数学疑难解惑（Mathematical puzzle）.doc

数学疑难解惑（Mathematical puzzle） Troubleshooting the fifth grade 2 Peoples education press primary school mathematics curriculum research and Development Center for teaching materials Liu Li What factors should be grasped when teaching rotation? 1. background knowledge about rotation. The descriptive definition of rotation is that, like this (Figure 4), a graph transformation that rotates an image around a point O is called rotation. According to the descriptive definition, to complete the rotation, you must determine two factors, namely the rotation center and rotation angle (including rotation direction). Any change in one factor, the rotation will change: two rotation in Figure 5, the center of rotation, the rotation angle is different, and finally get the pattern is different; similarly, two rotation in Figure 6, the center of rotation, rotation angle, the pattern is also different. Therefore, when rotating, it is necessary for the student to make clear which point he rotates around and which angle is the angle of rotation. Figure 4, figure 5, Figure 6 The rotation transformation has three characteristics: (1) the shape and size of the same graphics (pictured above 4 triangles in A B C with the same shape and size of the triangle ABC); (2) corresponding to a distance equal to the center of rotation (as in Figure 4 in the length OC and OC is equal to the length of); (3) the corresponding point and the center of rotation of the segment of the angle is equal to the rotation angle (i.e. above 4 angle AOA size and the angle of rotation angle equal to the size of COC and the angle of rotation is equal to the rotation angle here is 90 degrees). Figure 7 Figure 8 According to the definition of rotation, the oscillation is also a rotating phenomenon in Mathematics (Figure 7 and figure 8). 2. for the teaching of this part, please pay attention to the following points. (1) grasp the teaching requirements. Through the teaching of this unit, the student describes the phenomenon o