Math lesson notes.
Class: 2nd class “B”.
Teacher: Bukhteeva I.M.
Subject: A three-digit number as a sum of digit terms.
Lesson objectives:
Further study of the bit (positional) principle of numbering three-digit numbers;
The procedure for decomposing a number into digit terms (the sum of the digit terms of a three-digit number);
Recognizing the bit composition of a number by its short decimal notation;
Formation of UUD: self-test according to the model, communicative UUD (pair work).
Propaedeutics: addition and subtraction of three-digit numbers.
Repetition: “round” numbers, digit terms.
Methods and techniques for organizing student activities:explanation of new material based on assignments and illustrations in the textbook with the gradual inclusion of students in independent activities; verbal counting.
Educational and didactic support:U-2, T-2, Z., models of the number 100, colored and simple pencils, pointer.
During the classes:
- Organizing time.
Greeting from the teacher. Preparation of jobs. Inclusion in the business rhythm of the lesson.
- Updating students' knowledge.
- We repeat the sixth column of TU along the chain.
- Lesson topic message. Setting goals.
- We suggest opening the textbook on p. 15, read the topic of the lesson (“A three-digit number as a sum of digit terms”) and name any three-digit number.
- What will we learn in the lesson?
- Setting a learning task.
Task No. 1 (U-2, p. 15)
*We ask students to look at the drawing of three models of the number 100 and answer the questions: how many cells are colored red? (200) Blue? (50) Yellow? (8)
We explain while writing on the board.
Shaded:
200+50+8 cells, which is equal to the number 258.
200+50+8 is the sum of the digit terms of the number 258, because this is 2 hundred. +5 dec. + 8 units (hundreds place, tens place and units place).
After all the numbers are written in the form of a sum of digit terms, we check the solutions by writing on the board under the dictation of the children:
258 - 200 + 50 + 8 1 65 = 100 + 60 + 5
319 = 300 +10 + 9 689 = 600 + 80 + 9 940 = 900 + 40 + 0
208 = 200 + 0 + 8 208 = 200 + 0 + 8 = 200 + 8
- We draw the children's attention to the digit terms - 940 = 900 + 40 + 0 and 208 = 200 + 0 + 8 - and explain that these sums of the digit terms can be written differently: 940 - 900 + 40; 208 = 200 + 8, omitting the digit 0 in the bit terms.
- Let's complete the second part of the task. We name the digit terms of each of the numbers,starting from the hundreds place, For example:
place numbers are 258. The hundreds place is 2 hundreds, the tens place is 5, the ones place is 8;
digit terms of the number are 208. The hundreds place is 2 hundred, the tens place is 0 des, the units place is 8.
- Primary consolidation.
Task No. 3 (U-2, p. 16)
- Students read the task independently and verbally name the numbers that Masha missed (141, 146).
- We pay special attention to the wording “no more than 9 units”, explaining that in the number 149 there are 1 hundred, 4 tens and 9 ones. The number of units here is 9, that is, no more than 9.
- We ask the children to write down in their notebooks all the numbers in order, in which there are 3 hundreds, 5 dec. and no more than 7 units.
- We give time to complete the task, after which we conduct an oral test (350, 351,352... 357).
Task No. 4 (U-2, p. 16)
- Children perform the task orally.
- Students, as a rule, do not name the number 340. It is advisable to explain that the uncertainty in the digit of units (“several ones”) allows you to indicate the number 340, where the number of units is written as 0: 340 is 3 hundreds and 4 more tens, and a few more units that are equal to 0.
Task No. 5 (U-2, p. 16) is combinatorial in nature and refers to tasks of increased difficulty
- We invite students to read the task independently and compose three-digit numbers from place value terms such as 500 and 800, 40 and 70, 3 and 9.
- We give time for an independent search, and then we propose a solution algorithm based on fixing the bit term of the high-order digit and manipulating the bit terms of the low-order digits:
- 543, 549, 843, 849 (students fill in the missing numbers - 573, 579, 873, 879).
Task No. 6 (U-2, p. 16)
We give students time to complete the task independently and ask: why equality 437= 400 + 37 cannot be called the sum of digit terms? (The tens place and the units place are not highlighted.)
We propose to transform this equality into a sum of bit terms and write it on the board:
437 = 400 + 30 + 7
- Independent work with checking against the standard.
Task No. 1 (T-2, p. 7)
- Students read and complete the assignment independently.
