Subtraction of natural numbers. Reduced, Subtracted, Difference

Subtraction- this is the arithmetic operation inverse to addition, by means of which as many units are subtracted (subtracted) from one number as they are contained in another number.

The number to be subtracted from is called reduced, the number that specifies how many units to subtract from the first number, is called deductible. The number resulting from subtraction is called difference(or remainder).

Let's take subtraction as an example. There are 9 sweets on the table, if you eat 5 sweets, then there will be 4 of them. The number 9 is reduced, 5 is subtracted, and 4 is the remainder (difference):

The - (minus) sign is used to write subtraction. It is placed between the minuend and the subtrahend, while the minuend is written to the left of the minus sign, and the subtrahend is written to the right. For example, the entry 9 - 5 means that the number 5 is subtracted from the number 9. To the right of the subtraction entry, put the sign = (equal), after which the result of the subtraction is written. Thus, the complete subtraction entry looks like this:

This entry reads as follows: the difference between nine and five is four, or nine minus five is four.

In order to get a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.

Consider how, using the natural series, you can perform subtraction and find the difference of two natural numbers. For example, we need to calculate the difference between the numbers 9 and 6, mark the number 9 in the natural series and count 6 numbers to the left from it. We get the number 3:

Subtraction can also be used to compare two numbers. Wanting to compare two numbers with each other, we ask ourselves how many units one number is more or less than the other. To find out, you need to subtract the smaller number from the larger number. For example, to find out how much 10 is less than 25 (or how much 25 is more than 10), you need to subtract 10 from 25. Then we find that 10 is less than 25 (or 25 is more than 10) by 15 units.

Subtraction check

Consider the expression

where 15 is the minuend, 7 is the subtrahend, and 8 is the difference. To find out if the subtraction was performed correctly, you can:

1. add the subtrahend with the difference, if it turns out to be reduced, then the subtraction was performed correctly:
2. subtract the difference from the minuend, if the subtrahend is obtained, then the subtraction was performed correctly:

1. Introduce students to the name of the components and the result of the subtraction action.
2. With difference as an expression.
3. Strengthen problem solving skills.
4. Develop computational skills, attention, thinking, memory, raise interest in the lesson of mathematics.

Equipment:

1. Clock face.
2. Figurine of the Dunno.
3. House of the Unknown.
4. Picture “Old Man-Lesovichok”.
5. Poster “Reduced. Subtrahend. Difference".
6. Poster “Forest clearing”.
7. Berries with examples.
8. Textbook.
9. Notebook.

1. Organizational moment.

Teacher: Dear children, today we are visiting fairy tale hero Dunno, he asks you for help. He decided to prepare unusual gifts for girls from the flower town by March 8 and went alone to get gifts, but the trouble is, he could not go along the road, because he did not really like to study at school. Let's help him prepare a gift for the girls. Dunno came out of his house very early, the other shorties were still sleeping. Look at the clock and tell me what time the clock shows? (On the dial 6 hours 30 minutes), and now look at Dunno's house and count all the rectangles.

The teacher shows the numbers and the sign between them with a pointer, and the children count verbally.

xn--i1abbnckbmcl9fb.xn--p1ai

How to Find the Difference of Numbers in Math

The word difference can be used in many ways. It can also mean a difference in something, for example, opinions, views, interests. In some scientific, medical and other professional fields, this term refers to various indicators, for example, blood sugar levels, atmospheric pressure, weather conditions. The concept of "difference", as a mathematical term, also exists.

Arithmetic operations with numbers

The basic arithmetic operations in mathematics are:

Each result of these actions also has its own name:

• sum - the result obtained by adding numbers;
• difference - the result obtained by subtracting numbers;
• product - the result of multiplying numbers;
• quotient is the result of division.

Explaining the concepts of sum, difference, product and quotient in mathematics in a simpler language, we can simply write them down only as phrases:

• amount - add;
• difference - take away;
• product - multiply;
• private - share.

