Lesson type: consolidation of the studied material.
Lesson Objectives:
To form the skills of finding GCD with the help of decomposition into prime factors, to solve problems with the help of GCD.
To form the ability to independently check the correctness of the task.
Raise the level of mathematical culture.
Build an interest in mathematics.
Develop students' logical thinking.
Teaching aids: personal computer (work in the POWER POINT environment), interactive whiteboard. (Presentation)
During the classes
I. Organizational moment.
Hello guys! Check if everything is ready for the lesson: diary, textbook, notebook, pen. Drafts, for those who find it difficult to calculate in the mind.
II. The message of the topic of the lesson and the purpose.
What did we do in the last lesson? (We learned to find the greatest common divisor). Today we will continue to work with the greatest common divisor. The topic of our lesson is “Greatest Common Divisor”. In this lesson, we will find the greatest common divisor of several numbers, and solve problems using the knowledge of finding the greatest common divisor.
Open your notebooks, write down the number, class work and the topic of the lesson: “Greatest Common Divisor”.
III. oral work.
So, let's stir up your gray cells and answer the question: "Is the statement true?". You need to explain your answer. (slide 2)
A prime number has exactly two divisors. (Yes, one and this number itself)
A composite number has one divisor. (No, since a composite number must have more than 2 divisors)
The smallest two-digit prime number is 11. (Yes, 10 is composite)
The largest two-digit composite number is 99. (Yes, it is divisible by 1, 3, 99. And the next number is three-digit).
Some composite numbers cannot be factored into prime factors. (No, any composite number can be factored into prime factors)
The number 96 is prime. (No, it is divisible by 1, 3, 96 - 3 divisors - a composite number)
The numbers 8 and 10 are relatively prime. (No, there is a common divisor of 2)
IV. Doing exercises.
Check if the decomposition into prime factors is correct. (No, the number 10 is composite, and we factor it into prime factors. 10 can be replaced by the product of prime numbers 2 and 5). (Slide 3)
Find the error. (The number 9 is composite). How do you find the greatest common divisor? (Slide 4)
What is wrong? (The numbers 28 and 21 have one common divisor - 7). (Slide 5)
Find the greatest common divisor of the numbers 72, 54 and 36. Performing the task, we pronounce each stage. We work at the blackboard in notebooks (Slide 6)
GCD (72, 54, 36) = 2*3*3 = 18
Are the numbers 64 and 81 relatively prime?
gcd (64, 81) = 1
Answer: The numbers 64 and 81 are coprime.
V. Problem solving.
Solve the problem. (At the blackboard and in the notebook)
For first-graders, 270 felt-tip pens and 675 pencils were bought. What is the largest number of gifts that can be prepared so that they contain the same number of felt-tip pens and the same number of pencils? How many felt-tip pens and pencils will be in each gift? (Slide 7)
Felt pens - 270 pcs. PC. in 1 p.
Pencils - 675 pcs., by? PC. in 1 p.
Total gifts - ? PC.
1) 3 3 3 5 \u003d 135 (p.) - they will cook
2) 270:135=2 (f.) - in 1 gift
3) 675:135=5 (k.) - in 1 gift
Answer: 135 gifts, 2 markers, 5 pencils.
VI. Fizminutka.
Sit equally. Put your hands behind your back. Without turning your head, look at the window, at the stand on the opposite side, up, at the desk, at the blackboard. Close your eyes, imagine blue sky. Open your eyes. Put your hands on the table. Let's continue...
Next task.
In the depot, 2 trains were formed from identical cars. The first - for 456 passengers, the second - for 494 passengers. How many wagons are in each train if it is known that the total number of wagons does not exceed 30? (Slide 8)
1 train - 456 passengers, ? vag.
2 train - 494 passengers, ? vag.
Total number of wagons< 30 шт.
1) 19 2 = 38 (m.) - in each car
2) 456:38=12 (v.) - in 1 composition
3) 494:38=13 (v.) - in the 2nd composition
Check: 12+13=25 (in.)
Answer: 12 wagons, 13 wagons.
VII. Independent work.
When completing assignments in independent work, do not forget about the signs of divisibility and other rules. Good luck! (Slide 9)
Hand over your notebooks. Now we will check if you completed the tasks correctly. (Analysis of the mistakes made.) (Slide 10)
VIII. Homework
Let's write down the homework, and then summarize the lesson. So, open your diaries and write down your homework:
p. 6 p. 21, No. 161, 182, 192 (oral). (Slide 11)
IX. Summarizing.
What is our goal today? (Learn to solve problems by finding GCD).
