Common multiple and minimum common multiple: lecture notes 1 I. Teaching materials
(1) teaching material analysis:
1, teaching content: the least common multiple of the first kind. It is a process of guiding students to know, establish and understand the concept of least common multiple on the basis of independent participation, discovery and induction.
2. According to the learning situation and the requirements of the new curriculum standards, analyze the intention of compiling teaching materials:
Grade five students have richer life experience and knowledge background. The new curriculum standard requires that teaching materials should be realistic and interesting, and adopt a spiral way to promote students to establish the concepts of common multiple and minimum common multiple in exploration and communication.
Before that, students have learned divisibility, multiple, factor, common factor and greatest common factor. By writing multiples of several numbers, we can find the common multiple, and then find the smallest one from the common multiple, thus leading to the concepts of common multiple and minimum common multiple. Then, the multiples of 4 and 6 and the common multiples of these two numbers are graphically represented by * graphs. The study of this part of the content also laid the foundation for studying the general theory and reducing the score in the future, which has scientific and strict logic.
(B) the handling of teaching materials
1. The understanding of common multiple and minimum common multiple in the textbook is abstract bricklaying, which is not conducive to the understanding of concepts. Therefore, the title of "original wall brick" was changed to "find two people with the same rest day" to establish the concept. There are three reasons: first, students' learning content should be realistic, meaningful and challenging; Secondly, effective mathematics activities must be based on students' cognitive development level and existing knowledge and experience; Furthermore, the most effective time for class is the first 15 minutes. Doing a good job in teaching during this period is conducive to improving learning efficiency. Therefore, this difficult link was left behind.
2. Add life cases to the new teaching to guide students to understand meaning, solve practical problems and understand meaning by solving problems. The reason is that mathematics teaching should be closely linked with students' real life, so that students can feel that mathematics is around.
3. Classroom exercises have been clearly targeted and purposeful. (described later)
(3) Teaching objectives, teaching emphases and difficulties.
1, teaching objectives
(1) Understand the meaning of common multiple and minimum common multiple of two numbers.
(2) By solving practical problems, we have a preliminary understanding of some applications of common multiple and minimum common multiple of two numbers in real life, and experience the diversification of problem-solving strategies.
(3) Cultivate students' abstract generalization ability.
2. Teaching focus
The establishment of the concepts of common multiple and minimum common multiple. The reason is that the standard requires students in grades 4-6 to find the common multiple and the minimum common multiple of any two natural numbers within 10. Therefore, the focus of this lesson should be on the understanding of students' logarithmic concept.
3. Teaching difficulties
Using the knowledge of "common multiple and minimum common multiple" to solve simple practical problems in life. The reason is that "standard" means that people should learn valuable mathematics and let students acquire basic mathematical skills through activities such as observation, writing and reflection. The ability of primary school students to solve practical problems in life is generally low, so it is undoubtedly a difficulty to meet the requirements in the standard.
Second, the method of speaking and learning
1, learning situation analysis
Pupils have a strong desire to start work, and students are more willing to participate in the concept of numbers and find out for themselves. Furthermore, students' individual problem-solving ability is limited, and group cooperation can better stimulate their mathematical thinking and obtain mathematical information through communication.
2. Guidance on learning methods
Ask the students to find and circle on the calendar paper. By speaking, students say the concept before it is revealed. Give students the opportunity to say how they feel after starting work, or listen to what others say while expressing themselves personally.
Third, oral teaching methods
In order to achieve the teaching objectives, meet the requirements of the standards and better solve the difficulties in teaching, I designed this course as an entertaining form, and integrated the teaching content into the process of students' independent exploration and discovery.
1. Use the situation to introduce new lessons and explore new knowledge through the monthly calendar.
Students look for the date on the calendar and see clearly and vividly the multiple relationship between two numbers.
2. The concept of natural infiltration, a preliminary understanding of common multiple and minimum common multiple.
After students explore and organize new knowledge in their own language, in the interlocking teaching process, students can naturally understand concepts and communicate the relationship between concepts.
3. Create problem situations and try to apply and refine methods.
Combining the characteristics of teaching content, we create interesting problem situations, use students' life experience and knowledge background, encourage students to solve simple practical problems, activate students' mathematical thinking and improve their problem-solving skills.
4. Consolidate practice, constantly inspire, and constantly consolidate and improve.
Fourth, prepare teaching tools:
Print with calendar paper and multimedia courseware.
Five, the specific teaching process:
The general idea of my design: let students feel, understand, apply and consolidate on the basis of independent participation. The combination of intuitive demonstration and abstract thinking. My teaching process is as follows:
(A), the use of learning tools, the introduction of new lessons (this link is to solve the teaching focus)
1. Students find out the dates of multiples of 4 and 6 on the pre-distributed calendar paper according to the teacher's requirements.
2. Guide students to observe the number of dates found, and consciously guide students to find the number of features on the calendar, so as to get the common multiple and the minimum common multiple.
3. Refine life problems into mathematical problems, and students summarize the concepts of common multiple and minimum common multiple in their own language.
(2) Creating situations and applying knowledge: (This link is to solve teaching difficulties)
1, showing the problem of students queuing. The reason is to stimulate interest in learning with situations full of life problems and break through the gap between life and mathematics again.
