Lecture Notes on "Prime Numbers and Composite Numbers" in Elementary Mathematics

Lecture Notes on "Prime Numbers and Composite Numbers" in Elementary Mathematics

Let's start with teaching material analysis.

"Prime number and composite number" is the content of Unit 2, Section 3, Book 10 of Nine-year Compulsory Education Primary School Mathematics published by People's Education Press, on pages 23-24 of the textbook. Before this, students have learned the relationship between factors and multiples, as well as the characteristics of multiples of 2, 3 and 5, paving the way for the transition to this section. This section is the basis for students to learn to decompose prime factors and find the greatest common factor and the smallest common multiple, and occupies an important position in the teaching content of this chapter.

As a primary school mathematics teacher, we should not only teach students mathematical knowledge, but also teach students mathematical thinking, mathematical consciousness and mathematical logic analysis ability. Therefore, according to students' existing knowledge structure and psychological characteristics, I have formulated the following teaching objectives:

1, knowledge goal: a, make students understand the meaning of prime numbers and composite numbers, and know their connections and differences; B, will correctly judge whether a number is a prime number or a composite number, and remember prime numbers within 20.

2. Ability goal: By making high-quality tables within 100, let students learn how to choose learning materials reasonably, and at the same time cultivate the ability of induction, summary, observation and analysis.

3. Emotional goal: to cultivate students' cooperative spirit through group discussion; Solve problems through independent observation and analysis, cultivate students' independent thinking ability and stimulate students' interest in learning.

At the same time, according to the requirements of curriculum standards, I have identified the following key points and difficulties in teaching: through the observation and analysis of students, the significance of prime numbers and composite numbers, which are the key contents of this lesson, is discussed and summarized; How to correctly judge whether a number is prime or composite?

Second, talk about teaching methods.

Mathematics teaching under the new curriculum emphasizes to train students to understand their own environment and society from the perspective of mathematics, learn mathematical thinking, and initially learn to analyze things and think about problems with mathematical knowledge and methods. At the same time, the new curriculum standard requires changing students' learning methods and changing passive learning into active learning. Teachers should provide students with sufficient opportunities to engage in mathematical activities, help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent inquiry and cooperation, and gain rich experience in mathematical activities. Therefore, according to the knowledge characteristics of this section, the cognitive rules of primary school students and the spirit of curriculum standards, I adopted the teaching methods of hands-on, guiding inquiry, discovering the rules and teachers' explanation, and constructed the inquiry-based teaching mode, which fully embodied the educational concept of "student development-oriented".

Third, the guidance of speaking and learning methods.

The task of teachers is not only to impart knowledge to students, but also to impart learning methods to students, so that students can learn. So I'm going to let students learn to analyze, sum up and sum up problems by observing and comparing, using the methods from individual to general, comparing and contrasting, and distinguishing similarities and differences.

Fourth, talk about teaching procedures.

The new curriculum standard points out that effective teaching activities should be based on students' existing cognitive level, so according to students' ability to master old knowledge, I have formulated a teaching idea of "seeking divisor, laying a foundation-finding rules, exploring independently-classifying and summarizing, understanding meaning-explaining application and verifying conclusions". Strive to build an exploratory classroom teaching model.

1, review preparation: In the last class, let students review the relationship between factors and multiples, mainly reviewing the meaning of factors, so as to lay the foundation for the following new lessons.

2. New lesson introduction: Whether natural numbers can be divided by 2 can be divided into odd and even numbers, which leads to today's new lesson content. Natural numbers can also be divided into prime numbers and composite numbers (blackboard titles). Then let the students work out the factors of 2, 3, 5, 7 and 4, 6, 8 and 9 respectively, carefully observe the characteristics of their respective factors and discuss them in groups. (mainly cultivate students' independent thinking ability and the spirit of communication and cooperation)

