Operations with decimal fractions. Subtracting decimals: rules, examples, solutions Adding and subtracting decimals

Arithmetic calculations such as addition And subtracting decimals, are necessary in order to obtain the desired result when operating with fractional numbers. The particular importance of carrying out these operations is that in many areas of human activity the measures of many entities are represented precisely decimals. Therefore, to carry out certain actions with many objects of the material world, it is required fold or subtract exactly decimals. It should be noted that in practice these operations are used almost everywhere.

Procedures adding and subtracting decimals in its mathematical essence it is carried out almost exactly in the same way as similar operations for integers. When implementing it, the value of each digit of one number must be written under the value of a similar digit of another number.

Subject to the following rules:

First, it is necessary to equalize the number of those characters that are located after the decimal point;

Then you need to write the decimal fractions one below the other in such a way that the commas contained in them are located strictly below each other;

Carry out the procedure subtracting decimals in full accordance with the rules that apply to subtracting integers. In this case, you do not need to pay any attention to commas;

After receiving the answer, the comma in it must be placed strictly under those that are in the original numbers.

Operation adding decimals carried out in accordance with the same rules and algorithm as described above for the subtraction procedure.

Example of adding decimals

Two point two plus one hundredth plus fourteen point ninety-five hundredths equals seventeen point sixteen hundredths.

2,2 + 0,01 + 14,95 = 17,16

Examples of adding and subtracting decimals

Mathematical operations addition And subtracting decimals in practice they are used extremely widely, and they often relate to many objects of the material world around us. Below are some examples of such calculations.

Example 1

According to design estimates, the construction of a small production facility requires ten point five cubic meters of concrete. Using modern building construction technologies, the contractors, without compromising the quality characteristics of the structure, managed to use only nine point nine cubic meters of concrete for all work. The savings amount is:

Ten point five minus nine point nine equals zero point six cubic meter of concrete.

10.5 – 9.9 = 0.6 m3

Example 2

The engine installed on an old car model consumes eight point two liters of fuel per hundred kilometers in the urban cycle. For the new power unit, this figure is seven point five liters. The savings amount is:

Eight point two liters minus seven point five liters equals zero point seven liters per hundred kilometers in urban driving.

8.2 – 7.5 = 0.7 l

The operations of adding and subtracting decimal fractions are used extremely widely, and their implementation does not pose any problems. In modern mathematics, these procedures have been worked out almost perfectly, and almost everyone has been fluent in them since school.

Adding and subtracting decimals is similar to adding and subtracting natural numbers, but with certain conditions.

Rule.

is performed by the digits of the integer and fractional parts as natural numbers. In writing adding and subtracting decimals

the comma separating the integer part from the fractional part should be located at the addends and the sum or at the minuend, subtrahend and difference in one column (a comma under the comma from writing the condition to the end of the calculation). Adding and subtracting decimals

243,625 + 24,026 = 200 + 40 + 3 + 0,6 + 0,02 + 0,005 + 20 + 4 + 0,02 + 0,006 = 200 + (40 + 20) + (3 + 4)+ 0,6 + (0,02 + 0,02) + (0,005 + 0,006) = 200 + 60 + 7 + 0,6 + 0,04 + 0,011 = 200 + 60 + 7 + 0,6 + (0,04 + 0,01) + 0,001 = 200 + 60 + 7 + 0,6 + 0,05 + 0,001 = 267,651

843,217 — 700,628 = (800 — 700) + 40 + 3 + (0,2 — 0,6) + (0,01 — 0,02) + (0,007 — 0,008) = 100 + 40 + 2 + (1,2 — 0,6) + (0,01 — 0,02) + (0,007 — 0,008) = 100 + 40 + 2 + 0,5 + (0,11 — 0,02) + (0,007 — 0,008) = 100 + 40 + 2 + 0,5 + 0,09 + (0,007 — 0,008) = 100 + 40 + 2 + 0,5 + 0,08 + (0,017 — 0,008) = 100 + 40 + 2 + 0,5 + 0,08 + 0,009 = 142,589

in a column:

Adding decimals requires an additional top line to record numbers when the sum of the place value goes beyond ten. Subtracting decimals requires an extra top line to mark the place where the 1 is borrowed.

If there are not enough digits of the fractional part to the right of the addend or minuend, then to the right in the fractional part you can add as many zeros (increase the digit of the fractional part) as there are digits in the other addend or minuend. is performed in the same way as multiplying natural numbers, according to the same rules, but in the product a comma is placed according to the sum of the digits of the factors in the fractional part, counting from right to left (the sum of the digits of the multipliers is the number of digits after the decimal point of the factors taken together).