- We ask the children, using the model written on the board, to check by exchanging notebooks that the task was completed correctly:
643 = 600 + 40 + 3 999 = 900 + 90 + 9 207 = 200+ 7
910 = 900 4 10
207 = 200 + 7
909 = 900 + 9
We identify the presence of errors and analyze each of them.
As a rule, errors occur in cases where the bit terms are written as 0: 910 = 900 + 10:
207 = 200 + 7: 909 = 900 + 9 .
Let us clarify that the entries: 910 = 900 + 10 and 910 = 900 +10 + 0, 207 = 207 = 200 + 0 + 7, 909 = 900 + 9 and 909 = 900 + 0 + 9 are equal.
The bit term, which is denoted by the number 0, is not written down by mathematicians. But if you write the digit with the number 0, showing that in the tens place there are 0 tens or in the ones place there are 0 units, then there will be no error.
Task No. 2 (T-2, p. 7)
Students read and complete the assignment independently.
Task No. 3 (T-2, p. 7) Task 1
- Students read the problem independently. Please use a red pencil to underline the key words of the condition (“500 quintals were taken out”, “200 quintals remained less”), and with a blue pencil - the key words of the requirement (“How many quintals”, “remained”).
- We read aloud the key words of the condition and answer the requirement of the task - we look fora value that is less than 500 centners by 200 centners:
500 quintals - 200 quintals = 300 quintals Answer: 300 quintals left.
- We ask: is it possible to find out how many centners of vegetables were in the warehouse?
- We write a brief condition for the new problem on the board, askingdecide for yourselfand write down the answer.
They took out 500 c
300 cents left 500 cents + 300 cents = 800 cents Answer: There were 800 cents.
Homework: repeat the seventh column of the Multiplication Table; No. 3, task 2and No. 4 (T-2, p. 7); Cut a rectangle (13 cm * 8 cm) from a sheet of clean paper.Assignments that were not completed in class.
- Reflection of activity.
To perform some operations on natural numbers, you have to represent these natural numbers in the form sums of bit terms or, as they also say, sort natural numbers into digits. No less important is the reverse process - writing a natural number by the sum of its digit terms.
In this article, we will use examples to understand in great detail the representation of natural numbers in the form of a sum of digit terms, and also learn how to write a natural number using its well-known digit decomposition.
Page navigation.
Representation of a natural number as a sum of digit terms.
As you can see, the title of the article contains the words “sum” and “addends”, so first we recommend that you have a good understanding of the information in the article, a general understanding of the addition of natural numbers. It also wouldn’t hurt to repeat the material from the section digit, the value of the digit of a natural number.
Let's take on faith the following statements that will help us define bit terms.
Place terms can only be natural numbers whose entries contain a single digit other than the number 0 . For example, natural numbers 5 , 10 , 400 , 20 000 and so on. can be digit terms, and numbers 14 , 201 , 5 500 , 15 321 and so on. - can not.
The number of digit terms of a given natural number must be equal to the number of digits in the recording of a given number other than the digit 0 . For example, a natural number 59 can be represented as a sum of two digit terms, since this number involves two digits ( 5 And 9 ), different from 0 . And the sum of the digit terms of a natural number 44 003 will consist of three terms, since the number record contains three digits 4 , 4 And 3 , which differ from the numbers 0 .
All bit terms of a given natural number in their notation contain a different number of characters.
The sum of the digit terms of a given natural number must be equal to the given number.
Now we can give a definition of bit terms.
Definition.
Bit terms of a given natural number are such natural numbers as
- in which there is only one digit other than the number 0 ;
- the number of which is equal to the number of digits in a given natural number other than the digit 0 ;
- whose records consist of a different number of characters;
- the sum of which is equal to a given natural number.
From the above definition it follows that single-digit natural numbers, as well as multi-digit natural numbers, the entries of which consist entirely of digits 0 , with the exception of the first digit on the left, do not decompose into the sum of digit terms, since they themselves are digit terms of some natural numbers. The remaining natural numbers can be represented as a sum of digit terms.
It remains to deal with the representation of natural numbers in the form of a sum of digit terms.
To do this, you need to remember that natural numbers are inherently related to the number of certain objects, while in writing a number, the values of the digits set the corresponding quantities of units, tens, hundreds, thousands, tens of thousands, and so on. For example, a natural number 48 answers 4 dozens and 8 units, and the number 105 070 corresponds 1 a hundred thousand 5 thousands and 7 dozens. Then, due to the meaning of addition of natural numbers, the following equalities are true: 48=40+8 And 105 070=100 000+5 000+70 . This is how we represented natural numbers 48 And 105 070 in the form of a sum of bit terms.
