Svetlana Vladimirovna Ternovykh, mathematics teacher
MKOU Berezovskaya secondary school, village. Berezovka
Description of material: I offer a summary of a mathematics lesson in 5th grade.
The lesson notes are intended for mathematics teachers and young professionals. Helps develop students' cognitive interest, test knowledge of the material covered, studying using the textbook Mathematics 5, a textbook for secondary schools, N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Shvartsburg
Lesson topic: Addition and subtraction of decimal fractions (generalization and systematization of knowledge)
Class 5
Lesson type: consolidation of the material covered.
Forms of student work: frontal, individual, group
Lesson objectives:
1.Summarize and systematize the material on the topic “Adding and subtracting decimal fractions.” Enrich knowledge, establish connections between theory and practice.
2.Develop computing skills, memory, thinking and ingenuity.
3.Cultivate cognitive interest in the subject.

DURING THE CLASSES:
I. Organizational moment.
Good afternoon guys!
Teacher: Check your readiness for the lesson. On the desk there should be a textbook, notebook, diary, pencil case with writing materials; carefully place everything on the edge of the table.
II. Motivational start to the lesson.
Teacher: Let's get ready for work. Wish yourself to think clearly, remember firmly and be attentive. Repeat after me:
I really want to study!
I'm ready for successful work!
I'm doing a great job!
Teacher: The motto of our lesson is the following words: Listen and hear, look and see, think and reason.
Teacher: How do you understand the words? What will we develop? What is needed for this?
III. Setting lesson goals.
Teacher: What mathematical concept were discussed in our previous lessons?
Students: About the decimal fraction.
Teacher: Think about what we will do in class?
Students: Summarize knowledge on the topic “Decimal”, repeat the rules for adding and subtracting decimals.

Teacher: Open your notebooks, write the number and the topic of the lesson “Adding and subtracting decimals.”
IV. Verbal counting.
Mathematical football.

V. Updating knowledge.
Teacher: Let’s conduct a short survey and remember the necessary knowledge for the lesson.
1. What fractions can be written as decimals?
2. Read decimals: 131.5; 0.126; 17.29; 1269, 567; 13, 3791.
3. How can you change the number of decimal places in a decimal fraction?
4. Can a natural number be represented as a decimal fraction?
5. How to add decimals?
VI. Formation of skills and abilities.
Teacher: The warm-up showed that the class is ready to travel through the “Land of Decimals.” So, let's begin our journey.
Teacher: First stop “Count the port”
Teacher: We do it in a chain at the board, and the rest in notebooks. Let's find the values ​​of these expressions.
A) 5.1 + 3.687
B) 7.5 + 82.157
B) 8 + 2.6
D) 4.7 + 1620.7
D) 7.9 – 5.623
E) 8.4 – 8.103
Teacher: Our second stop is “Historical Port”
Teacher: (name) has prepared a message about the history of the origin of decimal fractions. Let's listen.
Student message: “In science, industry and agriculture, decimal fractions are used much more often than ordinary fractions. This is due to the fact that operations with these fractions are simpler and resemble the rules for operations with natural numbers. The rules for working with decimal fractions were first described by the famous medieval scientist al-Kashi - Jemshid Ibn Masud at the beginning of the 5th century.
When writing decimal numbers, he highlighted the entire part in red ink or separated it from the fractional part with a vertical line.
In Europe, decimals were reinvented 150 years later by the Flemish engineer Simon Stevin. However, their recording was difficult. The comma in recording decimal numbers began to be used in the 17th century.
Teacher: Thank you. Now let's rest a little.
Fizminutka (musical)
Teacher: Third stop “Mysterious Port”
Teacher: Discuss in pairs a plan for solving this problem. Who wants to come to the board and show the solution to this problem.
Three friends - Kolya, Vitya and Misha - decided to buy a puck that costs 100 rubles. Kolya and Vitya had 37.3 rubles each, and Misha had 24.6 rubles. Will they play hockey in the evening?
Solution:
1) 37.3 +37.3 = 74.6 rub. Vitya and Misha had it
2)74.6 + 24.6 = 99.2 rub. had three boys together.
Answer: They won’t play hockey.
Teacher: Fourth stop “Port Thinking”
Open textbooks No. 1238 (d, f). Solve the equation.
Teacher: Fifth stop “Port of Hope”
To consolidate knowledge, we will do independent work.
Independent work. Independent work.
Option 1. Option 2.
1. Calculate: 1. Calculate:
2,83+(8,7-7,35) 2,31+ (8,93-1.212)
2. Solve the equation: 2. Solve the equation:
a) 17 – x = 0.87 a) 11 – x =7.39
b) 45.6 – p = 13 b) 65.3 – p =27
c) y + 4.837 = 6.5 c) y + 2.109 = 5.9
VII. Summarizing.
Teacher: Sixth stop “Terminal”
Teacher: Let's summarize the lesson.
- So what did we do in class today?
- What goal did we set for ourselves at the beginning of the lesson?
- Have we achieved our goal?
VIII. Reflection.
Teacher: On the desks there are geometric figures that correspond to your grade (triangle - 3, quadrangle - 4, pentagon - 5).
-Evaluate your work in class.
Giving ratings, with comments on each.
Homework: paragraph 32 No. 1262, No. 1265
Thank you for the lesson!!!