Example:

At multiplying decimals in a column, the first significant digit on the right is signed under the first significant digit on the right, as in natural numbers:

Record multiplying decimals to the line:

Record division of decimals to the line:

The underlined characters are the characters that are followed by a comma because the divisor must be an integer.

Rule. At dividing fractions The decimal divisor is increased by as many digits as there are digits in the fractional part. To ensure that the fraction does not change, the dividend is increased by the same number of digits (in the dividend and divisor, the comma is moved to the same number of digits). A comma is placed in the quotient at that stage of division when the whole part of the fraction is divided.

For decimal fractions, as for natural numbers, the rule remains: You cannot divide a decimal fraction by zero!

In this article we will focus on subtracting decimals. Here we will look at the rules for subtracting finite decimal fractions, focus on subtracting decimal fractions by column, and also consider how to subtract infinite periodic and non-periodic decimal fractions. Finally, we'll talk about subtracting decimals from natural numbers, fractions, and mixed numbers, and subtracting natural numbers, fractions, and mixed numbers from decimals.

Let’s say right away that here we will only consider the subtraction of a smaller decimal fraction from a larger decimal fraction; we will analyze other cases in the articles subtraction of rational numbers and subtraction of real numbers.

Page navigation.

General principles of subtracting decimals

At its core subtracting finite decimals and infinite periodic decimals represents the subtraction of the corresponding ordinary fractions. Indeed, the indicated decimal fractions are the decimal notation of ordinary fractions, as discussed in the article converting ordinary fractions to decimals and vice versa.

Let's look at examples of subtracting decimal fractions, starting from the stated principle.

Example.

Subtract the decimal fraction 3.7 from the decimal fraction 0.31.

Solution.

Since 3.7 = 37/10 and 0.31 = 31/100, then . So the subtraction of decimal fractions was reduced to the subtraction of ordinary fractions with different denominators: . Let's present the resulting fraction as a decimal fraction: 339/100=3.39.

Answer:

3,7−0,31=3,39 .

Note that it is convenient to subtract final decimal fractions in a column; we will talk about this method in.

Now let's look at an example of subtracting periodic decimal fractions.

Example.

Subtract from the periodic decimal fraction 0.(4) the periodic decimal fraction 0.41(6) .

Solution.

Answer:

0,(4)−0,41(6)=0,02(7) .

It remains to voice principle of subtraction of infinite non-periodic fractions.

Subtracting infinite non-periodic fractions is reduced to subtracting finite decimal fractions. To do this, subtracted infinite decimal fractions are rounded to some place, usually to the lowest possible (see rounding numbers).

Example.

Subtract the finite decimal 0.52 from the infinite non-periodic decimal 2.77369….

Solution.

Let's round the infinite non-periodic decimal fraction to 4 decimal places, we have 2.77369...≈2.7737. Thus, 2,77369…−0,52≈2,7737−0,52 . Calculating the difference between the final decimal fractions, we get 2.2537.

Answer:

2,77369…−0,52≈2,2537 .

Subtracting decimal fractions by column

A very convenient way to subtract trailing decimal fractions is by column subtraction. Column subtraction of decimal fractions is very similar to column subtraction of natural numbers.

To execute subtracting decimal fractions by column, need to:

equalize the number of decimal places in the records of decimal fractions (if it is different, of course), by adding a certain number of zeros to the right of one of the fractions;
write the subtrahend under the minuend so that the digits of the corresponding digits are under each other, and the comma is under the comma;
perform column subtraction, ignoring commas;
In the resulting difference, place a comma so that it is located under the commas of the minuend and subtrahend.

Let's look at an example of subtracting decimal fractions in a column.

Example.

Subtract the decimal 10.30501 from the decimal 4452.294.

Solution.

Obviously, the number of decimal places of fractions varies. Let's equalize it by adding two zeros to the right in the notation of the fraction 4 452.294, which will result in an equal decimal fraction 4 452.29400.

Now let’s write the subtrahend under the minuend, as suggested by the method of subtracting decimal fractions in a column:

We carry out the subtraction, ignoring the commas:

All that remains is to put a decimal point in the resulting difference:

At this stage, the recording has taken on a complete form, and the subtraction of decimal fractions in a column is completed. The following result was obtained.

Answer:

4 452,294−10,30501=4 441,98899 .

Subtracting a decimal fraction from a natural number and vice versa

Subtracting a final decimal from a natural number It’s most convenient to do it in a column, writing the natural number being reduced as a decimal fraction with zeros in the fractional part. Let's figure this out when solving the example.

Example.

Subtract the decimal fraction 7.32 from the natural number 15.

Solution.

Let's imagine the natural number 15 as a decimal fraction, adding two digits 0 after the decimal point (since the subtracted decimal fraction has two digits in the fractional part), we have 15.00.

