Revision on the topic of decimals. Summary of the mathematics lesson "actions with decimals"

Lesson topic: "Decimal fractions and operations with them."

Lesson objectives: to repeat and systematize students’ knowledge and skills on the topic “decimal fractions”, to determine the level of knowledge acquisition on this topic, to check the degree of mastery of the material; develop attention, memory, speech, logical thinking, independence; cultivate the desire to achieve goals, a sense of responsibility, self-confidence, and the ability to work in a team.

Lesson objectives: Show the importance of practicing computational skills at this stage of training. Stimulate students' motivation to study mathematics;

Lesson type: lesson on generalization, systematization and correction of knowledge and skills on the topic: “Decimal fractions”

Forms of student work: frontal, group, individual

Equipment: laptop, presentation, test on the topic “All operations with decimals”, task cards, a set of signal cards for each student (red, green, yellow).

Lesson progress

Organizational moment.

Hello guys!
Please take your seats.
Today is February 13th,
Day of the week – Friday
Today we will spend
The lesson is this
which will be dedicated
One interesting person.
Listen to me carefully
Answer the questions
That's it, guys, take note.
Don't forget anything
Please don't let me down.

Come on, my young friend,

Are you ready to start the lesson?

Is everything okay on the table?

Is there order in your head?

To have knowledge

It will take patience and effort.

Lesson motivation.

We studied fractions for a long time,
Compare, round,
Added, subtracted,
Multiplied and divided
The arithmetic mean was found.
And now the time has come
To check everything with you.
How do you solve problems?
Multiply the fraction by ten
How do you solve equations?
Do you know many examples?
We will check everything with you
And at the end we give an order:
Or give you an A, or teach you to send you away!

And to cope successfully we must:

Answer questions asked clearly and concisely;

Quickly and correctly calculate proposed tasks;

Provide assistance in work;

Be able to listen to others, etc.

Lesson motto: Have excellent knowledge on the topic “Decimal Fractions!”

3. Historical background slide 3-5

4. Updating basic knowledge

a) Game “Chamomile”. The goal of the game is to repeat the rules that will be required when solving problems.

(A chamomile flower is attached to the board using a magnet, with questions written on each petal. Opening the petal, the student answers the question posed):

Rules for adding and subtracting decimals

Rules for multiplying decimal fractions by 10, 100, 1000:.

Rules for dividing decimal fractions by 10, 100, 1000:.

Rules for multiplying decimals by natural numbers

Rules for multiplying decimals by decimals

Rules for dividing decimal fractions by natural numbers

Rules for dividing decimals by decimals

Rules for comparing decimal fractions

b). And now oral calculation will be useful to us.

“Health is not everything, but everything without health is nothing.” Socrates

5. Consolidation of acquired knowledge. Work in notebooks.

Assignment for students.

1. Mathematical dictation

Students write down only their answers on pieces of paper.

1) 24,04: 2= 12,02

2) 1.3 1.5 + 1.5 1.7 = 4.5

3) 8,07 + 4,1 = 12,17

4) 1,28 +3,4 +1,72 -2,4 = 4

6) 0.7 · * =0.007 (instead of * put a number to get the correct equality) 0.01

7) 7.8 · 3.5 – 7.8 · 3.4 =0.78

8) 2,54: * = 2540 = 0,001

9) 9,6: 100 =0,096

2). Correct answers:

Students exchange papers and give marks

Arrange the letters in the table according to the answers.

2) The clown came up with several examples of adding, subtracting and multiplying decimal fractions, and to make it funnier, he erased the commas in them. Here are the equalities he came up with:

34 * 0,01 = 0034

Putting commas in the right place

3) Solve problems:

1. On Monday, 37.6 tons of grain were threshed, on Tuesday - 3.8 tons more than on Monday, and on Wednesday - 1.5 times less than on Tuesday. How many tons of grain were threshed in these three days?

2. The tourists walked to the river at a speed of 6.6 km/h, and along the river bank at a speed of 4.2 km/h. In total they walked 9.06 km. How long did the tourists walk along the shore if they walked 0.8 hours to the river?

6. Physical education minute

In class we wrote,

They answered everything they knew.

Now we'll rest

And let's start writing again!

Having relieved the tension that had accumulated while solving the problem and equations, let’s continue working in the notebook.

