining goals and communicating the topic of the lesson.

Let's remember what you know about numbers? What about numbers??? (Numbers are signs that represent numbers.) Different peoples came up with different signs to represent numbers p.4.

Signs can be very different. Since ancient times, people have invented them to convey important information, their thoughts, feelings to children, friends, and enemies. They used different methods for this. The most ancient writings were, as you know, cave paintings. They were made by primitive people in order to leave a memory of military or hunting exploits. Consider what an unusual letter the Persian king Darius wrote in ancient times. Page 28

In mathematics, they often use not only numbers, but also pictures to convey information. We will learn to understand not only the language of numbers, but also the language of pictures. Page 4 No. 1.

Let's review the composition of single-digit numbers. Page 4№1

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

Let's repeat even and odd numbers. Page 5 No. 3, 4.

In task No. 4, remember the rule about rearranging terms.

In task No. 5, guess which numbers are written using addition and which numbers are written using subtraction. You can check your findings by looking at page 29.

Open all notebooks on page 3, let's complete the tasks.

Look at page 5 in the textbook, task No. 6, answer the questions.

Eight

Nine (picture 9 shaft)

Open page 126 and read the information.

Workbook page 4 No. 5 homework.

6. Lesson summary

So, let's summarize the lesson.

What goals did we set at the beginning of the lesson?

What should have been repeated?

Have we achieved our goals?

Now let’s stand up and everyone will say what they learned in the lesson, what new things did they learn, what did they remember?

This means our lesson was not in vain. This concludes the lesson.

Development of cognitive interests

brain teaser

Puud synthesis as the composition of a whole from parts;

LUUD formation of installation on healthy image life;

Kuud The ability to express one's thoughts fully and accurately;

Ruud Goal setting as setting an educational task based on the correlation of what is already known and learned by the student and what is still unknown

ability to listen and engage in dialogue;

Ruud assessment - the student’s identification and awareness of what has already been learned and what remains to be learned, awareness of the quality and level of assimilation;

The ability to express one’s thoughts fully and accurately;

Mathematics 4.09.

Topic: Calculating within tens.

Objectives: Repetition: calculation techniques using an addition table, using a number line and a number series, using rearrangement of numbers in a sum, based on knowledge of the composition of single-digit numbers.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

Come on, check it out, my friend.

Are you ready to start the lesson?

Is everything in place? Is everything all right?

Pen, book and notebook?

Is everyone sitting correctly?

Is everyone watching carefully?

2.Oral counting

Solving examples within 10.

What is the topic of our lesson? (We calculate within tens).

5.Learning new material and consolidating it.

For a long time, people added and subtracted up to ten on their fingers; we also have other assistants for calculations: an addition table (p. 38), a number ray and a series of numbers.

Let's complete task No. 1 in the textbook in notebook No. 1 independently, and then check it.

Task No. 2, 3.6 orally.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

In task No. 4 we will write several options for the sum of odd numbers.

Let's complete task No. 7.

Textbook page 7 No. 6 in the notebook homework.

6. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

brain teaser

analysis of objects to identify features

Luud formation of adequate positive conscious self-esteem.

Mathematics 5.09.

Topic: Gathering groups.

Objectives: Repetition: names of round numbers, reading, writing. Getting to know the numbers one hundred and one thousand, writing them in numbers.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

2.Oral counting

3. Defining goals and communicating the topic of the lesson.

What is the topic of our lesson? (Gathering groups).

Why are we doing this? (repeat)

5.Learning new material and consolidating it.

One object can be represented by one sign. Come up with and draw your own sign for one item.

Groups of objects can be represented by a group of signs.

To avoid drawing a lot of signs, people came up with signs for groups of objects and gave them names. Ten is ten. Etc.

Let's complete task No. 3, 7 in the textbook orally.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

In task No. 4 we will depict the numbers 20, 30 using Roman numerals.

Let's complete task No. 6 Write in numbers: two hundred, four hundred, eight hundred. Come up with and draw your own sign to represent a hundred. Using this sign, depict three hundred, five hundred.

Textbook page 9 No. 5 in the notebook homework.

6. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

Development of cognitive interests

brain teaser

analysis of objects to identify features

Puud synthesis as the composition of a whole from parts.

Luud formation of adequate positive conscious self-esteem.

Mathematics 7.09.

Topic: Counting by tens.

Objectives: Review: round numbers. Introducing writing in numbers of several hundred.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

2.Oral counting

Solving examples within 10 for a while.

Writing and reading round numbers.

3. Defining goals and communicating the topic of the lesson.

What is the topic of our lesson? (Collecting dozens).

Why are we doing this? (repeat)

5.Learning new material and consolidating it.

