Manuscript of the lecture "Characteristics of multiples of 3" 1 1. A brief analysis of the teaching materials
The characteristic of multiples of 3 is the content of the ninth volume of Beijing Normal University Edition, which belongs to the knowledge of multiples and factors in the field of numbers and algebra. Students have learned the characteristics of multiples of 2 and 5, and continue to learn the characteristics of multiples of 3.
Second, the teaching objectives
1, through the process of exploring the characteristics of multiples of 3, understand the characteristics of multiples of 3, and judge whether a number is multiples of 3.
2. Cultivate the ability to analyze, compare, guess and verify.
Third, teaching ideas
In this class, I firmly grasp the main line of conjecture → observation → proof → induction to start teaching, so that students can experience the learning process of effective inquiry.
Based on the above ideas, this lesson has designed the following two links:
explore
deepen
Fourth, the teaching process
First, explore
In this part, I provide four inquiry platforms for students:
(1) conjecture
Review: Multiple characteristics of 2 and 5. Guess the characteristics of multiples of 3.
(2) Observation
Find all multiples of 3 in the hundred tables and deny the conjecture by observation.
With the help of a counter, a multiple of 3 is randomly selected from 100 tables, and it is dialed out with a counter to record how many beads are used to dial this number. Look at the record again What can you find?
Students will soon find that the number of beads used is a multiple of 3.
When students have cognitive difficulties, using counters to study the characteristics of multiples of 3 directly reduces the difficulty of students' observation and discovery of characteristics, and makes new knowledge closer to students' "nearest development zone".
If you are given three beads, can you guess that the number dialed on the counter within 100 will be a multiple of 3? Call four, five ... dial yourself. What did you find?
Students found that the range of 100 is a multiple of 3, the number of beads used is a multiple of 3, not a multiple of 3, and the number of beads used is not a multiple of 3. That is to say, the number within 100, if dialed on the counter, the number of beads used is a multiple of 3, and this number is a multiple of 3.
(3) Proof
Do our previous findings apply to all figures? Students will immediately propose to learn a number greater than 100.
Teamwork: Come up with more than 100 at will, work it out with a calculator first, and then record it. Finally, dial it with the counter and see what you find.
After cooperative discussion and exchange of reports, the students found that the previous research conclusions are still applicable in these larger figures.
The wider and more representative the research object, the more reliable the research conclusion. In this link, through the two aspects of "large number" and "random thinking", the scope of the research object is wider, and the students' consciousness and habit of careful thinking are cultivated.
(4) induction
Now if you are given a number without division, how can you quickly judge whether it is a multiple of 3? Hey! I found that some students judged correctly without using a counter, and it was still fast! what do you think? Students will say that the number of beads used is actually the sum of the numbers on each number.
The slightly complicated expression of "the sum of numbers on each digit" is naturally summed up in students' operation, which highlights the autonomy of students' inquiry learning and highlights their subjective status.
Second, deepen
Ask the students to take out ten cards from 0 to 9 prepared in advance and solve the following problems in the game:
(1) Can you choose 3 cards and put multiples of 3? With the three cards you choose, can you still pose different multiples of 3? How many poses can a * * * pose?
(2) Randomly draw 3 cards and add cards on them, so that the number is still a multiple of 3. If I add one, how do I add it? How about two more? Three? ..... How many can I use at most?
(3) When all ten cards are used, we get a larger multiple of 3. Can you get rid of some cards quickly so that this number is still a multiple of 3?
What should you do if you want to remove a card? If you want to get rid of two? Three? ……
Did this exercise give you any inspiration?
Use your method to determine whether the following numbers are multiples of 3:
36996969336,
1827457874。
It is troublesome to judge whether a number with more digits is a multiple of 3 by conventional methods. How to break through this difficulty? Through this series of card games, students naturally explored the shortcut of solving problems in operation and completed the expansion of their knowledge.
Dear teachers, the teaching process I just described is to enable students to accumulate not only the experience of mathematical activities for students, but also the basic mathematical ideas in the process of exploring the characteristics of multiples of 3: let students gradually realize that guessing, observing, giving evidence and inducing are the general methods to solve mathematical problems.
thank you
Lecture Notes on Characteristics of Multiplies of 3 2 I. Analysis of Teaching Materials and Learning Situation
This lesson is the content of the fourth grade of primary school mathematics in Qingdao edition textbook. It is taught on the basis that students have mastered the characteristics of factors and multiples and multiples of 2 and 5. It is an important basis for finding the greatest common factor and the least common multiple, and it is also a necessary prerequisite for learning reduction and general scores. Therefore, it is of great significance for students to master the characteristics of multiples of 3.