Reasoning in a similar way, we can decompose any natural number into digits.
Let's give another example. Let's imagine a natural number 17 in the form of a sum of bit terms. Number 17 corresponds 1 ten and 7 units, therefore 17=10+7 . This is the decomposition of the number 17 by category.
And here is the amount 9+8 is not the sum of the digit terms of a natural number 17 , since in the sum of the bit terms there cannot be two numbers whose records consist of the same number of characters.
Now it has become clear why bit terms are called bit terms. This is due to the fact that each digit term is a “representative” of its digit of a given natural number.
Finding a natural number from a known sum of digit terms.
Let's consider the inverse problem. We will assume that we are given the sum of the digit terms of some natural number, and we need to find this number. To do this, you can imagine that each of the digit terms is written on a transparent film, but the areas with numbers other than 0 are not transparent. To obtain the desired natural number, you need to “superpose” all the bit terms on top of each other, matching their right edges.
For example, the amount 300+20+9 represents the expansion into digits of a number 329 , and the sum of bit terms of the form 2 000 000+30 000+3 000+400 corresponds to a natural number 2 033 400 . That is, 300+20+9=329 , A 2 000 000+30 000+3 000+400=2 033 400 .
To find a natural number from a known sum of digit terms, you can add these digit terms in a column (if necessary, refer to the material in the article adding natural numbers in a column). Let's look at the solution to the example.
Let's find a natural number if given the sum of the digit terms of the form 200 000+40 000+50+5
. Writing down the numbers 200 000
, 40 000
, 50
And 5
as required by the column addition method:
All that remains is to add the numbers in columns. To do this, you need to remember that the sum of zeros is equal to zero, and the sum of zeros and a natural number is equal to this natural number. We get 
Under the horizontal line we got the required natural number 240 055 , the sum of the bit terms of which has the form 200 000+40 000+50+5 .
In conclusion, I would like to draw your attention to one more point. The skills of decomposing natural numbers into digits and the ability to perform the inverse operation allow one to represent natural numbers as a sum of terms that are not digits. For example, expansion into digits of a natural number 725 has the following form 725=700+20+5 , and the sum of the bit terms 700+20+5 due to the properties of addition of natural numbers, it can be represented as (700+20)+5=720+5 or 700+(20+5)=700+25, or (700+5)+20=705+20.
A logical question arises: “What is this for?” The answer is simple: in some cases it can simplify calculations. Let's give an example. Let's subtract natural numbers 5 677
And 670
. First, let's imagine the minuend as a sum of bit terms: 5 677=5 000+600+70+7
. It is easy to see that the resulting sum of bit terms is equal to the sum (5,000+7)+(600+70)=5,007+670. Then
5 677−670=(5 007+670)−670=
5 007+(670−670)=5 007+0=5 007
.
Bibliography.
- Mathematics. Any textbooks for 1st, 2nd, 3rd, 4th grades of general education institutions.
- Mathematics. Any textbooks for 5th grade of general education institutions.
Math lesson in 2nd grade.
Subject. Representation of two-digit numbers as a sum of digit terms
The purpose of the lesson : Learn to decompose numbers into the sum of digit terms.Develop the student’s personality based on the formation of the ability to learn, develop attention, thinking, memory, independence, and improve computing skills. Foster a culture of behavior in frontal and group forms of work. To cultivate hard work and responsibility, as well as cognitive interest.
Planned results .
In the subject area:
Students will learn, with the help of various exercises, to represent a two-digit number as a sum of digit terms, analyze, prove assumptions, draw conclusions orally and in writing, and perform tasks to gain new knowledge. In the personal area:
Be able to conduct self-assessment based on the criterion of successful educational activities.
In the meta-subject area:
Be able to determine and formulate the topic and purpose of the lesson,accept(set) an educational-cognitive task and maintain it until the end of the educational activities;
plan your action in accordance with the task, express your judgments based on performing various exercises (Regulatory UUD)
Realizesearching for information necessary to solve educational problems from textbook materials,understandinformation presented in verbal, pictorial, schematic form. (Cognitive UUD)
Consciously and voluntarilybuildspeech expression in oral and written form;
give a reasoned answeranswer questions, justify your point of view, construct statements that are understandable to your partner, adequately use verbal means to solve communication problems
enter into educational cooperationwith the teacher and classmates, carry out joint activities in small groups;
admitthe possibility of people having different points of view, showing tolerance towards the statements of others, showing a friendly attitude towards partners. (Communicative UUD)
Basic concepts developed in the lesson . The first digit term in the sum shows the number of tens in the number, the second - the number of units in the number.