Now let's subtract decimal fractions in a column:

As a result, we get 15−7.32=7.68.

Answer:

15−7,32=7,68 .

Subtracting an infinite periodic decimal from a natural number can be reduced to subtracting an ordinary fraction from a natural number. To do this, it is enough to replace the periodic decimal fraction with the corresponding ordinary fraction.

Example.

Subtract the periodic decimal fraction 0,(6) from the natural number 1.

Solution.

The periodic decimal fraction 0.(6) corresponds to the common fraction 2/3. Thus, 1−0,(6)=1−2/3=1/3. The resulting ordinary fraction can be written as a decimal fraction 0,(3).

Answer:

1−0,(6)=0,(3) .

Subtracting an infinite non-periodic decimal from a natural number comes down to subtracting the final decimal fraction. To do this, an infinite non-periodic decimal fraction must be rounded to a certain digit.

Example.

Subtract the infinite non-periodic decimal fraction 4.274... from the natural number 5.

Solution.

First, let's round the infinite decimal fraction, we can round to the nearest hundredth, we have 4.274...≈4.27. Then 5−4.274…≈5−4.27.

Let's imagine the natural number 5 as 5.00, and subtract decimal fractions in a column:

Answer:

5−4,274…≈0,73 .

It remains to voice rule for subtracting a natural number from a decimal fraction: to subtract a natural number from a decimal fraction, you need to subtract this natural number from the integer part of the decimal fraction being reduced, and leave the fractional part unchanged. This rule applies to both finite and infinite decimal fractions. Let's look at the example solution.

Example.

Subtract the natural number 17 from the decimal fraction 37.505.

Solution.

The whole part of the decimal fraction 37.505 is equal to 37. Subtract the natural number 17 from it, we have 37−17=20. Then 37.505−17=20.505.

Answer:

37,505−17=20,505 .

Subtracting a decimal from a fraction or mixed number and vice versa

Subtracting a finite decimal or infinite periodic decimal from a fraction can be reduced to subtracting ordinary fractions. To do this, it is enough to convert the decimal fraction to be subtracted into an ordinary fraction.

Example.

Subtract the decimal fraction 0.25 from the common fraction 4/5.

Solution.

Since 0.25=25/100=1/4, then the difference between the common fraction 4/5 and the decimal fraction 0.25 is equal to the difference between the common fractions 4/5 and 1/4. So, 4/5−0,25=4/5−1/4=16/20−5/20=11/20 . In decimal notation, the resulting common fraction is 0.55.

Answer:

4/5−0,25=11/20=0,55 .

Likewise subtracting a trailing decimal or periodic decimal from a mixed number comes down to subtracting a common fraction from a mixed number.

Example.

Subtract the decimal fraction 0,(18) from a mixed number.

Solution.

First, let's convert the periodic decimal fraction 0,(18) into an ordinary fraction: . Thus, . The resulting mixed number in decimal notation has the form 8,(18) .

LESSON PLAN in mathematics in grade 5 on the topic “Adding and subtracting decimals”

	Full name (full name)	Nikulina Irina Evgenevna
	Place of work	State Budgetary Educational Institution boarding school No. 1 Chapaevsk
	Job title	Mathematic teacher
	Item	mathematics
	Class
	Lesson topic	Adding and subtracting decimals (40 min)
	Basic tutorial	N.Ya.Vilenkin. Mathematics: Textbook for 5th grade of general education institutions. -21st ed., - M.: Mnemosyne, 2007

Lesson objectives:

1) consolidate the skill of adding and subtracting decimal fractions;

2) develop logical thinking, oral mathematical speech, and memory of students;

3) cultivate activity, independence, interest in the subject.

9. Tasks:

Educational (formation of cognitive UUD):

repetition, testing and correction of students’ knowledge, skills and abilities; highlight and formulate cognitive goals, consciously and arbitrarily construct your statements;

Developmental (formation of regulatory control systems)

the ability to process information and rank it on the specified grounds; plan your activities depending on specific conditions; reflection on methods and conditions of action, control and evaluation of the process and results of activity, development of cognitive interest in the subject;

Educational (formation of communicative and personal educational skills):

the ability to listen and engage in dialogue, participate in collective discussion of problems, cultivate responsibility and accuracy.

Lesson type: a lesson in applying students' knowledge, skills and abilities in adding and subtracting decimals.

Forms of student work: frontal, group, individual

13. Necessary equipment: computer, projector, mathematics textbook, handouts ( cards with test work, cards with oral and written tasks, signal cards of three colors (yellow, red, green), emoticons of three types (, , ), electronic presentation made in the program Power Point, magnets.

