Textbook status:

Before learning this lesson, this textbook has arranged all the cognitive and numerical factors, which are closely related to this lesson and are the foreshadowing and foundation for learning this lesson. At the same time, finding common factor is the basis of divisor, and divisor is an important basis for four decimal operations. Therefore, it is particularly important to understand and master the common factor. It can be seen that this course plays an important role in fractional operation.

When writing this lesson, the textbook writers carry out the concept of Mathematics Curriculum Standard (20 1 1 Edition), and attach great importance to encouraging students to experience learning activities such as observation, operation, comparison, discussion and induction, developing the ability of abstraction and generalization in the process of "finding common factors", cultivating students' practical ability and innovative consciousness, and helping students achieve sustainable development.

Analysis of learning situation:

Before learning this lesson, the fifth-grade students already know the multiples and factors, and can find out all the factors of a natural number within 100; I have accumulated some experience in observation, operation, induction and other mathematical activities, and have a preliminary ability of abstract generalization. Students in this age group are in the transition stage from concrete thinking in images to abstract logical thinking. An important feature of their mathematics learning is that they need concrete and vivid mathematical examples to support their exploration, discovery and abstract generalization. At the same time, they often have incomplete mathematical generalization and imprecise mathematical expression, and need careful guidance.

Teaching objectives:

1. Understand the meaning of common factor and common factor in the process of solving problems, and explore the method of finding common factor, and then you will correctly find the common factor and common factor of two numbers.

2. Infiltrate stereotypes and experience the diversity of problem-solving strategies.

3. Cultivate students' thinking ability such as analysis and induction, stimulate students' enthusiasm for independent learning and active exploration, and cultivate good habits of cooperation and communication.

Teaching focus:

Understand the meaning of common factor and common factor, and explore ways to find common factor.

Teaching difficulties:

Can correctly find the common factor and common factor of two numbers.

Textbook processing:

The textbook first gives a general method to find the common factor: first, find the factors of 12 and 18 by multiplication, and then let students fill these factors in two intersecting sets, thus guiding students to focus on the following questions: What factors should be filled in at the intersection of two sets? On this basis, the concepts of common factor and common factor are introduced. The textbook presents ideas in a set way, allowing students to experience the formation process of knowledge and trigger students' mathematical thinking.

In the practice of teaching materials, there are two groups of exercises to find factors, common factors and common factors One group is 8 and 16, and the other group is 5 and 7. The first group is to find the common factor of two numbers with multiple relations; The second group is to find the common factor of prime numbers. When I was teaching these two special situations, I gave more numbers and arranged three logarithms. The first group is 4 and 8, 16 and 32, 6 and 24, and each pair has multiple relationships. Let the students find the common factor and common factor first, then observe the common factor and find the common factor law of each group. In the second group, three logarithms 3 and 7, 8 and 9, 15 and 16 are arranged, and they all have coprime relations. Ask the students to find the common factor and the common factor first, then observe that the common factor of each group is 1, and then think about the characteristics of each group, so as to sum up the methods of finding the common factor in these two special situations.

Teaching rules:

According to Mathematics Curriculum Standard (20 1 1 Edition), mathematics teaching activities should pay attention to the organic combination of four basic goals and realize them as a whole; In order to attach importance to students' dominant position in learning activities, I mainly chose inquiry learning in this class. Similarly, according to the mathematics curriculum standard (20 1 1 version), in order to make students' dominant position and teachers' leading role harmonious and unified, I also chose heuristic teaching method.

Teaching methods:

1. Operation of learning tools: Reasonable use of learning tools can promote students' personal experience and help them learn to establish mathematical modeling.

2. Whiteboard application: Appropriate courseware demonstration will bring a clear sense of hierarchy to the classroom, reflecting the leading role and guidance of teachers. A powerful electronic whiteboard can better assist the interaction between teachers and students.

3. Physical display platform: it is conducive to the timeliness of feedback, making feedback more beneficial, and allowing individual students to produce representative and typical learning resources for all.

4. Classroom blackboard writing: The necessary blackboard writing is conducive to the synchronization of students' thinking and teaching process, and helps students better grasp the context of teaching content.

Teaching process:

First, check the import. (Review the method of finding factors)

Recalling old knowledge paves the way for the extension of new knowledge.

