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一、打破常规思维模式,引导学生转换思路。例:把一个表面积为64平方厘米的正方体平均分成8个大小一样的小正方体,每个小正方体的表面积是多少平方厘米?分析:按常规的解题方法,因为无法求出大正方体的棱长,所以也无法求出每个小正方体棱长,故此题无法求解。由于此路不通,逼得学生另寻新径。这时教师可引导学生先画图,当学生画出图形后很快发现,分割后大正方体的表面被分成6×4=24个小正方形,而小正方体的表面积刚好是这样的6份。从而得解:64/6×4=16(平方厘米)还有部分学生这样分析:分割后的每个小正方体有3个面是原来大正方体的表面,有3个面是新截的面。这样,截割后8个小正方体的表面积之和刚好是原正方体表面积的2倍,从而得出另一种解题思路:64×2÷8=16(平方厘米)
First, break the normal mode of thinking, guide students to change ideas. Example: A square with a surface area of 64 square centimeters is divided equally into 8 small cubes of the same size, and the surface area of each small cuboid is a few square centimeters. Analysis: According to the conventional solution method, , So it can not find each small cube edge length, so this problem can not be solved. Due to this road barrier, forcing students to find another new path. At this time, the teacher can guide the students to draw first. When the students draw a picture, they quickly find that the surface of the divided large cube is divided into 6 × 4 = 24 small squares, and the surface area of the small cube is exactly 6 pieces. To understand: 64/6 × 4 = 16 (square centimeter) There are some students to do this analysis: Each split small cube has three faces is the original large cube surface, there are three new faces. In this way, the surface area of eight small cubes after cutting is just twice the surface area of the original cuboid, thus leading to another solution: 64 × 2 ÷ 8 = 16 (square centimeters)