What numbers are called coprime?
How to find NOD?
Who should be recognized for good work? (Grading for work in the lesson)
Type of work -working out the technique of drawing and displaying object images.
Target: PC 2.5 organize the productive activities of preschoolers (drawing, modeling, applique, design; PC 2.7 analyze the process and results of organizing various types of activities and communication of children; OK 2 organize their own activities, determine methods for solving professional problems, evaluate their effectiveness and quality; OK 5 use information and communication technologies for the improvement of professional activity.
The assignment is scheduled for 3 hours.
Task: Using an Internet resource (methodological guide, see "Catalog of Internet Resources"), get acquainted with the technique of drawing various images. Practice the technique of showing 3-4 images of birds and animals.
In the process of developing the display technique, it is necessary to use a vertically placed sheet of A3 paper, gouache paint, and a brush. Sketch 3-4 images in the manual using gouache, colored pencils and felt-tip pens.
Prepare to demonstrate the technique of showing birds and animals in a practical lesson outside of the GCD (you can use a weakly drawn outline with a simple pencil).
Reporting form: drawn images and readiness for practical demonstration (samples in the "Pedagogical piggy bank").
Criteria for evaluation:
The quality of the resulting image (recognizability of the image, compositional correspondence to the sheet and paper);
· Verbal accompaniment;
· The process and result of the show should be clearly visible to children.
Possible tasks that allow you to study the features of the pedagogical conditions for the artistic and aesthetic development of preschoolers that exist in the practice of preschool educational institutions
Type of work:
Parent survey: in order to identify their ideas on the problem of artistic and aesthetic development of preschoolers.
Conclusion:
Questionnaire for parents
Dear Parents ________________________ (child's name)
Please answer the questions in the questionnaire.
Your sincere answers will help to study the problem most deeply and outline ways to improve the pedagogical process of the kindergarten.
1. In your opinion, at what age is the purposeful artistic and aesthetic development of a child necessary?
2. From your point of view, the artistic and aesthetic development and education of children, to a greater extent, should be directed to (select the statement that suits your opinion):
Developing the ability to feel beauty, respond to beauty
Formation of some art history knowledge
Developing an interest in art
Development of interest in creative leisure, crafts (embroidery, weaving, design)
Mastering productive activities (sculpt, draw, design)
Self-expression, expression of emotions, feelings
Creative experience
Experience in working with different materials (sand, clay, sanguine, coal, etc.), experimenting with them;
Development of certain qualities (independence, organization, ability to plan activities)
Another variant_____________________________________________________________
3. What kinds of productive activities for children are most interesting for your child (mark with a + symbol)? Do you consider it mandatory for preschool attendance (mark with a v)?
Drawing
Application
Artistic work (embroidery, weaving, etc.)
Construction and design
Comments
4. What direction of design activity is more preferable for you (in the development of decorative activity in your child and are you ready to participate with him)?
Painting toys in the style of folk crafts
- “designing” puppet and carnival clothes
Making postcards, bookmarks, etc.
Decoration of items (boxes, vases, disposable cups, etc.) and making simple items (key rings)
Making a patchwork doll, etc.
production of New Year's toys, Christmas tree layouts, costumes
production of city layouts, insolations, unusual souvenirs
Layout decorations visiting for the holidays (garlands, etc.)
Your choice ___________________________________________
5. Does your child often draw, sculpt, construct?____
6. Does your child often pay attention to the “beauty” in the world around him (natural objects, beautiful little things in everyday life, etc.) ______ ____________________________________________
7. Does the child use interesting words (figurative comparisons, exaggerations, comparative forms) when he sees something beautiful or ugly (Name typical or favorite) ______________________________________________________________