Ask the students to find all the factors of 12. Tell me how to find it. What should I pay attention to when looking for factors?

(Numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20 and assembly circle 1 20. )

Let the students drag the factor of 12 into the set circle and recall the method of finding the factor. How to find the factors quickly and orderly?

The use of multiplication formula is orderly and not easy to miss.

Second, explore

Explore 1: Understand the common factor.

Find all the factors of 18 again and show the set circle 2. Ask the students to drag all the factors of 18 into the set circle 2.

9、 18

Students may drag it to 9, 18, and other factors? Can you find a way to represent all the factors of 12 and 18 with two sets of circles?

Move the assembly ring. Show the process of intersection dynamics.

Teacher: What's in the assembly circle on the left? (Factor 12) What is filled in the set circle on the right? (a factor of 18) What is the middle circle? (that is, the factor of 12 is also the factor of 18).

Then we can give him a name? (Common factors)

Can we put 4 in the middle circle? Why?

According to the students' answers, it is concluded that even the factor of 12 is the factor of 18, so we call it the common factor of 12 and 18.

Consolidate the exercises.

Have you learned to find the common factor of two numbers? Just try it.

Find the common factor of 6 and 9, find the common factor of 30 and 45.

Inquiry 2: Understanding Common Factor and Minimum Common Factor

If you find the common factor of 12 and 18, which number do you think it is?

Consolidate the exercises.

Find 6 and 9 on the basis of the previous exercise; Common factor of 30 and 45.

We learned to find common ground. Can the students find the least common factor of these three groups of numbers? What did you find?

The lowest common factor of all numbers is "1".

Inquiry 3: Find the common factor of a special array.

Find the common factor of each group of numbers below.

1, 4 and 8 16 and 326 and 24.

2, 3 and 78 and 9 15 and 16.

Talk to each other in groups when you are finished. What can you find?

What are the characteristics of each group of two numbers and what are their common factors? Do the common factors of two numbers with these characteristics have these laws? Group verification.

Feedback comes to the conclusion that two numbers are multiples, and the larger number is the common factor of two numbers.

When two numbers have only one common factor 1, their common factor is 1.

Third, practical feedback.

There are two, the length is 12 cm and 18 cm respectively. Cut them into equal-length sticks, and no extra ones are allowed. How long is each stick?

Teacher: What do you think when you see this question? Here are a few key words: the same length, no surplus, what is the longest? What are we asking for when confronted with such a problem?

Fourth, induction and summary.

1. What have we learned in this lesson?

2. How did we acquire this knowledge?

(Not only let students talk about the gains in knowledge and skills, but also pay more attention to the gains in learning methods and emotional attitudes, which once again arouses good emotional experience. )

Mathematics Courseware for Grade Five in Primary School Part II: Searching for Common Factors

Teaching objectives:

Knowledge and skills: go through the process of finding the common factor of two numbers and understand the meaning of common factor and common factor. Exploring the method of finding the common factor will correctly find the common factor and common factor of two numbers.

② Mathematical thinking: Combining with concrete examples, we should infiltrate collective thinking, cultivate students' ability of orderly thinking, and let students develop the habit of thinking without repetition or omission.

③ Problem-solving: Cultivate students' ability to express their findings in their own language, be good at discovering laws and use them to solve problems.

④ Emotional attitude: actively participate in mathematics activities, experience the happiness of autonomous learning, and experience the happiness of learning mathematics.

Teaching focus:

Go through the process of finding the common factor of two numbers and understand the meaning of common factor and common factor. This is the core task of this lesson.

Teaching difficulties:

Will use enumeration to find the common factor and common factor of two numbers, and use set circle to record and present the thinking process. This is because although enumeration is the lowest method, it is also the most important and intuitive method. Students must fully understand the meaning of common factor and use set circle to represent the thinking process.

Teaching methods:

1. Make the teaching content active and let students learn while doing. The arrangement of teaching materials in this section is rather boring and can't stimulate children's interest in learning. Therefore, the problem of writing multiplication formula to find the factor in the textbook is full, which has become a queue-like activity of the male and female teams of the school gymnastics team, which leads to the topic of finding the common factor.

2. Use group cooperative learning to make students interact in middle school. The cooperation ability of talents needed by modern society is the most important. In order to be responsible for children's future study and lifelong development, the design of this course adopts the way of group cooperation, which also paves the way for highlighting the "inquiry and discovery method" and "discussion and induction method".

