Tisch
First create a scene, feel the rotation 1, and show three pictures: fan, windmill and fireworks.
Teacher: How do these objects move? Can you show it by gesture?
Summary: This movement phenomenon is called rotation.
Teacher: There are still many spinning phenomena in life. Can you give me an example?
Teacher: Today, in this class, let's study the rotation phenomenon of graphics. (uncover the topic)
Show the concept of rotation: in a plane, a figure rotates an angle around a vertex in a certain direction, and such a graphic movement is called rotation.
Second, know clockwise and counterclockwise rotation
Show me a picture of the rotating rod.
Ask questions:
(1) What do you see from this picture?
(2) How do the rotating rods rotate respectively? What other similar rotation examples are there in life?
(3) Understand the meaning of clockwise and counterclockwise rotation. What are the similarities between the rotating process when the rotating lever is opened and closed? What is the difference? Which rotation direction is the same as clockwise?
Summary: clockwise rotation is the same as clockwise rotation, and counterclockwise rotation is in the opposite direction. The lever rotates 90 counterclockwise when it is opened and 90 clockwise when it is closed.
Third, understand the three elements of rotation.
Display the grid diagram: rotate the triangular ruler 90 degrees around point A.
Teacher: What do you mean by "rotating around point A"? Can this point move? Students practice by themselves.
Teacher: What is the relationship between the edge after rotation and the edge before rotation? Who can tell me how he painted it?
Teacher: What do you think should be determined when rotating a graph?
Displays three elements of rotation: rotation center, rotation direction and rotation angle.
Fourth, solve practical problems in life.
1, do the "think about it" question 1
(1) observation and communication; Students do it independently.
(2) Communication: 6:00-9:00, 9:00- 12:00, the clock rotates 90 degrees.
(3) If the items on the scale are removed, how can the pointer rotate? What about the pointer on the turntable?
2. "Thinking and Action" Question 2
Question: How did you draw it?
Common summary: the key to determine the position of a rotating rectangle is to determine the positions of two adjacent sides that intersect at point A; The key to determine the position of the rotated flag map is to determine the position of the flagpole.
3. "Thinking and Action" Question 3
Ask questions:
(1) Observe two numbers in each group. What did you find?
(2) Can you rotate one figure in each group so that each group of figures becomes a rectangle?
(3) How to draw? Can the last number only be rotated once How many degrees did it rotate?
Verb (abbreviation of verb) class summary
What did you get from this lesson?
What should I pay attention to when rotating the graph at a certain angle?
extreme
[Teaching content]
Beijing normal university printing plate fourth grade unit 54-56 graphic transformation.
[teaching material analysis]
Before learning this part of the content, students have already experienced the phenomenon of translation and rotation in their lives in the third grade, and can draw a figure with horizontal and vertical translation on the grid paper. The content of this lesson is an extension of the above, which introduces the students' perspective into the rotation of graphics, aiming to let students experience the process of changing simple graphics into complex patterns through a series of activities such as appreciation, exploration and creation, and understand that the central point, direction and angle of rotation are different, and the patterns formed are also different, so as to further develop students' spatial concept and lay the foundation for continuing to learn graphic transformation in the future.
1. In the process of operation, let students experience the characteristics of graphic transformation.
In the teaching of this unit, students should be encouraged to operate and think actively during the operation. For example, in the activity of "Rotation of Graphics" (page 54 of the textbook), two beautiful patterns displayed in the textbook were obtained by rotating a simple graphic. When teaching, you can prepare four pieces of paper with the same pattern, then rotate around a certain point one by one, rotate 90 degrees, paste one piece of paper, rotate 90 degrees, and paste another piece of paper until a complete pattern is formed. In the process of rotation, teachers should remind students to observe and think: what changes have taken place in the pattern and what points it rotates around.
Many exercises in this unit can be operated, so students can be required to prepare some small learning tools before class, so that students will have the opportunity to operate in the teaching process. Some questions in the exercise are also answered by students, which improves students' perceptual knowledge.
2. In the transformation of graphics, advocate different operation methods.
After a graph is transformed, a new graph can be obtained, but the same new graph can be obtained by different operation methods. So, let the students think about it first, then try it on the square paper, and then talk about it in the class. In the teaching process, teachers should go deep into students' activities, find out students' unique operating methods, encourage and affirm them, and provide conditions for students to learn and communicate with each other.
3. In the process of appreciation, encourage students to design and make exquisite patterns.
The content of mathematics appreciation in this unit is any simple figure. When it rotates around a point and draws the figure after each rotation along the outline, it will form a beautiful pattern. By the third grade, the students have appreciated the process of square rotation and made it. This unit further expands this content, which can be any simple graphic. In teaching, students are invited to appreciate it first, then each student cuts out an arbitrary simple figure with cardboard, and then carries out transformation. As long as the patterns made by students basically meet the requirements, teachers should affirm them. For some students with excellent design, they can also demonstrate it on the spot to encourage students with weak hands-on ability.