7. Test on the topic “Addition, subtraction, multiplication, division of decimals”

Now let's test our knowledge with a test.

Option 1

1) Perform addition:

2) Do the multiplication:

3) Find the value of the quotient:

Additionally:

Find the meaning of the expression:

4,36: (3,15 + 2,3)

Option 2

1) Perform addition:

2) Do the multiplication:

3) Find the value of the quotient:

Additionally:

Find the meaning of the expression:

6,93: (0,028 + 1,512)

Key to the test:

1) 2) 3) Add.

I. option B) A) B) C)

II. option A) B) C) C)

We check the work ourselves. Next to each task we put a “+” or “–” sign.

Let's evaluate the result

Evaluation criteria:

“5” – 5 tasks; “4” – 4 tasks; “3” – 3 tasks.

Show with the help of a signal card which score you received: “5” – red, “4” – green, “3” – yellow.

8. Work in pairs

Follow the steps. Cross out the answers and the letters corresponding to them in the table. The remaining letters will allow you to read the word.

1) 5,8 + 22,191=

2) 6.025 x 5.6 =

3) 1.15 x 0.4 =

5) 131,67: 5,7 =

1,4 23,1 0,46 2,11 0,14 0,4 27,991 3,4 33,74 27 8,22 2,6

M P Y O Z L O V D E C

Answer: the word WELL DONE

9. Homework:

Well done to all of you!
You are all daredevils!
And let my beloved for years
Math will always be there for you!

Repeat steps 22-37. Solve tasks No. 1317, 1321, 1333

Come up with and beautifully draw up a problem on a landscape sheet that could be solved using addition and subtraction of decimal fractions, write down the condition of the problem on a piece of paper and draw a picture based on this condition, and write down its solution in a notebook. Try to ensure that the students in the class like your task so that the data in the condition corresponds to reality.

10. Lesson summary. Reflection. Microphone principle. (Students take turns giving a reasoned answer to one of the questions).

I enjoyed my lesson today...

Today in class I repeated...

Today in class I reinforced...

Today in class I graded myself...

What types of work caused difficulties and require repetition...

What knowledge are you confident in...

Did the lesson help you advance in your knowledge, skills, and abilities in the subject...

Who needs more work, on what...

How effective was the lesson today...

The work is used for display on the screen using a multimedia projector.

Subject : operations with decimal fractions.

Lesson objectives:

Creating a favorable, friendly environment.

1. consolidate the operations of addition, subtraction, multiplication, division by natural numbers.
2. develop logical thinking, attention, memory
3. cultivate kindness, independence, teach mutual assistance.

Lesson progress

1. Organizational moment.

The teacher introduces himself. (slide 1) “Hello guys. My name is Tatyana Ivanovna. I heard that you have the most inquisitive and friendly children in your class. And I really wanted to get to know you better. And good old fairy tales will help us with this.

Hurry up because the days are passing

You are visiting a fairy tale again

Don't count on help

Remember: everything is in your hands.

And I would like the last lines to become the motto of all our work.

Teacher: “Guys, do you believe in wizards? I believe it.

And today a kind sorceress will come to visit us (slide2) for our good work the sorceress promised to give everyone a gift.

2. Oral work:

To do this, we need to solve examples. (Slide 3). Guys, each row has its own task. But to complete it, you must pay attention to the number that is attached to your desk. This is the number of your example.. Having received the answer, find it in the alphabet a letter that corresponds to this example. And only by collecting all the letters together will you guess who came to us. Now we will find out whose row will complete the task faster. Check (slide 3, click)

Teacher: “Well done guys! Cartoon characters came to visit us (slide 4)

3 . Repetition of what has been covered.

Music plays (slide 5), Dunno appears (click on slide 5)

Teacher: “Guys, Dunno was in a hurry to come to our home. I wanted to show that he knows how to add and subtract decimal fractions. (Slide 6) But he got caught in the rain and the droplets washed away all the commas from the assignments. I heard that you are very attentive and kind. And I think that you can help Dunno place the commas.

We successfully completed the task. Look how happy Dunno is.

Oh, and someone else came to visit us.