3, make full use of the original cognitive experience, in the transfer of middle school. Curriculum standards point out that the teaching of mathematical knowledge should pay attention to the "growing point" and "extending point" of knowledge. The "growing point" of this lesson lies in "finding factors" Using the idea of mathematical migration can guide children to understand the concepts of common factor and common factor well, and expand and extend them in the continuous migration.

Teaching process:

First, create situations to pave the way for new knowledge.

1, create a situation: the students of the school gymnastics team, with 12 girls and 18 boys, are about to compete. Please line up the boys' and girls' groups.

2. Can you use an expression to express the formation of your platoon?

Courseware demonstration of students' speech:12 =1×12 = 2× 6 = 3× 4.

18= 1× 18=2×9=3×6

(Design purpose: Conduct communication activities in specific situations to help students review factors, perceive common factors, and pave the way for learning new knowledge. At the same time, the situational questions can stimulate students' interest in learning and make knowledge no longer boring. )

Second, explore independently and gain new knowledge.

1, observed that

Teacher: What do you find from these two lines of equations?

Health: 1, 12,3,4,2,6 are the factors of12. 1, 18,2,9,3,6 are the factors of18. Where 1, 2,3,6 are factors of 12 and 18.

The courseware shows the assembly ring.

Step 2 reveal the concept

Since 1, 2, 3, 6 is both a factor of 12 and a factor of 18, we can merge two sets in the set circle and fill in their common factors at the middle intersection, that is, their common factors (courseware demonstration).

Step 3 deepen understanding

Ask a question: How many common factors will they have? Who is the youngest?

After discussion, students come to the conclusion that the number of factors of a number is limited, so the number of common factors of two numbers is also limited. The common factor of 12 and 18 here is 6.

4. Reveal the topic: Today, our lesson is to learn to find common factors. (blackboard writing)

5. Method: Looking back, how did we find the common factor of 12 and 18?

Student: First list the factors of two numbers, then find out their common factors, and finally find out the common factors among the common factors.

(At the same time, the teacher writes down the factors of: 12: 1, 2, 3, 4, 6, 12.

Factors of 18: 1, 2, 3, 6, 9, 18.

Common factors of 12 and 18: 1, 2,3,6.

Common factor of 12 and 18: 6.

6. Consolidate in time: after practicing 1, 2. Let the students make a list independently, find out the common factors and fill them in the notebook, and then evaluate them collectively.

The exploration of new knowledge is the focus and difficulty of the whole class. Heuristic teaching helps to implement students' dominant position, give play to teachers' guiding role, and make students become the main body of learning and learn to learn gradually. )

Third, practice expanding and consolidate new knowledge.

1, finish the fourth question. Because there are many topics in this topic, the focus of practice is to discover the law of common factors of special numbers, so I intend to practice this topic in groups (vertical three rows, aiming at letting students experience and refine the solution of common factors of three coprime relational numbers, multiple relational numbers and common factors), and communicate collectively after practice, and then guide thinking: Are the common factors of these numbers regular? After students think independently, it is found that the common factor of the two numbers in the first question is 1 (at the same time, the number introduced by the teacher is called prime number), the number in the second row has a multiple relationship, and the common factor is decimal. These laws do not need a unified language, as long as students describe them in their own language.

2, complete an exercise 3: (The third question designed in the book is mainly to consolidate the idea of set, and the depth of the exercise is not enough. We will find the common factor of two numbers, so will you find the common factor of 12, 15, 18? Students independently show the enumeration process with a collection circle on the homework paper.

3. Then complete exercise question 5.

Exercise design is from understanding to expanding application, gradually deepening, and cultivating students' abstract generalization ability and cooperation consciousness. Teaching extends from two to three, from simple enumeration to regular refining methods, which enhances the depth of knowledge and students' awareness of drawing inferences from others. )

Fourth, the whole class summarizes, reviews and integrates.

1. In this lesson, we know the common factor and common factor of two numbers. Tell me about the method you have mastered.

2. Complete mathematical inquiry: guide students to find common factors, and there are many discoveries. You can finish the math exploration in the book by yourself after class.

Students recall what they have learned in the whole class and think about problems. 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. )