The first level: analysis of teaching background.
First, teaching analysis
1, the position and function of teaching materials
"Motion and Coordinate of Graphics" is in the second lesson of the fifth section of Chapter 18 "Similarity of Graphics" in the eighth grade of Mathematics published by China Normal University. This chapter introduces the similarity after axial symmetry, translation and rotation. Similarity is also a transformation between graphics. There are a lot of similar graphics in life. Starting from the reality of life, we can understand the characteristics of similar figures and use them to solve some simple practical problems, so that students can understand the changes of coordinates after translation, rotation, axial symmetry and similar transformation. Deepen the understanding of graphics, and initially understand the idea of combining numbers with shapes.
2. Teaching objectives
Knowledge goal: in the same rectangular coordinate system, feel the change of coordinates of each point and the change of the graph (translation, axis symmetry, rotation, enlargement and reduction) after the graph changes; Cultivate students' idea of combining numbers with shapes.
Ability goal: to cultivate students' observation ability and practical ability.
Emotional attitude goal: let students get the happiness of discovery in the process of observation and exploration, and experience mathematical activities full of exploration and creation; Guide students to face the difficulties and setbacks in their study and life, and cultivate strong will.
3. Teaching emphases and difficulties
Key points: in the same rectangular coordinate system, the figure is translated, rotated, axisymmetrical, enlarged or reduced, and the change of coordinates of points caused by the change of figure position and the change of figure position caused by the change of points are explored.
Difficulties: Through observation, analysis and generalization, the idea of coordinate is linked with the idea of graphic transformation, and the consciousness of combining numbers with shapes is formed.
Second, the analysis of learning situation
1, student starting point analysis
The students of Grade 8 in the next semester have acquired the knowledge of translation, rotation, symmetry and similarity of graphics, and learned to establish a suitable coordinate system to describe the position of objects. They can flexibly use various forms to determine the position of the object according to the specific situation, which also brings the possibility of learning the coordinate changes of each point after the graphic changes in this section, but they lack the consciousness of combining numbers and shapes, which should be guided, guided and inspired.
2. Analysis of teaching environment
This part is designed in an environment of equality, democracy and cooperation; At the same time, modern teaching methods are introduced to form a variety of teaching environment choices.
Third, teaching methods and means
Teaching method: exploratory teaching method. The whole teaching process is from problem raising to problem solving, and teaching is organized around three links: observation, discovery and induction. The whole teaching mode has changed from "how teachers teach" to "how students learn" and from teacher-centered classroom to student-centered development, which is the embodiment of innovation.
Teaching means: computers, physical projectors and other modern teaching equipment.
Fourth, study the guidance of law.
1. Perception and cognition: Students know that the position change of graphics causes the coordinate change of points. This section introduces the coordinate change caused by the position change of points from the game.
2. Practical exploration: further observe the translation, rotation, axial symmetry, enlargement or reduction of the figure through examples, and explore the changes of points caused by position changes. Through group discussion, unity and cooperation, discover, summarize and summarize the laws. At the same time, each student tries to draw a figure he likes in the rectangular coordinate system and write the coordinates of the corresponding points after the figure changes, so as to achieve the purpose of consolidation.
3. Migration and expansion: How to measure the flagpole height of our school with what we have learned? (connecting the preceding with the following)
Five, theoretical basis, mathematical thought
1, theoretical basis: this section focuses on students' development in teaching, so that students can truly become the masters of the classroom. The whole section focuses on students' observation, perception and practice, and summarizes the idea of coordinate and graphic change.
2. Mathematical thought: This section develops mathematical thought of combining numbers with shapes and thinking in images.
The second level: teaching analysis.
(1) Topic introduction: Design a simple game, creatively establish a rectangular coordinate system on the class seat, determine the position of each student in this coordinate system, and then move a ball in a straight line in the class coordinate system to guide students to discover the influence of the ball's movement on the coordinate change, so as to transition to the coordinate change of key points in the graphic change. This design can vividly guide students to enter the teaching situation of this class, and at the same time feel the process of "game problems turning into math problems".
