Summary of the lesson "number systems". Lesson outline: Number systems What is the basis of this number system

Goals: Generalization and application for solving problems of knowledge about the ways and methods of transferring numbers.

Development of cognitive interest, creative activity of students.

Lesson objectives: Develop algorithmic thinking, memory and mindfulness.

To deepen, generalize and systematize the methods of transferring numbers from one number system to another.

Expand ideas about number systems, show the variety of applications of numbers.

Develop cognitive interest and logical thinking.

During the classes:

1. Organizational moment.

For the lesson, a presentation was prepared using Power Point in order to visualize information in the course of summarizing the material.

On the board: the topic of the lesson is “Number systems”.

Textbooks, workbooks, a booklet for the lesson are laid out on the children's desks.

The teacher greets the children.

2. Motivational start of the lesson.

Teacher: In the last lesson, we learned about how to convert binary numbers to decimal and from decimal to binary. Therefore, the purpose of today's lesson is Generalize and apply knowledge about the ways and methods of transferring numbers to solve problems.

Teacher: Today we will continue to work on converting numbers from decimal to binary; from binary to decimal.

Our lesson will begin with the words of Johann Goethe: "Numbers do not rule the world, but show how the world is ruled."

And ahead of us is waiting for the “Merry warm-up”.

Open your notebooks, write down the date and topic of the lesson.

Answers to the questions will be written down in a notebook.

(Guys work simultaneously in a workbook)

1. When is two times two equal to 100?

I have 100 brothers. The younger one is 1000 years old, and the older one is 1111 years old.

The eldest is in class 1001. Could it be?

Answer: I have 4 brothers. The youngest is 8 years old and the oldest is 15 years old.

The oldest is in 9th grade.

3. Generalization of knowledge.

We move on to the next steps of our lesson. You will need not only the skills and abilities to translate from one number system to another, but also your attentiveness, quick wit, ingenuity, and then you will be able to make a very important discovery for yourself.

But first answer the questions:

1. What number system do we use in everyday life?

2. What is the basis of this number system?

3. How is numerical information represented in a computer? What number system is being used?

4. How to convert a number from binary to decimal?

"Eureka"

Guys, do you know how many eyes a leech has? And what size boots did Uncle Styopa wear? These questions will help us answer the tasks that you will now complete.

Tasks of different difficulty levels:

1. LEVEL

2. LEVEL

1. How many big planets revolve around the sun?

Hint: 10012 answer 9

2. How many vershoks are in an arshin?

Hint: 100002 Answer 16

3. What size boots did Uncle Styopa wear?

Hint: 1011012 Answer 45

4. How many eyes does a leech have?

Hint: 10102 Answer 10

3. LEVEL

1. Determine whether the number is even or odd:

A) 10012

B) 110002

C) 11001002

D) 100112

Formulate a parity criterion in the binary system.

Answers 9, 24,100,19

2. What is the maximum number that can be written in binary with eight digits?

111111112=25510

Students complete tasks at the selected level. Checking from the projector screen from the presentation SLIDES. For correctly performed work, they receive tokens of yellow (level 1), green (level 2), red (level 3) colors.

4. The stage of consolidating, testing the acquired knowledge.

-It is necessary to remember two ways of processing the transfer from the decimal number system to the binary system(table and column).

The group that will be able to: quickly solve tasks will win; make an explanation; will be able to organize their activities so that the number of completed tasks is maximum. The winning group will be the first to process the data on the computer and perform the construction.

1 level

Convert from decimal to binary number system: 100; 37.

2 level

Convert from decimal to binary number system: 168; 241.

3 level

Convert from decimal to octal number system: 168; 241.

PHYSICAL MINUTE(See presentation)

5. The stage of systematization, generalization of the studied.

The class is divided into groups of two.

The group starts the task on the computer.

Exercise 1:

It is necessary in the Calculator environment to convert numbers from binary to decimal. Values ​​should be formatted as a record of point coordinates. The obtained coordinates, mark on the plane (in the workbook), alternately connect the points, demonstrate the resulting figure.