14. Lesson format: computer presentation.

15. Lesson motivation: stimulate interest in studying mathematics.

16. Techniques:- creating fun and surprise in the lesson;

Creating a situation of success;

Operational control over compliance with requirements.

17 . Lesson plan: 1. Organizational moment - 2 min.

2. Oral exercises - 9 min.

3. Physical exercise - 1 min.

4. Solving problems - 10 min.

5. Physical exercise for the eyes - 1 min.

6. Work on the card - 6 min.

7. Test work - 8 min.

8. Setting homework - 1 min.

9. Summing up the lesson. Reflection - 2 min.

Lesson structure and flow

Teacher activities

Student activity

UUD

Organizational moment (2 min). Objectives: create a favorable psychological mood for work.

Personal oud:

1.self-determination,

3.readiness for life and personal self-determination.

Regulatory activities:

1.goal setting,

General education:

1.semantic reading,

1. summing up the concept.

2. ability to listen.

Hello guys.

The key direction (2 slide) of our lesson will be the words of the famous teacher Soloveichik, whose portrait you see now on the screen:

"Lesson with passion"

everyone needs it

without exception.

Learning with passion -

this is not at all

not learning and entertainment."

During the lesson, you will help various fairy-tale characters answer questions, count orally and in writing, solve problems and equations, find the meaning of numerical expressions individually and in groups. (4 slide) Some of your tasks are numbered on pieces of paper for those who have difficulty seeing. Please be careful. Some tasks require a written solution, so you will do the calculations in your notebook.

What was the last topic we studied?

The topic of our lesson: “Adding and subtracting decimals.” (3 slide)

Given the above, say: “What goals should you achieve during the lesson?”

Open your notebooks. Write the date and topic of the lesson.

Students listen to the teacher and look at the screen as needed.

Students answer the teacher's questions.

Students take notes in notebooks.

Oral exercises (9 min). (5 slide) Objectives: updating basic knowledge and methods of action, developing logical thinking; ensuring perception, comprehension, generalization of the studied material, using new information technologies

Personal oud:

2. knowledge of moral standards and the ability to highlight the moral aspect of behavior.

Regulatory activities:

2. goal setting,

3.control,

4.correction,

5.volitional self-regulation, mobilization of strength and energy, overcoming obstacles.

Cognitive focus:

General education:

- universal logical actions:

1.synthesis,

2.analysis,

3.building a logical chain of reasoning.

Communication activities:

“Lost Words” (6 slide)

Dunno lost not only commas, but also words.

Your task is to find words - mathematical terms - among the letters. You need to look line by line. Underline terms with a pencil. Whoever finds the “lost words” first raises his hand, goes to the board, writes them down.

AVGKSPZRFDESIATICNAYASVSHCHTRADROBRS

MTSKBGFMNSCHADDUCTIONPRIV

. IVKASON SUBTRACT FROM THE DISCHARGE

DIRECT VENIKPTOMCHKATRONS

. DESIGNATORSVFMIOKRPIKTOTUBAKR

IMONEYBNRPSCOUNTER

(7 slide with answers: 1.decimal, 2.fraction, 3.addition,

8.numerator)

Students listen to the teacher, look through the set of letters, look for mathematical terms, underline those found on a piece of paper with this task, raise their hands, and with the teacher’s permission, go to the board and write them down.

The teacher reads the task from the slide and explains how to complete it.

“Gather a rule” (8 slide)

Set up the algorithm for adding and subtracting decimal fractions in the required order:

To add or subtract decimals:

. perform addition or subtraction operations without processing

paying attention to the comma;

. in the answer, place a comma under the comma in the data

fractions;

. equalize the number of decimal places;

. write the fractions so that the comma is under

comma.

Draws attention to the slide where the algorithm is installed in the required order. Makes adjustments as needed with students.

Students listen to the teacher, read the proposed algorithm on a slide or piece of paper, and establish the desired order on the piece of paper. Check your answer on the slide. Corrections are made as necessary together with the teacher.

The teacher reads out the task from slide No. 9.

3.- Place commas in the terms so that the number"3"

in each of them there wasin the tenth place.

. What is the amount?

1032 + 153 = 104,73

The teacher reads out the task from slide number 10.

Complete with commas add the terms so that the indicated amount is obtained:

1032 + 153 = 104,73

The teacher asks the answer of one student with a full explanation of the task.

Students listen to the teacher. They think about the answer and raise their hands. One of the students voices the answer with a full explanation, the others listen to the answer of this student.

The teacher draws students' attention to slide number 11.

- Guys, a parrot has flown to us. It turns out he can't solve the examples. Let's help him and find the mistake.

13,48 _ 123

6,8 1,5

The teacher asks the answers of two students with a full explanation of the task.