8. How does a child typically behave when he notices something beautiful?
9. What is the manifestation of your child's desire for beauty?_________________________________________________________________
10. Does your child ask questions about art? asks for clarification of some words (for example - what is beauty? Landscape? Sculpture? Designer?) __________________________________________
11. Does your child ask to buy new pencils, paints, plasticine, books with interesting illustrations?_______________________________________________________________
12. When your child brings works (drawings, applications) from kindergarten, to whom he strives to show them, what is his “pride” or unwillingness to show ___________________
13. Are you engaged in any artistic activity, craft, “artistic leisure”?___________________________
14. Is there a collection of children's work at home? Comments (who began to collect, what is presented, how do the works "get" into the collection?)? _____________________________________________
15. If a child gets carried away and begins to stain a piece of paper or “play around” with paints, your typical reaction is ______________________________________________
16. Please name the difficulties that arise in the process of drawing (sculpting, application or design) for your child? _____________________________________________
17. Are you ready to take part in some kind of activities organized in kindergarten in the direction of the artistic and aesthetic development of preschoolers (making costumes, drawings, creative competitions with children)? What? _________________________ Comments_______________
18. Formulate wishes for teachers, preschool educational institutions in terms of organization, conduct, content of work on the artistic and aesthetic development of children _________________________
APPLICATION
FINE ARTS, DECORATIVE AND APPLIED ARTS
http://inka.duma.midural.ru/
If you are interested in teaching fine arts - come on in! On the site you will find developments on the course "Fine Arts", MHK. Methods, programs, articles. The program "Fine Arts and Its History". Methods for diagnosing the level of development of visual thinking. To help the educator and primary school teacher.
All-Russian Museum of Decorative Applied and Folk Arthttp://vmdpni.ru/
Similar information.
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Technological map of the lesson
| Lesson type | Combined | ||
| The purpose of the lesson | Repeat and consolidate the signs of divisibility; prime and composite numbers, to form the ability to find GCD and LCM and apply the algorithm for finding GCD and LCM to solve problems. | ||
| Lesson objectives | educational | developing | educational |
| Update knowledge on topics: decomposition of a number into prime factors; prime and composite numbers, GCD and LCM. Repetition and consolidation of acquired knowledge. Ability to apply mathematical knowledge to problem solving. |
Expanding students' horizons. The development of methods of mental activity, memory, attention, the ability to compare, analyze, draw conclusions. Development of cognitive activity, positive motivation for the subject. Development of the need for self-education. |
Education of a culture of personality, attitude to mathematics as a part of human culture, which plays a special role in social development. Responsibility, independence, ability to work in a team |
|
| Cognitive UUD: | They develop the skills of cognitive reflection as awareness of the actions taken and thought processes, master the skills of solving problems. learning the ability to independently identify and formulate a cognitive goal, search and highlight the necessary information with the help of independent work and questions from the teacher. Improve the ability to consciously and voluntarily build a statement in oral and written form, analyze objects in order to highlight essential features for compiling an algorithm, learning the ability to put forward a hypothesis; | ||
| Communicative UUD: | Develop the ability to participate in the discussion; clearly, accurately and logically state your point of view; | ||
| Regulatory UUD: Personal UUD: |
They learn to independently evaluate and make decisions that determine the strategy of behavior, taking into account civil and moral values. creating a situation for setting a learning problem based on knowledge about divisors and multiple natural numbers; predicting the result of the level of assimilation based on the concepts of divisors and multiples, GCD and LCM. Teaching control skills in the form of comparing the result of independent work with solving tasks on the board in order to detect deviations and differences from the sample, assess what has already been learned and what is still to be learned on the topic; Learn the ability to conduct a dialogue based on equal relations and mutual respect |
||
During the classes
Stage 1. Organizing time.
Stage 2. Updating knowledge and fixing difficulties in activities.
Checking homework (task and equation)
Oral work (children assess their knowledge at the beginning of the lesson)
Questions:
- What numbers are called natural?
- Definition of prime and composite numbers (give examples)
- And 1 - what is this number? (neither simple nor compound) Why?
- Signs of divisibility by 2, 3, 5, 9, 10
What is the largest number of identical gifts that can be made from 48 Belochka sweets and 36 Inspiration chocolates if all the sweets and chocolates must be used? GCD (36.48)=?
Formulation of the problem: Today we will summarize all the knowledge gained on this topic.
Open notebooks, write down the number, class work, topic: “GCD and LCM of numbers”.
Stage 3.
What numbers are called coprime? (gcd = 1)
Find the GCD and LCM of the numbers 6 and 15
GCD(6; 15) = 3, LCM(6; 15) = 30
- What is the product of GCD and LCM of these numbers? 3 * 30 = 90
- What is the product of the numbers a and b? 6 * 15 = 90
- What we conclude: gcd(a; b) LCM(a; b) = a * b .