Teacher: “Music sounds (slide 7) and Winnie the Pooh appears (click on slide 7)

Teacher: “This is Winnie the Pooh. He is a big fan of solving interesting examples and also brought us unusual examples. Shall we show him how we can solve examples?

Students complete the task independently, then change sheets and check the answers on the slide. (slide 8)

And Winnie the Pooh is a big fidget and he prepared an unusual warm-up for us as a gift. Get up from your seats. Don’t say yes and no, but show with your hands. (slide 9)

Well done.

And another guest is already rushing to us. Who is he? Pinocchio really loves difficult tasks. And he prepared a test for you. Having solved each task, circle the letter of the answer option. By putting together a word from the letters, you can find out how each of you worked today? (time to work)

Well? How did the guys do in the first draft? What about the second option?

Our road was difficult

But you coped with it, friends.

What talented kids!

I see in the ninth school.

And here is our sorceress. (slide 10), (slide 11)

5 Relaxation.

Guys, I leave you in a very good mood. Show me and with What mood are you leaving in?

I give you these funny faces. And I hope that you will always go to mathematics lessons with this mood.

Thanks for the interesting introduction.

Student workbook.

(fragment of a workbook for one lesson)

Cool job.

Solving problems using equations.

№1

4x + 3x = 77,

7x=77,

X=77:7,

X=11.

Answer: x=11.

19x-3x+5=133,

16x+5=133,

16x =133-5,

16x=128,

X=128:16,

X=8.

Answer: x=8.

№2

(7+8)*a=7a+8a

(r-12)*5=5r-60

3v-12=(v-4)*3

(v-7)*3=3v-21

№560

3a +17+ 3a +14=6a+31

k +35+ 4k +26=5k+61

№574

Let the mass of one part be x kg

Water – 7 kg

Milk fat – 2 kg 4400 kg

Sugar – 2 kg

Let's create and solve the equation:

7x+2x+2x=4400,

11x=4400,

X=4400:11,

X=400

400 kg – mass of one part.

7*400=2800(kg) – mass of water

2*400=800(kg) – fat mass

2* 400=800(kg) – mass of sugar

Answer. 2800kg, 800kg. 800kg.

Math lesson in 6th grade. (FSES)

Subject.Operations with decimal fractions. Repetition.

Lesson type. A lesson in generalizing and systematizing knowledge on the topic “Decimal Fractions”, repeating what was learned in 5th grade.

Goals: formation of UUD.:

Personal.

Respect for the individual and his dignity,

stable cognitive interest,

the ability to conduct dialogue on the basis of equal relations and mutual respect,

sustainable cognitive interest;

Subject.

Read decimals, compare decimals, add and subtract decimals, use commutative and combinational laws in calculations, multiply decimals, use commutative and combinational laws in calculations, use division of decimals in problem solving

Metasubject. Formation of universal educational actions.

Regulatory UD.

Set goals for activities in the lesson,

Plan ways to achieve the goal;

Make decisions in problem situations based on negotiations;

Cognitive UD.

Possess general techniques for solving problems, performing tasks and calculations;complete tasks based on the use of the properties of ordinary fractions.

Communication UD. Use speech adequately to plan and regulate your activities,formulate your own opinion, argue and coordinate it with your partner’s position.

Formation of meta-subject universal educational activities.

Regulatory

Cognitive

Communication

I Organizational stage

Motivation for studying the lesson topic

Goal setting

Teacher's opening speech.

What fractions are we studying?

What actions can we perform with them?

The teachers are listening.

Answer questions.

Under the guidance of the teacher, lesson goals are set.

They plan ways to achieve them.

Repeat previously acquired knowledge.

children name familiar concepts.

Children offer possible answers.

Students express their opinions.

They learn to behave correctly, listen to the teacher, raise their hand, listen to a friend.

Express their thoughts orally.

II. Repetition. Oral counting

The task is to calculate examples orally. We monitor the answers of classmates and signal with cards (with natural numbers and decimal fractions)

Students learn to control their actions.

They learn to adequately assess the correctness of actions and make the necessary adjustments as the actions progress.

Students complete assignments and check the correctness of their answers.

Monitor actions

III. doing exercises.

Listen, write down.

Analyze the conditions of this problem, comment on the initial and final data.

Students remember and answer.

They adequately use speech to plan and regulate their activities.