Students listen to the teacher. They think about the answer and raise their hands. Two of the students voice their answers with a full explanation, the others listen to the answers of these students.

The teacher draws students' attention to slide number 12.

- Find the root of the equation:

a) x+2.5=3.7; b) y - 1.2=3.4; c) 27.8 - k=22.3.

Guys, you solve every equation in your head. Raise your hand, thereby showing your readiness to voice the solution to the equation.

Students listen to the teacher. They think about the answer and raise their hands. Three of the students voice their answers with a full explanation, the others listen to the answers of these students.

The teacher draws students' attention to slide number 13.

- Guys, now we will conduct a test with signal

cards. Place circles of 3 colors in front of you: yellow, red, green. Your task is to find the correct answer and raise the circle of the color under which your chosen answer is located.

a) 0.769 + 42.389=

○50,459 ○43,158 ○4,3158

b) 5.8+22.191=

○27,991 ○80,195 ○27,199

c) 11.1 - 2.8=

○8,3 ○83,0 ○0,83

d) 6.6 - 5.99=

○6,1 ○0,07 ○0,61

Students listen to the teacher. They think over the answer, raise the signal card. If necessary, corrections are made together with the teacher.

Physical exercise (1 min) . Slide number 14.

Objectives: health preservation.

The teacher addresses the children:

We will leave the desks together,

But there's no need to make any noise,

Stand up straight, legs together,

Turn around, in place.

Let's clap our hands a couple of times.

And we'll drown a little.

Now let's imagine, kids,

It’s as if our hands are branches.

Let's shake them together

Like the wind blows from the south.

The wind died down. We sighed together.

We need to continue the lesson.

We caught up. They sat down quietly

And they looked at the board.

Personal oud:

Problem solving. (10 min) (slide number 15) Objectives: generalization of the studied material, development of cognitive interest in mathematics, using new information technologies.

Personal oud:

1.readiness for life and personal self-determination,

Regulatory activities:

1.drawing up a plan and sequence of activities,

2. goal setting,

3.correction,

5. evaluation.

Cognitive focus:

General education:

1.search and selection of necessary information,

- universal logical actions:

1.synthesis,

2.analysis,

Communication activities:

1. ability to listen,

4. proficiency in monologue form of speech.

The teacher informs the students that they will solve problems from the slides, helping various fairy-tale characters.

and asks the rest to solve it in their notebooks on their own. For those students who find it difficult to solve, the teacher asks them to solve together with the answerer at the board.

-Help the gnomes! (16 slide)

Snow White decided to sew herself a new dress and asked her faithful gnomes to count how much fabric there was.

does she need to buy it if she needs 3.25m for a skirt and 1.2m for a blouse?

-Kikimora Duckweed and Zelenka went for a boat ride. (17 slide)

How hard it is to row against the current. I'm already tired.

I think the guys will find out how fast we are sailing.

The speed of the river current is 2.9 km/h, and the own speed of the boat with kikimorki is 6.2 km/h. What is the speed of a boat with kikimorks moving against the current?

(Slide 18)

-The little pig decided to fence the castle with a fortress, making it in the shape of a triangle. Two sides of the fortress are already ready. They are equal to 18.7m and 13.6m.

The perimeter of the triangle is 42.9 m. Find the length of the remaining side of the fortress.

-Let's explore... (slide 19)

I want to surround my hut with a fence so as not to be afraid

I prefer Koshchei. Its width is 5.6 meters, and its length is 0.8 meters more. What length of fence do I need?

The teacher grades students who solved at the board and independently.

Students solve problems in their notebooks. In turn, 4 students solve 4 problems at the board with a full explanation of the solution.

Exercise for the eyes. (1 min). (Slide 20)

Objectives: health preservation.

Personal oud:

1.readiness for life and personal self-determination.

(6min) Objectives: generalizing the material studied, developing cognitive interest in mathematics, using new information technologies and organizing group work for students.

Personal oud:

1.readiness for life and personal self-determination.

Regulatory activities:

1.drawing up a plan and sequence of activities,

2. goal setting,

3.correction,

4.volitional self-regulation, mobilization of strength and energy, overcoming obstacles,

5. evaluation.

Cognitive focus:

General education:

1.search and selection of necessary information,

2.the ability to structure knowledge, construct statements in oral and written form,

3. selection of the most effective ways to solve educational problems,

4.semantic reading,

- universal logical actions:

1.synthesis,

2.analysis,

3. establishing cause-and-effect relationships.

Communication activities:

3.the ability to express one’s thoughts sufficiently fully,

4.ability to participate in collective discussion.

The teacher draws students' attention to 21 slides.