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

Lesson No. 108(5/5).

Mathematic teacher Icategories: Nikulina Irina Evgenievna.

The purpose of the lesson: repeat, systematize, consolidate and apply the knowledge and skills of students on this topic.

Lesson objectives:

Educational(formation of cognitive UUD) -

● repeat and consolidate the studied material on the topic “Addition and

subtracting decimal fractions” in the process of solving various tasks;

to form students’ motivation to study the topic;

check students’ knowledge and correct them;

developing(formation of regulatory UUD) -

develop communication skills;

develop readiness for self-education;

develop attention, logical thinking, intuition, mathematical speech, ingenuity, the ability to self-test and analyze one’s mistakes;

educational(formation of communicative and personal UUD) -

cultivate discipline, high efficiency and organization;

cultivate feelings of collectivism, the joy of empathy for the successes of comrades.

Lesson type: lesson in correction and generalization of knowledge.

Equipment: computer, projector, monitor, screen, textbook, notebook, pen, diary, printed sheets with tasks for the lesson for 15 desks, 15 yellow pancakes made of colored paper for the number of the winner of the task: “Who will eat the most pancakes?” and assessments for independent work, 30 questionnaires for reflection.

Lesson format: computer presentation.

Lesson motivation: stimulate interest in studying mathematics.

Techniques:- creating fun and surprise in the lesson;

Creating a situation of success;

Operational control over compliance with requirements.

Lesson plan:

Organizational moment (1 min).

Updating knowledge. Oral work (5 min)

Repetition of basic knowledge (6 min).

Fixing the material. Work in pairs (6 min).

Physical education minute (1 min).

Independent work (6 min).

Solving problems and examples (10 min).

Summing up the lesson. Reflection (3 min).

Setting homework (2 min).

During the classes.

1. Organizational moment. Setting the topic and purpose of the lesson. Record the date and topic of the lesson in your workbooks. (Slide 1)

Today we have an unusual lesson - a holiday lesson. And what kind of holiday we are celebrating today, you will find out when you arrange the numbers in descending order. (Slide 2)

According to Ozhegov’s dictionary: “Maslenitsa is an ancient Slavic holiday of farewell to Winter, during which pancakes are baked and entertainment is held.” The ancients believed that together with a round, rosy, hot pancake, so similar to the sun, they eat a piece of its warmth and power. (Slide 3)

2. Updating knowledge. Oral work.

Monday - meeting.

Monday - On this day

We are not too lazy to meet Maslyana.

The day is called “meeting”

All day from morning to evening.