Second, the teaching objectives and teaching priorities and difficulties
According to the above analysis of teaching materials and learning situation, in order to make every student get different development from the research activities in this class, I have designed the following teaching objectives.
Knowledge goal: make students experience the activity of exploring the multiple characteristics of 3, know the multiple characteristics of 3, and skillfully judge whether a number is a multiple of 3.
Ability goal: Through observation, guessing, verification and other activities, let students experience the inductive process of the characteristics of multiples of 3. In order to cultivate students' ability to observe, analyze, calculate and summarize problems, and further develop students' sense of numbers. Experience some ways to explore the characteristics of numbers.
Emotional goal: let students experience the inquiry and challenge of mathematical problems, further stimulate students' interest in learning mathematics, and get positive emotional experience from it.
Based on the above understanding, I decided on the course.
Teaching emphasis: understand and master the characteristics of multiples of 3.
Correctly judge whether a number is a multiple of 3.
Teaching difficulties: explore and understand the characteristics of multiples of 3.
Third, teaching method design and learning guidance.
In order to achieve the teaching objectives of this class, highlight the teaching focus, break through the difficulties and better promote the development of each student, this class mainly adopts the following teaching methods:
1, conjecture verification discussion exchange
2. Self-exploration and experience
Fourth, teaching preparation:
1, teacher preparation: courseware, physical exhibition platform, experimental form.
2, student preparation: counter calculator
Verb (abbreviation of verb) teaching program
Suhomlinski said: "Among the many tasks faced by primary schools, the first task is to teach children to learn." Learning here refers to learning methods, which are characterized by multiples of 3, have rules to follow, and are easy to take mechanically boring classes. Students can judge according to the rules, but their ability has not been cultivated and their intelligence has not been developed. The design of this course aims to sublate the teaching of "full-hall irrigation" and replace it with the teaching method of combining inspiration and discovery, so as to encourage students to guess, practice and discover the law boldly, let all students actively participate and think, and stimulate their enthusiasm for learning. According to the characteristics of students, the following four activities are designed in teaching, which are closely related to students' knowledge base and personality development.
Activity 1 Review the old knowledge, lead to guess Activity 2 Independent inquiry and cooperative verification.
Activity 3: Apply the law, experience and feel Activity 4: Reflection and summary, self-improvement.
Activity 1 Review the old knowledge and cause a guess.
"Characteristics of multiples of 3" belongs to the category of number theory, which is far from students' life, and the characteristics of multiples of 2 and 5 are the basis for students to learn this lesson. Starting from the students' existing foundation, I first reviewed the characteristics of 2 and 5. Through the teacher's summary and guidance, I organically combined review and introduction to guide students to guess "What are the characteristics of multiples of 3?" Let the students fully express various conjectures. Maybe some students will say his guess without thinking: "The digits are 3, 6 and 9, all multiples of 3", while some students have different ideas. Then it causes cognitive conflicts, creates inquiry situations, stimulates students' desire for knowledge, feels the process of new knowledge, and clarifies the problems to be solved in the new curriculum. This leads to the topic. Parallel blackboard writing: the characteristics of multiples of 3
Activity 2: Independent investigation and cooperative verification
This link is intended to guide students to show their different learning levels and ways of thinking through hands-on practice and independent inquiry, so that students can initially understand and master the characteristics of multiples of 3 in mathematical activities of observation, experiment, guessing, verification, reasoning and communication. Three teaching levels are designed here:
1, use "hundred tables" to deny the wrong guess.
After the students come to a guess, I will guide them to find a multiple of 3 in the hundred tables to verify. In the verification, I will overturn the guess just now. Therefore, students realize that they can no longer use the original method (that is, from the case of a number) to judge whether a number is a multiple of 3, but should think from another angle. Eliminate the mindset and deny the old transfer, thus stimulating students' desire to explore.
2. Explore experiments and find features.
Students have just learned the characteristics of multiples of 2 and 5, and there is a great thinking span from observing the last number to observing the sum of this number. It is difficult for students to get the characteristics of multiples of 3 through independent inquiry. At this time, the teaching strategies adopted by teachers are particularly important. In this class, the teacher adopted the teaching strategy of letting students carry out pearl picking experiments, which solved this problem well. Teachers guide students to experience the process of drawing beads, filling in forms, observing, thinking and discovering. Therefore, with the deepening of the experiment, students' understanding of the characteristics of multiples of 3 becomes clearer and clearer. In the process of experiment, inquiry, guess and verification, they constructed an overall understanding of the multiple characteristics of 3. Although there is no vivid teaching situation in this class, it skillfully pushes students to the main position of learning, so that students are always immersed in a strong atmosphere of exploration and deeply attracted by the charm of mathematical knowledge itself. This kind of mathematics learning activity is a real, vivid and personalized cognitive process. Through the accumulation of appearances, students have made a leap in thinking and formed a clear mathematical model in their minds.