Guys, by solving tasks on this card

You and I will guess the encrypted word - the name of the plant with the help of which people overcome serious illnesses. There is no need to write a short note when solving problems. The answer to each task is hidden along the lines. You will work in teams. Each row is a team. Whose team finds the letter first, any team member raises his hand.

For those who have difficulty seeing, you can take the assignments from a piece of paper.


2,446	3,2245	5,155	4,21	5,65	3,21
104,24	100,2	98,92	107,04	96,41	33,5
	0,11	0,15	1,89	1,98
34,75	5,06	30,7	4,05	10,8	30,75
7,18	30,7	14,49	15,2	29,43	32,22
5,38	6,21	15,96	14,27	13,4	4,08

Tasks for the card:

2,145+3,01

105,11 - 8,7

Solve the equations: 1 - x=0.89.

Solve the equation: x+15.35=19.4.

On the first day they sold 12.52 m of fabric, and on the second day another 19.7 m. How much fabric did you sell in two days?

The mass of two heads of cabbage is 10.67 kg, and one of

there are 5.29 kg. What is the mass of the other head of cabbage?

After the word is solved, the teacher draws the students’ attention to slide 22.

The teacher reads the text on the slide.

Fireweed, or fireweed, is a medicinal plant. With the help of fireweed, people overcome many, even the most serious, diseases.

Test work. (8 min) Objectives: test the skill of adding and subtracting decimal fractions when finding the values of expressions and solving equations.

Students listen to the teacher's explanations on how to complete test tasks. Select a certain number of tasks and task numbers. Complete the tasks in the notebook independently within the allotted time.

Personal oud:

1.self-determination,

2. establishing a connection between the purpose of the educational activity and the motive.

Regulatory activities:

1.drawing up a plan and sequence of activities,

2. goal setting,

3.volitional self-regulation, mobilization of strength and energy, overcoming obstacles.

Cognitive focus:

General education:

1.search and selection of necessary information,

3. selection of the most effective ways to solve educational problems,

4.semantic reading,

- universal logical actions:

1.synthesis,

2.analysis,

3. establishing cause-and-effect relationships.

Communication activities:

1. ability to listen.

The teacher draws students' attention to slide 23, slide 24. Organizes independent work of students. Announces that students will work independently in their notebooks. The test sheets are on everyone's desk. Everyone, at will, calculating their strength, chooses to solve certain tasks. If tasks: No. 1 - No. 3 - grade “3”, No. 1 - No. 4 - grade “4”, No. 1 - No. 5 - grade “5”, provided that the tasks are completed correctly. The work will be checked by the teacher after handing in the notebooks after the lesson. The results of the test will be announced by the teacher the next day in class.

5th grade. paragraph 32.

Test work on the topic:

5th grade. paragraph 32.

Test work on the topic:

"Adding and subtracting decimals."

Exercise

Options

answer

Exercise

Options

answer

Find the amount

8,236 + 124,17 =

1) 20,653

2)132,406

3) 132406

4)115,934

Find the amount

5,642 + 10,16 =

1) 15,816

2) 15,802

3) 16,8

4) 15802

Find the difference between the numbers

61,5 - 4,837 =

1) 42,22

2) 13,13

3) 56,663

4) 1313

Find the difference between the numbers

24,3 - 6,742 =

1) 15,342

2) 18,4

3) 17,558

4) 17558

Solve the equation:

5.3 - x = 2.4

1) 29

2) 7,7

3) 3,9

4) 2,9

Solve the equation:

10.8 - x = 6.9

1) 39

2) 5,6

3) 17,7

4) 3,9

Solve the equation:

(x - 8.48) + 2.16 = 3.9

1) 10,22

2) 14,54

3) 2,42

4) 6,74

Solve the equation:

(x - 10.12) + 5.23 = 7.49

1) 12,38

2) 12,8

3) 14,01

4) 13,38

Find the meaning of the expression:

4,7 + (40 - (27 - 3,06)) =

1) 20,76

2) 8,7

3) 16,53

4) 63

Find the meaning of the expression:

6,4 + (53 - (36 -7,94)) =

1) 313,4

2) 31,34

3) 40,16

4) 33,24

Setting homework. (1 min) (25 slide)

Objectives: ensuring children understand the purpose, content and methods of completing homework.

Students open their diaries and write down the homework, listen to the teacher’s recommendations for completing the homework.

Personal oud:

1.readiness for life and personal self-determination.

Regulatory activities:

1.goal setting.

Communication activities:

1. ability to listen.

The teacher asks the students to open their diaries and write down: paragraph 32, repeat the rule of adding and subtracting decimal fractions, No. 1263 (c, d), 1261 / No. 1268 (c) for good students.