Task 2:

The second group receives cards on which numbers are written in the binary number system. Convert numbers to decimal number system. Select the result on the board. Then, using a calculator, find the sum of the decimal numbers in rows (horizontally), columns (vertically) and diagonally. Make a conclusion.

As a result, the resulting amounts are the same (equal to 34).

Ask the children if they know what these squares are called.

6. Message "Magic squares".

7. Summing up.

Teacher: What is the magic of number?

8. Creative Homework:

Come up with your own drawing, describe it in decimal and binary number systems.

Make a drawing on a sheet of paper in a cage.

Sections: Informatics

Class: 8

Lesson Objectives:

Educational:

• give a definition of the concept of "number system";
• derive an algorithm for converting numbers from binary to decimal and vice versa;
• learn how to convert numbers from decimal to arbitrary.

Educational:

• education of information culture, attention, accuracy, perseverance.

Developing:

• development of the ability to highlight the main thing (when compiling a lesson summary);
• development of self-control (analysis of self-control of the assimilation of educational material according to the statement);
• development of cognitive interests (use of gaming techniques in the lesson).

Lesson plan:

1. Organizing time.
2. Explanation of new material and implementation of the practical part of the lesson.
3. Summing up the lesson.
4. Homework.

During the classes

1. Organizational moment.

Announcement of the topic and objectives of the lesson. Designation of the lesson plan.

In order to move on to the study of decimal and binary number systems, let's figure out what number systems are and where they originate from. Presentation “Number systems. Historical essay "( Appendix 1).

Let's start studying the topic of today's lesson with one, at first glance, incomprehensible and confusing poem (Slide 19 of the presentation).

She was a thousand and a hundred years old
She went to the one hundred and first class,
In a portfolio of a hundred books she carried -
All this is true, not nonsense.
When, dusting with a dozen feet,
She walked along the road
She was always followed by a puppy
With one tail, but hundred-legged.
She caught every sound
With ten ears
And ten tanned hands
They held a briefcase and a leash.
And ten dark blue eyes
Considered the world habitually,
But everything will become quite normal,
When you understand our story.

In order to figure out what the author wanted to tell us, you need to study the topic “Binary and Decimal Number Systems”. So, as you may have guessed, the topic of today's lesson is "Binary and Decimal Number Systems".

2. Explanation of new material and implementation of the practical part of the lesson.

Theoretical material:

Notation- this is the accepted way of writing numbers and comparing these records with real values. All number systems can be divided into two classes:

• positional - the quantitative value of each digit depends on its position (position) in the number;
• non-positional - numbers do not change their quantitative value when their position in the number changes.

To write numbers in different number systems, a certain number of characters or digits are used. The number of such characters in the positional number system is called base of the number system.

Each number in the positional number system can be represented as the sum of the products of the coefficients by the degree of the base of the number system.

For example:

from left to right, starting from "0")

Now consider the algorithm for converting numbers from an arbitrary number system to decimal using an example.

Algorithm for converting numbers from an arbitrary number system to decimal:

(we arrange the degrees over the integer part of the number from left to right, over the fractional part - right to left, starting with "-1")

The binary number system is of particular importance in computer science. This is determined by the fact that the internal representation of any information in a computer is binary, that is, described by sets of only two characters (0, 1).

Consider an example of converting a number from decimal to binary:

Picture 1

Explanation: The decision is drawn up on the board by the teacher with a clear explanation of each of his actions.

The result is a number made up of the remainders of division by 2 (which we have circled), written from right to left.

342 10 = 101010110 2

Now try to write down the considered algorithm for translating a number from the decimal number system into words (2-3 minutes are allotted for completing the task, the teacher controls its implementation). After the allotted time, the teacher asks several students to read the algorithm they have compiled. Then the rest of the students, under the guidance of the teacher, correct the algorithm. The teacher formulates the algorithm, the students write it down in their workbooks.

Algorithm for converting decimal numbers to binary number system:

1. Divide the number by 2. Fix the remainder (0 or 1) and the quotient.
2. If the quotient is not equal to 0, then divide it by 2, and so on until the quotient becomes 0. If the quotient is 0, then write down all the resulting remainders, starting from the first, from right to left.

