Learning mathematics and graphics is an important content. The following is an excellent tutorial on graphic rotation that I collected for everyone to learn.

one

learning target

1. Experience the process of observing and analyzing the rotation phenomenon in life, and guide students to look at the related problems in life from a mathematical point of view;

2. Understand the essence of rotation through concrete examples;

3. Experience the observation, operation and drawing of rotating feature graphics, and master drawing skills.

study

The nature of graphic rotation and the drawing method of graphic rotation.

teaching process

Preview navigation 1. Handmade: Make a small windmill.

2. Appreciate the rotation of some objects in daily life.

Question: (1) What are the characteristics of the rotation phenomenon in the above situation?

(2) Is there a similar example in life?

Cooperative investigation

First, the concept of exploration:

In a plane, a figure rotates a certain angle around a fixed point, which is called the rotation of the figure. This fixed point is called the center of rotation and the rotation angle is called the rotation angle.

1. Operating activities

1 Turn the triangular ruler ABC counterclockwise around point C to the position of DCB.

Question: measure the degree of ∠ACD and ∠BCE, the length of AC and DC, BC and EC. What did you find?

Turn △ABC clockwise around point O to the position of △A/ B/C/.

Question: What did you find by measuring the lengths of ∠AO A/, ∠BO B/, ∠CO C/, line segments AO and A/O, BO and B/O, CO and c/o?

3 through the operation activities, let the students discuss:

What changes have taken place in the process of triangle rotation? What hasn't changed? Understand the essence of rotation through students' discussion;

2. Summary: the essence of rotation:

Second, the case analysis:

Example: Given the line segment AB and the point O, draw the graph after the line segment AB rotates counterclockwise around the point O 100:

Cooperative exploration iii. Exhibition and communication

1. As shown in the figure, line segment AO rotates clockwise around point O to get line segment BO. During this rotation, the rotation center is and the rotation angle is.

2. As shown in the figure, after rotating the left rectangle around point B for a certain angle, if the position is the right rectangle, then ∠ABC=.

3. As shown in the figure, P is a point in the equilateral triangle ABC. If △PAB rotates counterclockwise around point A to △ P ′ AC, then ∠ PAP ′ =.

4. As shown in the figure, the square is formed by rotating the square ABCD clockwise by a certain angle, where the center of rotation is, and the degree of rotation angle is.

5. The following statement is correct.

A translation will not change the shape and size of the graph, but rotation will change the shape and size of the graph.

B. The similarity between translation and rotation is to change the position of the graph.

C. Graphics can move horizontally for a certain distance in a certain direction or rotate for a certain distance in a certain direction.

D In translation and rotation graphics, the corresponding angles are equal, and the corresponding line segments are equal and parallel.

6. As shown in the figure, after rotating △ABC clockwise by 60, it can coincide with △ a ′ bc ′.

1 Find the center of rotation.

Point out the corresponding vertices and corresponding edges.

3 indicates the rotation angle.

If AA ′ and CC ′ are connected, what triangles are △ ABA ′ and △ CBC ′? Why?

When a class reaches the standard of 1, one of the following phenomena belongs to rotation.

(1) The groundwater level is decreasing year by year; ② the movement of conveyor belt; ③ the rotation of the steering wheel; (4) the rotation of the faucet switch; (5) the movement of the pendulum; 6. Swing.

A.2 B.3 C.4 D.5

2. The bauhinia pattern in the center of the regional flag of the Hong Kong Special Administrative Region consists of five identical petals, which are obtained by rotating one petal several times?

3. As shown in the figure, if the square CDEF can coincide with the square ABCD after rotation, then there are _ _ _ _ * points on the plane where the figure is located that can be used as the center of rotation.

4. As shown in the figure, rotate the graph in the grid 900 counterclockwise around the O point to draw the rotated graph.

5. At the isosceles right angle △ABC, ∠C=900, BC=2cm. If the midpoint o of AC is taken as the rotation center, rotate the triangle by 1800, and the point b falls on the point b', and find the length of BB'.

6. As shown in the figure, at △ABC, ∠BAC= 1200, an equilateral triangle △BCD is formed with BC as the side, and △ABD is rotated 600 clockwise around point D to obtain △ECD. If AB=3 and AC=2, find the degree of △ ∠BAD and the length of AD.

Two?

Teaching objectives:

1. After observing and analyzing the rotation phenomenon in life, learn to look at related problems in life from a mathematical point of view;

2. Through the understanding of specific cases, study and discover the essence of rotation;

3. Experience the observation, drawing and operation of graphics with rotating characteristics, and master and be familiar with drawing skills.

Emphasis and difficulty in teaching:

Explore and discover the definition and properties of rotating graphics, and master them skillfully. How to use the nature of rotation to make a rotating figure of a figure?

Pre-class preparation and guidance

In the plane 1. 1, rotate a graphic point around a fixed point to become _ _ _ _ _ _, and the rotation angle is called _ _ _ _ _ _.