(2) Perception stage:
Example: Translate the AOB in the figure on the right by 3 units to the right along the X axis to get the δCDE. What changes have been made to the coordinates of the three vertices? Please answer (1). What are the coordinates of Δ δCDE vertices after translation? (2) What did you find by comparing the vertex coordinates?
(After moving to the right along the X axis, the vertical coordinates of the three vertices have not changed, but the horizontal coordinates have increased by the same amount. )
Q: 1. How do their coordinates change when the vertices of a triangle translate in any direction?
2. How do the coordinates of the corresponding points change when the figure is symmetrical, rotated, enlarged or reduced?
Design intention: let students know that this section is about how the coordinates of corresponding points change in graphic changes, and understand the research methods from the perspective of translation; The teacher's question pointed out the direction for the students. But let students know that the translation direction is not unique.
(C) Deep exploration: demonstration courseware
1, let students observe AOB, draw a symmetrical figure with X axis and Y axis as symmetry axes, and write the coordinates of the corresponding points. Four-person group discusses the changes of corresponding points and reports (about X axis symmetry, the abscissa becomes the inverse number, about Y axis symmetry, the ordinate becomes the inverse number).
2. Let the students continue to observe AOB, draw the figure of 1800 rotating around O, and write the coordinates of the corresponding points. Discuss the changes of the coordinates of the corresponding points in groups of four and make a report. What about rotating at any angle? How to change the coordinates of the corresponding points? (for students to think about)
(the graph is symmetrical about the origin, and the number of horizontal and vertical directions is opposite. )
3. The change of vertex coordinates when the triangle becomes larger (smaller).
Q: What are the vertices of (1)δAOB and δδCOD triangles after reduction?
(2) Can you find their similarity ratio? (3) What is the relationship between the coordinates of the corresponding points?
(Enlarge or reduce, the abscissa enlarges or reduces by the same factor)
4. Students take out their prepared graphics paper to establish rectangular coordinate system, draw their familiar and favorite graphics at will, draw symmetrical graphics about X axis and Y axis symmetry, make translated, rotated, axisymmetric, enlarged or reduced graphics, and write the coordinates of corresponding points.
5. Complete the classroom exercise P9 1 exercise 1, 2.
Design intention: Let the students do it themselves, observe and use their brains, and cooperate with their classmates to achieve the goal of this section. Make students know the law of graphic movement and coordinate change, and solve the key problems in this section. Cultivate students' practical ability and observation ability, develop students' thinking of combining numbers and shapes, and solve difficult problems. Break the shackles of drawing triangles and quadrangles in textbooks, and students draw their own "favorite graphics" to further study the movement and coordinates of graphics; Stimulate students' interest in learning; Make students dare to face the difficulties and setbacks in their study and life, and cultivate their strong will.
(4) Migration and expansion: If you were given a ruler, would you measure the height of the flagpole in our school?
Design intention: expand the role of connecting the preceding with the following through knowledge.
(5) class summary:
(1) The graph is translated along the X-axis, and the lateral change is unchanged.
The graph is translated along the Y-axis, and the vertical change remains unchanged.
(2) The graph is symmetrical about X, the horizontal direction is unchanged, and the vertical direction is the opposite number;
The graph is symmetrical about y axis, the longitudinal direction is unchanged, and the transverse direction is the opposite number;
(3) The graph is symmetrical about the origin, and the horizontal and vertical directions are opposite numbers.
(4) zoom in or out, both horizontally and vertically by the same factor.
(6) Homework: Synchronize exercise P35 1, 2, 3.
The third level: teaching design and teaching result prediction and evaluation.
This class pays attention to cultivating students' hands-on, brain-thinking, observation and rigor, and the effect is good.
This lesson breaks the shackles of textbooks, allows students to draw their favorite graphics, studies the coordinate changes of corresponding points, and stimulates students' interest in learning.