Now we know how to convert numbers from decimal to binary and how to convert numbers from an arbitrary number system to decimal. We will solve several examples (one student goes to the blackboard, the rest do the task in the notebook and check the result on the blackboard).

Exercise:

1. Convert to decimal number system: 101111001 2 ,1231 3 , 110110101 2 , 1223 3 .
2. Convert from decimal to binary, and vice versa numbers: 256, 457, 845, 1073.
3. Write down an algorithm for converting a number from a decimal number system to an arbitrary number system.

Explanation: the task is performed at the blackboard by students who are appointed by the teacher.

In order to consolidate the knowledge and skills gained today in the lesson, we will play a little. Exercise "build by points". To complete this task, you will need not only the knowledge gained in today's lesson, but also mathematical knowledge.

Each student is given a notebook sheet with a coordinate system printed on it (prepared in advance by the teacher) - Appendix 2 .

Explanation for the task: each point coordinate is written in binary coordinate system. You need to convert the coordinates of the points to the decimal number system and, using knowledge of mathematics, build points on the coordinate system, connect them. Points of one object are designated by one letter.

Head:

• G1 (101; 1011)
• G2 (1100; 1011)
• G3 (101;100)
• G4 (1100; 100)

• Ш1 (111;100)
• Ш2 (1010;100)
• Ш3 (1010;11)
• Ш4 (111;11)

Eyes:

• Ch1 (110;1010)
• Ch2 (1000;1010)
• Ch3 (1000;1000)
• Ch4 (110;1000)
• Ch5 (1001;1010)
• Ch6 (1011;1010)
• Ch7 (1011;1000)
• Ch8 (1001;1000)

• H1 (1000; 111)
• H2 (1001; 111)

• P1 (110;110)
• P2 (110;101)
• P3 (1011;101)
• P4 (1011; 110)

Antennas:

• A1 (110;1011)
• A2 (110;1111)
• A3 (101;1111)
• А4 (111;1111)
• A5 (1011; 1011)
• A6 (1011; 1111)
• A7 (1010; 1111)
• A8 (1100; 1111)

As a result, you should get a portrait of a ROBOT you know well.

Figure 2

Students have been familiar with the image of the robot since the 7th grade: it is an assistant who helps with practical work and when studying the Paint graphic editor, they got acquainted with creating a drawing using the application method and drew a portrait of the robot.

3. Summing up the lesson.

Students complete the card. Self-analysis of the assimilation of educational material by students and hand it over to the teacher Annex 3).

Checking the completion of the task ("drawing by points").

Front poll:

• what is a number system;
• define the concept of "base of the number system";
• how to convert a number from decimal to binary (algorithm).

Grading a lesson.

4. Homework.

Now let's go back to the beginning of the lesson and remember the poem that we didn't understand.

Note: The teacher gives students a printout of the poem ( Appendix 4).

Homework: Reframe the poem using the knowledge gained in the lesson.

The decimal number system is known to all of us in great detail, we use it every day (when paying for transport, counting the number of pieces of something, arithmetic operations on numbers). The decimal number system includes 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The decimal number system is a positional system, because it depends on where in the number (in what digit, in what position) the digit is. Those. 001 is one, 010 - ϶ᴛᴏ is already ten, 100 is one hundred. We see that only the position of one digit (one) changed, and the number changed very significantly.

In any positional number system, the position of a digit is the number multiplied by the number of the base of the number system to the power of the position of that digit. Look at the example and everything will become clear.

Decimal number 123 = (1 * 10^2) + (2 * 10^1) + (3 * 10^0) = (1*100) + (2*10) + (3*1)

Decimal number 209 = (2 * 10^2) + (0 * 10^1) + (9 * 10^0) = (2*100) + (0*10) + (9*1)

Binary number system

The binary number system should not be familiar to us at all, but believe me, it is much simpler than the decimal system we are used to. The binary number system includes only 2 digits: 0 and 1. This is comparable to a light bulb when it is off - ϶ᴛᴏ 0, and when the light is on - ϶ᴛᴏ 1.

The binary number system, like the decimal one, is positional.