On this day, they celebrate Maslenitsa, dress up a stuffed doll in old women's clothes, put this stuffed animal on a pole and, singing, carry it on a sleigh around the village. They put Maslenitsa on a snowy mountain and ride down it on a sleigh. They start baking pancakes. (Slide 4)

1) To make it fun to celebrate Maslenitsa, the sun came to visit us. (Slide 5)

Fractions written: 0.24, 0.2400; 0.240; 2.4 and fraction 24/100. Which fraction is the odd one out? (24/100)

2) Find equal fractions among fractions: (Slide 6)

03 2,300 2,003 2,0300

2,30 2,3 2,030 2,0030

3) Compare the numbers: (Slide 7)

20,821 … 20,83;

0,27 … 0,278 .

4) Using one mathematical sign, get a number greater than 3, but less than 4, from the numbers 3;5;6;7: 3 ˂ x ˂ 4. (Slide 8)

Answer: x=3.567.

3. Repetition of basic knowledge.

Tuesday - flirting.

We'll play on Tuesday.

Let's play before the post.

Show yourself to us, Maslyona,

Shchanga, pancake, pie.

In the morning, young people were invited to ride from the mountains and eat pancakes. They called their relatives and friends: “We have the mountains ready and the pancakes baked—we ask you to be kind.” (Slide 9)

1) - Guys, let's review the rules of adding and subtracting decimal fractions in an unusual way! Your classmate will now tell us the rule in poetic form.

To add a fraction with a decimal fraction,
Remember the simple rule:
Write one fraction under another,
The comma should fit under the comma.
For convenience of working with fractions
Equalize the decimal places with zeros.
Now add up those numbers figuratively,
How did you do it in natural numbers?
And the answer tips will be very simple:
Sign the comma under the commas.

Do the same when subtracting decimal fractions.

2) - Guys, do the addition and subtraction of decimal fractions in your notebooks. One student comments on the solutions to the examples. (Slides 10,11)

3) - So Petrushka came to us to play with us. Let's complete the task orally. (Slide 12)

Place a comma in the correct place:

4. Fixing the material. Work in pairs.

Wednesday is a “gourmet”.

Wednesday is reputed to be delicious:

He'll cook it, he'll bake it!

Maslenitsa pleases,

He seats all the guests at the table. (Slide 13)

From that day on, pancakes were baked - yellow, round, hot as the sun. We ate a lot of pancakes. The Russian people ate and made fun of themselves: “The pancake is not a wedge, it won’t split your belly.” On this day, the son-in-law came “to his mother-in-law for pancakes.” In addition to the son-in-law, the mother-in-law invited other guests. (Slide 14)

1) - Let's find out which of the 8 participants in the competition “Who will eat the most pancakes?” will win. To do this, you need to find the meanings of the expressions and choose the highest result among the answers. You work as a couple. After consulting, show me a pancake with the winner’s number. (Slide 15)

Answer: No. 6.

5. Physical education lesson “We became students.”

- Now it's time to get some rest. (Slides 16-18)

We became students.

We follow the regime ourselves:

In the morning, when we woke up,

They smiled and stretched.

For health, mood

We do exercises:

Hands up and hands down

They stood up on their tiptoes;

They sat down and bent over.

And then we washed ourselves,

Dressed neatly.

We had breakfast and, slowly,

We went to school

Striving for knowledge.

6. Independent work.

Thursday - “Wide Maslenitsa”.(Slide 19)

Take a walk - Thursday has come,
From morning to table.
Maslenitsa covered - pancake eater
Will feed everyone until lunch.

Thursday is the most fun day. The people indulged in all sorts of fun: ice mountains, booths, swings, horse riding, carnivals, fist fights, pole climbing. In a word - the height of the festivities. From this day on, Maslenitsa unfolded in all its breadth. People prepare for this day for a long time to make the holiday fun and memorable.

