I said that the topic of this class is the principle of pigeon nest (blackboard writing). This lesson is the first section of Unit 5, Book 12 of primary school mathematics. Let me talk about this course from the following four aspects.

First, (let's talk about the first point first) Starting from the learning situation, determine the division of class hours and have a dialogue with the text.

There are three examples in this unit, including example 1 and example 2. The textbook introduces the principle of pigeon hole to students through several intuitive examples and practical operation. Based on students' understanding of the mathematical method of pigeon hole principle, they will use this principle to solve simple practical problems. The content of case 1 case 2 mainly experienced the exploration process of pigeon hole principle, focusing on guiding students to discover and summarize the law through practical operation, which laid a solid foundation for studying pigeon hole principle (II) and solving problems by using it in the future. Example 1 and example 2 can be completed in one class or two classes. I choose the latter and have the following thoughts.

The content of wide-angle mathematics contains rich mathematical thinking methods. The main purpose of wide-angle teaching is to let students be influenced by mathematical thinking methods and develop their mathematical thinking ability. Therefore, for most students, there are some thinking difficulties in learning. The pigeon hole principle is the jewel in the crown of wide-angle mathematics, which is more challenging than the study of chicken and rabbit in the same cage in 1 1. In the Principle of Pigeon Cave, it is quite difficult for students to explain the two key words "there is always one" and "at least", to achieve the idea of "average score" of "at least", and to establish a mathematical model of what is regarded as an object and what is regarded as a drawer, especially the understanding of "at least", which is different from that mentioned in previous mathematics learning. Here, in addition, it is difficult for students to express their thoughts in refined and accurate language.

Read the textbook again and sort out the knowledge sequence of pigeon hole principle according to example 1 and example 2. The example 1 describes that there are more objects than drawers 1. Example 1 The number of description objects is less than twice the number of drawers, but 2 or 3 more than the number of drawers. Example 2 describes that the number of objects is more than an integer multiple of the number of drawers 1. Example 2 shows that example 1 is the basis of learning example 2 well. Only through the teaching of Example 1, can all students really experience the inquiry process of "Pigeon Cave Principle", understand and understand several difficulties they may encounter in their study, and establish clear basic concepts, ideas and methods, can they successfully learn Example 2, otherwise, this part of the learning will only be cold to gifted students. So I choose to divide the case 1 and case 2 into two categories. Some teachers may say that the teaching content of this course is too little. Based on this, I will explain it in the fourth link.

Second, starting from the text

Determine the teaching objectives

According to the mathematics curriculum standards and teaching materials, I have determined the learning objectives of this lesson as follows:

1. After going through the inquiry process of "pigeon hole principle" and having a preliminary understanding of "pigeon hole principle", we will use "pigeon hole principle" to solve simple practical problems.

2. Develop students' analogical ability through operation and form abstract mathematical thinking.

3. Feel the charm of mathematics through the flexible application of pigeon hole principle.

The focus of teaching is to discover, summarize and understand the principle of pigeon cage through the inquiry process of the principle of pigeon cage.

I regard understanding the meaning of "always" and "at least" in the principle of pigeon hole as the teaching difficulty of this course.

The reason why I determine the teaching objectives and difficulties in this way is because the New Standard points out that students will understand the extensive relationship between mathematics and life through mathematical activities, learn to use the knowledge and methods they have learned to solve simple practical problems, deepen their understanding of the knowledge they have learned, and acquire the thinking method of using mathematics to solve problems.

Third, proceed from the reality of students.

Choose a reasonable teaching method

In terms of teaching methods, this course mainly adopts the methods of asking questions to stimulate interest, teaching and practical operation.

In the study of law, students mainly adopt independent, cooperative and inquiry learning methods.

The fourth aspect is: apply what you have learned and talk to the classroom.

In this lesson, I designed four teaching links: game introduction-exploring new knowledge-reflection, presentation-problem solving (game).

Let me talk about the intention of this design.

