这里我尝试着对课本中的一道例题进行科学的改造,提出具有开放性、挑战性的问题,其解答的不确定性及条件的发散性(依学生的素养而定)留给学生的思维空间很大.在数学应用与建模选修课上,充分地让学生“活动”起来,学生通过由折到画,由画到算,从课本知识延伸到课外知识,从课堂学习开拓到网络世界,积极地、不断地发现,不断地学习,充分认识到数学的巨大价值和无穷的魅力.下面是这节课的教学实录. Here I try to make a scientific transformation of an example problem in the textbook and ask questions that are open and challenging. The uncertainty of the solution and the divergence of the conditions (according to the students’ literacy) are left to the students’ thinking space. Great. In mathematics application and modeling elective classes, students are fully “active”. Students go from classroom learning to online world by learning from folding to painting, drawing to computing, and extending from textbook knowledge to extracurricular knowledge. Actively and constantly discovering, constantly learning and fully realizing the tremendous value and infinite charm of mathematics. The following is the teaching record of this class.