Let's complete task No. 1. How many tens of kilometers did the red car travel from the start?

What is the distance in tens of kilometers between the red and green cars?

Let's complete task 32 in your notebook.

Task No. 3 on your own.

We solve problem No. 4 in a notebook.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

To designate tens, the ancient Romans used numbers such as in No. 5.

Guess which numbers are written in Roman numerals?

Task No. 6 homework.

6. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

Development of cognitive interests

brain teaser

analysis of objects to identify features

Puud synthesis as the composition of a whole from parts.

Luud formation of adequate positive conscious self-esteem.

Mathematics 10.09.

Topic: Writing down numbers.

Objectives: Review: single and double digit numbers; decimal composition of two-digit numbers; designation of tens and units by numbers. Formation of primary ideas about the bit composition of numbers.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

2.Oral counting

Solving examples within 10 for a while.

3. Defining goals and communicating the topic of the lesson.

Kolya collects large beautiful apples from the apple tree and puts them in boxes of 10 pieces. That's how much he collected. How can you tell about the harvest?

What is the topic of our lesson? (Write down the numbers).

Why are we doing this? (repeat)

Let's complete task No. 1. Give examples of single and double digit numbers. Write them down.

Task No. 2. Write down the result of the addition.

Write it as the sum of tens and ones: 43, 34, 71, 17.

Let's solve problems.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

We will complete task No. 5 orally.

Let's write it in terady:

A) the smallest two-digit number

B) the largest two-digit number, etc.

We will complete task No. 7 on our own.

Task No. 3 homework.

5. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

Development of cognitive interests

brain teaser

analysis of objects to identify features

Puud synthesis as the composition of a whole from parts.

Luud formation of adequate positive conscious self-esteem.

Mathematics 11.09.

Topic: Comparing numbers.

Objectives: Review: ways to compare numbers. Introduction to the concept of “true inequality”.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

2.Oral counting

Solving examples within 10 for a while.

Adding and subtracting round numbers within 100.

3. Defining goals and communicating the topic of the lesson.

Numbers can be placed on a number line. Name the numbers that are located: show where the number 45 is located.

What is the topic of our lesson? (Compare numbers).

Why are we doing this? (repeat)

4.Learning new material and consolidating it.

Open your notebook, write down the number and great job.

Let's complete task No. 2. Give examples of single and double digit numbers. Write them down.

Task No. 3. Write down the result of the addition.

Write down the number of characters in each picture using numbers. Write down the inequalities between numbers.

Let's solve problems.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

We will complete task No. 6, 7, 9 orally.

Task No. 4, No. 5 (c) homework.

5. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

Development of cognitive interests

brain teaser

analysis of objects to identify features

Puud synthesis as the composition of a whole from parts.

Luud formation of adequate positive conscious self-esteem.

Mathematics 17.09.

Topic: Adding and subtracting single digit numbers.

Goals: Review: addition and subtraction of two-digit and single-digit numbers without passing through ten.

Equipment: textbook, notebook, colored pencils. Lesson progress

1.Organizational moment

Checking readiness for the lesson.

2.Oral counting

Solving examples within 10 for a while.

Adding and subtracting round numbers within 100.

3. Defining goals and communicating the topic of the lesson.

Help Jack who built the house count the bags?

What is the topic of our lesson? (Add and subtract single digit numbers).

Why are we doing this? (repeat)

4.Learning new material and consolidating it.

Open your notebook, write down the number and great job.

Let's complete task No. 1. Let's write down examples and remember that units add up to..., and tens add up to...

Task No. 2. Let's solve the examples and write them down.

Let's solve problem #4 and write it down.

Physical exercise.

One, two - there is a rocket,

Three, four - plane,

One, two - clap your hands,

And then on every account.

1,2,3,4 - arms higher, shoulders wider,

1,2,3,4 - and they were on the spot.

We will complete task No. 6 orally.

- No. 7, 8 in the notebook.

Assignment No. 3, No. 4 homework.

5. Lesson summary

So, let's summarize the lesson.

What should have been repeated?

Have we achieved our goals?

You did all the tasks well, learned a lot in class and learned a lot.

RUUD volitional self-regulation as the ability to mobilize strength and energy;

WPUD sign-symbolic - modeling

Ruud control in the form of comparison of a method of action and its result with a given standard in order to detect deviations and differences from the standard;

Luud formation of adequate positive conscious self-esteem;

Formation of value guidelines and meanings of educational activities based on

Development of cognitive interests

brain teaser

analysis of objects to identify features

Puud synthesis as the composition of a whole from parts.

Luud formation of adequate positive conscious self-esteem.

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