Summing up the lesson. Reflection (2 min)

(26, 27 slides)

Students answer the teacher’s questions, think about their attitude to the lesson, select the appropriate emoticon, and drop the selected emoticon into the appropriate file when leaving the classroom. (The files are pinned on the board.)

Personal oud:

2. moral and ethical assessment of the acquired content, based on personal and moral and ethical values.

Regulatory activities:

1.goal setting,

2. assessment.

Cognitive focus:

General education:

3.reflection,

- universal logical actions:

1.analysis

Communication activities:

1. ability to listen,

2.the ability to express one’s thoughts sufficiently fully,

5.ability to participate in collective discussion.

The teacher asks students questions:

Guys, what numbers did we work with today?

What tasks did we have to complete today?

What rules helped you solve problems?

Explain the algorithm for adding and subtracting decimals.

You will receive grades for the work on the card and the test after checking your notebooks.

Today the following grades are awarded for work in class:………….

There are three smiley faces in front of each of you. When you leave your account, you each drop one of the three emoticons into the corresponding file. What do each of the emoticons mean (slide 27): in class to me:

Liked

It was boring

Did not like

Good luck in the Land of Knowledge! (28 slide)

Thank you for the lesson! (29 slide)

The lesson was prepared and conducted by 1st category mathematics teacher I.E. Nikulina. (30 slide)

Technological lesson map

	Stage lesson	Lesson Objectives	Name the use of ESM	Teacher activities	Student activity	Time (per minute)	Formed UUD
	Stage lesson	Lesson Objectives	Name the use of ESM	Teacher activities	Student activity	Time (per minute)	Cognitive	Regulatory	Communication	Personal

1.	Organization ny moment	Create a favorable psychological mood for work.		Greeting students; teacher checking the class's readiness for the lesson; organization of attention; preparing students for activities in the lesson; highlighting the goals and objectives of the lesson.	Students listen to the teacher and look at the screen as necessary, answer the teacher’s questions, They make notes in notebooks.		General education: 1.semantic reading, - universal logical actions: 1. summing up the concept.	1.goal setting, 2. drawing up a plan and sequence of activities.	1. planning cooperation between teacher and students, 2.listening ability	1.self-determination, 2. establishing a connection between the purpose of the educational activity and the motive, 3.readiness for life and personal self-determination
2.	Oral exercises	Updating basic knowledge and methods of action, developing logical thinking; ensuring perception, comprehension, generalization of the studied material, using new information technologies		The teacher, using oral tasks from slides, organizes frontal work with the class. The teacher reads the tasks from the slides and explains how to complete them.	Students listen to the teacher. They think about the answer and raise their hands. One of the students voices the answer with a full explanation, the others listen to the answer of this student. Adjust the speaker's answer as necessary.		General education: 1.search and selection of necessary information, 2.the ability to structure knowledge, construct statements orally, 3. selection of the most effective ways to solve educational problems. - universal logical actions: 1.synthesis, 2.analysis, 3.building a logical chain of reasoning	1.drawing up a plan and sequence of activities, 2. goal setting, 3.control, 4.correction, 5.volitional self-regulation, mobilization of strength and energy, overcoming obstacles	1. raising questions in a team, 2.ability to listen and enter into dialogue, 3.the ability to express one’s thoughts sufficiently fully,	1.readiness for life and personal self-determination, 2. knowledge of moral standards and the ability to highlight the moral aspect of behavior
3.	Exercise	Health saving		The teacher tells the students the physical exercise commands in poetic form.	Students perform movements while listening to the teacher's commands.					1.readiness for life and personal self-determination
4.	Problem solving 19	The teacher informs the students that they will solve problems from the slides, helping various fairy tales heroes. For those who have poor vision, the texts of the tasks are printed on a separate sheet of paper. The teacher reads the text of the problem from the slide, calls one student to the board to solve it, and asks the rest to solve it in their notebooks on their own. For those students who find it difficult to solve, the teacher asks them to solve together with the answering student at the board. Evaluates students who solved problems at the board and independently.	Students solve problems in their notebooks. In turn, 4 students solve 4 problems at the board with full explanation of the decision.		General education: 1.search and selection of necessary information, 2.the ability to structure knowledge, construct statements in oral and written form, 3. selection of the most effective ways to solve educational problems, - universal logical actions: 1.synthesis, 2.analysis,	1.drawing up a plan and sequence of activities, 2. goal setting, 3.correction, 4.volitional self-regulation, mobilization of strength and energy, overcoming obstacles, 5.evaluation	1. ability to listen, 2.the ability to express oneself with sufficient completeness thoughts, 4. proficiency in monologue form of speech	1.readiness for life and personal self-determination, 2.establishment connections between the purpose of educational activity and motive
5.	Exercise for the eyes	Health saving		The teacher asks students to pay close attention to moving elements on the screen.	Students look at the screen, observing the movement of elements on the screen, and listen to calm music.					readiness for life and personal self-determination
6.	Reinforcing the material learned in the lesson. Card work.	Summarizing the material studied, developing cognitive interest in mathematics, using new information technologies and organizing group work for students.		The teacher directs students to group work. Explains how to complete tasks from the card on slide 21.	Students organize work in teams. Complete assignments in notebooks. Having guessed the letter, the children raisehand, they call it. They see letters appearing sequentially on the screen as they guess. Listen to interesting information about the plant and look at its photos.		General education: 1.search and selection of necessary information, 2. the ability to structure knowledge, construct statements in oral and written form, 3. selection of the most effective ways to solve educational problems, 4.semantic reading, - universal logical actions: 1.synthesis, 2.analysis, 3.establishing cause-and-effect relationships	1.drawing up a plan and sequence of activities, 2. goal setting,	1.ability to listen and enter into dialogue, 2.planning cooperation, 3.the ability to express one’s thoughts sufficiently fully, 4.ability to participate in collective discussion	1.readiness for life and personal self-determination
7.	Test work	Test the skill of adding and subtracting decimal fractions when finding the values of expressions and solving equations.		The teacher organizes testing, aiming at multi-level completion of tasks.	Students listen to the teacher's explanations on how to complete test tasks. Select a certain number of tasks and task numbers. Complete the tasks in the notebook independently within the allotted time.		General education: 1.search and selection of necessary information, 2.the ability to structure knowledge, construct statements in writing, 3. selection of the most effective ways to solve educational problems, 4.semantic reading, - universal logical actions: 1.synthesis, 2.analysis, 3.establishing cause-and-effect relationships	1.drawing up a plan and sequence of activities, 2. goal setting, 3.volitional self-regulation, mobilization of strength and energy, overcoming obstacles	1.listening ability	1.self-determination, 2. establishing a connection between the purpose of educational activity and motive
8.	Setting homework.	Ensuring that children understand the purpose, content and methods of performing homework.		The teacher asks students to open their diaries and write down the lesson, taking into account the level of mastery of the topic; gives recommendations for its implementation.	Students write down their homework in diaries, depending on the level of mastery of the lesson topic; listen to the teacher's comments.			1.goal setting	1.listening ability	1.readiness for life and personal self-determination