Difference in mathematics

Considering definitions, what is the difference of numbers in mathematics, this concept can be denoted in several ways:

And all these definitions are true.

How to find the difference in values

Let us take as a basis the notation of the difference that the school curriculum offers us:

• The difference is the result of subtracting one number from another. The first of these numbers, from which the subtraction is carried out, is called the minuend, and the second, which is subtracted from the first, is called the subtrahend.

Once again resorting to the school curriculum, we find a rule for how to find the difference:

• To find the difference, subtract the minuend from the minuend.

All clear. But at the same time, we got a few more mathematical terms. What do they mean?

• Decreasing is a mathematical number from which it is subtracted and it decreases (becomes smaller).
• The subtrahend is the mathematical number that is subtracted from the minuend.

Now it is clear that the difference consists of two numbers, which must be known in order to calculate it. And how to find them, we also use the definitions:

• To find the minuend, add the difference to the minuend.
• To find the subtrahend, you need to subtract the difference from the minuend.

Mathematical operations with the difference of numbers

Based on the derived rules, we can consider illustrative examples. Mathematics is an interesting science. Here we will take only the simplest numbers for solution. Having learned to subtract them, you will learn how to solve more complex values, three-digit, four-digit, integer, fractional, in powers, roots, others.

Simple examples

• Example 1. Find the difference between two values.

20 - decreasing value,

Solution: 20 - 15 = 5

Answer: 5 - the difference in values.

• Example 2. Find the minuend.

32 - subtracted value.

Solution: 32 + 48 = 80

• Example 3. Find the value to be subtracted.

17 - reduced value.

Solution: 17 - 7 = 10

Answer: the subtracted value is 10.

More complex examples

In examples 1-3, actions with simple integers are considered. But in mathematics, the difference is calculated using not only two, but also several numbers, as well as integer, fractional, rational, irrational, etc.

• Example 4. Find the difference between three values.

Integer values ​​are given: 56, 12, 4.

56 - decreasing value,

12 and 4 are subtracted values.

The solution can be done in two ways.

Method 1 (consecutive subtraction of subtracted values):

1) 56 - 12 = 44 (here 44 is the resulting difference between the first two values, which will be reduced in the second action);

Method 2 (subtracting two subtracted from the reduced sum, which in this case are called terms):

1) 12 + 4 = 16 (where 16 is the sum of two terms, which will be subtracted in the next step);

Answer: 40 is the difference of three values.

• Example 5. Find the difference between rational fractional numbers.

Given fractions with the same denominators, where

4/5 - reduced fraction,

To complete the solution, you need to repeat the actions with fractions. That is, you need to know how to subtract fractions with the same denominator. How to deal with fractions that have different denominators. They must be able to bring to a common denominator.

Solution: 4/5 - 3/5 = (4 - 3)/5 = 1/5

• Example 6. Triple the difference of numbers.

But how to execute such an example when you want to double or triple the difference?

Let's go back to the rules:

• A double number is a value multiplied by two.
• A triple number is a value multiplied by three.
• The doubled difference is the difference in values ​​multiplied by two.
• A triple difference is the difference in values ​​multiplied by three.

7 - reduced value,

5 - subtracted value.

2) 2 * 3 = 6. Answer: 6 is the difference between the numbers 7 and 5.

• Example 7. Find the difference between 7 and 18.

7 - reduced value;

Everything seems to be clear. Stop! Is the subtrahend greater than the minuend?

And again, there is a rule applied for a specific case:

• If the subtracted is greater than the minuend, the difference will be negative.

Answer: - 11. This negative value is the difference between the two values, provided that the subtracted value is greater than the reduced one.

Math for Blondes

On the World Wide Web, you can find a lot of thematic sites that will answer any question. In the same way, online calculators for every taste will help you in any mathematical calculations. All the calculations made on them are a great help for the hasty, uninquisitive, lazy. Math for Blondes is one such resource. And we all resort to it, regardless of hair color, gender and age.