Key Resources : Moro M.I. Textbook for grade 2
Additional: computer, multimedia projector, screen, cards with numbers, cards with amounts.
Organizational forms of work : frontal, group, independent
Technologies used:
Technology of personal-activity learning
Information and communication technologies
Communication technology
Health saving technology according to Bazarny
During the classes
1. Organizing time ( Greetings)
2. Motivation (self-determination) to educational activities.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Inclusion in educational activities
Answer questions, define the problem, formulate the topic and purpose of the lesson
Creates conditions for students to develop an internal need for inclusion in educational activities.
Learn to group two-digit numbers
Be able to listen to questions, comprehend and answer them
(communicativeUUD)
Oral exercises (on the cross there are cards with two-digit numbers in two colors - red and blue)
37 7777
Teacher : - What two groups can these numbers be divided into? (Work in groups)
Students: Color - red and blue25 37 59 16 44 22 33 74
Odd-even44 22 16 74 25 37 33 59
By the number of different digits for writing numbers22 44 33 25 37 59 16 74
Teacher: Write down the numbers on the cross in increasing order
Reconciliation against the standard: 16 22 25 33 37 44 59 74 (the record of numbers appears on the screen)
Teacher: How many tens and ones are in each number? (children's answers)
Why do you think we work with two-digit numbers at the mental counting stage? (children's assumptions)
Perhaps one of the children will suggest that during the lesson we will perform tasks with two-digit numbers or learn the place value composition of two-digit numbers. If there is no such statement, then the teacher formulates the topic and purpose of the lesson:
Representation of two-digit numbers as a sum of digit terms.
We will learn how to decompose numbers as a sum of digit terms.
3. Updating knowledge.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Testing previously acquired knowledge, updating the topic, posing the problem
Learn to decompose two-digit numbers into the sum of their digit terms
Organizes a dialogue with children, during which the problem of the lesson is formulated
Concepts are formedbit terms
Be able to present answers, listen to the answers of others,
(communicative, cognitive UUD)
Teacher . Write down equalities in which a number is represented as a sum of tens and units
45=40+5 16=12+4 25=30-5 83=80+3 39=30+9 74=72+2
Reconciliation according to the sample: 45=40+5 83=80+3 39=30+9
Teacher: What does the first term in each of the written equalities show?
Students: How many units are in the tens place.
Teacher: what does the second term in each equality show?
Students: How many ones are in the units place.
Teacher: If the terms show how many units of each digit are in the value of the sum, they are calledbit terms.
For example:40 and 5 – digit terms of numbers45
Teacher: name the digit terms of the remaining numbers 39 and 83
4 Primary assimilation of new knowledge.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Continued implementation of the set goal.
Primary consolidation of new material.
Teachers answer questions, work in pairs, test their knowledge, and make conclusions.
Directs students’ actions to consolidate new knowledge and helps them approach the concept in their conclusions representation of a number as a sum of digit terms
Be able to work in pairs (communicative)
Be able to acquire new knowledge, memorize it, and work in a group.
(Cognitive, communicative UUD)
Cards with amounts are hung around the classroom. Children, working in pairs, look for cards where the amounts are presented as the sum of place value terms and bring cards to attach them to the sensory cross.
Cards hung around the classroom:
20+8
48+`10
50+6
41+12
33+5
62+6
70+7
17+6
30+2
50+14
Teacher: Why weren’t some cards brought to be placed on the touch cross?
5 (a) Physical education minute .
Pinocchio stretched,
Bent over once, bend over twice
He spread his arms to the sides;
I can't seem to find the key
To get us the key
We need to stand on our toes!
(b)exercise for the eyes:
In the four corners of the classroom there are visual markers on which cards with amounts are placed. The teacher calls the numbers of the marks several times in different orders, the children look for them with their eyes. After this, he asks the question: Which expression does not fit the others?
52=50+2
№144+4=48
№275=70+5
№3№4
38=30+8
Pupils: The expression is not suitable44+4=48 . It is not presented as a sum of bit terms.
