The fifth unit of the fifth grade mathematics book published by People's Education Press, "Draw a rotating figure on a square paper", is another major geometric topic in the geometry part of primary school mathematics learning after translation. Compared with the translation of graphics, the rotation of graphics is more complicated, but its main methods and principles are highly unified. So before learning this part, students can review the principles and methods involved in graphic translation, which is very helpful for learning this part.

Before drawing, let's take a look at some knowledge points in this part.

1, the nature of rotation:

(1) The rotation of a graph is the positional movement of each point on the graph rotating around a fixed point at a fixed angle on the plane;

② The distance from the corresponding point to the rotation center is equal; The size and shape of the figure have not changed before and after rotation, but the position and direction have changed, and the rotation center is the only fixed point;

(3) The angles formed by the connecting line between the two groups of corresponding points and the rotation center are equal, which are all equal to the rotation angle;

2, how to draw the shape of the graphics rotation:

① First, observe the shape characteristics of the original image to find the key points;

② Identify the center, direction and angle of rotation; ③ If the vertex of the right-angled triangular plate coincides with the center of rotation, the rotated shape of the figure is on the other side of the triangular plate;

(4) Determine the length of each corresponding point and mark it with a dotted line;

⑤ Connect the corresponding points and mark the names.

3, symmetrical rotation: rotation should pay attention to: clockwise, counterclockwise, degrees.

In the exploration of how to rotate, we found that the rotated figure is basically centered on the rotation center and then rotates to other sides. As long as the length and rotation angle of the line segment remain unchanged, the positions of the rotated points and line segments can be found.

In addition, we can also think about the problem that the graph rotates 90 degrees: taking the vertex of the right angle as the rotation center, then the rotated right angle edge is perpendicular to the original right angle edge. When both right-angled sides find the vertical line segment, we can connect the third side and get the rotated right-angled triangle.

From the above practice and exploration, we can summarize the drawing method of rotated graphics into the following steps.

Write at the end: the principle of graphic rotation and graphic translation is basically the same. The shape and size of the object have not changed before and after rotation. The corresponding point and the corresponding line segment are equal, and the corresponding angle is unchanged. As long as you master this method, when you rotate, you only need to find the rotation angle and point-to-point rotation, and finally connect the rotating points to get the rotated graphics. This part of the study has high requirements for the students' actual operation, and everyone needs to be careful in constant practice to ensure that no mistakes are made.