3. Give examples to verify and summarize the rules.
Let the students verify the law with examples after they have found it preliminarily, which embodies the thinking process from special to general. In order to verify this conclusion, students use the fastest speed to calculate whether the sum of the numbers in each class is a multiple of 3, and use a calculator to calculate whether this number is a multiple of 3, and let students report the verification process, so as to provide students with as many opportunities as possible to learn in practice, which not only enables students to learn the method of verification by examples, but also embodies the idea of dialectical materialism.
Activity 3: Experience the feeling of applying the law.
In this part, I designed four different exercises to improve students at different levels. On the basis of following students' cognitive rules, we strive to highlight key points, break through difficulties, and embody foundation, hierarchy, flexibility, life and interest.
Question (1) is a basic question, which enables all students to have a further understanding of new knowledge and achieve the purpose of consolidating new knowledge. If possible, students can feel the judgment skill of removing the multiple of 3 first in quick judgment;
Questions (2) are presented in the form of pictures to guide students to use what they have learned to solve practical problems in life;
Question (3) is to fill in a number in the □ of each number so that this number is a multiple of 3. In order to test students' comprehensive ability to use knowledge, achieve the effect of drawing inferences from others and improve the flexibility of thinking.
Question (4) aims to spread students' thinking through flexible forms.
Activity 4 Reflection, Summary and Self-improvement
In this link, students can actively recall and talk about the gains of this class through the communication between teachers and students. Reproducing knowledge and methods also reflects students' emotional value, further reflecting and summarizing, and improving themselves.
The whole class allows students to experience the inquiry process of "guess-verify-operate-guess-verify-draw a conclusion-solve the problem" and realize the interaction among curriculum, teachers and students, knowledge and so on. The whole teaching is to combine the imparting of knowledge, the training of thinking, the guidance of learning methods, the cultivation of learning ability and the infiltration of mathematical thinking methods, so as to achieve the overall improvement of teaching efficiency and quality of life.
"Characteristics of multiples of 3" lecture 3 I. teaching material analysis:
This part of the content is taught on the basis of students mastering the concept of multiple. Finding the factor, the greatest common divisor and the least common multiple is an important basis for learning, and it is also conducive to learning the knowledge of reduction and general division. Therefore, understanding the characteristics of multiples of 2, 5 and 3 is of great significance to the content of this unit.
This part mainly involves collective thinking. Mastering set thinking can make mathematics problems easier to understand and remember, which is not only helpful for students to master the essence of knowledge, but also of great significance for developing students' intelligence, cultivating students' ability, optimizing students' thinking quality and improving the effect of classroom teaching.
In this class, I give full play to the students' main role and let them draw a hundred tables by themselves. By analyzing and comparing the data, I can find out the features and finally verify them and draw a conclusion. This process has been applied many times in the whole class, which has fully exercised students' awareness of autonomous learning and their ability to analyze and summarize.
Second, the analysis of learning situation:
Students have mastered the concepts of factors and multiples, and have some life experience in odd and even numbers, so it is not difficult for students to be interested in this part of knowledge. Through this part of the study, students can master the characteristics of multiples of 2, 5 and 3. On the other hand, it is helpful to develop students' abstract thinking and improve their pride in acquiring new knowledge independently.
The fifth grade is a turning point in the primary school stage, and the physical and mental growth and personality characteristics of the fifth grade students have a profound impact on the teaching effect. Through analysis, students can "tailor-made" a quality class for students. I find that students are enthusiastic about learning, but they are not focused; Strong interest in discussion, but not good at cooperation; Strong thirst for knowledge, but poor purpose. So I design fresh materials close to students' life in teaching as the focus of attracting students, and guide students to be goal-oriented and achieve precise cooperation.
According to students' analysis, I mainly adopt teaching methods such as "independent inquiry, cooperative communication and report verification" in this course. Stimulate students' thirst for knowledge by creating vivid teaching scenes. Students discover through observation, explore and communicate, and solve problems through cooperation and induction.