Problem solving.
Where do we already use our knowledge of GCD and LCM numbers?
When solving problems.
Students have handouts with tasks on the table.
Performing an exercise.
Exercise: Select true statements: (on screen)
gcd (13, 39) = 39
16 - multiple of 3
LCM (9.18) = 18
5 is a multiple of 6
7 is the divisor of 14
gcd(2; 15) = 1
Every number has a divisor of 1
LCM (2;3) = 6
From the proposed correct answers, make the largest natural number that is a multiple of 5.
Answer: correct 3,5,6,7,8. The largest natural number that is a multiple of 5 is 87635.
Physical education minute
I believe - they stretch up, I do not believe - they squat.
- The number 2 is a divisor of the number 16.
- The number 33 is a multiple of 5.
- The number 10 is a divisor of 40.
- 60 is a multiple of 10 and 7
- 7 has two dividers.
Stage 4.
In children, cards with the location of the NOD and NOC (perform according to the options, then heard at the blackboard)
| Task #1 The children received the same gifts on the New Year tree. All gifts together contained 123 oranges and 82 apples. How many children were present at the Christmas tree? How many oranges and how many apples did each get? (it is necessary to find the GCD of the numbers 123 and 82 123 = 3 * 41; 82= 2 41 gcd(123; 82) = 41 Answer: 41 guys, 3 oranges and 2 apples.) |
Task #2 Two ships left the river port at the same time. The flight duration of one of them is 15 days, and the second one is 24 days. In how many days will the ships start sailing again at the same time? How many trips will the first ship make during this time? How much is the second? It is necessary to find the LCM of the numbers 15 and 24. 1) 15 = 3 *5; 24 = 2 * 2 * 2 * 3 LCM(15; 24) = 2 * 2 * 2 * 3 * 5=120 2) 120: 15 = 8 (p) first; 3) 120: 24=5(p) second Answer: after 120 days, the first will make 8 flights, and the second - 5 flights. |
Card work:
What is the largest number of identical gifts that can be made from 32 felt-tip pens, 24 pens and 20 markers? How many felt-tip pens, pens and markers will be in each set?
Buses leave from the last stop on two routes. The first returns every 30 minutes, the second returns every 40 minutes. In what shortest time will they be at the final stop again?
Task number 3. (work in pairs)
Decipher the name of one of the species of African antelopes. (Springbok)
To do this, find the least common multiple of each pair of numbers, then enter the letter corresponding to this number in the table.
| 1) LCM(3,12) = 12 R | 5) LCM(9;15) = 45 b |
| 2) LCM(4;5;8)= ___40 O | 6) LCM(12;10)= 60 To |
| 3) LCM(8;12)= 24 With | 7) LCM(9;6) = 18 And |
| 4) LCM(16;12)= 48 n | 8) LCM(10;20)= 20 G |
Fill in the free column in the table, taking into account the data:
LCM(25;4) = 100 P
| 24 | 12 | 18 | 48 | 20 | 45 | 40 | 60 | |
| With | P | R | And | n | G | b | O | To |
Stage 4. Knowledge test (with further self-test)
Independent work.
Now let's test your knowledge with the help of independent work. Take a card on the table and make all the notes in it.
Find the GCD and LCM of numbers in the most convenient way.
| Option 1 | Option 2 |
| a) 12 and 18; | a) 10 and 15; |
| b) 13 and 39; | b) 19 and 57; |
| c) 11 and 15; | c) 7 and 12. |
Are the numbers relatively prime?
| 8 and 25 | 4 and 27 | |||||
| IN 1 | AT 2 | |||||
| A | b | V | A | b | V | |
| GCD | 6 | 13 | 1 | 5 | 19 | 1 |
| NOC | 36 | 39 | 165 | 30 | 57 | 84 |
| Yes | Yes | |||||
Stage 5 Summing up the lesson.
Today we have repeated almost all the rules on the topic “Greatest Common Divisor and Least Common Multiple” and are ready to write a test. I hope you do well with her.
Graded for the lesson:
Stage 6 Homework Information
Open your diaries and write down your homework. Repeat the rules from paragraph 2.3, follow No. 672 (1.2); 673 (1-3), 674..