The first link-game import

Because I only take the example 1 as the teaching content of this course, I made some preparations and supplements for the teaching of the example 1 when designing. In the lead-in part, a game is designed to guess that at least several students were born in the same month, which brings the relationship between mathematics and life closer and stimulates students' desire to explore. After the teaching of the example 1, the problem of putting five pencils into four boxes was added. The purpose is to let students feel, experience and discover the same phenomenon more fully through two different examples, which is helpful for students to abstract and summarize and make the conclusion more convincing. Then it is extended to the problem of seven pencils in five boxes, eight pencils in five boxes and nine pencils in five boxes. This remainder is 2, yes, 3 and yes, 4, and the first level of understanding of the pigeon hole principle is completed.

The second link is to explore new knowledge.

According to students' learning difficulties and cognitive rules, I designed three levels of teaching activities in the inquiry part. These three levels of teaching activities gradually transition from image thinking to abstract thinking, step by step, and cultivate students' logical thinking ability.

The first one emerges: physical operation, which puts four pencils into three boxes (blackboard books) to solve three problems:

1, how can I put it

Know the method of arrangement and combination, and make it clear that if the number of branches in each box is different, it will be regarded as division, which will guide students to think in an orderly way and clear the obstacles for the following enumeration.

2. * * * There are several ways to understand "release anyway".

3. Understand the meaning of "there is always one".

By observing the number of pencils in the box, we can find out the number of pencils in the box with the largest number of pencils in the four ways, understand the meaning of "there is always one", and get a preliminary impression: no matter how you put them, there is always a pencil box with the largest number of pencils, which are 2, 3 and 4 respectively.

The second level: from concrete operation, from abstraction to numbers, numbers are decomposed-thinking about what will happen if five pencils are put in four boxes (blackboard books include six and five boxes), students can directly complete the form. This level has achieved three purposes:

1. Understand the meaning of "at least" and accurately express the phenomenon.

By observing the data in the box with the largest number of branches in the table, let the students find out the least from the most, learn to express it with the least, and sum up the conclusion that there are always at least two pencils in a pencil box when "there are five branches in four boxes" and "there are four branches in three boxes".

2, understand the idea of "average score" (blackboard writing), know why "average score".

Grasp the situation that best reflects the conclusion and guide students to understand how to quickly know that there are always at least a few branches in a pencil box-that is, divide them equally according to the number of boxes. Only in this way can the number of branches in the most box be as small as possible.

3, abstract generalization phenomenon

Through the exercises of "3 boxes with 4 sticks", "4 boxes with 5 sticks" and "5 boxes with 6 sticks", let students abstractly sum up that "when the number of objects is more than the number of drawers 1, there will always be at least 2 objects in a drawer no matter how they are placed" (blackboard writing), and get a preliminary understanding of the principle of pigeon hole.

(3) Students choose their own questions and explore "If the number of objects is greater than 1, how many pencils should be put in a pencil box anyway?" (blackboard writing 789 object 5 drawer)

At this level, students should understand that when the remainder is not 1, they have to go through two average points, the first is by drawer, and the second is by remaining branches. Only in this way can we achieve the goal of "making the branches in the box as few as possible".

In the third part of the teaching process, all the examples learned in this lesson are presented as a whole, so that students can sum up the simplest situation in the pigeon hole principle by comparison: when the number of objects is less than twice that of drawers, there are always at least two objects (blackboard books) in a drawer no matter how they are placed.

In the last practice session, I appeared in the form of a game. I have designed several simple practical problems that need to be solved by applying the pigeon hole principle, so as to further cultivate students' model thinking, let students correctly find out what is "something to be divided" and what is "drawer" in the problems, and at the same time let students feel the application of mathematical knowledge in life and the charm of mathematics.

drawer principle

average score

Four pencils in three pencil cases.

Five, four

Six and five.

When the number of objects is more than the number of drawers 1, no matter how to put them, there are always at least two objects in a drawer.

7 items and 5 drawers

8 items and 5 drawers

9 items and 5 drawers

﹕ ﹕

﹕ ﹕

"... no matter how you put it, there is always a drawer that can hold at least two objects. "

This is the blackboard design for this lesson.

Thank you! My speech is over.