At school, we were taught to calculate such actions with mathematical quantities in a column, and later on a calculator. The calculator is also a handy tool. But, for the development of thinking, intellect, outlook and other vital qualities, we advise you to perform arithmetic operations on paper or even in your mind. The beauty of the human body is the great achievement of the modern fitness plan. But the brain is also a muscle that sometimes needs to be pumped. So, without delay, start thinking.

And even if at the beginning of the path the calculations are reduced to primitive examples, everything is ahead of you. And there is a lot to learn. We see that there are many actions with different values ​​in mathematics. Therefore, in addition to the difference, it is necessary to study how to calculate the rest of the results of arithmetic operations:

• sum - by adding the terms;
• product - by multiplying factors;
• quotient - dividing the dividend by the divisor.

Here is some interesting math.

obrazovanie.guru

How to find the minuend subtrahend difference?

Answers and explanations

• Veronica33
• average

To find the minuend, add the minuend to the difference.
To find the subtrahend, subtract the difference from the minuend.
To find the difference, subtract the subtrahend from the minuend.

• Comments
• Flag Violation

To find the minuend, add the minuend to the difference. take the minuend as X
let's say X - 1 = 3 to find X, we need to add the subtrahend to the difference, that is, to 3, that is, 1, we get a total of 4
and 4-1 = 3.

Subtraction of numbers

What is subtraction?

Subtraction- this is the arithmetic operation inverse to addition, by means of which as many units are subtracted (subtracted) from one number as there are in another number.

The number to be subtracted from is called reduced, the number that specifies how many units to subtract from the first number, is called deductible. The number resulting from subtraction is called difference(or remainder).

Let's take subtraction as an example. There are 9 candies on the table, if you eat 5 candies, then there will be 4 of them. The number 9 is reduced, 5 is subtracted, and 4 is the remainder (difference):

The minus sign is used to write subtraction. It is placed between the minuend and the subtrahend, while the minuend is written to the left of the minus sign, and the subtrahend is written to the right. For example, the entry 9 - 5 means that the number 5 is subtracted from the number 9. To the right of the subtraction entry, put the sign = (equal), after which the result of the subtraction is recorded. Thus, the complete subtraction entry looks like this:

This entry reads as follows: the difference between nine and five is four, or nine minus five is four.

In order to get a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.

Consider how, using the natural series, you can perform subtraction and find the difference of two natural numbers. For example, we need to calculate the difference between the numbers 9 and 6, mark the number 9 in the natural series and count 6 numbers to the left from it. We get the number 3:

Subtraction can also be used to compare two numbers. Wanting to compare two numbers with each other, we ask ourselves how many units one number is more or less than the other. To find out, you need to subtract the smaller number from the larger number. For example, to find out how much 10 is less than 25 (or how much 25 is more than 10), you need to subtract 10 from 25. Then we find that 10 is less than 25 (or 25 is more than 10) by 15 units.

Subtraction check

where 15 is the minuend, 7 is the subtrahend, and 8 is the difference. To find out if the subtraction was performed correctly, you can:

1. add the subtrahend with the difference, if it turns out to be reduced, then the subtraction was performed correctly:

subtract the difference from the minuend, if the subtrahend is obtained, then the subtraction was performed correctly:

Summary of the lesson "Finding an unknown reduced"

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State budgetary educational institution school No. 565 of the Kirovsky district

Topic: "Finding an unknown minuend"

Malina Anastasia Gennadievna

Subject : finding the unknown reduced.

The purpose of the lesson : creating conditions for the formation of ideas about arithmetic operations with an unknown minuend.

repeat the names of the difference components;

learn to find the unknown reduced through the solution of arithmetic examples;

learn to make the correct notation when solving examples with an unknown minuend.

consolidate knowledge of the multiplication table;

carry out the correction of thinking through exercises to establish simple patterns;

improve the skill of oral counting;

upbringing respectful attitude to their own work and the work of others;

education of emotional adequacy of behavior.

Dictionary : minuend, subtrahend, difference.

