Teaching reflection on finding the greatest common factor 1

In Teaching Example 3, square pieces of paper with side lengths of 6 cm and 4 cm were used to pave rectangles with lengths of 65,438+08 cm and widths of 65,438+02 cm, respectively. Teachers choose to spread square pieces of paper into rectangles to teach public factors, because this kind of activity can attract students to find problems, ask questions and guide students to think. Students spread out a different rectangle with the same two square pieces of paper. Faced with these two results, they will find some problems worthy of study, such as "why it was just built and sometimes it can't be built" and "when it was just built and when it can't be built". When they spread the square piece of paper along the edge of a rectangle, they will think that the reason why it is just covered or uncovered may be related to the side length, so they have the desire to further study the relationship between the side length of a rectangle and the side length of a square. This paper analyzes the relationship between the length, width and side length of a rectangle, and designs it into two levels according to students' cognitive rules. The first level is related to the paving process and results. From the level where the length and width of a rectangle are divided by the side length of a square without remainder and with remainder, we can understand why it has just been paved or not. Secondly, according to the experience that a square with a side length of 6 cm just covers a rectangle with a length of 18 cm and a width of 12 cm, but a square with a side length of 4 cm cannot just cover a rectangle with a length of 18 cm and a width of 12, Lenovo thinks that a square with a side length of several cm can also cover a rectangle with a length of12. Then, "it is both a factor of 12 and a factor of 18" to describe the characteristics of the side lengths of these squares. Obviously, the thinking in images at the previous level is heavy and difficult, which plays an important supporting role in the abstract understanding at the latter level.

Reflection: highlight the connotation and extension of the concept, so that students can understand the concept accurately.

I use the description "both" ... and ... "to help students understand the meaning of" public ". Example 3 first describes the phenomenon that squares with sides of 1, 2, 3 and 6 cm can just cover a rectangular paper with a length of 18 cm and a width of 12 cm. If the length and width of the rectangle are divided by the side length of the square, there is no remainder, and it is concluded that the side length of the square is a factor of 12 and 18. Then it is further summarized as "1, 2,3,6 are all factors of 12 and 18, and they are common factors of 12 and 18", forming the concept of common factors.

Because of the transfer of knowledge, it is easy for students to think of using set diagram to show the meaning of common factors intuitively. On page 27, write the factor of 8 and the factor of 12 into two groups of circles respectively. The two sets of circles partially overlap. The numbers written in the overlapping part are all factors of 8, also factors of 12, and common factors of 8 and 12. Observe this assembly diagram first, and then fill in the assembly diagram on page 28. Students can further understand the meaning of common factor. The extension of the concept refers to all the objects contained in this concept.

Using mathematical concepts, let students explore the method of finding the greatest common factor of two numbers.

There are two ways to find the greatest common factor of two numbers in teaching. Some students write down the factors of 8 and 12 respectively, and then find out their common factor and the greatest common factor. Some find the factor of 12 in the factor of 8, which is convenient to operate, but easy to miss. I intend to guide students to choose the first one. The third question in Exercise 5 is the application of this method.

Make full use of educational resources, make self-made courseware and assist teaching.

Limited to local operation, I have carefully made practical courseware, so that the intuitive and clear pages can directly assist my teaching. Students are active, the classroom atmosphere is more active, and the enthusiasm for asking questions, dispelling doubts and dispelling doubts is high.

The purpose of this course design is to make students learn the meaning of common factor and greatest common factor, and learn how to find the greatest common factor of two numbers. Judging from the performance of students in the whole class and the feedback of homework after class, students have a good grasp of this part of knowledge, are enthusiastic about learning, and are very satisfied with the effect.

