Lesson 1 "Pigeon Cage Principle"

Teaching content: Examples 1 and Example 2 on pages 70 and 7 1 of the textbook.

Teaching objectives:

1, experienced the exploration process of "pigeon hole principle" and got a preliminary understanding of "pigeon hole principle".

2, can use the "pigeon cage principle" to solve simple practical problems.

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

Teaching emphasis: understanding "pigeon cage principle".

Difficulties in teaching: Flexible application of "Pigeon Cage Principle" to solve practical problems.

Teaching methods: group cooperation and independent inquiry.

Teaching preparation: several sticks and four paper cups.

Teaching process:

First, create situations and introduce new knowledge.

Teachers organize students to play "chair grab" games (

Ask three students to come up and spread out two chairs) and announce the rules of the game.

Teacher: What's the mathematical mystery behind this phenomenon? Let's learn this principle together in this class.

Second, autonomous learning, initial perception

(1) Example 1: 4 pencils, 3 pencil cases.

1, observe and guess

Guess what will happen if you put four pencils in three pencil boxes?

2. Independent investigation

(1) put forward a guess: "Anyway, there are always at least two pencils in a pencil box."

(2) Verification of group cooperation: Please take out your pencil and pencil box and put them into group cooperation.

(3) Exchange discussions and reports. It may be as follows:

The first type: enumeration method.

Put the real thing and list all the results.

The second type: hypothesis method.

If only 1 pencil is put in each pencil box, put at most 3 pencils. The remaining 1 pencils will be put in one of the pencil boxes, so at least two pencils will be put in the same pencil box.

The third kind: the decomposition of numbers.

Decomposition of 4 into three numbers, * * * has four cases, (4, 0, 0), (3, 1, 0), (2, 2, 0), (2, 1, 1), and each result has at least one of the three numbers.

(4) Comparison and optimization.

Let the students keep thinking: If you put five pencils in four pencil boxes, will the result be the same? Put 100 pencils in 99 boxes? How to explain this phenomenon?

Teacher: Why not use enumeration to verify it?

When the amount of data is small, we can think directly by enumeration or hypothesis, but when the amount of data is large, it is simpler to think by hypothesis.

Step 3 guide discovery

As long as there are more pencils than boxes 1.

Anyway, there are always at least two pencils in a box.

(2) Example 2: Put five books in two drawers. No matter how you put it, there are always at least a few books in a drawer.

What about seven books? What about nine books?