一、案例背景这节课是九年制义务教育课程标准实验教科书八年级第一节探索勾股定理第一课时.勾股定理是几何中几个重要定理之一,它揭示的是直角三角形中三边的数量关系,它在数学的发展中起过重要的作用.学生通过对勾股定理的学习,可以在原有的基础上对直角三角形有进一步的认识和理解.我校是一所农村学校,学生的思维与城里学生有一定距离,并且每个学生的知识、经验、思维、灵感、兴趣都不尽相同.因此学习活动中会呈现出丰富性、多变性和复杂性,会生成一些老师课前没想到的问题,有的能当场解决,有些则与本课无关,或不能当堂解 Case Background This lesson is the first lesson of the Pythagorean Theorem, the first section of the eighth grade of the nine-year compulsory education course standard experiment textbook. The Pythagorean Theorem is one of several important theorems in geometry, which reveals that in a right-angled triangle The relationship between the number of the three sides, which played an important role in the development of mathematics students through the study of the Pythagorean theorem, can be based on the original right triangle has a further understanding and understanding of our school is a rural school , Students’ thinking is far from urban students, and each student’s knowledge, experience, thinking, inspiration and interests vary, so learning activities will show richness, variability and complexity, which will generate some The teacher did not expect the problem before class, and some can be resolved on the spot, while others have nothing to do with this lesson, or can not be a solution