Binary number 1111 = (1*2^3) + (1*2^2) + (1*2^1) + (1*2^0) = (1*8) + (1*4) + (1 *2) + (1*1) = 8 + 4 + 2 + 1 = 15 (decimal).

Binary number 0000 = (0*2^3) + (0*2^2) + (0*2^1) + (0*2^0) = (0*8) + (0*4) + (0 *2) + (0*1) = 8 + 4 + 2 + 1 = 0 (decimal).

Whether we wanted it or not, we have already converted 2 binary numbers to decimal. Let's consider in more detail further.

From binary to decimal number system

Converting from binary to decimal is not difficult, you need to learn the powers of two from 0 to 15, although in most cases from 0 to 7 will be sufficient. This is due to the eight bits of each octet in the ip address.

To convert a binary number, you will need to multiply each digit by the number 2 (the base of the number system) to the power of the position of that digit, and then add those digits. The examples below will make it clear.

Let's start with prime numbers and end with eight digit numbers.

Binary number 111 = (1*2^2) + (1*2^1) + (1*2^0) = (1*4) + (1*2) + (1*1) = 4 + 2 + 1 = 7 (decimal).

Binary number 001 = (0*2^2) + (0*2^1) + (1*2^0) = (0*4) + (0*2) + (1*1) = 0 + 0 + 1 = 1 (decimal).

Binary number 100 = (1*2^2) + (0*2^1) + (0*2^0) = (1*4) + (0*2) + (0*1) = 4 + 0 + 0 = 4 (decimal).

Binary number 101 = (1*2^2) + (0*2^1) + (1*2^0) = (1*4) + (0*2) + (1*1) = 4 + 0 + 1 = 5 (decimal).

In exactly the same way, you can convert any binary number to decimal.

Binary number 1010 = (1*2^3) + (0*2^2) + (1*2^1) + (0*2^0) = (1*8) + (0*4) + (1 *2) + (0*1) = 8 + 0 + 2 + 0 = 10 (decimal).

Binary number 10000001 = (1*2^7) + (0*2^6) + (0*2^5) + (0*2^4) + (0*2^3) + (0*2^2 ) + (0*2^1) + (1*2^0) = (1*128) + (0*64) + (0*32) + (0*16) + (0*8) + (0 *4) + (0*2) + (1*1) = 128 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 129 (decimal).

Binary number 10000001 = (1*2^7) + (1*2^0) = (1*128) + (1*1) = 128 + 1 = 129 (decimal).

Binary number 10000011 = (1*2^7) + (1*2^1) + (1*2^0) = (1*128) + (1*2) + (1*1) = 128 + 2 + 1 = 131 (decimal).

Binary number 01111111 = (1*2^6) + (1*2^5) + (1*2^4) + (1*2^3) + (1*2^2) + (1*2^1 ) + (1*2^0) = (1*64) + (1*32) + (1*16) + (1*8) + (1*4) + (1*2) + (1*1 ) = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 (decimal).

Binary number 11111111 = (1*2^7) + (1*2^6) + (1*2^5) + (1*2^4) + (1*2^3) + (1*2^2 ) + (1*2^1) + (1*2^0) = (1*128) + (1*64) + (1*32) + (1*16) + (1*8) + (1 *4) + (1*2) + (1*1) = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 (decimal).

Binary number 01111011 = (1*2^6) + (1*2^5) + (1*2^4) + (1*2^3) + (1*2^1) + (1*2^0 ) = (1*64) + (1*32) + (1*16) + (1*8) + (1*2) + (1*1) = 64 + 32 + 16 + 8 + 2 + 1 = 123 (decimal).

Binary number 11010001 = (1*2^7) + (1*2^6) + (1*2^4) + (1*2^0) = (1*128) + (1*64) + (1 *16) + (1*1) = 128 + 64 + 16 + 1 = 209 (decimal).

Here we did it. Now let's convert everything back from binary to decimal.

Decimal number system - concept and types. Classification and features of the category "Decimal number system" 2017, 2018.

Lesson summary on the topic:

« Number systems»

Completed by: computer science teacher

Yarovenko S.S.