Equipment : a set of digital cards, an individual handout, a textbook, a rule on the board.

Technologies: personality-oriented, health-saving, information-computer, correctional and developing.

Desktop preparation.

Checking homework.

We write down today's date in a notebook, "Class work".

Let's do math exercises. We answer orally. (multiplication table for each student individually).

Students count orally.

Today we will solve examples with an unknown minuend. Write down the topic of the lesson. But first, let's remember what a minuend is.

Write the topic on the board.

Post a note on the board.

Learning new material.

I have five red apples on the board. I removed one. There are 4 left. Let's write this as a mathematical example. 5-1 = 4.

We have performed a subtraction action. Let's remember what numbers are called when subtracting.

What if we don't know how many apples we had. And we will only know that 1 apple was removed, and 4 remained. How to find how much it was? What are we looking for? Minuend.

Let's see what we did. We added the subtrahend to the difference (remainder).

We just made up our own rules. Turn to page 16, read the rule in the box.

Now I propose to practice in search of an unknown reduced. Usually, the unknown minuend is denoted as X.

Let's solve it like this:

Board work.

Write in your notebook the names of the numbers when subtracting.

Example on the board. A reminder about the names of the components of the subtraction action.

Page 16 rule we read in chorus.

Board rule.

P. 17, ex. 86/ p. 16 ex. 83, 84

Today we found an unknown reduced. Let's remember the rule. How do we denote the unknown minuend?

What did we talk about today?

What did you like the most?

Worked really well today....

Will work better next time....

Page 17, ex. 85, learn rule p. 16/ p. 17 ex. 88

Evaluation of student work

Literature: Perova M.N. Methods of teaching mathematics in a special (correctional) school of the VIII type - M .: Humanit. ed. center VLADOS, 2001. - 408 p.: ill. - (Correctional pedagogy).

If the subtrahend is added to the difference (remainder), then the minuend will be obtained.

minuend subtrahend difference

• Malina Anastasia Gennadievna
• 08.11.2016

Material Number: DB-331031

The author can download the certificate of publication of this material in the "Achievements" section of his website.

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"lesson summary"

Public lesson math in 1st grade.

Item:(Textbook No. 2, p. 29)

Class: 1 class

Lesson type:ONZ

Equipment:

laptop, multimedia projector, screen,

multimedia application for the lesson (presentation),

cards with inscriptions: "reduced", "subtracted", "difference"

number cards.

reflection cards (emoticons, apples, leaves and flowers)

textbook Moro M.I., Volkova S.I., Stepanova S.V. "Mathematics",

1st grade, part 2;

workbook for the textbook Moro M.I., Volkova S.I., Stepanova S.V. "Mathematics", grade 1, part 2;

Subject
Target
Lesson objectives	educational developing educators:
Planned results	Subject: Personal: Metasubject: Regulatory UUD Determine and formulate the purpose of the activity in the lesson with the help of the teacher; pronounce the sequence of actions in the lesson; (version) based on work with the textbook illustration; learn to work according to the plan proposed by the teacher. Means of formation of these actions: Cognitive UUD Means of formation of these actions: Communicative UUD Means of formation of these actions: organization of work in pairs