We also studied several lessons on the topic “Comparison, addition and subtraction of decimal fractions.” Let's check what we have learned over these days and do some independent work.

Let's check the independent work. Pick up pencils or a green pen. If the answers are correct, put “+”, if incorrect, then “-”. (Slide 22)

We'll give you ratings. (Slide 23) Write your names and grades on the pancake. Pass the pancakes from the back desks.

7. Solving problems and examples.

Friday is mother-in-law's evening.

Although mother-in-law's pancakes are tasty and sweet,

But mothers-in-law are treated to Maslena by their sons-in-law.

Sons-in-law invited their mothers-in-law to visit and treated them to pancakes.

(Slides 24, 25)

1) Solving a practical problem (slide 26)

In order to bake pancakes for his mother-in-law, the son-in-law bought from the store:
* bottle of milk weighing 0.7 kg,
* 1.5 kg flour,
* 0.75 kg sugar.
He put all his purchases in a 3 kg bag. Will the package hold up?

1) 0.7+1.5+0.75=2.95 (kg) - weight of all products,

2) 2.95kg ˂ 3kg, i.e. will withstand the package.

Answer: yes.

Saturday - sister-in-law's get-togethers.

Wide Maslenitsa

Helps brides

The sister-in-law collects

He treats you to pancakes,

Gives gifts.

Sister-in-law is the husband's sister.
On this Saturday, young daughters-in-law received their relatives. (Slide 28)

Maslenitsa also gifted us with an unusual task. You need to guess the encrypted word. (Slide 29)

Answer: pelican. (Slide 30)

8. Summing up the lesson. Reflection.

The last day of Maslenitsa week was called "Forgiveness Sunday" or farewell. (Slide 31)

Sunday - farewell

And also forgiveness for everyone!

We will ask for forgiveness

Let's kiss one last time.
On this day, a straw effigy is burned - a symbol of winter. The ashes are scattered across the field to ensure a good harvest. They see off the winter until next year. Everyone asks each other for forgiveness for intentional and accidental insults and upsets. They bow at their feet. And in response they hear the familiar words: “God will forgive.” The party ends, fires are lit on the ice slides to melt the ice and destroy the cold. Maslenitsa is leaving, and with it winter. He leaves to the sound of a drop. Spring is coming into its own. (Slide 32)

So, our acquaintance with the Russian folk holiday “Maslenitsa” has come to an end. Let's summarize.

Did you like the Russian folk holiday “Maslenitsa” in mathematical processing?

Remember what goal we set at the beginning of the lesson?

Repeat, systematize, consolidate and apply your knowledge, skills and abilities on the topic: “Adding and subtracting decimal fractions.”

Do you think we achieved this goal?

We did it.

Let's see how everyone did in the lesson?

Grading.

Reflection of mood and emotional state. (Slide 33)

Questionnaire for reflection:

9. Setting homework.

Anyone who loves to learn and be creative never stops at the result achieved! They are always moving forward! And they set new goals. A new task for you: come up with a task with encrypted words for adding and subtracting decimal fractions, but make it interesting and educational. Fill out the task on a scrapbook sheet. This will be your next math project. If difficulties arise, discuss them together. (Slide 34)

Goodbye, Maslenitsa! (Slide 35)

In the Astrakhan Art Gallery named after Kustodiev, you can admire the marvelous paintings of a master from Astrakhan, dedicated specifically to Maslenitsa. Here are some of them. (Slides 36-39)

Thanks everyone for the lesson! (Slide 40)

Bibliography

Chastushki_Babok-Ezhek.www.leopold-baby.com

Technological lesson map

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Lesson summary sent by: mathematics teacher of the highest category, Olga Vasilievna Popovich, secondary school No. 5, Severodonetsk, Lugansk region email: [email protected]

Lesson for 5th grade

Lesson topic: Adding and subtracting decimals. (Journey through the stations of mathematics)

Goals:

• Educational: familiarize students with problems of moving with the flow and against the flow; develop the ability to solve such problems using addition and subtraction of decimal fractions; practice adding and subtracting decimal fractions.
• Developmental: development of cognitive interest, logical thinking. Develop teamwork skills combined with independent work, interest in mathematics, logic and ingenuity, communication and work competence, and broaden your horizons.
• Educational: fostering hard work, accuracy, and developing a communicative culture. Increase responsibility not only for your own knowledge, but also for the success of the entire team. Cultivate curiosity in students.