6. Updating the acquired knowledge - developing practical skills.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
consolidation of new material
Independently and jointly represent equalities in the form of a sum of bit terms
Guides children to develop practical skills
Be able to perform work independently (regulatory)
Think logically, compare, generalize, draw conclusions (cognitive)
Be able to use the acquired knowledge for numbers, expressions, given at the beginning of the lesson in order to identify existing knowledge, work in a group (Cognitive, regulatory communicative)
Teacher: imagine the numbers that were given at the beginning of the lesson as a sum of place value terms.
Option 1: red numbers (25,37,59,16 )
Option 2: blue numbers (44, 22, 33,74)
Comparison with the sample - the following entry appears on the screen:25=20+5 37=30+7
59=50+9 16=10+6
44=40+4 22=20+2
33=30+3 74=70+4
(one person from each option works at the board)
Group work
2* Teacher: each group will take the card that you left in different places in the class, because the expression on the card was not presented as a sum of place value terms, change the terms so that they become place value terms for the same sum values and write it down.
33+5=38 41+12=53 62+6=68 50+14=64 48+10=58 17+6=23
30+8=38 50+3=53 60+8=68 60+4=64 50+8=58 20+3=23
7. Lesson summary. Reflection.
What are called bit terms?
What does the first term in the sum show? And the second?
Which task was more difficult to complete? Why?
What task did you enjoy doing? Why?
6. Organization of information.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Continued implementation of the set goal
Children observe new experiences
Demonstrates two experiments in order to identify new properties
Learn more about new properties of water
Be able to navigate your knowledge system (Regulatory UUD)
Teacher. What properties of water did you discover during your experiments? Children list. Slide No. 3 (diagram)
Teacher . What do the question marks on the diagram mean?
Children . There may be more properties that we have not considered
The teacher demonstrates two more experiments: he heats and cools water to reveal two more properties - the expansion of water when heated and the compression of water when cooled. Now all the properties have been studied, again you can see the diagram on the slide, but without question marks.Slide No. 4
Linking information. Generalization.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Summarize acquired knowledge, independent work
Children summarize their acquired knowledge and fill out a comparison table
Organizes a dialogue with children and gives practical tasks.
Be able to compare the properties of water and air
Be able to perform actions with signs and symbols (knowledge
vative UUD)
Teacher. Where in everyday life, in life, do we use the property of water - a solvent?
Children . When we stir sugar in water.
teacher b. Can knowledge about the property of water as expansion when heated be useful to us?
Children. Yes, when we boil a kettle, we must not pour water to the very edge of the kettle.
Teacher . How can you purify contaminated water?
Children . Pass through the filter.
teacher b. Is this enough to drink this water?
Children . No.
Teacher . What else needs to be done?
Children. Boil
Teacher. What properties of substance did we get acquainted with in the last lesson?
Children . Air.
Teacher . Compare the properties of water and air. Draw a conclusion.
(Children fill out the table) and then check it against the standard.Slide No. 5
Properties
Water
Air
Transparency
No color
No taste
Without smell
Fluidity
Solvent
Expands when heated
Compresses when cooled
Reflection.
Lesson Stage Objectives
Student activities
Teacher activities
Planned results
Subject
UUD
Record new lesson content, organize reflection and self-assessment of students’ own learning activities
Answer questions, give self-assessment of activities in the lesson
Organizes recording of new content, reflection, and self-assessment of educational activities.
Be able to independently adequately assess the correctness of an action, the ability to have a positive self-assessment based on successful educational activities. (regulatory UUD)
Teacher . What properties of water do you now know about?
How did we study these properties?
What surprised you during the process?
What did you find interesting while studying the topic?
What did you find most difficult?
What's the most important thing you learned?
Topic: Sum of digit terms
Lesson type: learning new material
Lesson type: lesson-travel
Target: familiarization with the definition of the sum of bit terms
Tasks:
Educational:
Summarize, systematize and consolidate acquired knowledge on the topic;
Improve the ability to write two-digit numbers as the sum of digit terms, perform operations with two-digit numbers;
Develop problem solving skills of the types studied
Educational:
Create a situation conducive to the development of the intellectual abilities of each student
Organize activities to develop the skill of adequate self-esteem
Create conditions for the formation of cognitive interest of students
Focus on developing logic of thinking, sustained attention, and mathematical speech
Educators:
To promote the formation of moral qualities of students: diligence, mutual respect, responsibility for their work
Equipment: textbook for grade 2 Mathematics G.L. Muravyova, M.A. Urban; puzzles, multimedia installation, “Write numbers correctly” poster, cards, ball, self-esteem ruler, “Knowledge Bank” scale.