Let students go through a series of processes, such as understanding goals, cooperative discussion, making plans, analyzing and judging, verifying and thinking, and summarizing. Cultivate the spirit of exploration and cooperation and realize the mathematical thought of classification.
Third, the learning objectives:
This section belongs to the field of "number and algebra" in the mathematics curriculum standard. Curriculum standards clearly put forward the characteristics of understanding multiples of 2, 3 and 5 in the specific objectives of this field. According to the requirements of curriculum standards and referring to teachers' books, I set the following teaching objectives:
1, so that students can master the characteristics of multiples of 2 and 5 through independent exploration.
2. Let students experience the process of observation, analysis, abstraction and generalization, and cultivate their thinking ability of abstraction and generalization.
3. Experience the happiness brought by mathematics through independent exploration and cooperative communication.
Teaching emphasis and difficulty: the process of students exploring the multiple characteristics of 2 and 5 independently.
Fourth, teaching activities:
According to the requirements of curriculum standards, according to my analysis of teaching materials, combined with students' learning foundation and experience, I designed the following teaching activities around classroom teaching objectives:
The first link: create situations and introduce new lessons.
This is how I introduced this lesson: Students, some time ago we learned multiples. Who can tell how many times 2 is? Students can say anything as long as they are right. ) Who can tell how many times 5 is?
We know that a number has countless multiples. If you are given a number at random, is there a better way to judge whether it is a multiple of 2 or a multiple of 5? Yes, if you listen carefully in this class, you will certainly master the mystery. This leads to the topic, which not only greatly mobilizes students' enthusiasm for learning, but also naturally throws questions at students and arouses their desire for inquiry. A good beginning is half the battle.
The second link: independent exploration and discovery of laws.
Mathematics curriculum standard points out that hands-on operation, independent exploration and cooperative communication are important ways for students to learn mathematics. Mathematics teaching is the teaching of mathematics activities. When teaching the characteristics of multiples of 2, I designed the following links:
The first step is to find the multiple of the circle, so that students can find the multiple of 2 in the inner circle of the hundred-digit table.
The second step is to find the law, let students observe and think about the characteristics of multiples of 2, and let students express their ideas boldly. Guide students to summarize the characteristics of multiples of 2: numbers with 0, 2, 4, 6 and 8 are multiples of 2.
The third step is to verify the teacher's question with examples: whether the newly discovered law can be used for all natural numbers, the students' answers may be different. Teacher's guidance: Whether it is suitable or not is just our guess. In order to prove that the guess is right, we should give examples to verify it. How to verify? For example, numbers ending in 0, 2, 4, 6, and 8, also find some numbers that do not end in 0, 2, 4, 6, and 8, and calculate whether they are divisible by 2, that is, multiples of 2. Then ask the students to verify it.
The fourth step is to draw a conclusion according to the student's report. Numbers in units of 0, 2, 4, 6 and 8 are multiples of 2. At the same time, the teacher gave the research scope: we only study multiples within the range of natural numbers.
The fifth step, through the characteristics of multiples of 2 summarized by students, it is further concluded that among integers, numbers that are multiples of 2 are called even numbers (0 is also even numbers), and numbers that are not multiples of 2 are called odd numbers.
This design cultivates students' mathematical thinking and language expression ability, initially establishes the mathematical thinking of guessing-verifying-drawing conclusions, and improves self-reflection consciousness.
Teaching the multiple characteristics of "5" is helpful for students to find the multiple characteristics of "5" by using the method of finding the multiple characteristics of "2" that they have just learned, which is helpful for students to form good learning quality.
Contrast observation, let students observe hundreds of tables and find out what multiples of 2 and 5 have in common. Through students' observation, we can draw the conclusion that numbers with 0 are both multiples of 2 and multiples of 5.
The third link: consolidate practice and improve cognition.
After-class exercises 1 and 2.
The fourth link: class summary
"What do you know through this lesson?" What are you confused about? What else do you want to know? Summarize and reflect on this lesson to pave the way for the following content.
In short, the design of this class is teacher-oriented, students' independent thinking, independent exploration and personalized expression run through, the teaching objectives are clear, students' dominant position is fully respected, and a student-oriented classroom is created. Shortcomings, I hope experts will criticize and correct me. Thank you. blackboard-writing design
Characteristics of multiples of 2 and 5
Characteristics of multiples of 2: Numbers with units of 0, 2, 4, 6 and 8.
Characteristics of multiples of 5: Numbers with 0 or 5 bits.
Natural numbers are even and odd.