This is a mathematics class. The lesson plan is designed as follows: The problem of "chicken and rabbit in the same cage" appears in the first volume of fifth grade. It is a question recorded in the ancient Chinese mathematics masterpiece "Sun Zi Suan Jing". The original question is: "Today there are chickens and rabbits in the same cage. There are thirty-five heads on top and ninety-four legs on the bottom. What are the geometry of each chicken and rabbit?" Based on this mathematical question, the editor changed "difficult" to "simple".

Convert larger numbers into smaller numbers. It appears as the first example question in the textbook, that is, a chicken and a rabbit share a cage with 9 heads and 26 legs. How many chickens and rabbits are there? After solving this problem, the textbook presents questions from "Sun Tzu's Suan Jing", so that it goes from simple to complex, which is in line with students' cognitive rules.

There are many ways to solve the problem of "chicken and rabbit in the same cage", which also contain many mathematical thinking methods. For example, the list method provided in the textbook is permeated with the thinking method of enumeration and conjecture; the drawing method is permeated with the mathematical thinking method of hypothesis. The problem-solving process of enumeration and drawing can be used to summarize mathematical models for solving such problems, and at the same time it is permeated with mathematical model ideas; equations can also be used to solve such problems, which is permeated with algebraic thinking methods.

In class, I focused on discussing the list method with students. In teaching, these mathematical thinking methods should be connected and used together to establish mathematical models. Let students experience the modeling process in the process of solving problems.

1. Present the question and clarify its meaning.

In class, I first showed the "chicken and rabbit in the same cage" problem in "Sun Zi Suan Jing" to guide students to understand the meaning of the question and clarify its meaning. Then, organize students to discuss how to solve this problem. During discussions and exchanges, clarify the general path to solving more complex problems: you can start with simple problems first, look for patterns, and then solve more complex problems.

Then, I showed the first example question of this lesson, "A chicken and a rabbit share a cage with 9 heads and 26 legs. How many chickens and rabbits are there each?" The number was obviously smaller than before. There are many, so it is naturally easier to solve them.

This makes my students feel that when solving problems with relatively large numbers, they can make the numbers smaller and simplify the complex ones, and the solution will be much easier. At the same time, the idea of ??transformation began to sprout.

2. Independent thinking and group communication.

Faced with this problem, I asked students to think. Guess what can be done to solve it. Students will think of the list method based on their existing experience with the car rental problem, or use equations to solve this problem based on what they have learned, or use hypothetical methods to solve this problem. With the method in place, I give students a few minutes to think independently.

Let them clarify their ideas for solving problems and then communicate in groups. I think group communication is based on the independent thinking of each member of the study group, and this kind of communication is effective.

3. Communicate with the whole class and build models.

After the group members finished communicating, I asked the students to calm down, organize their thoughts based on the communication, and practice speaking. This can give students sufficient preparation to produce efficient results in whole-class communication.

Then the students reported their thoughts. In the report, the students used different methods. We combined induction and gave these methods names: list method, algebra method, hypothesis method, drawing method, and foot-raising method.

There are many methods, but each method contains a rule - for every time the number of chickens decreases by 1, and for every time the number of rabbits increases by 1, the number of feet will increase by 2. Only. Based on this rule, it is not difficult for students to summarize a mathematical model, which is the number of chickens = (total number of heads × 4 - total number of legs) ÷ (4-2). Students are participating in the entire modeling process, and gradually learn this mathematical idea through participation.