Subject: mathematics
Topic: Adding decimals.
Goal: To consolidate skills and acquire skills in solving examples and addition problems
decimal fractions,
develop mathematical thinking, logical thinking, computational
skills, formation of a scientific worldview
Type: lesson - competition
Epigraph: “A person is like a fraction: the denominator is what he thinks about himself,
in the numerator is what it really is. The larger the denominator,
the smaller the fraction." Lev Tolstoy.
During the classes
1. Org. moment. Psychological warm-up “Let’s create a good mood.”
Turning to your neighbor, look at him friendly, with a smile in the eyes and say
together: “Hello, neighbor! "
2. Warm up. Solving fun problems.
1) Ducks were flying: one in front, two behind; one behind and two in front; one between
two and three in a row. How many ducks are there in total? (3)
2) 10 people came to the meeting, and they all shook hands.
How many handshakes were there? (90)
3) The safe code consists of three different numbers: 1,3 and 5. How many different numbers are there?
combinations for the code can be made? (135, 153, 315, 351, 513, 531) .
3. Theorists
1) What notation is called a decimal fraction?
2) What common fraction can be represented as a decimal?
3) Where is the comma placed when writing a decimal fraction?
4) Will the decimal fraction change if or is added to the end of the decimal fraction?
discard zeros?
5) In what ways can you compare decimals?
5) Formulate the rule for adding decimal fractions?
4. Oral work
1) Read the fractions: 16.023; 98.704; 17.027; 9.006; 5.00005; 34.3008.
2) Write down the decimal fractions: 0.9; 0.17; 0.03; 2.315; 3.054 9.207.
3) Find the error: 3.7 + 0.02 = 3.9 5.04 + 1.1 = 5.14 1.2 + 0.3 = 1.23
5. Guess the word.
Card number 1. In Russian, this word appeared in the 8th century, it comes from the verb
“split” - break, break into pieces.
Card No. 2. This unit of length was first introduced by merchants. It was also called “elbow”.
Card No. 3 Birds live on the globe - the infallible “compilers” of the forecast
weather for summer. The name of these birds is encrypted in card No. 3.
Answer key:
6. Cross - survey
1 team
1. The number above the fraction line?
2. Result of subtraction?
4. A number that is neither prime nor composite?
5. Circle tool?
6. Speed times time?
7. Result of division?
8. A natural number that has more than two divisors?
9. Distance divided by time?
10. The result of division?
2 teams
1. A tool for measuring and constructing segments?
2. Result of multiplication?
3. A natural number that has only two divisors?
4. The number under the fraction line?
5. Tool for plotting and measuring angles?
6. The result of addition?
7. The number that is the solution to the equation?
8. Distance divided by speed?
9. The sign that separates the whole part of a decimal fraction from a fraction?
10. A fraction whose numerator is greater than its denominator?
7. Reflection
Summarizing.
Grading.
8. Homework
Page 256 – advanced task.
Topic: Adding and subtracting decimals
Lesson objectives: educational: consolidate and improve skills in performing addition and subtraction of decimal fractions; practicing mental counting skills; check the degree of mastery of the material by conducting a test with verification. developing: development of logical thinking, cognitive interest, curiosity, ability to analyze, observe and draw conclusions. educational: increase interest in studying the subject of mathematics; nurturing independence, self-esteem, activity. Lesson type: lesson to consolidate and improve skills.Equipment: interactive whiteboard, projector, document cameraDuring the classes
1.Emotional mood for the lesson. Children, are you warm? (Yes)Is it light in the classroom? (Yes)Did the bell ring? (Yes)Is the lesson over already? (No)Has class just started? (Yes)Do you want to study? (Yes)So everyone can sit down.2. Lesson motivation. The poet R. Sef wrote “Whoever does not study anything notices nothing. He who doesn’t notice anything is always whining and bored.”And so that you guys don’t get bored in class, everyone should take an active part in the work3. Oral work. 1. Individual work on site (three students work).(Children solve cards independently. Checking is carried out using a document camera)
Exercise 1. Calculate the meaning of expressions in a convenient way.3,875 – (1,3 + 1,875) = (0,75) 8,12 + 1,93 + 1,88 = (11,93) Task 2. Solve the equation 2x – 3.48 = 4.52 (x=4)Task 3. Compare the numbers 4.375 and 4.38; 2.4 and 2.397; 0.67 and 0.599.2. Front work (together with the teacher)Link to presentation Today in class we will continue to work with decimals.