Lesson progress:

Checking homework. Consultants talk about the results of checking homework.

The class is divided into three teams: three rows. The competition takes place between three teams, but everyone can win at once. When calculating points, speed is not taken into account, only tasks completed correctly are taken into account. Thus, by the end of the competition it may turn out that everyone has the same number of points. This will help maintain a friendly atmosphere in the classroom. But to do this, we need to remind students that they are not competing with each other, but with their knowledge.

For each station, its own guide sheet is opened, the name of the station and the motto are read out. The teacher explains how students will encounter this station during extracurricular activities throughout the school year. The conditions of the competition are described. The tasks are designed for 7 people in a row and are checked immediately in class. You can check completed assignments when the next competition takes place, or you can select consultants before the lesson. Points are calculated regularly and written on the board.

Let's start the lesson with a poem:

Verbal counting! We're doing this thing

Only by the power of mind and soul!

The numbers converge somewhere in the darkness

And the eyes begin to glow!

And there are only smart faces around!

Verbal counting! We count in our heads!

1 station. Verbal counting

Motto:

The one of you is dearer to me than all of you,

Who counts everyone the fastest?

Relay race in rows.

For each row, a sheet is distributed for recording answers in a chain (the relay race begins from the first desk), the previous answer is involved in the next action.

The action is dictated by the teacher (you can prepare a recording on a tape recorder). The example is not recorded on the relay sheet, only the answer is recorded. You are given 10 seconds to solve the example.

Exercise:

Answers:

For each correct answer - 1 point.

2nd station. Geometric figures

Individual work.

A drawing with squares is hung on the board (or drawn on the board):

The work is individual and each student writes down the answer on a card distributed for recording answers (you can distribute the same squares, but in a smaller size, and each will write down their answer in a separate cell).

About 1 minute is given to complete the task (during this time all students must write down their number).

Exercise:

3rd station. Savvy

Motto:

If you use your wits,

The problem can be solved faster.

Work in pairs.

Each pair is given a sheet to write down answers; the solution can be discussed in pairs (a competition can be held in the form of an individual solution). The teacher reads the problems out loud, 15 seconds are given to solve the problem, and students write down the answers.

Tasks:

1. Three horses ran 30 km, how many kilometers did each horse run?
2. A flock of geese was flying: one goose in front and two behind; one behind and two in front; one goose between two and three in a row. How many geese were there in total?
3. There are 10 fingers on two hands, how many fingers on 10 hands?
4. Seven brothers have one sister. How many children are there in total?
5. What is lighter than a kilogram of cotton wool or a kilogram of iron?

Answers:

For each correct answer - 2 points.

Physical education minute. Sujuk.

Historical reference

Mathematicians of ancient Egypt used the signs (legs go) instead of the usual “+” and “-” signs for us.

The doctrine of decimal fractions was first taught in the 15th century by the Samarkand mathematician and astronomer Jemshid ibn Masud al-Kashi. In 1585, the Flemish scientist Simon Stevin published a small book called The Tenth, in which he outlined the rules for working with decimal fractions.

In 1592, they began to separate the whole and fractional parts of the comma.

In the USA, a period is used instead of a comma. Due to the rapid development of programming, the dot is used more and more often

4 station. Gymnastics of the mind

Motto:

Prove your friendship with fractions

Show addition and subtraction.