Stage 7. Reflection.
Determine the truth for yourself of one of the following statements:
- “I figured out how to find the GCD of numbers”
- “I know how to find the GCD of numbers, but I still make mistakes”
- “I have unanswered questions”
Independent work on the topic "Greatest Common Divisor"
Find all common divisors of numbers and underline their greatest common divisor:
a) 50 and 70; b) 34 and 51; c) 8 and 27. Name a pair of relatively prime numbers, if there is such a pair.
2. Write down two numbers for which the greatest common divisor is the number: a) 7; b) 24.
3. Find the GCD of numbers: a) 55 and 88; b) 72 and 96; c) 720 and 90; d) 255 and 350; e) 675 and 825.
Option 2
1. Find all common divisors of numbers and underline their greatest common divisor:
a) 30 and 40; b) 39 and 65; c) 25 and 9;. Name a pair of relatively prime numbers, if there is such a pair.
2. Write down two numbers for which the greatest common divisor is the number: a) 9; b) 21.
3. Find the GCD of numbers: a) 44 and 99; b) 630 and 70; c) 64 and 80; d) 242 and 999; e) 7920 and 594.
Independent work on the topic "Greatest Common Divisor"
Find all common divisors of numbers and underline their greatest common divisor:
a) 50 and 70; b) 34 and 51; c) 8 and 27. Name a pair of relatively prime numbers, if there is such a pair.
2. Write down two numbers for which the greatest common divisor is the number: a) 7; b) 24.
3. Find the GCD of numbers: a) 55 and 88; b) 72 and 96; c) 720 and 90; d) 255 and 350; e) 675 and 825.
Option 2
1. Find all common divisors of numbers and underline their greatest common divisor:
a) 30 and 40; b) 39 and 65; c) 25 and 9;. Name a pair of relatively prime numbers, if there is such a pair.
2. Write down two numbers for which the greatest common divisor is the number: a) 9; b) 21.
3. Find the GCD of numbers: a) 44 and 99; b) 630 and 70; c) 64 and 80; d) 242 and 999; e) 7920 and 594.
Independent work in mathematics Greatest common divisor. Coprime numbers 6 class with answers. Independent work includes 2 options, each with 6 tasks.
Option 1
1.
a) 4 and 8
b) 18 and 48
c) 45 and 98
2.
a) 425 and 625
b) 532 and 665
c) 36, 72 and 198
3.
a) 28 and 36
b) 3; 5 and 26
4. In each of the identical sets of dishes there are glasses and glasses. Only 35 glasses and 21 glasses. How many sets in total? How many shot glasses and glasses are in each set?
5. Write down all the proper fractions with a denominator of 18 whose numerator and denominator are coprime numbers.
6. In how many ways can 5 passengers be accommodated in a 6-seater boat?
Option 2
1. Find all common divisors of numbers:
a) 5 and 15
b) 12 and 48
c) 51 and 65
2. Find the greatest common divisor of numbers:
a) 232 and 261
b) 124 and 148
c) 24; 48 and 54
3. Are the numbers relatively prime?
a) 36 and 37
b) 2 and 14
4. In the same New Year's gifts, there are only 26 chocolates, 11 7 chocolates and 169 caramels. How many gifts are there? How many chocolates, chocolates and caramels are in each set?
5. Write down all proper fractions with a denominator of 22 whose numerator and denominator are not coprime numbers.
6. In how many ways can 4 passengers fit in a 6-seater boat?
Answers to independent work in mathematics Greatest common divisor. Coprime numbers Grade 6
Option 1
1.
a) 1, 2, 4
b) 1, 2, 3, 6
in 1.
2.
a) 25
b) 133
c) 18
3.
a) no
b) yes
4. 7 sets, 5 shot glasses and 3 glasses
5. 1/18, 5/18, 7/18, 11/18, 13/18, 17/18
6. 720 ways
Option 2
1.
a) 1.5
b) 1, 2, 3, 4, 6, 12
in 1.
2.
a) 29
b) 4
at 6.
3.
a) yes
b) no
4. 13 gifts; 2 chocolates; 9 chocolates and 13 caramels
5. 2/22, 4/22, 6/22, 8/22, 10/22, 11/22, 12/22, 14/22, 16/22, 18/22, 20/22
6. 360 ways