Summing up the lesson. Reflection.

Evaluate the results of your activities and the entire class.

The teacher asks students questions; evaluates the quality work of the class and individual students; organizes reflection.

Students answer the teacher’s questions, think about their attitude to the lesson, choose the appropriate emoticon, and drop the selected emoticon into the appropriate file when leaving the classroom. (The files are pinned on the board.)

Students hand over their notebooks to the teacher's desk to check the test.

General education:

1.the ability to structure knowledge, construct statements orally,

3.reflection,

4.the ability to adequately convey thoughts in a concise manner,

- universal logical actions:

1.analysis

1.goal setting,

2. assessment

1. ability to listen,

2.the ability to express one’s thoughts sufficiently fully,

4. proficiency in monologue form of speech,

5.ability to participate in collective discussion

1.readiness for life and personal self-determination

2.moral and ethical assessment of the acquired content, based on personal and moral and ethical values

The main purpose of studying the topic “Adding and subtracting decimals”:

Objectives for studying the topic “Adding and subtracting decimals”:

Form a clear understanding of the decimal places of the numbers in question, be able to read, write decimal fractions, add and subtract decimal fractions, use the properties of addition and subtraction, solve word problems involving addition and subtraction, data in which are expressed in decimal fractions.

Requirements for mathematical preparation of 5th grade students when studying the topic

“Adding and subtracting decimals”:

As a result of studying a mathematics course on this topic, students should:

Correctly use terms associated with various types of numbers and methods from the notation: natural, fractional, decimal, etc.;

Perform arithmetic operations with decimals and natural numbers;

Combine oral and written methods when making calculations;

Solve basic word problems;

Round decimals; make estimates of calculations;

Correctly use the terms “expression”, “numerical expression”, “literal expression”, “meaning of expression”, understand their use in the text, in the teacher’s speech, understand the wording of tasks: “find the meaning of the expression”, “simplify the expression”, etc.;

Compose simple letter expressions and formulas; carry out numerical substitutions in expressions and formulas and perform corresponding calculations;

Correctly use the terms “equation”, “root of equation”; understand them in the text, in the teacher’s speech, understand the formulation of the problem “solve the equation”;

Solve linear equations with one variable;

Solve problems on calculating the lengths of segments, the perimeters of a rectangle, square, triangle, using the studied properties of shapes.