Teaching reflection on finding the greatest common divisor II

First, the teaching design theme name:

Beijing Normal University Edition, Grade Five Mathematics, Volume One, Searching for the Greatest Common Factor

Second, the class situation, student characteristics analysis:

Our school is in the suburbs, and there are 25 students in the class. Students are active in thinking, good at asking mathematical questions and actively exploring knowledge in group cooperative learning. In the first unit of this book, students have understood the meaning of factors and multiples, and can list the factors of a number through multiplication and set. Therefore, it is not difficult to find the greatest common factor through enumeration. But it is still difficult to find the relationship between factors and prime numbers. Because it is not easy for students to find these relationships between these two numbers.

Three. Analysis of teaching content:

The textbook directly gives the general method of finding the common factor: first, the factors of 12 and 18 are obtained by multiplication, and then the common factor and the maximum common factor are obtained. On this basis, the concepts of common factor and greatest common factor are introduced. The textbook presents the process of exploration in a fixed way. Exercises 1 and 2 introduce how to find the greatest common factor by using factor relation and coprime relation. Teachers should guide students to find this method and apply it. Teachers should pay attention to let students experience the formation process of knowledge and stimulate their mathematical thinking.

Four. Teaching objectives:

Knowledge and skills: explore the method of finding the common factor of two numbers, and find the common factor and the greatest common factor of two numbers by enumeration.

Process and method: Go through the process of finding the common factor of two numbers and understand the meaning of the common factor and the greatest common factor.

Emotion, attitude and values: cultivate students' interest in learning mathematics. Through observation, analysis, induction and other mathematical activities, we can experience the exploration and challenge of mathematical problems and feel the order of mathematical thinking.

Analysis on the teaching difficulties of verbs (abbreviation of verb);

Teaching emphasis: explore the method of finding the common factor of two numbers, and find the common factor and the greatest common factor of two numbers by enumeration.

Teaching difficulties: go through the process of finding the common factor of two numbers and understand the meaning of common factor and the greatest common factor.

Teaching time of intransitive verbs:

One class hour

Seven. Teaching process:

(1) review

Teacher: Show me 3×4= 12, and () is the factor of 12.

Health: 3 and 4 are factors of 12.

(2) Explore new knowledge

1, understand the common factor and the greatest common factor.

(1) Teacher: What is the factor of 12 except that 3 and 4 are the factors of 12?

The factors of blackboard writing 12 are: 1, 2, 3, 4, 6, 12.

Teacher: What should I pay attention to if I ask for all the factors of a number?

Health: Write one-on-one in an orderly way so as not to miss anything.

Teacher: According to this method, please write all the factors of 18.

The factors for students to report: 18 after writing independently are: 1, 2, 3, 6, 9, 18.

(The assembly drawing is displayed)

Teacher: What numbers should be filled in these two circles? Please complete page 45.

Report to the teacher on the blackboard after birth.

(2) Teacher: Please find out whether there are the same factors in 12 and 18, and which ones are the same.

Students find that the same factors as 12 and 18 are: 1, 2, 3, 6.

Teacher: Like this, it is both a factor of 12 and a factor of 18, so we say that these numbers are the common factors of 12 and 18.

Teacher: What is the greatest common denominator here?

Health: Maximum 6.

Teacher: 6 is the greatest common factor of 12 and 18. This is what we learned in this class-finding the greatest common divisor.

Writing on the blackboard: finding the greatest common divisor

(The assembly drawing is displayed)

Teacher: What are the characteristics of this middle area? What number should I fill in? Group discussion after independent thinking

(Students discuss in groups)

Report: The middle area is the intersection area of factor 12 and factor 18. The number filled in should be both a factor of 12 and a factor of 18, that is, the common factors of 12 and 18 are filled in here.

Teacher: Please finish this problem. (Post-production revision)

2. Explore ways to find the greatest common factor.

(1) enumeration method

The method that we just found the greatest common factor is called enumeration. (blackboard writing: enumeration method)

Please find the greatest common factor of each group number in this way. 9 and 15

(2) Using factor relation to find

Teacher: Please turn to page 45 of the book and finish the first question by yourself.