IV. oral work

Performing oral exercises and working from ready-made drawings

Children express their opinions.

They make a decision based on negotiations with the teacher.

Children look for answers to questions posed by the teacher

They learn to listen carefully to a friend and respectfully accept his point of view.

VI. problem solving

Independently analyze ways to solve the problem. Complete tasks in a notebook.

Calculate in notebooks.

Check for correct execution.

Plan general methods of activity. Establish a working relationship as a couple

Exercise control. correction of the partner's actions.

VI I. Reflection

What new did you learn in the lesson?

What did they repeat?

What did you remember?

What caused the difficulties?

What hindered, what helped?

They learn to adequately assess their capabilities in achieving goals and the level of implementation of assigned tasks.

Students analyze their activities in the lesson.

Adequately use linguistic means to display their thoughts and feelings, motives for actions.

VI II . Information about homework, instructions on how to complete it

The teacher offers homework.

№14, 15, 25

The teacher gives grades. Thanks for your help with the lesson

The guys write down their homework.

Each correspondent introduces himself and asks a question.

Correspondent for Kolobok magazine.

Question 1. Readers of the magazine ask if it is true that there are some magic rules for dividing and multiplying by 0.1; 0.01; 0.001, etc. What are they?

Question 2. The editor received a letter from friends of Winnie the Pooh. They are worried about whether their friend, who bought 12 jars of jam for his birthday and invited Piglet to visit, will get sick. But Piglet eats jam 1.4 times slower than Winnie the Pooh. How many jars of jam will Piglet eat and how many will Winnie the Pooh eat on this day? Help Winnie the Pooh.

Solution: Winnie the Pooh - ?

Piglet - ? 1.4 times less

Let Piglet eat X cans

1.4x + x = 12

2.4x = 12

x+12: 2.4

x = 5 1.4 5 = 7

Answer: Piglet will eat 5 cans, Winnie the Pooh will eat 7 cans.

Correspondent for Dengi magazine.

Question 1. Each state has its own monetary unit. In Russia it is 1 ruble, in the USA it is 1 dollar. 1 kopeck – 0.01 ruble; 1 cent – ​​0.01 dollar. People often have to exchange money from one state for money from another. Now our banks give 28.8 rubles for 1 US dollar. How much Russian money should you pay for 10, 100, 1000 dollars?

(288 rubles; 2880 rubles; 28800 rubles)

Question 2. How much will a computer cost in Russia if it costs $2,000 in America?

Solution: 28.8 2000 = 57600 (rub.)

Answer: in Russia a computer will cost 57,600 rubles.

Correspondent for “Around the World” magazine.

Help young geographers from the Planet club solve the following problems:

Question 1. The highest peaks in Europe are Elbrus and Kazbek in the Caucasus and Mont Blanc in the Western Alps. The height of Elbrus, and Mont Blanc is 0.835 km lower than Elbrus. What is the height of Kazbek, Mont Blanc?

Solution: Elbrus - ? 5,642 km.

Kazbek - ? 0.609 less than Elbrus

Mont Blanc - ? 0.835 less than Elbrus

5.642 – 0.609 = 5.033 (km) height of Kazbek

5.642 – 0.835 = 4.807 (km) height of Mont Blanc

Answer: the height of Kazbek is 5.033 km, the height of Mont Blanc is 4.807 km.

Question 2. A flock of birds, flying away for the winter, flew for 2 hours at a speed of 50.4 km/h and for 3 hours at a speed of 52.3 km/h. Find the average speed of movement of the flock during these 5 hours.

Solution: 1) 2 * 50.4 + 3 * 52.3 = 257.7 (km) distance in 5 hours.

2) 257.7: (2+3)= 51.54 (km/h) average speed

Answer: The average driving speed is 51.54 km/h.

4) Correspondent for the magazine “Man and the Law”

Question 1. Readers of the magazine know the legal laws of our state well. They would like to know whether the commutative and associative laws of multiplying decimals are fulfilled in mathematics?

Give examples.

Question 2. Recently at customs, during an inspection of a man’s personal belongings, a palette from an unknown artist was discovered. The customs officers are asking you guys to decipher the artist's name in order to find out what value the painting is.