- What do we know about them?
- What are decimals used for?
- How are decimals compared?
4. Graphic dictation (the guys check the correctness of the calculations, the expressions are hidden behind the curtain, the key to the graphic dictation is hidden behind the border of the page)
The answer “yes” corresponds to -, the answer “no”^ 5,48 – 3 = 2,48 0,9 – 0,5 = 0,4 0,28 – 0,04 = 0,24 0,94 – 0,5 = 0,44 0,86 – 0,08 = 0,06 3 – 0,6 = 2,4 5 – 0,3 = 4,7 6,58 – 4,24 = 2,34 7,32 – 2,23 = 5,09 9,38 – 4,3 = 5,8 Key: -- ^ ------ ^ 5. Work on the topic of the lesson. (children solve the problem independently, the solution and answer are written down with a marker on the board, then checked by lowering the curtain)
Working with the textbook Page 193, No. 1216
- Read the problem. How much area did the first tractor driver plow? Is it known how much area the second tractor driver plowed? Read what the problem says about this.
- Which tractor driver plowed more? How much more? What will we learn as the first step? Make a plan to solve the problem. Solve the problem.
Page 193, No. 1224
- Read the problem. How many pieces is the rope cut into? What does it say about the first piece? What is said about the fourth piece? Write down a brief statement of the problem.
- Can we find out the length of the fifth piece? How? What length of the piece can we still find out? What can we find now? The length of which piece is still unknown to us? How to find her? Can we now answer the main question of the problem? Solve the problem.
- How many different triangles do you see? (12) How many quadrilaterals do you see? (8) How many pentagons do you see? (1) Show the pentagon.
Fizminutka
7. Independent work. (Students solve equations independently. To check, they “drag” answers and action signs)
Solve the equationOPTION 1 OPTION 2Y + 0.83 = 1.1 y – 2.7 = 3.4 Y = - y = 3.4 2.7 Y = y = Answer: Answer:
(7.1 – x) + 3.9 = 4.5 3.84 – (x + 0.89) = 2.37.1 – x = 4.5 3.9 x + 0.89 = 3.84 2.3 7.1 – x = x + 0.89 = X = - x = - X = x = Answer: Answer:
8. Homework. (students write down homework)
P. 32; p. 197 No. 1262; p.198 No. 1268 (c,d)
9. Summing up the lesson. Evaluate yourself and draw a conclusion for yourself. “Microphone” principle (students take turns giving a reasoned answer to one of the questions)
- During the lesson I worked actively/passively I am satisfied / not satisfied with my work in class The lesson seemed short/long for me During the lesson I was not tired / tired My mood has become better / has become worse The material in the lesson was useful / useless to me
- Homework seems easy to me / difficult
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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 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:
- Three horses ran 30 km, how many kilometers did each horse run?
- 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?
- There are 10 fingers on two hands, how many fingers on 10 hands?
- Seven brothers have one sister. How many children are there in total?
- 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 signs “+” and “-”
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
Boat's own speed | River flow speed | Boat speed downstream | Speed of the boat against the current |
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 expression in meters of the sum: 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.
Test response codes |
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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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This is a lesson in systematizing and consolidating the material studied. ICT technology is used to comprehensively test students’ educational and cognitive competencies. When practicing the skills of adding and subtracting decimal fractions, independent work with self- and peer-testing is used. The predominant method of organizing educational activities is interactive: comparison, analysis, observation are accompanied by a computer presentation.
The use of ICT technology allows you to develop logical thinking, mathematical speech, promote rapid updating and practical application of previously acquired knowledge, skills and methods of action in a non-standard situation.
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Municipal educational institution
basic secondary school No. 122
Kirovsky district of Volgograd
Subject: "Adding and subtracting decimals"
Prepared by: Saenko Irina Nikolaevna,
Mathematics teacher, Municipal Educational Institution No. 122
Lesson summary "Adding and subtracting decimals."
Class: 5
Goals and objectives:
Create conditions for the development of students’ computing skills, ability
to solve problems.