Grade: 8

Lesson topic: Number systems.

Lesson type: learning new material.

Lesson Objectives:

To acquaint students with the history of the emergence and development of number systems.

Point out the main disadvantages of non-positional number systems.

To form in students the concept of "positional number systems"

Requirements for knowledge and skills:

Students should know:

Definition of the following concepts: "digit", "number", "numeral system", "non-positional number system";

Disadvantages of non-positional number systems;

What number system is called "positional" and why;

Give examples of positional number systems;

An expanded form of writing a number in a positional number system.

Students should be able to:

Write numbers in non-positional number systems;

Give examples of numbers of various positional number systems, determine the base of the number system;

Be able to write the numbers of the positional number system in expanded form.

Software: Microsoft PowerPoint program,

presentation "Number systems".

Lesson Plan

Types and forms of work

Time

1. Org. moment

Greetings

0.5 min

2. Presentation of new material

The teacher presents the material, simultaneously demonstrating the presentation of the "Number System". Complete the tasks given in the presentation.

25 min

3. Consolidation of the material covered.

Working with the textbook

10 minutes

4. Summing up

Grading

2 minutes

5. Lesson reflection

1 min

7. Homework

1.5 min

During the classes

Organizing time

Presentation of new material

The presentation of new material is accompanied by a presentation "Number systems". The presentation is attached.

1. The history of the emergence and development of number systems

(Slides 1-4)

People have always counted and written down numbers. But they were written in a completely different way, according to different rules. However, in any case, the number was depicted using certain symbols, which are called numbers.

Question: What are numbers? (Students try to answer this question). Numbers- these are the characters involved in writing a number and making up a certain alphabet.

Question: What is a number?

Initially, the number was tied to those items that were recounted. But with the advent of writing, the number separated from the objects of recalculation and the concept of a natural number appeared. Fractional numbers appeared due to the fact that a person needed to measure something, and the unit of measurement did not always fit an integer number of times in the measured value. Further, the concept of number developed in mathematics, and today it is considered a fundamental concept not only of mathematics, but also of computer science. Number is a certain value.

Numbers are made up of numbers according to special rules. At different stages of human development, these rules were different for different nations, and today we call them number systems.

1. Number systems.

Notation is a way of writing numbers using numbers.

(Slide 5)

All known number systems are divided into non-positional and positional.

Non-positional number systems arose earlier than positional ones. A non-positional number system is such a number system in which the quantitative equivalent (“weight”) of a digit does not depend on its location in the number entry. Positional number systems, in which the quantitative equivalent ("weight") of a digit depends on its location in the notation of the number.

Consider examples of writing numbers in positional and non-positional number systems.

The number 333. In the record of this number, the number 3 is used three times. But the contribution of each number to the value of the number is different. The first 3 means the number of hundreds, the second - the number of tens, the third - the number of units. If we compare the "weight" of each digit in this number, it turns out that the first 3 is "greater" than the second by 10 times and "greater" than the third by 100 times.

This principle is absent in non-positional number systems. Consider the Roman number XXX. In the decimal number system, this number is 30. When writing the number XXX, the same “digits” were used - X. And if we compare them with each other, we get absolute equality. Those. no matter where the digit stands in the notation of the number, its “weight” is always the same. In this example, it is 10.

1. Non-positional number systems

(Slide 6)

In ancient times, when people began to count, there was a need to record numbers. The number of items, such as bags, was depicted by drawing dashes or notches on some solid surface: stone, clay, wood (it was still very far from the invention of paper). Each bag in such a record corresponded to one dash.

Scientists called this way of writing numbers the unit or unary number system.

The inconveniences of such a number system are obvious: the larger the number you need to write down, the more sticks. When writing a large number, it is easy to make a mistake - apply an extra number of sticks or, conversely, not add sticks. Therefore, later these icons began to be combined into groups of 3, 5, 10 sticks. Thus, more convenient number systems arose.

(Slide 7)

The ancient Egyptian decimal non-positional system arose in the second half of the third millennium BC. The paper was replaced by a clay tablet, and that is why the numbers have such a mark.