During the classes
1.Organizational and installation stage
Can we start the lesson?
Mood?
Excellent!
Behavior?
Decent!
Then let's start the lesson.
You will smile at each other
And sit down quietly.
2. Stage of communicating the topic and purpose of the lesson
What lesson are you prepared for?
What do you expect from the lesson?
(interesting tasks, new knowledge, difficult tasks)
So: Time for business, time for fun. In this lesson, guys, we will improve our mental arithmetic skills, solve problems, examples, and learn how to write two-digit numbers as the sum of digit terms.
3. Motivational stage
Today we have an unusual lesson. I propose to take a trip on the “Locomotive from Romashkino” and make an interesting path to the “Mountain of Success” (slide 1 little engine). A lot depends on your efforts. Anyone who shows diligence, attentiveness, and good knowledge may find themselves on the top of the mountain (slide 2, mountain of success).
Do you want to visit the top of the mountain?
Here are the rules that you need to follow while traveling (slide 3) 1. Raised hand rule - “If you want to answer, raise your hand”
2. Rule of silence - “If you want to answer, don’t make noise, just raise your hand”
3. Rule of friendship - “One for all, all for one”
4. Homework checking stage
Peer review.
And so the starting point is the Proveryakino station (slide 4 “Proveryaykino”).
Open your notebooks. Exchange notebooks with a friend. Check the answers on the screen. Evaluate your neighbor's performance using the self-assessment ruler.
( slide 5).
1) 13 - 9 = 4 (kg)
Answer: 4 kg heavier.
50 +10 = 60 30 + 30 = 60
80 - 20 = 60 100 - 40 = 60
Does anyone have any comments?
Who has a wish?
Praises:
Place your right hand on your head, stroke it and say: Oh, what a great fellow I am! Now put your hand on your neighbor’s head, stroke it and say: Oh, what a great fellow you are!
5. Stage of updating student experience
next station
(slide 6 “Chistopisaykino”)
Let's write down the date of our trip in a notebook.
Classwork
(on the board there is a poster “Write the numbers correctly”)
It was 9:25 am, 19 students from grade 2a went on a trip. There was only one teacher with them. On the way they met 5 women and 8 men.
Self-test:
In notebooks
9,25,19,2,1,5,8 (slide 7: 9,25,19,2,1,5,8)
Self-esteem (ruler) is recorded in the margins
What is the number of the third ten? (25)
6. Oral counting
(slide 8 “Chitaikino”)
We continue our journey. next station "Chitaykino"
Motto: together we learn accurate counting
Hurry up guys, get to work quickly.
Ball game:
Name the number in which: 3 des 1 units; 4 dec 0; 8ed 2 des; 10 des; 9 dec.
Say the next number after number: 23; 78; 61; 49; 50
Name the previous number, number: 19; thirty; 45; thirty; 1
70 +10 80 -20 60 +30 90 -40 50 +20 70 ?
Solve the math puzzle and read the words;
cards on the board
(BASEMENT) (PILLAR) (MAGIE)
Tasks
1. A chicken on two legs weighs 2 kg. How many kg does a chicken weigh on 1 leg? (2 kg) (Play out the situation with the children). The teacher asks students to stand on 2 legs and then stand on one leg.
2. The ducks were flying. One in front, two behind; one behind and two in front; one between two, and three in a row. How many ducks were there in total? (3)
Praise:
one, two - oh, yes we are (claps hands)
three, four - well done!
(slide 9 “Repetition”)
Let's review what we learned in the previous lesson.
Repetition is the mother of learning.
Students complete tasks on cards (front)
|
5 dec. 6 units = |
|
1 dec. 8 units = |
|
37 = ... des ... units |
|
14 = ... des ... units |
|
25 = ... des ... units |
|
4 dec. 2 units = |
7.Stage of learning new material
Our little train brought us to the station "Izuchaykino"(slide 10)
Look at the picture
How many dozens of circles are there in the picture? (3)
What number is this? (thirty)
How many green circles? (6)
How many circles are there in total? (36)
Conclusion: 36 = 3 des. 6 units
Problematic question: how to write the number 36 as a sum of digit terms? 36 = +
Students offer their answers. The answers are summarized and a conclusion is drawn.