Health report:

Factor of 8: 1, 2, 4, 8

The factor of 16: 1, 2,4,8, 16.

Common factor of 8 and 16: 1, 2,4,8.

The greatest common factor of 8 and 16 is 8.

The teacher guides the students to observe the last sentence and think about the relationship between 8 and 16 and their greatest common factor.

Students think independently and then discuss in groups.

Health report: 8 is a factor of 16, so the greatest common factor of 8 and 16 is 8.

The teacher guides the students to sum up and write it on the blackboard: if the smaller number is a factor of the larger number, then the smaller number is the greatest common factor of the two numbers. (blackboard writing: search by factor relationship)

Exercise: Find the greatest common factor of each group of numbers below. 4 and 12 28 and 7 54 and 9

(3) using the relationship of prime numbers to find.

Teacher: Please finish the second question by yourself.

Health report:

Factor of 5: 1, 5

Factor of 7: 1, 7

The greatest common factor of 5 and 7 is 1.

The teacher guides the students to observe the relationship between 5 and 7 in the last sentence and their greatest common factor.

Students think independently and then discuss in groups.

Health report: 5 and 7 are prime numbers, so the greatest common factor of 5 and 7 is 1.

Teacher: Like this, two numbers with only one common factor 1 are called prime numbers. If both numbers are prime numbers, their common factor is only 1. (blackboard writing: using the relationship of prime numbers)

Exercise: Find the greatest common factor of each group of numbers below. 4 and 5 1 1 and 7, 8 and 9

(4) Sort out the method of finding the greatest common factor.

Teacher: Today we learned how to find the greatest common factor.

Health: enumeration method, using factor relation to find, using prime relation to find.

Teacher: When you do the problem, you should observe the characteristics of the given number and choose different methods.

(3) Practice

Page 46, questions 3, 4 and 5. Students finish independently, and teachers patrol and guide.

(4) class summary

What did you learn from this course?

Eight. Classroom exercises:

Fill in the brackets with the greatest common factor of each group of numbers.

6 and 18() 14 and 2 1() 15 and 25 ().

12 and 8() 16 and 24() 18 and 27 ()

9 and 10() 17 and 18() 24 and 25 ()

Nine. Operation arrangement:

Complete the exercises in the workbook.

X appendix (teaching materials and resources):

1, teacher's book: the first volume of fifth grade mathematics published by Beijing Normal University.

2. Digital card

XI。 Self-question:

Finding the greatest common factor by short division has not appeared in the book for the time being, but it appears in the form of "Do you know" after finding the smallest common multiple, but I think this method is very practical. I don't know what the purpose of the textbook is. How to deal with it?

Teaching reflection:

This lesson is based on students' mastery of factors, multiples and factors. By solving the problems in the story, students can deeply understand the basic methods of finding common factors step by step. On this basis, the concepts of common factor and greatest common factor are introduced. When filling in the common factor, students are often prone to repetition.

In the teaching process, I encourage children to sum up and find the characteristics and methods of the greatest common divisor. Let's see if two numbers are multiples. If they are multiples, then the smallest number is the greatest common factor. If two numbers are prime numbers or two adjacent natural numbers, then the greatest common factor of these two numbers is 1.

When looking for the greatest common divisor, I introduced short division to my classmates. It is easier to use short division when the number is large.

Teaching reflection on finding the greatest common factor (3)

? Common factor and greatest common factor are part of the teaching that students accumulate "close-shop" experience when they understand the relationship between factors and multiples, find the factors of natural numbers in the range of 1 to 100, and learn the concept of area. For the teaching of concept class "common factor and greatest common factor", I think the key and difficult point is to understand the meaning of the word "public", that is, how to experience this number is not only a factor of one number, but also a factor of another number, and it is a "public" factor of two numbers. In order to highlight the teaching focus of this class and break through the teaching difficulties, combined with our teaching and research theme of this semester, "How to design effective teaching activities and achieve teaching objectives", I mainly try to teach from the following aspects:

First, attach importance to activity experience, so that students can experience the formation process of mathematical concepts.