Tasks: 1. Subject: Promote the development of numerical skills in adding and subtracting decimals
Regulatory: to develop the ability to accept and maintain a learning task;
take into account the guidelines identified by the teacher in the educational material;
Communicative: develop the ability to take part in work in pairs and groups, negotiate and come to a common decision;
Personal: continue to form an idea of the reasons for success in school, develop the student’s internal position at the level of a positive attitude towards mathematics.
Lesson type : lesson - workshop (practicing and testing knowledge on the topic)
Forms of work : assignments are selected so that the work in the lesson has:
Practicing listening comprehension of mathematical speech;
Mutual examination, independent checking by students of their work;
Work in groups of 2 people.
Types of educational activities:
Listening (listening to scientific speech);
Individual work, work in pairs;
Practical tasks;
Speaking;
Mental analysis;
Self-test;
Peer review
DURING THE CLASSES
1. Organizational moment
Hello! Have a seat!
2. Setting the lesson goal (slide 2)
French writer Anatole France once remarked: “You can only learn through fun... To digest knowledge, you need to absorb it with appetite.” Let’s follow this advice from the writer, try to be attentive, let’s “absorb knowledge” with great desire, because it will be useful to you in the future.
(Slide 3) The topic of our lesson is “Adding and subtracting decimals.”
We opened our notebooks and wrote down the date and topic of the lesson.
The study of fractions has always been considered difficult. The Germans have preserved a proverb: “Getting into fractions,” which means getting into a difficult situation. And the task of today's lesson is to prove that fractions cannot put you in a difficult position. We will confidently add and subtract them. I will be glad to see your good answers.
3. Generalization of the material covered (frontal survey) (Slide 4)
Let's remember:
1. How to add decimals?
Answer: To add decimals you need:
c) perform addition without paying attention to the comma,
2. How to subtract decimals? (Slide 5)
Answer: To subtract decimals you need:
a) equalize the number of decimal places in these fractions,
b) write them one below the other so that the comma is written under the comma,
c) perform the subtraction without paying attention to the comma,
d) put a comma in the answer under the comma in these fractions.
4. Oral counting (Slide 6)
8,7 - 1,8 =
6,3 + 2,4 =
7,2 - 2,9 =
9,1 - 3,6 =
2,5 + 1,8 =
8,3 - 1,2 =
5,6 - 3 =
5 + 2,6 =
Solve the equations (Slide 7)
a) 2.5 + x = 7
b) 5 - x = 3.4
c) x - 6.8 = 3.4
d) x + 8.7 = 15
5. Working with the textbook (Slide 8)
Complete task No. 684, No. 692
6. Physical education minute (slide 9)
Now guys, stand up
Raise your hands slowly
Squeeze your fingers, then unclench them,
Hands down and stand like that.
My head is tired too.
So let's help her!
Right and left, one and two.
Think, think, head.
Lean right, left
And get down to business again.
7. Oral work
It is known how important the comma is in the Russian language. The meaning of a sentence can change dramatically if commas are placed incorrectly. For example, “You can’t execute, you can’t have mercy” and “You can’t execute, you can’t have mercy.” In mathematics, the position of the comma determines whether an equation is true or false.
Task: Place commas so that the equality is true (Slide 10)
32 + 18 = 5
3 + 108 = 408
42 + 17 = 212
736 - 336 = 4
63 - 27 = 603
57 - 4 = 17
8. Independent work with self-test in pairs and self-assessment.
(Slide 11)
Students in pairs exchange work and check the work using the answers indicated on the board (slide 12) and rate each other
Option 1 Option 2
1.Follow the steps 1.Follow the steps
0,613 + 32,7 = 0,894 + 89,4 =
5,2 + 317,9 = 241,608 + 24,7 =
0,41 - 0,385 = 6,4 - 2,96 =
62,5 - 8,419 = 50,1 - 9,323 =
2. Solve the equation 2. Solve the equation
Y + 0.83 = 1.1 Y + 3.54 =8.2
3.84 - (x + 0.89) = 2.3 (x - 3.48) + 2.15 = 3.9
9. Lesson summary
What task did we set in the lesson? (confidently add and subtract decimals)
- Do you think we accomplished it?
10.Homework (slide 13)
At home, you will also practice adding and subtracting decimals confidently and correctly by completing the following numbers:
№ 686, № 694
Thank you for the lesson. (slide 14)