Working with the textbook. The student reads the rule p. 78
Where will you apply this knowledge? (when solving examples, problems.)
8. Stage of consolidation of acquired knowledge
(Slide 11 “Zakreplyaikino”)
Pupils comment on the chain and write numbers in their notebooks in the form of a sum of digit terms under the guidance of the teacher.
Physical education minute
We arrived at the station "Otdykhaykino"(slide 12)
Motto:
Move more - you will live longer.
"Two Flowers": The teacher calls out 1 phrase, the children repeat and perform.
Two flowers
Two flowers
Hedgehogs, hedgehogs
Anvil, anvil
Scissors, scissors
Running in place, running in place
Bunnies, bunnies
And now we're together
let's say: girls, girls!
boys boys!
How are you?
How do you live: like this
How do you swim? Like this
Are you waiting for an answer? Like this
Are you waving after me? Like this
How are you running? Like this
Do you sleep in the morning? Like this
Are you looking into the distance? Like this
How do you sit at your desk? Like this!
Independent work
Find task p.78, No. 2
Compare this task with the previous one.
What can we say?
(the bit terms are known, you need to find the sum)
Write down only the answers on the line.
(slide 13: 14,18,34,73,67,42,59,87)
Our train took us to the Zadachkino station(slide 14)
- What task do you think lies ahead of us?
Right. Let's solve the problem. For good luck, let's solve problem p. 79 No. 6 together. Write the word task in your notebook.
The student reads the problem. Then the children read to themselves.
Task analysis.
What does the problem say? (students' answers)
What does the number 5 mean? — bought 5 dozen Christmas balls
What does the number 40 mean? - bought 40 more balloons
Repeat the question.
How many balloons did you buy?
To solve the problem, let's model the condition using a segment.
The teacher draws a picture on the board.
What action can solve the problem? (by addition)
One student writes the solution to the problem on the board.
1) 50+40 = 90 (w).
Answer: 90 balls.
Exercise minutes for the eyes
"Butterfly"
A butterfly has arrived
She sat on the pointer.
Try to follow her
Run your eyes (students follow the “flight” of the butterfly on the tip of the pointer).
9. Stage of expanding and deepening knowledge on this topic
Differentiated work in groups
Our funny little train brought us to the station "Choose Kino"(slide 15)
Group 1 of students (with high motivation to learn) completes task No. 8 p. 79 of increased difficulty.
Group 2 students (average level of knowledge acquisition) task No. 5 p. 79
Group 3 students (low level of attainment of ranks) No. 3 p.78.
Checking assignments: from each group of students, 1 student presents a solution to the assignment.
Students check the correctness of the work in their notebooks and record it in the margins using the magic ruler.
10. Control and evaluation stage
And so, we arrived at the Vypolnyaykino station
Station "Vypolnyaykino"(slide 16)
Complete the test: from the written expressions on the board, mark the sum of the bit terms and write the answer in your notebook
- a) 50 + 20 b) 28 - 1 c) 6 + 12 d) 40 + 3
Answer: 1.-r
Key check. Self-esteem.
11. Reflection stage
How was our lesson?
Let’s sum it up now (slide 17 “Zavershaikino”)
Continue the sentence:
Today in class I learned... (write two-digit numbers as a sum of digit terms)
repeated... (bit composition of two-digit numbers)
consolidated...(ability to solve problems)
Using the “Knowledge Bank” scale, students mark the volume and correctness of the material learned in the lesson.
(Slide 18 “Mountain of Success”)
Use the self-esteem ruler to show who has climbed to the very top (position at the top).
Who ended up on the mountainside? (middle position)
Who stayed at the foot of the mountain (position below)
12. Homework
page 79 No. 1,2
The lesson is over.
(slide 19, Thank you for your work.)
The presented article is devoted to an interesting topic about natural numbers. In order to perform some actions, it is necessary to represent the original expressions as the addition of several numbers - in other language, sorting numbers into digits. The reverse process is also very important for solving exercises and problems.
In this section, we will consider in detail typical examples for better assimilation of information. We will also learn how to convert natural numbers and write them in a different form.
How can you decompose a number into digits?
Based on the title of the article, we can conclude that this paragraph is devoted to such mathematical terms as “sum” and “commands”. Before you start studying this information, you should study the topic in detail in order to have an understanding of natural numbers.