Name of the lesson	During the classes		Formed UUD
Motivation for learning activities. (1 min.) Target: Stage 2 Calligraphic minute. 2 minutes Stage 3 Verbal counting	Org. moment. The cheerful bell rang He invited us to a lesson To walk the path of knowledge And make discoveries. Good morning, Guys! My name is Anna Sergeevna and today I will give you a lesson in mathematics! Let's start our lesson with a smile. Look at each other and smile. Smile at your guests. Sit down! What is your mood? Show it with emoticons. (reflexion smiley) I see that you are in a great mood. I think that this mood will remain with you until the end of the lesson. After all, today we are again waiting for discoveries, in the lesson we will go to the mysterious city of Tsifr and make a small discovery for ourselves. What qualities do you need to have in order to make a small discovery for yourself in the lesson? (be careful, listen to the teacher) Show with your landing that you are ready for new discoveries. The motto of the lesson: "You know - speak, if you don't know - listen." Wish you luck. Open workbooks. Guys write down the number, cool work, continue the series of numbers through the box. Before you is a series of natural numbers. Name them in chorus in direct and reverse order. What is the smallest number? Name the largest number What number comes after number 2? Follows the number 3? Follows the number 6? Follows the number a with the number 8? Comes before the number 2? Comes before the number 5? Is it before the number 7? Name the neighboring numbers numbers 3, 7, 9 2. The game "Name your neighbor." 3. The game "Name the neighbors." 4. Orally solve the problem: Brought goose - mother Six children walk on the meadow. All goslings are like balls. Three sons, how many daughters? (answer 3)		Personal UUD 1) Adopting the image of a "good student" 2) development of interest in mathematics.
Updating knowledge and trial learning action. (5 minutes) Target:	Gymnastics for the eyes. First we need to rest our eyes so that they can see well. We follow the movements of the inhabitants of this city "Tsifr". Examples on the slide: Guys, let's turn to the slide. Let's count examples. 8 – 2 6 + 3 1 + 7 8 – 4 9 – 3 5 + 4 2 + 6 7 – 3 – What did you notice? What groups can these expressions be divided into? What are numbers called when adding? - Read this expression using the terms "term", "sum". slug + slug = sum, sum of 6 and 3 is 9 slug + slug = sum, sum of 5 and 2 is 7 slug + slug = sum, sum of 1 and 7 is 8 slug + slug = sum, sum of 2 and 6 is 8 - What is 8? 2 and 6?		Regulatory UUD 1) 2) 3) Monitor and evaluate your work and its results. 4) learn together with the teacher to discover and formulate a learning problem 5) learn to speak your mind 6) We form the ability to determine the success of our task in a dialogue with the teacher;
Identification of the place and cause of the difficulty (2 min) Target: discussion of difficulties	Why didn't it work? (Identify the cause of the difficulty) So what do we not know yet? What question do we have to answer? (as numbers are called when subtracted)
Goal-setting and building a project for getting out of difficulty Target:	Do you want to know what numbers are called when subtracting? We will learn this in class today. So what is the topic of our lesson? (names of numbers when subtracting) Will it be a lesson of repetition or discovery of new knowledge? (discovery of new knowledge) Why do we need this knowledge? And in the future, to learn how to solve equations and problems. So, you will need this knowledge for further training. So what is your goal for the lesson? (Remember; 2. Building a project for getting out of a problem situation. Let's start our research. There is a cake in front of you. How many parts does it consist of? (7) How many parts were removed from this whole cake? (2) What happened to the cake? It has decreased, which means that the number 7 has increased or decreased? (decreased) If it decreases, what can it be called? ("MINUEND") And what did we do with one part? (cut off, removed, subtracted) What is the name of this part? "SUBTRAHEND" How many pieces are left? (5) How would you call this number? ("DIFFERENCE") Let's