Professor Wu Zhengxian from Beijing Academy of Educational Sciences.

Ask questions first, and use letters to represent numbers.

Teacher: Students, in your experience, have you ever seen anything expressed in letters?

Hygiene: wc (toilet). Health: UFO.

Teacher: Have you ever seen anyone who uses letters to represent numbers? Have you seen this (showing playing cards J, Q, K)

Health: Yes.

Teacher: Do you have any questions about using letters to represent numbers?

Health: How to use letters to represent numbers? Student: What letters are used to represent numbers?

Student: Why do letters represent numbers? Student: What do you mean by using letters to represent numbers?

Second, explore why letters represent numbers.

Teacher: Math class is a place to solve problems, and today we will study with these problems. Suppose your age this year is 10, and Miss Yang is 20 years older than you. How do you express Miss Yang's age?

Health: 10+20=30 years old.

Teacher: Next year, you will be 1 1 years old. How old is Miss Yang? Health: 1 1+20, representing 3 1 year.

Teacher: When you are 1 year old, Mr. Yang's age is ... Student: 1+20, which means 2 1 year old.

Teacher: When you are 10 years old, can we use (10+20) years old to represent Miss Yang's age?

Health: 30 years old. Psychologically, she is 30 years old.

Teacher: Actually, 10+20 is also a result, but it is not the final result. Today, we use this way to express Miss Yang's age.

Teacher: Come back when you are 1 year old? Student: Teacher Yang is 2 1 year old.

Teacher: It must be 2 1 year old. Do you want to change the word? Health: 1+20 (years old)

Teacher: Did you go to school when you were 6 years old? Student: Teacher Yang 6+20 (years old)

Teacher: Did you go to college when you were 18? Student: Teacher Yang 18+20 (year old)

Teacher: 30 years old. Are you married? Student: Teacher Yang 30+20 (years old)

Teacher: Look at these formulas. What did you find?

Student: Teacher Yang 1 year old, so are we. The age difference is always 20 years old.

Teacher: Can you still write like this? Can you finish it? (endless)

Teacher: Human life is limited. How do you express the age gap between Mr. Yang and you? Can you come up with a formula for everyone to see at a glance and also reflect the age relationship between the two of you in any year? You can write anything you want.

(Student activities, teachers collect and generate resources and number them)

No. 1: A B

student teacher

2nd: Our age +20= Miss Yang's age.

Third: n+20=m

Fourth place: (C+20) years old

Teacher: Let's look at the number 1 first. what do you think? Health: Not good.

Teacher: Student 1, what number can your A stand for? What number can b stand for?

Health 1: can be any number.

Teacher: Then ask him, A and B can say whatever they like. Why not?

Student: No.65438 +0 can't see that the teacher is 20 years older than us.

Teacher: Mathematics is about expressing quantitative relations. No.65438 +0 can't see the age relationship between the teacher and you. How about the 2nd?

Health: No.2 made it clear, but it was a little troublesome.

Teacher: Who do you like better, Number Three or Number Four?

Health: I like No.4, but I don't know No.3.

Teacher: Whose age is N+20 in No.3 Middle School? Whose age does m refer to?

Student: The teacher's age is indicated, and the instructions are repeated.

Teacher: In No.4 Middle School, when C can be 1 year, 5 years old and 50 years old, C is a variable. Can c be 200 years old? Man's life is limited, and under certain circumstances, C has a range of values. What does C+20 see?

Student: I saw the teacher's age and the gap between the teacher's age and my own age.

Teacher: You can see the result of one quantity with letters, and you can also see the relationship between two quantities. Do you feel anything about letters now? (Yes)

Third, how to use letters to represent numbers

Show me the plate of 1: 1. How many peaches are there in each plate? Health: 10

Teacher: Put it another way. Health: (2×5)

Teacher: What are the numbers of 3, 5, 6, 100,10, 300,596 and 1000 respectively? (Performance of original board: 3×5, 5×5, 6× 5 ...)

Teacher: Can you stand it? If you can't stand it, find a way. If you can't stand it, keep writing. 100 1 disk ...

Health: I have an idea. Write X×5 (pieces).

Teacher: What does X mean? Health: Many plates. Health: Many plates, 5 each.

Teacher: How much is X five? Health: X×5

Teacher: What does X×5 mean?

Health: In X plates, there are five in each plate, and one * * * is (X×5) peaches.

Teacher: What else can we learn from it? Health: Five per plate.

Summary: X×5 not only expresses how many peaches are there in a * * *? It also expresses the relationship between peach and plate.

Exhibit 2: There are two meeting places. There is a person in the meeting place A, and mathematics needs to study relationships. The relationship between meeting place B and meeting place A is as follows. Listen and write the formula:

1.Hall B has 200 more people than Hall A.