The first guess: rectangle, 4 cm long and 2 cm wide. If you use a square of the same size and a full centimeter in length, and it happens to be full and there is no extra, you can choose a square a few centimeters long. Let students use their own thinking to operate and verify, and experience "a square with the same size" and "full without profit" in operation. At first, they felt that the square should not only fill the length of the rectangle without surplus, but also fill the width of the rectangle without surplus.

The second guess: now make the rectangle bigger, 6 cm long and 4 cm wide. For the same requirement, how long can the side of the square be this time? Students can skillfully operate and verify, and when they further perceive and choose a square in the activity experience and communication, they must ensure that the long square and the wide square are not redundant.

The third guess: continue to grow bigger, and the rectangle with the length of 18 cm and the width of 12 cm still has the same requirements. Just put it in squares of the same size, just fill it up and there is no redundancy. Can I choose a square with a few centimeters on each side this time? Students continue to verify the operation. At this time, students have already had the first two kinds of operation perception, accumulated enough activity experience, can support them to reason and imagine, find the essence of "full without profit", and thus perceive the law of square side length as a whole.

Then, give play to the teacher's leading role: "Let's put three rectangles in front of each other and take these data to the blackboard. Think about it. What are the side lengths of these squares related to? What does it matter? " Guide students to observe the data, find the law, and introduce the concepts of common factor and greatest common factor.

By creating the above-mentioned teaching activities, students can truly experience the process of generating the common factor, accumulate rich experience in the activities and fully experience the significance of the common factor.

Second, with the help of geometric intuition, improve students' understanding of conceptual meaning.

Through the above operating experience and thinking cognition, students know the common factor and the greatest common factor, and have gone through the process of finding the common factor and the greatest common factor. Students can perceive some relationships among the three concepts: factor, common factor and greatest common factor. In order to help students understand these concepts deeply, ask such a question: "Compare these three concepts, now can you talk about their connections and differences?" You can choose two of them to talk about. "Guide students to think further. At this time, students communicate: "The factor is a number, and the common factor is the common factor of two or more numbers" and "the greatest common factor" are first of all one of the common factors and the largest one among them. According to students' communication, I intuitively demonstrated the relationship between "factor" and "common factor", "common factor" and "greatest common factor" through courseware and with the help of Wayne diagram images, which enhanced students' understanding of the concept.

Third, communicate the connection between mathematical concepts and the real world through practical problems.

After students fully understand and distinguish the three concepts of "factor", "common factor" and "greatest common factor", they ask the question: "The length of a ribbon is 16 decimeter. If you want to cut it into small pieces to decorate the packaging box, you must ask that each piece is the same length, and there is no excess after cutting. How many decimeters can each piece have? Students think that this is a problem to be solved with the knowledge of factors, and each segment can be a few decimeters, which is the factor of 16. At this time, to guide students to adapt it into a problem solved by common factors, students first thought of it.

Two data are needed, so some students think it can be adapted into: "Two ribbons, one is 16 decimeter and the other is 12 decimeter. Cut them into small pieces of the same length, and there is nothing left. How many decimeters can each piece have? (Select whole decimeter) ". In the process of students' thinking, they not only further understand the meaning of concepts, but also find the practical significance of concepts such as "common factor formula" and "greatest common factor formula" to cultivate students' mathematical abstraction ability.

After a class, I found that students are the best! In the continuous practice and exploration, their understanding has been continuously improved, and I seem to hear their thinking voices.

Of course, when you think about it, there are still many remarkable places in this class, such as:

1. After three operations, find out what is the relationship between the side length of a square and the length and width of a rectangle. Some children can't observe and think with mathematical eyes, and still stay in operation. This shows that as teachers, they did not build a suitable bridge between these two links for their children and did not help them find a good fulcrum of thinking.