guys open the textbook to page 29. P look at the illustration. How many snowmen were there? How many have flown? Teacher – Atlesser 5; subtrahend 2; difference equals three. difference of numbers 5 and 2 equals 3. So what is the name of the first number when subtracted? (reduced, integer) What is the name of the second number when subtracted? (subtracted, part) Name the result (difference, part) Guys read the rule on page 29 Guys, what new words have you learned now? (reduced, subtracted, difference) This is the topic of today's lesson. The wind blows in our face The tree swayed. The wind is quieter, quieter, quieter. The tree is getting higher and higher.		Communicative UUD 1) Be able to jointly agree on the rules of behavior and communication in the classroom and follow them. 2) Listen and understand the speech of others. 3) 4) to form the ability to argue one's opinion 5) be respectful of the position of the other 6) develop the ability to work in pairs Cognitive UUD 1) 2) Use sign-symbolic means, including models and diagrams. 3) Use mathematical terminology. 4) 5) navigate a page in a textbook 6) we form the ability to draw conclusions based on the analysis of objects.
Primary fixing (5 min)	Primary fastening. Let's do it collectively #1, on p.29. (One student with commenting writes an expression on the board, and the rest in notebooks). 9 – 4 = 5 (9 - minuend, 4 subtracted, 5 difference) (Well done sit down!) Check it out guys. Everyone has done it Well done!
Inclusion in the system of knowledge and repetition.	Textbook work 1. Solution of expressions No. 4 The guys carefully consider the expressions in task No. 4 (p. 29 of the textbook, part 2), What is the pattern of each column and what another example can each column be added. 3 + 4 – 2 9 – 3 + 1 8 + 2 – 1 4 + 3 – 3 8 – 2 + 2 7 + 3 – 2 5 + 2 – 4 7 – 1 + 3 6 + 4 – 3 6 + 1 – 5 6 – 0 + 4 5 + 5 – 4 Decide for yourself Check on the slide Who has 1-2 mistakes, pick up a green apple. Who has 3 mistakes, raise the flower Who has 4 or more mistakes, raise a piece of paper Well done! 2. Problem solving task number 2 p.29.-collective analysis of the problem, and the solution independently. (The teacher reads the problem) What is this task about? What is known about the problem? What is the task question? Write down the solution in your notebook. (slide) Answer: 2 apples Examination. Read the solution using the name of the components when subtracting chorus Who decided without mistakes pick up a red apple. Problem solving task number 3 p.29.-collective analysis of the problem. (The teacher reads the problem) What is this task about? What is known about the problem? What is the task question? What action do we solve the problem? Make a schematic drawing and solve the problem Answer. 4 markers.
Stage 9 work in a printed notebook Stage 10 consolidation of the studied Summary of the lesson. Reflection. (2-3 min) Target:	VII. Work on the development of logical thinking of students. Guys, look at the margins of the textbook, what figure did you cut out? (p. 29, part 2, margins of the textbook). № 3 pinocchio Pinocchio stretched, Once - bent over Two - bent over Raised hands to the sides, Apparently the key has not been found. To get us the key You need to get on your toes. Guys open the printed notebook on page 16. Examination Who decided without mistakes pick up a red apple. Whoever has mistakes, raise a green apple. (Reserve card) Examination term term Who decided without mistakes pick up a red apple. -Who has errors, raise a green apple. Minuend Subtrahend Difference Well done! Here we have completed the task in the mysterious city of "Tsifr" What discovery did you make for yourself? What are numbers called when subtracted? (reduced, subtracted, difference) - What did you study? Name the numbers in chorus when subtracting – Atlesser 5; subtrahend 2; difference equals three. difference of numbers 5 and 2 equals 3. Reflection on a slide That's the end of the lesson. Thanks to well-coordinated work, mutual assistance and support of each other, we were able to repeat the studied material and discover new knowledge. What is your mood now? Show with emoticons. Thank you for the lesson!