There are 200 more people in Hall A than in Hall B..

Site b is three times as big as site a.

Site a is three times as big as site b.

Formula: a+200 a-200 a÷3 a×3

Teacher: What do these expressions mean?

Student: The number of people in the second meeting.

Teacher: What else did you see?

Student: the relationship between the number of people in venues A and B.

Summary: The letters we learned today can represent both a result and the relationship between two quantities.

4. What numbers can be represented by letters?

Show frog song: 1 frog 1 mouth, 2 eyes, 4 legs.

A frog has a mouth, an eye and a leg.

Go ahead. Can you finish it? Whether the number of frogs, the number of eyes and the number of legs can be expressed by today's knowledge can not only express the results, but also express the relationship between them. (Student activities, collecting results)

Health 1: (a) frog (b) mouth, (c) eyes (d) legs.

Health 2: (x) Frogs (x) have mouths, (2:(x) eyes (4x) legs.

Teacher: Who did you choose and why?

Health: No.2 and 1 only indicate quantity, and I don't know the relationship between them.

Teacher: 1 has (a) a frog (b) a mouth (c) an eye (d) two legs. If A is 1, do you know what B, C and D are here?

Health 1: I know that if a is 1, then b= 1, c=2 and d=4.

Teacher: You know, from your expression, can others know? (Sheng 1 Silence)

Teacher: And from "(x) frog (x) mouth, (2x) eyes (4x) legs", suppose x is 1. Do you know anything else?

Health 1: Yes, it is (1) mouth, (2) eyes and (4) legs, which can be counted.

Teacher: Now, do you understand why frogs have mouths, eyes and legs? Although a, b, c and d can represent any number, they can't.

Health: He knows, but we don't.

Summary: Mathematics is the language of all human communication, without which there will be more trouble.

Verb (abbreviation of verb) course summary

Teacher: What do you want to say to Teacher Wu in this class today?

This is the class record of the class discussion held by the network research community mathematics group on Wednesday evening of February, 20081February, 2008 18, and the lesson "Representing Numbers with Letters" by Mr. Wu Zhengxian.

Reflective experience:

This lesson is the fifth unit of the first volume of the fifth grade mathematics textbook published by People's Education Press. It is the first lesson of simple equations and the first lesson of students' thinking from "arithmetic to algebra". This lesson should not only make students feel the necessity of the generation of letters representing numbers, master the method of letters representing numbers, and understand the meaning of formulas containing letters, but also let students experience symbolic thoughts and infiltrate algebraic thoughts.

In this lesson, Mr. Wu leads today's topic from the letters in common playing cards in life, and at the same time lets the children enter today's inquiry learning with their own doubts and questions, thus mobilizing the students' enthusiasm.

For today's first question, how did Mr. Wu grasp the essence of using letters to represent numbers and guide students to understand them step by step?

Classroom is the place to solve problems. Teacher Wu used examples from life: the teacher-student era to guide everyone to exchange ideas. Students already have knowledge and experience in this field, so it is not a problem to calculate. The students come to the conclusion that 10+20 is a result, and Teacher Wu instructs the children to use this result to calculate the teacher's age in any year. By calculating the formula representing the teacher's age, we can sum up the rules and find some methods to express the age relationship between students and teachers. As a result, various relationships came out. Teacher Wu said: "Mathematics is to express quantitative relations." In the constant recognition and overthrow, the formula of the fourth student (C+20) years old can best express the age relationship between students and teachers. From this formula, we can see not only the age of teachers, but also the age gap between teachers and students. Children naturally understand that the letter C in the formula also has a range of values. In this way, Mr. Wu led the children to inadvertently understand the numbers represented by letters, and also understood that letters can not only see the result of one quantity, but also see the relationship between two quantities. Next, through different forms of practice, let children understand and master the application of letters representing numbers.

The second question: for the cultivation of children's good study habits, Mr. Wu uses the way of dialogue and communication to guide children to think step by step about solving problems with examples, and children naturally develop the habit of thinking in dialogue. Teacher Wu's class is relaxed and enjoyable, and children can imagine and give full play in class. For example, when writing about the age relationship between teachers and children, after analyzing the specific figures, Mr. Wu asked the children to write if they wanted to, and let them sum up the relationship themselves. Such a relaxed learning environment has created the habit of children's independent learning.

The third question: I feel that Mr. Wu pays special attention to students and knowledge generation in this class. In Mr. Wu's class, children are always guided to discover and explore through some familiar concrete examples in life, thus generating new knowledge. Teacher Wu emphasizes the life of mathematics, pays attention to life and the classroom. Mathematical knowledge is no longer pure knowledge, but mathematical thought serving life.