2. Because of the long time of operation perception, it is a pity that the second knowledge goal of this lesson-finding the common factor and the greatest common factor, does not have enough time to communicate with children's various methods.

With initial thinking, we made the above attempt. However, the time of a class is limited, and the personal professional quality needs to be improved, so it is not comprehensive. Fortunately, the end of a class does not mean the end of thinking. I am on my way with new problems in practice. Looking forward to thinking, I can get more guidance and criticism from leaders and colleagues!

Teaching reflection on finding the greatest common factor (IV)

"Common factor and greatest common factor" is the content of the third lesson of Unit 3. Before that, I have learned the common multiple and the minimum common multiple, and mastered the concepts and solutions of the common multiple and the minimum common multiple. The teaching process of this class is very similar to the teaching of common multiples, and I have learned a lesson from the teaching of common multiples. When teaching the concept of public factor in this class, I will let the students look at the questions first, make the meaning of the questions clear, and then do the calculation, so that the students can walk with the questions. When teaching the method of finding common factor, I also ask students to compare it with the method of finding common multiple. Through comparison, students find that the common multiple is infinite, and ellipsis should be written when there is no given range, while the common factor is limited, and a period should be written to indicate completion; It is also found that when looking for common multiples, we are looking for the smallest common multiple, while looking for common factors is the largest common factor. It is also found that in the method of finding common factor, the factor of decimal is found first, and then the factor of large number, while in the method of finding common multiple, the multiple of large number is found first, and then the multiple of decimal number is found. The two examples are similar not only in the teaching process, but also in the design of exercises. Therefore, when students finish the exercise, they are already familiar with the form of the exercise and have completed the exercise well. Just because the two classes are too similar, a small number of students are confused, and they can't tell how to find common multiples and common factors, which should be avoided in future teaching.

The homework of this class can also reflect some problems of this class. When teaching common multiples, I didn't emphasize the differences between the elements in the set. In the homework, many students filled in the common multiple columns and appeared in the left and right parts of the collection at the same time. When I practiced in this class, I especially emphasized this point. I hope students can remember that when they finish Exercise 5, they also find that some students can't remember clearly the characteristics of multiples of 2, 3 and 3. So when judging whether it is their multiple, some people use the method of dividing large numbers by 2, 3 and 5 to judge, which has delayed a lot of time, which I didn't expect before class. If students are asked to recall the characteristics of multiples of 2, 3 and 5 before doing this problem, more time will be saved.

Teaching reflection on finding the greatest common factor (5)

In this class, I carefully designed a fairy tale situation according to the students' existing knowledge and experience, which stimulated students' desire for learning. Let the students operate and discuss first, and help Uncle Wang choose the floor tiles. Think again and explore the relationship between the side length of square floor tile and the length and width of rectangular floor. Then, in the form of questions, by reviewing the factors of 16 and 12, let the students find out the factor of two numbers, the common factor of two numbers and the largest factor in the common factor of two numbers. It is found that the square with sides of 1 cm, 2 cm and 4 cm is just covered by the square with length of 16 cm and width of 65438+. On this basis, guide students to think about the relationship between numbers 1, 2, 4 and 16, 12, and reveal the concepts of common factor and maximum common factor.

In short, in the process of teaching, I not only review and consolidate old knowledge, but also let students learn new knowledge unconsciously. It is also necessary to let students take their own mathematical reality to participate in the mathematics classroom and constantly use the original experience background to explain new problems. In this process, I also pay attention to encouraging every student to participate in exploration, to arouse students' thinking, to pay attention to the communication between students, and to let students express their findings in their own language. For students with difficulties, I gave further guidance on methods, with the help of the group leader and mutual help among students. Students are the masters of learning, and teachers are the organizers, guides and collaborators of mathematics learning. Cultivate students' practical ability and let them learn the content of this lesson in a pleasant learning atmosphere.