Teaching content: mathematics, experimental teaching material of compulsory education curriculum standard (People's Education Edition), sixth grade, wide angle of mathematics.

Teaching objectives:

1. Let students understand and master the meaning of reciprocal by exploring some examples. Mastering the method of finding the reciprocal of cooperative inquiry will find the reciprocal of a number.

2. Make students experience the generalization process of reciprocal meaning, and improve the ability of observation, comparison, generalization, induction and flexible use of knowledge to solve problems.

3. Through students' personal participation in inquiry activities, experience the fun of mathematics learning, stimulate their positive learning emotions, and develop the habit of cooperative inquiry.

Teaching process:

First, the introduction of situations, leading to problems

1. Conversation understanding is "mutual".

Teacher: As the saying goes, you depend on your parents at home and your friends when you go out. Besides your relatives, you should also have friends in society. Do you have any friends?

Let the students (a) tell who is his good friend. (2)

Teacher: Can you express the friendship between two people in one sentence? What else can I say? Can you say that A is a friend and B is a friend? Why?

It is difficult for students to understand the word "mutual", which is a difficult point in teaching. Here, I make use of the relationship that you are my friend and I am your friend to make many transformations, and create situations in nature, so that students can have a life experience and know what "caring for each other" is in the life situation, thus mobilizing students' enthusiasm, enabling students to unconsciously understand the meaning of "caring for each other" and dispersing the difficulties in teaching.

2. Play games and fill in the blanks according to the rules.

Swallow-Wu Dai -() 3/8-(/) 10/7-(/)

(1) Students observe and fill in the blanks, answer by name and express their thoughts.

(2) Teacher: Can you name several groups of numbers according to the above rules? (Students give examples and the teacher writes them on the blackboard)

3. Students observe several groups of scores on the blackboard to see what are the characteristics of the two numbers in each group?

Discuss and communicate at the same table, then the whole class reports the characteristics of two scores in each group, and the teacher pays attention to guidance. (Mainly the product of numerator, denominator and two fractions. )

4. Teacher: Can you give these groups a proper name according to the characteristics of two scores in each group?

The teacher revealed the theme: the understanding of reciprocal.

5. Teacher: What questions do you want to ask when you see this topic?

Choose the blackboard according to the students' answers. (1) What is reciprocal? (2) How to find the reciprocal of a number? (3) What is the function of knowing the reciprocal? ……

The problem is the heart of mathematics, the starting point and motivation of students' inquiry, and guides students to find and ask questions in dialogue and game situations.

Second, cooperate to explore and solve problems.

1. Explore the meaning of reciprocal.

(1) Observe 3/8 and 8/3. Tell me which two numbers are reciprocal. What else can I say?

(2) Who can tell us who is the reciprocal of 10/7 and 7/ 10? what can I say?

(3) Group discussion, what is reciprocity?

After students think independently, communicate in groups.

The class reports, and the teacher gives guidance according to the students' reports. Students may have the answer is:

A: Two numbers with the numerator and denominator reversed are called reciprocal.

B: Two numbers whose product is 1 are called reciprocal.

Significance of reciprocal induction between teachers and students: Two numbers whose product is 1 are called reciprocal. (Teacher writes on the blackboard)

2. Explore the method of finding the reciprocal.

(1) Learning example 1: Write the reciprocal of 7/8 and 5/2.

A: Students try to write, and teachers patrol to remind them of the writing format.

B: call the roll. The teacher wrote on the blackboard: the reciprocal of 7/8 is 8/7, and the reciprocal of 5/2 is 2/5.

Teacher: Are the two reciprocal numbers equal? How to express its results? It can also be represented by-(dash).

C: Students communicate and look for a way to score each other.

(2) Teacher: Students can already find the reciprocal of a score. Think about it, what other numbers have we learned? (integer, decimal, with fraction), then how to find the reciprocal of integer, decimal and with fraction? Choose one and explore in the group.

A: Students choose a kind of research, and teachers patrol for guidance.

B: Students exchange reports and teachers write them on the blackboard.

C: Guide students to summarize the method of finding the reciprocal.

(3) Teachers ask questions: Is there a countdown to 0? Why? The students discussed and dispelled doubts.

1×( )= 1, so the reciprocal of 1 is 1. And 0×( )= 1?

The reciprocal of 1 is itself, and 0 has no reciprocal.

To find the reciprocal of a number (except 0), just exchange the numerator and denominator of this number.

