After one year's junior high school study, students have certain abilities of induction, summary, analogy, transformation and mathematical expression, and are full of strong curiosity and interest in real-life mathematical knowledge, and can express their views through the mutual assistance and cooperation of group members under the guidance of teachers. In addition, in the course of this lesson, students can have a preliminary understanding of right-angled triangles by learning the previous knowledge, and can intuitively grasp some characteristics of right-angled triangles. Therefore, we should grasp these characteristics of students in teaching, stimulate students' interest in learning mathematics, establish students' self-confidence, and provide opportunities for the development of students' spatial concept, the accumulation of experience in mathematics activities and the display of their personality.

Second, teaching material analysis

(A) the status and role of teaching materials

Pythagorean theorem is learned on the basis that students master the related properties of right triangle. It has played an excessive role in the teaching material, paving the way for studying the inverse theorem of Pythagorean theorem in the future, and also laying the foundation for studying "quadrilateral" and "solving right triangle" in the future. The exploration and proof of Pythagorean theorem contains rich mathematical ideas and scientific research methods, which is the carrier of cultivating students' good thinking quality. It plays an important role in the development of mathematics. Pythagorean theorem describes the harmonious and unified relationship of nature with its concise and beautiful form and rich and profound connotation, and is a beautiful example of the combination of numbers and shapes.

(B) Teaching objectives

1. Knowledge and skills: Understand and master Pythagorean theorem, and use Pythagorean theorem to input simple calculations.

2. Mathematical thinking: By exploring the process of Pythagorean theorem, improve students' reasoning ability and experience the idea of combining numbers with shapes.

3. Problem-solving: In the inquiry activities, the inquiry results are obtained through cooperation and exchange.

4. Emotional attitude: Through the historical introduction of Pythagorean theorem, let students realize the cultural value of mathematics and improve their interest and confidence in learning mathematics.

In the inquiry activities, experience the diversity of problem-solving methods, and cultivate students' awareness of cooperation and communication and exploration spirit.

(C) Teaching focus and difficulties

1. Teaching emphasis: master Pythagorean theorem, so that students can deeply understand the special relationship of three sides of right triangle.

2. Teaching difficulties: the exploration process of Pythagorean theorem and the proof of Pythagorean theorem.

(d) Prepare teaching AIDS: a triangle, some paper, multimedia, onion lessons, etc.

Thirdly, the analysis of teaching methods and learning methods

1 Analysis of teaching method: Based on the knowledge learned and mastered by students in junior high school, the rational thinking ability of geometric figure observation and geometric proof is initially formed. Therefore, in teaching, we should strive to realize the teaching concept of taking teachers as the leading factor, students as the main body, knowledge as the carrier, and paying attention to cultivating students' thinking ability, practical ability and inquiry ability. Try to create a scene of "doing math and playing math" so that students can change from "learning" to "learning" and become the masters of learning.

2. Analysis of learning methods: Students at this stage lack rigorous logical reasoning ability. Therefore, when exploring Pythagorean theorem, we mainly introduce the situation through onion micro-class, and then verify Pythagorean theorem with intuitive and acceptable equal area method. The mode of "operation+thinking" conforms to the cognitive level of eighth-grade students, adapts to their thinking development law and psychological characteristics, and makes students realize that the best way to learn any knowledge is to explore, understand in exploration and understand in understanding, so that they can learn to learn.

Fourth, the teaching process

The new curriculum standard points out that the process of mathematics teaching is the process of teachers guiding students' learning and the process of interactive development between teachers and students. In order to teach in an orderly and effective way, I mainly arranged the following teaching links in this class:

(1) Watch the onion micro-lesson and introduce new lessons.

[Activity 1] Question and situation: Watch the onion micro-lesson carefully to understand the research of Pythagorean theorem in the East and the West.

The onion micro-course is introduced into the course to stimulate students' enthusiasm and enthusiasm for learning and exploration.

(B) teacher-student interaction, exploring new knowledge

[Activity 2] Question and situation: 2500 years ago, Pythagoras, a famous mathematician in ancient Greece, discovered that the floor paved by a friend's floor tiles reflected some characteristics of a right triangle.

(1) Please observe now. Can you find anything?

? How to find the square area with hypotenuse as side? What are the three sides of an isosceles right triangle? "

(2) The isosceles triangle is a special triangle. Does the general triangle have such characteristics?

(3) Do you have a new conclusion? Please make a bold guess.

(C) proof theorem of hands-on reasoning

[Activity 3] Question and Situation: Do all right triangles have such characteristics? Next, let's explore the string diagram of China mathematician Zhao Shuang.

(1) Take two right angles of a right triangle as sides, make two squares, and make a picture by cutting and splicing.

(2) How to represent the area of triangle and quadrilateral respectively? What is the relationship between them?

From this, the Pythagorean theorem can be obtained: if the two right-angled sides of a right-angled triangle are A and B respectively and the hypotenuse is C, then A 2+B 2 = C 2.

In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse.

(5) Class summary to improve knowledge.

I ask questions and then review.

1. What are your main gains from this course?

2. What kind of triangle does this theorem reveal?

3. What methods have we used in the process of exploring and verifying theorems?

4. What interests you most? Do you have any difficulties?

(6) assign homework and deepen thinking.

1. Collect the proof methods of Pythagorean theorem, try different methods to prove Pythagorean theorem (common 16 proof method), and show the communication in the next class.

Teacher's tips: jigsaw puzzle method, Zou method, Zhao Shuang method, president method, Mei Wending method, Euclid method, right triangle inscribed circle, reduction to absurdity and so on.

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