三角形等积变形本质探究及反思

Exploration and Reflection on Nature of Triangle Equal Area Deformation

反比例函数背景下,探究几何图形的面积以及几何图形面积与比例系数k之间的关系,是典型的数形结合题,中考也常涉及该知识点。因此在反比例函数新课结束后,安排一节复习课,让学生对新学的知识作回顾和巩固。原计划为反比例函数复习课,因学生对其中一个知识点“等积变形”不熟悉,转而利用教材中的探究活动,进行追本溯源,探寻问题本质。

Under the background of inverse proportional function,exploring the area of geometric figures and the relationship between the area of geometric figures and the proportional coefficient k is a typical number and form combination question,which is often involved in the senior middle school entrance examination.Therefore,a new lesson on inverse proportional function is followed by a revision one so that students can review and consolidate the new knowledge.Reflecting that an original plan was a revision lesson on inverse proportional function,however,students were not familiar with the knowledge of“equal product deformation”,and the teacher turns to the exploration activities in the textbook to trace back to the source and explore the essence of the problem.