2. Cooperate and communicate to solve problems and refine methods.
(3) Practice consolidation (explain the level of practice)
1, learn to find the least common multiple of two numbers in the most basic way.
2. Use this knowledge to solve problems in life.
(1) Looking for a birthday. Basic extension
(2) wall tiles. Explaining life phenomena by mathematical methods implies the relationship between finding common factors and finding common multiples.
(4), class summary
Students recall what they have learned in the whole class. Through this link, students can review the whole learning process, sort out new knowledge according to certain clues, form an overall impression, and facilitate the understanding and memory of knowledge.
The theory of common multiple and least common multiple draft 2 finished the lesson of least common multiple, and I felt a lot and gained a lot. Looking back at some highlights, there are mainly the following points:
The creation of 1. situation effectively stimulates students' interest in learning and improves classroom efficiency.
Before class, I think that if students can find the least common multiple through their own study, deeply understand what is the least common multiple and how to calculate it, and let all this be done by students themselves, then their memories will be more profound. Considering that this is a pure math class, full of abstract math knowledge, I wonder if it can provide a scene to stimulate students' interest. So I created the scene of students laying bricks. Ask the students to find the least common multiple through enumeration in this process. Then take a number axis as an opportunity, squirrels can jump 2 squares at a time, and monkeys can jump 3 squares at a time. By drawing and talking, it can be concluded that they jump forward from the same point and which square they jump to, and they meet for the first time. What about the second time? In order to further improve students' understanding of common multiple and minimum common multiple. Finally, while affirming everyone's enthusiasm for learning, I came up with the idea of taking several good students out to participate in an activity, which can be divided into groups of four or six, all of which have just ended. Do you know how many people I have at least? This greatly stimulates students' interest, makes students' learning mood high and their thinking is always active.
2. Bring forth the old and bring forth the new, and infiltrate and reform ideas.
In class, when students experience that it is tedious to find the least common multiple by multiplying, it is timely to find the least common multiple of two numbers by short division, because the greatest common divisor of two numbers is also found by short division, and the method of short division is consistent, so students can explore on the basis of existing knowledge and transform new knowledge into old knowledge. The key point of this lesson is to make students understand: why are these multiplied together to be the least common multiple? In the teaching of this course, we can discuss it more deeply, but we feel that the students are not deep enough. Therefore, when learning the least common multiple, we need to further strengthen our study.
3. Give students enough space to learn knowledge in self-study since enlightenment.
In teaching, I give students enough space to think about problems, so that students can learn knowledge from enlightenment and experience. After a long time, students can develop good thinking habits, with targeted thinking and orderly thinking.
Lecture notes on common multiples and minimum common multiples 3. First of all, it can make students experience and understand mathematics in real situations.
Before the lecture, I learned about the students' existing knowledge background before this class, showed examples directly, let students try to solve them themselves, and then reported personalized solutions. In the constant communication and reporting, the students found the solution of the least common multiple of two numbers with special relationship. The teacher asked the students to give examples to test. The least common multiple of two numbers whose common factor is only 1 is their product. The least common multiple of two numbers with multiple relations is the larger one. Then apply this discovery to try. Let students experience observation, thinking, comparison, reflection and other activities, and gradually understand the process of the emergence, formation and development of mathematical knowledge.
Second, guide students to think and cooperate in teaching.
When teaching the least common multiple of two numbers with special relationship, the teacher asked the students to talk about the difference between the least common multiples of each group. After the process of searching, students observe carefully, think seriously, report their thoughts, and change passive cognition into active inquiry. When finding the difference between the greatest common factor and the least common multiple in teaching, the teacher showed the topic of finding the greatest common factor and the least common multiple of 20 and 48. Let the students try it by themselves, and then discuss the similarities and differences between finding the greatest common divisor and the least common multiple of two numbers in groups. In the discussion, communication and exploration among students, students have discovered the characteristics of new knowledge, and through constant comparison, they have learned the similarities and differences between new knowledge and old knowledge. In this way, the activities of sorting, induction and communication enrich the experience of mathematics activities and improve the ability to solve problems. In this class, students become the masters of learning.
Third, there are shortcomings.
1, the form of praise and encouragement to students is relatively simple, which does not really play much role.
2. The introduction at the beginning was far-fetched, because teachers and students were nervous and took a detour. It should be studied deeply, because the introduction at the beginning is very important.
3. The use of interlanguage is carefully designed by teachers, but it has little incentive effect on classroom teaching. Use simple language.
The example of 4, 1 allows students to rehearse, which limits students' personalized problem-solving methods and should not be done. Students should be encouraged to use more methods.
There is no need for students to discuss the content of "talk". Students should be allowed to talk about it fully and show their personalized ideas.
6. The content of "Yiyi" is not enough time, and students are not allowed to really discuss it in depth.
7. The use of multimedia is not effective, so it is more appropriate to use a small blackboard.
8. The understanding of "textbook suggestions" is not in place. Talking about it is different from discussing it. "Seeking" and "calculating" are two different concepts, so the understanding is not in place.
9. For the "Protestant content", students can say that the teacher wrote it on the blackboard, which plays a role in strengthening knowledge.
10. Teachers should pay attention to language refinement in class. For example, the least common multiple of 7 and 5 is 35. The teacher asked: Why? This is not an appropriate question. Q: What do you think?