0,31 1,09 600

T I N

0,89 535 40,37

WEIGHT

0.5 + 12.38 + 11.5 + 7.62 + 8.37 (40.37 – C)

1.55:5 (0.31 – T)

7 * 0.3 – 1.01 (1.09 – I)

3.875 * 10.35 *0 * 5 + 0.89 (0.89 – V)

0.535 * 100: 0.1 (535 – E)

4.99: 0.01 + 101 (600 – N)

5) Correspondent for the magazine “Funny Pictures”.

The magazine's readers are small children. Often in their letters they ask us to talk about fractions. What do you guys know about them?

Nikiforova Marina Nikolaevna

mathematics teacher, Secondary School No. 1968, Moscow

Summary of a 6th grade math lesson on the topic

"Repetition: operations with decimals"

Goals: repetition of operations with decimal fractions.

Equipment:

computer multimedia projector, screen, presentation created in Power Point

Progress of the lesson.

1. Organizational moment (1 min.)

1. Oral exercises ( 4 min.)

Solution of exercises. (12 min.)

Gymnastics for the eyes (1 min.).(Slide No. 10)

Solution of exercises (12 min.).

3.8 - 2.736: 0.76 + 0.04 0.45

1 option

1) Subtraction

2) Division

3)Multiplication

4) Addition

Option 2

1) Division

2)Addition

3)Multiplication

4) Subtraction

Option 3

1)Addition

2) Division

3)Multiplication

4) Subtraction

Option 1

(3.8 - 2.736) : 0.76 + 0.04 0.45

2. 0.04·0.45=0.018

Option 2.

3.8 – (2.736: 0.76 + 0.04) 0.45

1)2,736:0,76=3,6

3)3.64·0.45=1.638

4)3,8-1,638=2,162

Option 3.

3.8 - 2.736: (0.76 + 0.04) 0.45

2)2,736:0,8=3,42

3)3.42·0.45=1.539

4)3,8-1,539=2,26

Physical exercise (1 min.).(Slide 13).

Solving problems. (11 min.) (slide No. 14)

1) 1500·1.8=2700 (m) - the distance that the sound traveled to the bottom and back. 2)2700:2=1350(m) Answer: 1350 m – sea depth.
1) 11.022 2 = 22.044 (km) = 22044 (m) - the distance that the sound traveled to the bottom and back. 2)22044:1500=14.696≈14.70(s) Answer: 14.70 s – time measured by echo sounder.

1. Reflection. Summing up. (2 min.) (slide No. 15)

IX. Homework.(1 min.)(slide No. 16)

Literature (slide No. 17):

Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics: Textbook. for 5th grade general education. institutions - M.: Mnemozina, 2006. Shevrin L.N., Gein A.G., Koryakov I.O., Volkov M.V. Mathematics: textbook - interlocutor for 5th grade of general education institutions - M.: Prosveshchenie, 2001. www fsu expert ru node page http://matroskin.su/ http :// office . microsoft . com / ru - ru / images / results . aspx ? qu =% D 0% BE % D 0% B 1% D 0% B 5% D 0% B 7% D 1%8 C % D 1%8 F % D 0% BD % D 0% B 0& origin = FX 010132103# ai : MM 900040925| http :// office . microsoft . com / ru - ru / images / results . aspx ? qu =% D 0% BE % D 0% B 1% D 0% B 5% D 0% B 7% D 1%8 C % D 1%8 F % D 0% BD % D 0% B 0& origin = FX 010132103# ai : M.C. 900426420| http :// office . microsoft . com / ru - ru / images / results . aspx ? qu =% D 0% B.F. % D 1%82% D 0% B 8% D 1%86% D 0% B 0# ai : MM 900236249 http :// korabli . ucoz . ru /_ miranimashek . ucoz . ru / photo /100-0-14848 miranimashek . ucoz . ru / photo /100-0-10371 miranimashek . ucoz . ru / photo /100-0-1531 http :// go . mail . ru / frame . html ? q =% EF % E 5% F 7% E.A. % E 8% ED & rch = e & jsa =1& sf =0& cf =5& is =0& type = all # cf =5 http :// go . mail . ru / frame . html ? q =% E 4% FF % E 4% FF %20% F 4% E 5% E 4% E.E. % F 0& rch = e & jsa =1& sf =0& cf =3& is =0& type = all # cf =3