2 Before and after the rotation, the figure _ _ _ _ _ _ corresponds to the line segment _ _ _ _ _, and corresponds to the angle _ _ _ _ _.

3 The distance from the corresponding point to the center of rotation is _ _ _ _ _ _ _.

4 The angle formed by the connecting line of each pair of corresponding points and the rotation center is _ _ _ _ _ _ _ _.

5 As shown in the figure, draw the figure after ⊿ABC rotates 90 counterclockwise around point A. ..

2. Group communication and cooperation:

1 Give a life example about rotation.

2 choices: ① The following phenomena belong to rotation.

A. When the motorcycle brakes suddenly, it slides forward; B. the process of the plane rushing into the air after taking off

C. the process of turning the lucky wheel; D. a train that flies by on a straight track

(2) In graphic rotation, the following statement is wrong.

A. The rotation angles of each point on the diagram are the same; B. Rotation does not change the size and shape of the graph;

C. The figure obtained by rotation can also be obtained by translation; D, the distance between the corresponding point and the rotation center is equal.

3 Point out the rotation, rotation center and rotation angle in the figure below.

Two. Class discussion:

1. As shown in the figure, △ABC is an equilateral triangle, and point D is a point on BC. After rotation, △ABD reaches the position of △ACD'. What is the center of rotation of 1? How many degrees did it rotate? If m is the midpoint of AB, where does the point M turn after the above rotation?

2. The figure below is formed by rotating the square ABCD. The rotation center of 1 is _ _ _ _

2 The rotation angle is _ _ _ _ 3 If the side length of a square is 1, then C'D=_____

Step 3 rotate the drawing

1 Rotate the line segment AB clockwise around the O point 1000 and draw a graph.

2 Rotate △ABC counterclockwise around point C 1200 and draw the corresponding triangle.

Draw a graph that △ABC rotates 90 counterclockwise around point C.

4. As shown in the figure, if the square CDEF can coincide with the square ABCD after rotation, then the graph

There are _ _ _ _ * points on the plane that can be used as the center of rotation.

5. As shown in the figure, at △ABC, ∠BAC= 1200, an equilateral triangle △BCD is formed with BC as the side, and △ABD is rotated 600 clockwise around point D to obtain △ECD. If AB=3 and AC=2, find the degree of △ ∠BAD and the length of AD.

6. As shown in the upper right, after AB rotates around point O, the line segment corresponding to AB is A ′ B ′. Try to determine the position of the rotation center point o.

7. Inquiry: As shown in Figure 3. 1- 19, in Rt△ABC, ∠ ACB = 90.

AC=, BC= 1, rotate Rt△ABC around point C by 90.

Is Rt△A'B'C, and then rotate Rt△A'B'C around point B.

Rt △ a "b" c "makes a, c, b' and a" on the same straight line.

So the length from point a to point a is.

Three. Course summary

Postscript of teaching:

Graphic rotation has three key elements: first, the center of rotation, that is, which point to rotate around; The second is the direction of rotation, clockwise or counterclockwise; The third is the angle of rotation. In order to break through the difficulty of students rotating simple graphics 90 clockwise or counterclockwise on grid paper, the author thinks about whether static grid graphics can move in students' hands, so that students can clearly see its complete rotation process. Then use the method of "inquiry verification" to test your learning results. In the process of "operation-verification", the method and key points of graphic rotation are gradually constructed.

Class name and student number of second-grade math classroom practice.

1. As shown in figure 1, the graph can be rotated by a certain angle to coincide with itself, so the rotation angle may be

A.30 B.60 C.90 D. 120

2. As shown in Figure 2, △ABC rotates clockwise by an angle of △A/B/C/, which means that the center of rotation in the figure is point A.A, point B.B, point C.C and point D.B/.

3. As shown in Figure 3, △ABC is an equilateral triangle, and d is a point within △ABC. If △ABD rotates to △ACP position, the rotation center is _ _ _ _ _ _ _ _ _, the rotation angle is equal to _ _ _ _ _ _ _ _ _, and △ADP is _ _ _ _ _ _ _.

4. As shown in Figure 4, △ABC and △CDE are equilateral triangles, and △ _ _ _ _ _ _ and △ _ _ _ _ _ in the figure can surround each other.

Point rotation _ _ _ _ _ degrees are mutually obtained.

5. As shown in Figure 5, △ABC rotates counterclockwise by 80 degrees to become △A/B/C/. It is known that ∠B=60 degrees ∠C=55 degrees, then ∠BAC/= degrees.

6. As shown in the figure, in the isosceles right angle △ABC, ∠C=900, BC=2cm. If the midpoint o of AC is taken as the rotation center, rotate the triangle by 1800, and the point b falls on the point b', and find the length of BB'.

7. According to the need to draw rotating graphics:

1 Draw △ABC, and rotate 90 clockwise around the O point to get △

2 rotate the quadrilateral ABCD 90 counterclockwise around the O point to get the quadrilateral.