Self-analysis of the lesson on GEF.

Item: Mathematics (Moro M.I., Volkova S.I., S.V. Stepanova)(Textbook No. 2, p. 29)

Class: 1 class

Lesson type:ONZ(technology of activity learning)

Lesson type: ONZ (technology of activity training)

Subject	Minuend. Subtrahend. Difference.
Target	introduce students to the components of subtraction, read expressions using these terms.
Lesson objectives	educational: to introduce students to the concepts of "reduced", "subtracted", "difference"; teach how to apply new terms when compiling and reading mathematical expressions for subtraction; developing: to promote the development of thinking, memory, attention; educators: to cultivate the ability to communicate with peers in pair, teamwork, to instill interest in mathematics lessons.
Planned results	Subject: Students will learn to use mathematical terminology when compiling, reading and writing mathematical equalities for subtraction; perform verbal and written arithmetic operations with numbers (addition and subtraction within 7). Personal: Adoption of the image of a "good student", the development of interest in mathematics. Monitor and evaluate your work and its results. Learn to self-assess based on the criterion of success of educational activities. Metasubject: Regulatory UUD Means of formation of these actions: problematic dialogue technology at the stage of studying new material. Learn to distinguish a correctly completed task from an incorrect one; to study together with the teacher and other students to give an emotional assessment of the activities of the class in the lesson. Means of formation of these actions: technology for assessing educational achievements (educational success) Cognitive UUD Be able to navigate in your system of knowledge; to distinguish the new from the already known with the help of a teacher; acquire new knowledge; find answers to questions using the textbook, your life experience and the information received in the lesson; extract relevant information from messages different types; use sign-symbolic means, including models and diagrams; build reasoning in the form of a connection of simple judgments about an object; establish analogies; be able to express your thoughts orally and in writing. Means of formation of these actions: educational material and tasks of the textbook, focused on the lines of development by means of the subject. Communicative UUD Listen and hear the speech of the teacher; listen to the answers of classmates, supplement and clarify them; The means of shaping these actions: problematic dialogue technology. Jointly agree on the rules of behavior and communication in the classroom and follow them; negotiate and come to a common decision in joint activities. Means of formation of these actions: organization of work in pairs

I will analyze my lesson, adhering to the structure of the lesson, which suggests the "technology of activity learning."

Motivation (self-determination) for learning activities

Target: the inclusion of students in activities at a personally meaningful level.

Work methods: I said at the beginning of the lesson good wishes children; wished good mood and good luck; picked up The motto "You know - speak, if you don't know - listen" I think is the most suitable for first-graders at this time.

2. Actualization of knowledge and trial educational action.

Target: repetition of the studied material necessary for the "discovery of new knowledge", and the identification of difficulties in the individual activity of each student.

At this stage, I prepared to get acquainted with new material based on the knowledge gained earlier, I tried to interest children (motivation). For this I created problem situation. (- Is it possible to read it using the same terms? Let's try? Did it work? Why?) Tried to identify the cause of the difficulty. Cognitive UUD 1) Be able to navigate your system of knowledge: to distinguish the new from the already known with the help of a teacher. Regulatory UUD 4) learn together with the teacher to discover a learning problem

Target: discussion of difficulties (“Why are there difficulties?”, “What do we not know yet?”); pronouncing the purpose of the lesson in the form of a question to be answered, or in the form of a lesson topic.

Using the dialogue leading up to the topic, I identified the cause of the difficulty in the children. I needed them to independently determine that they lack specific knowledge and skills to solve the task. Regulatory UUD 5) learn to speak your mind Communicative UUD 3) We form the ability to build a speech statement in accordance with the tasks;

1. Goal-setting and building a project for getting out of difficulty

Target: solution of the KM (oral tasks) and discussion of the project of its solution.

With the help of a dialogue with the teacher, the children learned to determine the topic of the lesson and set goals for themselves. And also found out why students need this knowledge. Since children have just become students, they do not know how to build a work plan, so I used a dialogue at this stage that leads to the discovery of new knowledge. And the children learned to work in pairs.

Personal UUD

2) development of interest in mathematics

Regulatory UUD

1) Learn to identify the topic and formulate the goal in the lesson with the help of a teacher.

2) Accept and maintain the goals and objectives of educational activities.

5) learn to speak your mind

Communicative UUD

1) Be able to jointly agree on the rules of behavior and communication in the classroom and follow them.

6) to form the ability to work in pairs

Cognitive UUD

4) Be able to formulate your thoughts orally

5. Primary fastening.

Target: pronunciation of new knowledge

My task as a teacher at this stage was to help students connect new knowledge with previously acquired ones. Children had to clearly see and understand the relationship between the concepts of "parts and the whole" on the one hand and "Smart. Subtract. Diff.» with another. That they are one and the same and are the same. Children solved typical problems, but with the use of new knowledge. The work was both individual and frontal.

