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一、案例简述有个教学案例,任课教师通过对一道常见题“将一个棱长为6厘米的正方体,切削成一个最大的圆柱体,求这个圆柱体的体积是多少立方厘米?”进行师生合作分析、探究并进行变式练习:将一个棱长为6厘米的正方体,切削成一个最大的圆锥体,这个圆锥体的体积是多少立方厘米?(注:此改编题在网络上出现次数很多)经过一节课的师生探究活动,通过画图,对图1和图2进行直接分析以及推理(具体探究过程在此不再赘述),最终得到了圆柱体的体积占正方体的78.5%,以及圆锥体的体积占正方体的26.2%。并利用这两个比率常数进行了实际运用,让学生充分体会到这种常数的作用。
First, a brief description of the case There is a teaching case, the teacher through a common title "will be a prism length of 6 cm, cut into one of the largest cylinder, and find the volume of this cylinder is the number of cubic centimeters? Conduct a collaborative analysis of teachers and students to explore and carry out variant exercises: a cube of 6 cm long edge is cut into a maximum cone, the volume of the cone is how many cubic centimeters? (Note: This adaptation of the title on the web A lot of times) after a class of teachers and students to explore activities, through drawing, direct analysis of Figure 1 and Figure 2 and reasoning (the specific inquiry process will not repeat them here), and finally the volume of the cylinder accounted for 78.5 %, And the cone volume accounted for 26.2% of the cube. And the use of these two ratio constants were actually used, so that students fully appreciate the role of this constant.