[Teaching objectives]
1. Further understand the rotation transformation of graphics and explore its characteristics and properties.
2. Be able to rotate simple graphics 90 degrees on square paper. .
3. Initially learn to design patterns on square paper by rotating method, and develop students' concept of space.
4. Appreciate the beauty created by graphic rotation and transformation, and cultivate students' aesthetic ability; Feel the application of rotation in life and appreciate the value of mathematics.
[Teaching Focus]
1. Understand the meaning of graphic rotation transformation.
2. Explore the characteristics and nature of graphic rotation.
[Teaching difficulties]
1. Explore the characteristics and properties of graphic rotation.
2. Be able to rotate a simple figure 90 clockwise around a fixed point on the grid paper, and tell the rotation process.
[Teaching tools]
Multimedia courseware, one learning kit (basic graphics, marker) for each table.
teaching process
First, the scene introduction:
This is the windmill that children like to play with.
Let two children play with the teacher. (biological operation)
Other children, please pay attention to how the windmill moves.
Who can say what you see in the movement of the windmill?
(Solve rotation, rotation center and rotation direction)
Display clock face
Mathematically, I call the rotation direction in this direction clockwise;
Counter-clockwise.
Gestures. Gestures.
Summary: In the exercise mode just now, we can say,
The windmill rotates clockwise around the center point;
Or the windmill rotates counterclockwise around the center point.
Can you say it?
Second, the new grant:
In life, there are all kinds of beautiful patterns, some of which are simply translated and rotated.
Do you want to know how these patterns are designed? Do you want to know? )
Then we will further study the "rotation of graphics" today. (blackboard writing topic)
Then let's choose a simple pattern, from easy to difficult, and study how simple patterns are made and how to rotate. Please observe carefully.
Courseware display
In order to facilitate the study, the teacher also made a model and posted it on the blackboard.
Discussion:
Talk to each other in groups. What did you see just now?
(shape and size unchanged)
Teacher: What is the conversion from Figure A to Figure B?
How it rotates. (clockwise around point o). . . . . . )
How many degrees did it rotate?
How to judge that it has rotated by 90?
What can we do? Think about it and talk to each other.
Combined with the legend, draw the corresponding edge and mark the rotation angle. Measure.
This degree is called rotation.
To sum up, Figure B can be regarded as Figure A rotating 90 clockwise around the O point.
Who can say it again completely?
Emphasize three elements.
Teacher: What is the conversion from Figure B to Figure C?
What about pictures a to c?
Students, we can say that figure A rotates clockwise around point O 180 to get figure C; Is there another way to say it? (with gestures)
counterclockwise
Can you still say such a thing when you see this picture?
Teacher's summary: Only when the rotation center, rotation direction and rotation degree are determined can the position after rotation be determined.
Third, consolidate the exercises:
1. Turn around. (hands-on operation)
Tell me which point these triangles revolve around.
2.
Fourth, appreciate sublimation.
Feel the beauty of rotation and mathematics.
What simple figure is rotating?
Tisso
Teaching objectives
1. Through the observation of examples, we can understand the process of rotating a simple graph to make a complex graph.
2. Simple graphics can be rotated 90 degrees on square paper.
Emphasis and difficulty in teaching: Simple graphics can be rotated 90 degrees on square paper.
Activity flow:
Activity 1: Create scenarios and solve problems.
(1) In life, there are all kinds of beautiful patterns, but many of them are obtained by translation or rotation of simple graphics. This activity introduces the process of forming complex patterns by rotating simple patterns.
(2) In the lead-in stage of the activity, a set of patterns can be displayed for students to enjoy. Then, these patterns are decomposed according to a certain shape, and a small part of them is taken out and rotated on the Fang Gezi to gradually show the process of forming complex patterns from simple patterns after rotation. Of course, every time you rotate, you have to tell the students what figure rotates around which point. What is the rotation angle? Students can also use learning tools to operate by themselves, so that students can experience the process of rotation.
Activity 2: Practice.
On the basis of students' independent completion, the whole class communicates and the teacher guides.
Question 1
The exercise of this topic is mainly to understand which point the rotation of the figure revolves around, so this activity allows students to try it independently first, and then discuss the central point of rotation. In the activity, each student can prepare some white paper and triangles. In order to let students feel the changes of the figure before and after rotation, please draw a triangle on your hand along the edge of the triangle, then rotate it around a vertex of the triangle (the rotation angle can be arbitrary), and finally talk about which point the triangle rotates around.
Question 2
Similarly, this question can also ask students to rotate as required, and describe the graphics obtained each time they rotate. Then discuss the rotation angles from Figure 1 to Figure 2 and from Figure 2 to Figure 4.
Mathematical kaleidoscope
Conditional schools can use multimedia to demonstrate the rotation process of this problem. If students are interested, they can also cut an arbitrary triangle by themselves, and then describe the rotated figure while rotating, so that each student can make beautiful patterns.
Question 2
In practice, students can use triangular squares to operate as needed. After the students are more skilled, they can draw rotating figures as required.
Question 3
Similarly, the practice of this question also requires students to put it on their own. In the process of putting it on, let the students accumulate some experience and then color it.