Cognitive UUD

2) Use sign-symbolic means, including models and diagrams.

4) Be able to formulate your thoughts orally.

5) navigate the page in the textbook

6) we form the ability to draw conclusions based on the analysis of objects.

Communicative UUD

2) Listen and understand the speech of others.

6. Inclusion in the knowledge system and repetition

Cognitive UUD

1) Be able to navigate in your knowledge system: to distinguish the new from the already known with the help of a teacher.

3) Use mathematical terminology.

Communicative UUD

3) We form the ability to build a speech statement in accordance with the tasks;

7. Reflection of educational activity in the lesson (outcome of the lesson)

Target: students' awareness of their SD (learning activity), self-assessment of the results of their own and the whole class.

The concept of subtraction is best understood with an example. You decide to drink tea with sweets. There were 10 candies in the vase. You ate 3 candies. How many candies are left in the vase? If we subtract 3 from 10, then 7 sweets will remain in the vase. Let's write the problem mathematically:

Let's take a closer look at the entry:
10 is the number from which we subtract or which we reduce, therefore it is called reduced.
3 is the number we are subtracting. Therefore it is called deductible.
7 is the result of subtraction or is also called difference. The difference shows how much the first number (10) is greater than the second number (3) or how much the second number (3) is less than the first number (10).

If you are in doubt whether you have found the difference correctly, you need to do verification. Add the second number to the difference: 7+3=10

When subtracting l, the minuend cannot be less than the subtrahend.

We draw a conclusion from what has been said. Subtraction- this is an action with the help of which the second term is found by the sum and one of the terms.

In literal form, this expression will look like this:

a -b=c

a - reduced,
b - subtracted,
c is the difference.

Properties of subtracting a sum from a number.

13 — (3 + 4)=13 — 7=6
13 — 3 — 4 = 10 — 4=6

The example can be solved in two ways. The first way is to find the sum of numbers (3 + 4), and then subtract from the total number (13). The second way is to subtract the first term (3) from the total number (13), and then subtract the second term (4) from the resulting difference.

In literal form, the property for subtracting the sum from a number will look like this:
a - (b + c) = a - b - c

The property of subtracting a number from a sum.

(7 + 3) — 2 = 10 — 2 = 8
7 + (3 — 2) = 7 + 1 = 8
(7 — 2) + 3 = 5 + 3 = 8

To subtract a number from the sum, you can subtract this number from one term, and then add the second term to the result of the difference. Under the condition, the term will be greater than the subtracted number.

In literal form, the property for subtracting a number from a sum will look like this:
(7 + 3) — 2 = 7 + (3 — 2)
(a +b) —c=a + (b - c), provided b > c

(7 + 3) — 2=(7 — 2) + 3
(a + b) - c \u003d (a - c) + b, provided a > c

Subtraction property with zero.

10 — 0 = 10
a - 0 = a

If you subtract zero from the number then it will be the same number.

10 — 10 = 0
a -a = 0

If you subtract the same number from a number then it will be zero.

Related questions:
In the example 35 - 22 = 13, name the minuend, the subtrahend and the difference.
Answer: 35 - reduced, 22 - subtracted, 13 - difference.

If the numbers are the same, what is their difference?
Answer: zero.

Do a subtraction check 24 - 16 = 8?
Answer: 16 + 8 = 24

Subtraction table for natural numbers from 1 to 10.

Examples for tasks on the topic "Subtraction of natural numbers."
Example #1:
Insert the missing number: a) 20 - ... = 20 b) 14 - ... + 5 = 14
Answer: a) 0 b) 5

Example #2:
Is it possible to subtract: a) 0 - 3 b) 56 - 12 c) 3 - 0 d) 576 - 576 e) 8732 - 8734
Answer: a) no b) 56 - 12 = 44 c) 3 - 0 = 3 d) 576 - 576 = 0 e) no

Example #3:
Read the expression: 20 - 8
Answer: “Subtract eight from twenty” or “Subtract eight from twenty.” Pronounce words correctly