(2) From the rotation of line segments to the rotation of graphics, learn to describe the rotation process with the center point, direction and rotation angle. Specific practices:
① Observe carefully the rotation process of the pointer. (The pointer points from 12 to 1) Who can describe this rotation process completely in one sentence, if the pointer continues to rotate clockwise around the O point from "6" 180? What will it point to?
There is so much rotation. Think about it. What should be said to describe a rotating phenomenon?
③ Explore the rotating characteristics of windmills.
How did the windmill change from figure 1 to figure 2? Let the students work in groups.
* * * Solve the problem together.
From figure 1 to figure 2, the windmill rotates counterclockwise _ _ _ degrees around point O.
How to judge the angle of windmill rotation? Through observation, we found that after the windmill rotates, not only each triangle rotates 90 counterclockwise around the O point, but also each line segment and each vertex rotates 90 counterclockwise around the O point. )
④ Reveal the characteristics and properties of rotation.
From the picture, we can clearly see that the position of each triangle has changed after the windmill rotates, so what hasn't changed? The shape and size of the triangle have not changed. The position of point o has not changed. The length of the corresponding line segment has not changed. The included angle of the corresponding line segment has not changed. )
If we rotate the windmill on the basis of Figure 2, continue to rotate counterclockwise around point O 180. So where should the yellow triangle turn?
3) Improving the spatial imagination and describing the process of graphic rotation correctly can increase the phenomenon of both clockwise and counterclockwise in the process of rotation, thus consolidating the understanding of rotation transformation.
2. The understanding of the meaning of rotation and the application of the characteristics and properties of rotation make this unit more difficult. To break through this difficulty, it is best to follow the principle of from easy to difficult and from special to general. The specific methods are as follows:
1) right triangle. Think independently about how to rotate the triangle 90 degrees clockwise and draw the rotated pattern. On the basis of independently completing the requirements, through communication and sharing strategies: rotate 90 clockwise, OA and OA' are perpendicular to each other, OA = OA', OB and OB' are perpendicular to each other, OB = OB' (point B and point B' can also be symmetrical), and connect A' and B'.
(2) Example 4, completed independently according to the strategy just now. What do you find by comparing these two questions? (It's a little difficult to find the line perpendicular to OB)
3, warm tips
(1)p6 Do it 1 ("which figure rotates around which point" and "which direction". ) p8 Exercise 1, Question 3, Band 1. (2)p6 does one thing and does two things, p8 questions 4 and 6 (The characteristics of another kind of graph "rotationally symmetric graph" were discovered through experiments. These figures rotate around their center at a certain angle and coincide with the original figures. You can use your own language to describe the characteristics of these graphics overlapping with the original graphics after rotating 360 degrees. The key is how to find the center point. )