3. Process development: (1) The team sent representatives to report the observation results, and the teacher summed up the meaning of prime number and composite number according to the students' observation-a number, and if there are only two factors, 1 and itself, it is called prime number (or prime number); A number is called a composite number if it has other factors besides 1 and itself. Students' own observation and induction can not only enliven the classroom atmosphere, but also return the classroom to students, so that students can become the masters of learning and strengthen their understanding and mastery of knowledge points. (2) Ask students to judge whether the following numbers 17, 22, 35, 87 and 96 are prime numbers or composite numbers, and summarize the methods to judge whether a number is prime or composite. Make it clear that all divisors of each number can be found, and then judge according to the meaning of prime number and composite number; Only by finding 1 and the third divisor other than itself can a number be judged as a composite number or a prime number. You don't need to find all the divisors, which can improve the efficiency of judgment (in practice, summarizing methods can not only strengthen students' application ability, but also cultivate students' ability to analyze and solve problems independently and summarize the methods to solve problems). (3) Ask the students whether they have forgotten the existence of 1? The derivative of 1 is neither prime nor composite. Then let the students practice orally and talk about the smallest prime number, smallest odd number, smallest composite number and smallest even number, aiming at distinguishing the concepts of prime number, odd number, composite number and even number. (4) Let the students make a table of prime numbers according to the table on page 24 of the textbook, and find out the prime numbers within 100. The group can discuss how to make this prime number table, how to quickly judge whether this number is a prime number or a composite number, and then report the method. The teacher can give appropriate suggestions. For example, you can cross out numbers that are multiples of 2, then cross out numbers that are multiples of 3, 5 and 7, and finally check the remaining numbers.

4. Classroom development: judging right or wrong.

A, the minimum prime number is 1, and the minimum composite number is 2. ( )

B. All prime numbers are odd and all composite numbers are even. ( )

C, in natural numbers, except prime numbers, they are composite numbers. ( )

5. Classroom games

Let the students stand up in turn and answer whether their student numbers are prime numbers or composite numbers. For example, I am 1, and I am neither a prime number nor a composite number; I am 2, and I am a prime number. ...

6. Summary: What have you gained from today's study? Summarize the meanings of prime numbers and composite numbers, and how to judge whether a number is a prime number or a composite number according to their meanings. It is emphasized that 1 is neither a prime number nor a composite number. The minimum prime number is 2 and the minimum composite number is 4, so as to impress students. The fifth-grade students are still in the transition period of thinking. Although they can remember on the basis of understanding, they still need the teacher's repeated emphasis on knowledge points to deepen their memory.

7. Homework after class: independently complete the exercises on page 25 of the textbook 1, 2, 3 to consolidate the knowledge learned today.

Blackboard design:

Prime number and composite number

2 3 5 7

↙↘↙↘↘↙↘→ There are only two factors: 1 and itself.

1 2, 1 3, 1 3, 1 7 ↓

Prime number (prime number)

4 6 8 9

↙↘↙↘↘↙↘→ There are other factors besides 1 and itself.

1 2 4, 1 2 3 6 , 1 2 4 8, 1 3 9 ↓

composite number

1 → is neither a prime number nor a composite number.

Teaching reflection:

Mathematics Curriculum Standard advocates students' active participation and willingness to explore, and cultivates students' ability to acquire new knowledge. Focus on cultivating students' ability to analyze and solve problems. The content of this lesson is taught on the basis of learning factors and multiples. After mastering the knowledge of factors and multiples, students can accurately find out all the factors of each number, and then learn the concept of composite number of prime numbers by observing the number of factors, which is more acceptable. Using old knowledge to draw out new knowledge, understand the formation process of knowledge and let students know the learning methods, which not only cultivates students' habit of autonomous learning, but also creates a good autonomous learning environment for students. However, there are still many shortcomings: in the classroom, teachers should give less or no hints about the knowledge that students can discover by themselves, and in the teaching process, students should be given sufficient opportunities to practice, think and discover in person and enough time to explore and discover. In this way, students can master the basic knowledge of mathematics and develop their thinking in a relaxed and harmonious learning environment.

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