Students think about each question independently before group discussion.

Concern: (1) Can students draw a correct conclusion by quadrilateral analogy?

(2) Whether students can adopt different methods.

Students discuss and communicate in groups (sum of internal angles of pentagon)

Methods 1: Divide the Pentagon into three triangles, and the sum of the three 180o is 540o.

Method 2: Starting from a point inside the Pentagon, divide the Pentagon into five triangles, and then subtract a fillet 360o from the sum of five 180o. The result is 540o o o.

Method 3: Divide the Pentagon into four triangles from any point on one side of the Pentagon, and then subtract a right angle of 180o from the sum of four 180o to get 540o.

Method 4: Divide the Pentagon into triangles and quadrilaterals, and then add 360o to 180o to get 540o.

Teacher: How clever you are! I have applied what I have learned.

After the communication, students use the geometric sketchpad to demonstrate and verify the method.

After getting the sum of the internal angles of the pentagon, the students seriously discussed the sum of the internal angles of the hexagon and the decagon. By analogy with the discussion method of quadrilateral and pentagon, it is finally concluded that the sum of internal angles of hexagon is 720o and the sum of internal angles of decagon is1440 o.

(2) Extend thinking and cultivate innovation.

Teacher: From the previous discussion, can you know the sum of the inner angles of polygons?

Activity 3: Explore the internal angles and formulas of arbitrary polygons.

Thinking: (1) What is the relationship between the sum of internal angles of polygons and the sum of internal angles of triangles?

(2) What is the relationship between the number of sides of a polygon and the sum of internal angles?

(3) What is the relationship between the number of diagonal triangles drawn from a vertex of a polygon and the number of sides of the polygon?

Students discuss with thinking questions and exchange the results after discussion.

It is found that the sum of 1: quadrilateral internal angles is the sum of two 180o, pentagonal internal angles is the sum of three 180o, hexagonal internal angles is the sum of four 180o, and decagon internal angles is eight 180o.

Discovery 2: The number of sides of a polygon increases by 1, and the sum of internal angles increases by180o. ..

It is found that there is a (n- 2) relationship between the number of diagonal triangles drawn from the vertices of N-polygons and the number of sides N. ..

It is concluded that the formula of the sum of the interior angles of a polygon is (n-2)? 180。

(3) Practical application and complementary advantages.

1, oral answers: (1) and ()

(2) nonagon's internal angle and ()

(3) The sum of the internal angles of the decagon ()

2. Answer first: (1) The sum of the internal angles of a polygon is equal to 1260o. How many polygons does it have?

(2) If the sum of the internal angles of a polygon is 1440o and the internal angles are equal, then the degree of each internal angle is ().

3. Discuss the answer: The sum of the internal angles of a polygon is 540o more than the sum of the internal angles of a quadrilateral, and all the internal angles of this polygon are equal. How many degrees is each internal angle of this polygon?

(4) General storage.

Students' self-summary:

1, polygon internal angle and formula.

2. Use transformation ideas to solve mathematical problems.

3. Solve problems by combining numbers with shapes.

(5) Homework: Page 93, 1, 2, 3.

Six, teaching reflection:

1, the change of teaching. In this class, the role of teachers has changed from imparting knowledge to organizing, guiding, cooperating and researching students' learning. After guiding students to draw, measure and find the conclusion, they can show it intuitively with the geometric sketchpad, so as to stimulate students to consciously explore mathematical problems and experience the fun of discovery.

2. Changes in learning. The role of students has changed from learning to learning. The students in this class don't stop at the level of learning textbooks.

Surface, but from the perspective of researchers into its territory.

3. Changes in classroom atmosphere. The whole class? Smooth, open and cooperative. Hide? A tour guide? As a basic feature, teachers should try their best to let students discuss, think and draw their own conclusions, and the teaching process is relatively smooth.

The whole class and classmates, classmates and teachers? Dialogue? 、? Discuss? Starting from mutual assistance and cooperation and aiming at solving problems, students can choose their own direction of success and judge the value of discovery in a relatively relaxed environment.

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