In this number system, the key numbers 1, 10, 100, 1000, etc. were used as digits. and they were written using special hieroglyphs: a pole, an arc, a folded palm leaf, a lotus flower.

It was from combinations of such “numbers” that numbers were written and each “number” was repeated no more than nine times.

Question: Why? (Students try to answer this question).

Answer: Since ten identical digits in a row can be replaced by one number, but a bit older.

All other numbers were compiled from these key numbers using ordinary addition.

Question: What number is written? (Students try to answer this question).

Answer : 2342

(Slide 8)

The Roman system familiar to us is fundamentally not much different from the Egyptian one. But it is more common these days.

It uses the signs I (one finger) for the number 1, V (open palm) for the number 5, X (two folded palms) for 10 to indicate numbers, and for the numbers 50, 100, 500 and 1000, capital Latin letters of the corresponding Latin letters are used. words.

I, V, X, L, C, D and M are the "digits" of this number system. A number in the Roman numeral system is denoted by a set of consecutive "numbers".

Rules for compiling numbers in the Roman numeral system: The value of a number is defined as the sum or difference of the digits in the number. If the smaller number is to the left of the larger one, then it is subtracted. If the smaller number is to the right of the larger one, then it is added.

(Slide 9)

Consider how the number 444 is written in the Roman numeral system.

444 \u003d 400 + 40 + 4 (the sum of four hundred, four tens and four units).

400 = D - C = CD, 40 = L - X = XL, 4 = V - I = IV

444 = CDXLIV

Please note that the decimal notation uses three identical digits, while the Roman number system uses different ones. The number of digits used when writing the same number is not the same in decimal and Roman systems (in Roman - twice as much).

(Slide 10)

Question: What numbers are written in Roman numerals?

MMIV = 1000 + 1000 + (5 - 1) = 2004

LXV = 50 + 10 + 5 = 65

CMLXIV = (1000 - 100) + 50 + 10 + (5 - 1) = 964

Question: Take action.

MMMD + LX = (1000 + 1000 + 1000 + 500) + (50 + 10) = 3560

Question: When performing this arithmetic operation, did you experience any inconvenience, and what was it? (Students try to answer this question).

(Slide 12)

The Greeks used several ways of writing numbers. The Athenians used the first letters of numerals to designate numbers. With the help of these numbers, a resident of Ancient Greece could write down any number.

Question: Try to determine what number is written in the Greek number system? (Students try to answer this question).

(Slide 13)

More advanced non-positional number systems were alphabetic systems. Such number systems included Slavic, Ionian (Greek), Phoenician and others. In them, numbers from 1 to 9, whole numbers of tens (from 10 to 90), and whole numbers of hundreds (from 100 to 900) were denoted by letters of the alphabet.

The alphabetic system was also adopted in ancient Russia. Until the end of the 17th century (before the reform of Peter I), 27 Cyrillic letters were used as "numbers".

To distinguish letters from numbers, a special sign was placed above the letters - a title. This was done in order to distinguish numbers from ordinary words.

Question : What number is written in the Slavic number system? (Students try to answer this question).

We see that the entry turned out to be no longer than our decimal. This is because alphabetic systems used at least 27 "digits". But these systems were only convenient for writing numbers up to 1000.

(Slide 14)

True, the Slavs, like the Greeks, were able to write numbers and more than 1000. For this, new designations were added to the alphabetical system.

So, for example, the numbers 1000, 2000, 3000 ... were written in the same “numbers” as 1, 2, 3 ..., only a special sign was placed in front of the “number” from the bottom left.

The number 10,000 was denoted by the same letter as 1, only without a title, it was circled. This number was called "darkness". Hence the expression "darkness of the people."

Question: What number in the Slavic number system corresponds to the expression "dark darkness"? (Students try to answer this question).

Answer: 100 000 000.

This way of writing numbers, as in the alphabetical system, can be considered as the beginnings of a positional system, since it used the same symbols to designate units of different digits, to which only special characters were added to determine the value of the digit.

Alphabetical number systems were not very suitable for operating with large numbers. When writing a large number, for which there was no sign denoting it yet, there was a need to introduce a new character to designate this number.