(Design intention) Fully mobilize students' enthusiasm for learning, provide students with sufficient opportunities to engage in mathematical activities, guide students to study in groups, explore knowledge in discussion, understand and master the meaning and solution of reciprocal, and cultivate students' inquiry ability and consciousness.

Third, consolidate contacts and expand and deepen.

1. Which two numbers are reciprocal?

4/3 , 7/6 , 8 , 6/7 , 3/4 , 1/8

2. Write down the reciprocal of the following numbers.

4/ 1 1 , 16/9 , 35 , 15/8 , 1/5

Students write down the reciprocal of these numbers in their exercise books, call the names and answer them, and say how to get them and evaluate them collectively.

3. Try to be a little judge with keen observation.

The reciprocal of (1) 1 is 1. (2) All numbers have reciprocal numbers.

(3)3/4 is the reciprocal. (4) The reciprocal of a is1/a.

(5) Because 0.5×2= 1, 0.5 and 2 are reciprocal.

(6) The reciprocal of 7/5 is 7/2.

(7) The reciprocal of the true score is greater than 1. (8) The reciprocal of the false score is less than 1.

(9) Because 8-7 = 1, 3÷3= 1, 8 and 7, 3 and 3 are reciprocal.

4. Fill in the blanks.

3/4×( )= 1 7×( )= 1

2/5×( )=( )×4= 5/4×( )=0.5×( )= 1

5. Game: Find friends.

Teacher: Just now, each of us talked about our good friends in class. The teacher thinks you have too few friends. Now let's find some more friends in the class, shall we?

A student says a number, and whoever can say the reciprocal of the number correctly and quickly is a good friend with this classmate.

Multi-level exercises help students to consolidate new knowledge and activate their thinking. With the students' emotional participation, the game exercises arouse the students' enthusiasm and initiative in learning, arouse their thinking climax again, and make students get a pleasant emotional experience.

Fourthly, summarize the experience of reflection and evaluation.

What did you learn from this course? Is there a problem?

(Design intent) Help students sort out their knowledge, reflect on their own learning process, understand learning methods, and gain experience in mathematics learning.

Fifth, assign homework.

Reflections on interactive cognitive teaching;

At the beginning of this class, we will create a situation of "let students find friends", help students understand the meaning of "interaction" through this activity, and clear the obstacles to language understanding for building new knowledge. In class, the accuracy of expression is emphasized many times, and students are guided to express their thinking process clearly and methodically by using mathematical language in communication with others, and to discuss and ask questions.

I adopted the discovery teaching method in this class. Teachers only guide students to actively participate in the whole learning process through the identities of organizers, guides and collaborators, let students organize their own learning materials, provide students with free thinking space, respect students' autonomy, allow students to make mistakes in exploring new knowledge and experience success in correcting mistakes. Stimulate students' enthusiasm for inquiry with an equal and tolerant attitude. Especially when exploring the meaning of reciprocal and the method of finding reciprocal, let the students explore, observe, summarize and summarize by themselves. The design of this link is to guide students to carefully understand the positional relationship between numerator and denominator on the basis of careful observation of data characteristics, and try to find a method to find the reciprocal. The design strives to make students the masters of learning, so that "all truths must be obtained by students themselves, or rediscovered by students, or at least reconstructed by students".

"Reciprocal" learning is suitable for students to observe, compare, communicate and summarize. In order to better guide the study of law, I also organize teaching in the form of group cooperation. On the one hand, students can try to discover and experience the creative process; On the other hand, it can also enhance students' sense of cooperation, so that students can learn from each other and learn from each other in the process of group communication and class communication, and gradually complete the understanding of "countdown". Sometimes, generate is inspired by classmates and full of wisdom. And fully mobilize students' learning enthusiasm, provide students with sufficient opportunities to engage in mathematics activities, guide students to study in groups, explore knowledge in discussion, understand and master the meaning and solution of reciprocal, and cultivate students' inquiry ability and consciousness.

In the consolidation exercise after class, I designed such questions as "Be a little judge and be good at observing", "Fill in the blanks" and "Play: Find friends". Through these multi-level exercises, I helped students to consolidate new knowledge, activate their thinking, play games with students' emotional participation, arouse their enthusiasm and initiative in learning, arouse their thinking climax again, and make them get a happy emotional experience.

Finally, in the class summary, ask questions again, summarize and reflect, help students sort out their knowledge, reflect on their own learning process, understand learning methods, and gain experience in mathematics learning.