1.Remember the chain of expressions

2.Solve equations

3. Perform the action, choosing the most rational course of action

1). 3,3+(0,7+5,2); (9,2) 2). 3,3+5,9+0,1 (9,3);3). 3,3-(0,1+0,3) (2,9);

4. Calculate in meters

1). 5.2m-3cm;

2). 5.2m-3dm;

3). 5.2km-3m;

(1m=100cm; 5.2m-0.03=4.77;)

(1dm=10cm; 5.2m-0.3=4.9m;)

(1km=1000m; 5.2-0.003=5,197;)

According to the calculations of modern cybernetics and mathematician von Neumann, it turned out that the brain can accommodate approximately 1020 units of information. This means that each of us can remember all the information contained in the millions of volumes of the world's largest Library.

Working with the textbook. Look at the cover of the textbook, where we will look at tables of large numbers.

5 station. Movement

Motto:

Everyone, young and old, should know

Main characteristics of movement:

Distance-S

Speed-V

Formula S = V t

Movement along the river

Own speed V – speed in still water of the lake

Flow speed V t

Speed ​​along the current V by t. Vby t.=V+Vt.

Speed ​​upstream Vagainst t.Vagainst t.=V-Vt.

V t = (V along t. + V against t.) : 2

Solution of exercises: No. 841.843,858(2),860(3),865(1).

Exercise for the eyes.

6 station. Test

Motto:

You solve test problems

Prove your skills

Mutual verification.

Option 1

1. Which of the mixed expressions are given by (y g) Sum:

2m 28Kg, 1G 5kg, 5g 4y.

1)8.568g; 2)8.73g, 3)8.433g; 4)8.326g.

2.Find an equation whose root is the number 10.

1)x-2.093=0.207; 2)2.093x=0.207; 3)12.903x=2.093; 4)x+2.093=12.93.

3.Which of the given numbers is equal to the difference 10-0.090908?

1)9,010101; 2)9,909092; 3)9,090902; 4)0,919192.

4.Which of these numbers is equal to the sum of the roots of the equation x-1.048=0.9094 1.005-x=0.044

1)2,92; 2)1,19; 3)1,2; 4)2,91.

5. Which of the pairs of numbers is the value of the boat’s own speed and the speed against the current, if the speed of the river is 2.3 km/h, and the speed of the current is 18.1 km/h.

1)16.2 and 13.9; 2)15.8 and 13.5; 3)20.44 and 18.1; 4)20.44 and 22.7.

Option 2

1.Which of these expressions is equal to the sum expressed in meters: 7m 5dm, 3m 7cm and 2m 88mm.

1)12.955m; 2)12.658m; 3)12.838m; 4)14.08m.

2.The root of which of the given equations is the number 2.005.

1)x+1.195=3.22; 2)3.2x=0.195; 3)2.005x=0; 4)1.005+x=2.005.

3.Which of these numbers is equal to the difference 4-2.9996?

1)2,9994; 2)2,0004; 3)1,9994; 4)1,0004.

4.Which of the given numbers is the sum of the roots of the equations.

x+5.4=10.31 and x-3.8=8.9 accurate to units.

1)17; 2)18; 3)17,6; 4)16.

5.Which of the given pairs of numbers is a record of the values ​​of one’s own speed and the speed along the river flow is 2.6 km/h, and the speed against the flow is 17.2 km/h.

1)14,6 and 12; 2)19.8 and 22.4; 3) 19.8 and 14.6; 4)19.8 and 17.2.

Summarizing

Then the points are counted and the winner is determined. At the end of the lesson, reward each team: for winning (competition winners), for quickly counting and solving problems (fast accountants), for drawing up a tangram and a beautifully composed drawing (artists). Remind that there will be another meeting with each of the stations during the school year.

The reader or teacher ends the lesson:

Homework:842,859(1),854. 865(3,4)n.30

The century continues.

And another century is approaching.

Along the flint steps

Climbing to dangerous heights,

Never, never, never

The person won't give it back

Of your superiority

The smartest machines.

Lesson summary "Adding and subtracting decimals. Traveling through mathematics stations"

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