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新课标中,提倡学生是数学学习的主人, 提出“有效的数学学习活动不能单纯地依赖模仿与记忆,动手实践、自主探索与合作交流是学生学习数学的重要方式”这一全新理念．既要动手操作,更要严谨计算,从中得到启示,来指导操作．在2005年的许多地区中考题中, 都体现出这一理念．例1 (2005年盐城)已知如图1, 现有a×a、b×b的正方形纸片和a×b的矩形纸片各若干块,试选用这些纸片(每种纸片至
In the new curriculum standard, students are advocated as masters of mathematics learning. They proposed that “effective mathematics learning activities cannot simply rely on imitation and memory, hands-on practice, independent exploration and cooperation and communication are important ways for students to learn mathematics”. It is necessary to operate, but also rigorous calculations, to get inspiration from it, to guide the operation. This idea was reflected in many examination questions in many regions in 2005. Example 1 (Yancheng, 2005) It is known that, as shown in Fig. 1, the existing a×a, b×b square sheets and a×b rectangular sheets each have several pieces, and these sheets are selected (each sheet