Let's get started and look at the basic concepts of bit terms.
Definition 1
Bit terms- these are certain numbers that consist of zeros and a single digit other than zero. Natural numbers 5, 10, 400, 200 belong to this category, but the numbers 144, 321, 5,540, 16,441 do not.
The number of digit terms of the presented number is equal to the number of digits other than zero contained in the record. If we imagine the number 61 as a sum of digit terms, since 6 and 1 differ from 0 . If we expand the number 55050 as the sum of bit terms, then it is presented as the sum of 3 terms. Three fives represented in the entry are different from zero.
Definition 2
It should be remembered that all digit terms of numbers contain a different number of characters in their notation.
Definition 3
Sum digit terms of a natural number is equal to this number.
Let's move on to the concept of bit terms.
Definition 4
Bit terms– these are natural numbers whose notation contains a digit other than zero. The number of numbers must be equal to the number of digits that are not zero. All addend numbers can be written with a different number of digits. If we decompose a number into digits, then the sum of the terms of the number will always be equal to this number.
Having analyzed the concept, we can conclude that single-digit and multi-digit numbers (consisting entirely of zeros with the exception of the first digit) cannot be represented as a sum. This happens because these numbers themselves will be bit terms for some numbers. With the exception of these numbers, all other examples can be expanded into terms.
How to arrange numbers?
To decompose a number as a sum of digit terms, you need to remember that natural numbers are related to the number of certain objects. In writing a number, the digits depend on the number of units, tens, hundreds, thousands, and so on. If you take the number 58 for example, you might note that it answers 5 dozens and 8 units. Number 134 400 corresponds 1 a hundred thousand, 3 tens of thousands, 4 thousand and 4 hundreds. These numbers can be represented as equalities - 50 + 8 = 58 and 134,400 = 100,000 + 30,000 + 4,000 + 400. In these examples, we clearly saw how a number can be decomposed into digit terms.
Looking at this example, we can represent any natural number as a sum of digit terms.
Let's give another example. Let's imagine the natural number 25 as a sum of digit terms. Number 25 corresponds 2 dozens and 5 units, therefore 25 = 20 + 5 . And here is the amount 17 + 8 is not the sum of the digit terms of the number 25 , since it cannot contain two numbers consisting of the same number of characters.
We have covered the basic concepts. Bit terms get their name due to the fact that each one belongs to a specific category.
In order to analyze this example, let's analyze the inverse problem. Let's imagine that we know the sum of the bit terms. We need to find this natural number.
For example, the amount 200 + 30 + 8 decomposed into the digits of the number 238, and the sum 3 000 000 + 20 000 + 2 000 + 500 corresponds to a natural number 3 022 500 . Thus, we can easily determine a natural number if we know its sum of reserve terms.
Another way to find a natural number is to add the digit terms in the columns. This example should not cause you any problems during execution. Let's talk about this in more detail.
Example 1
It is necessary to determine the original number if the sum of the bit terms is known 200 000 + 40 000 + 50 + 5
. Let's move on to the solution. You need to write down the numbers 200,000, 40,000, 50 and 5
for column addition:
All that remains is to add the numbers in columns. To do this, you need to remember that the sum of zeros is equal to zero, and the sum of zeros and a natural number is equal to this natural number.
We get: 
After performing the addition, we get a natural number 240 055 , the sum of the bit terms of which has the form 200 000 + 40 000 + 50 + 5 .
Let's talk about one more thing. If we learn to decompose numbers and represent them as a sum of digit terms, then we can also represent natural numbers as a sum of non-digit terms.
Example 2
Decomposition by digits of a number 725 will be presented as 725 = 700 + 20 + 5 , and the sum of the bit terms 700 + 20 + 5 can be represented as (700 + 20) + 5 = 720 + 5 or 700 + (20 + 5) = 700 + 25 , or (700 + 5) + 20 = 705 + 20 .
Sometimes complex calculations can be simplified a little. Let's look at another small example to reinforce the information.
Example 3
Let's subtract numbers 5 677 And 670 . First, let's imagine the number 5677 as a sum of digit terms: 5 677 = 5 000 + 600 + 70 + 7 . After performing the action, we can conclude that. amount ( 5,000 + 7) + (600 + 70) = 5,007 + 670. Then 5 677 − 670 = (5 007 + 670) − 670 = 5 007 + (670 − 670) = 5 007 + 0 = 5 007 .
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