In the course of the development of human society, these systems gave way to positional systems.

(Slide 15)

Question: Remember which number system (positional or non-positional) uses more digits when writing a number, in which number system (positional or non-positional) it is more convenient to perform arithmetic operations. And answer the question: What are the disadvantages of non-positional number systems? (Students try to answer this question).

1. Positional number systems

(Slide 16)

In connection with the above shortcomings, non-positional number systems gradually gave way to positional number systems.

The main advantages of the positional number system:

Easy to perform arithmetic operations.

Limited number of characters required to write a number.

(Slide 17)

Discharge is the position of the digit in the number.

Base (basis) of the positional number system is the number of digits or other characters used to write numbers in a given number system.

There are many positional systems, since any number no less than 2 can be taken as the base of the number system.

Data on some number systems are given in the table.

(Slide 18)

In the positional number system, any real number can be represented as:

A q = ±(a n-1 q n-1 +a n-2 q n-2 +…a 0 q 0 +a -1 q -1 +a -2 q -2 +…a -m q -m)

Here:

A is the number itself

q - base of the number system

a i - digits of this number system

n is the number of digits of the integer part of the number

m - the number of digits of the fractional part of the number

Let's represent the decimal number A = 4718.63 in expanded form.

What number system is the number in?

What is the base of this number system? (q=10)

What is the number of digits of the integer part of the number (n \u003d 4)

What is the number of digits of the fractional part of the number (m \u003d 2)

(Slide 19)

Question: What will the number A 8 \u003d 7764.1 look like in expanded form? (Students try to answer this question).

(Slide 20)

Question: How will the number A 16 = 3AF look in expanded form? (Students try to answer this question).

(Slide 21)

The folded form of writing a number is called writing in the form:

A = a n-1 a n-2 … a 1 a 0 , a -1 a -m

It is this form of writing numbers that we use in everyday life.

III. Fixing new material

Complete tasks:

№1

What number is written using Roman numerals: MCMLXXXVI?

№2

Follow these steps:

MCMXL + LX

№3

Are the numbers written correctly in the corresponding number systems

A 10 \u003d A.234 B) A 16 \u003d 456.46

A 8 \u003d -5678 D) A 2 \u003d 22.2

№4

Completing the tasks of the textbook 1-5 p. 48.

IV. Summarizing

The teacher evaluates the work of the class, names the students who excelled in the lesson.

V. Lesson reflection.

Questions for students:

- What new did you learn at the lesson today?

What new concepts did you get?

What tasks are difficult to complete?

VI. Homework

Gymnasium named after F.K. Salmanov, city of Surgut

Summary of the lesson in mathematics

Primary school teacher

Mulyukova Renata Ildusovna

Summary of the lesson in mathematics

Lesson topic: Name of measurements in decimal notation

Goals:

cognitive (didactic):

Acquaintance of students with the name of the measures of the decimal number system

Acquaintance with the new positional way of writing a multi-digit number

- developing

Development of the ability to correctly use the mathematical language (enrichment of the vocabulary of children, the ability to correctly name and read numbers in the decimal number system)

The development of students' thinking (the ability to analyze, compare, generalize)

- educational

Cultivating accuracy when making notes in a notebook

Lesson type: lesson in the formation of new knowledge

Lesson equipment for the teacher: Mathematics textbook for grade 2 No. 1 V.V. Davydov, S.F. Gorbov, G.G. Mikulina, O.V. Savelyeva, Mathematics workbook for grade 2 No. 1, teacher's guide "Teaching Mathematics" Grade 2 S.F. Gorbov, G.G. Mikulina, O.V. Saveliev, interactive whiteboard, computer, didactic material for the lesson.

Lesson equipment for students: Mathematics textbook for grade 2 No. 1 V.V. Davydov, S.F. Gorbov, G.G. Mikulina, O.V. Savelyeva, Mathematics workbook for grade 2 No. 1, checkered notebook.

Lesson plan:

Org. moment

Knowledge update

Formation of knowledge

Generalization and primary consolidation of knowledge

Summarizing

Homework, instruction