Teaching objectives
1, understand the concept of plane rectangular coordinate system; Can draw a plane rectangular coordinate system; Find out the symbolic characteristics of the coordinates of points in the quadrant and on the coordinate axis; Can write coordinates from the position of a point in the specified coordinate system, and draw corresponding points according to the coordinates; A preliminary understanding of the one-to-one correspondence between points on the coordinate plane and "ordered number pairs"
2. Infiltrate the mathematical thought of the combination of number and shape to develop students' sense of symbol; Cultivating students' divergent thinking and innovative thinking ability in mathematical modeling.
3. Experience the process of abstracting the plane rectangular coordinate system from practical problems, realize the idea of mathematical modeling, and stimulate students' interest and enthusiasm in learning; By introducing the background of Cartesian coordinates, students are encouraged to establish the spirit of daring to explore.
Teaching focus
The rectangular coordinate system can be drawn correctly, and the points can be found according to the coordinates in the rectangular coordinate system, and the coordinates can be obtained from the points.
Teaching difficulties
One-to-one correspondence between the midpoint of the plane rectangular coordinate system and the ordered number pairs.
Teaching process design
(A) create scenarios and introduce topics
1, review the knowledge of the number axis and describe the position of each point on the line.
2. Tell your position in the classroom.
3.300 years ago, French mathematician Descartes, inspired by ordered number pairs, proposed a coordinate method to determine the position of points. Scientists took a small step forward and made a big step forward in the history of mathematics. Today, let's follow the footsteps of our forefathers and learn about the "plane rectangular coordinate system" first.
The teacher reveals the topic, puts forward the teaching goal and writes the topic on the blackboard.
Design intent
1, lead the class from the questions that students are familiar with.
2. I feel that the position is decided by myself, and I realize that mathematics comes from life.
3. Analogize ordered pairs of numbers and draw coordinates to ensure the continuity of knowledge.
4. Introduce Descartes briefly, infiltrate the history of mathematics, and stimulate students' curiosity.
(2) Introduce new knowledge and lay a solid foundation.
I. Definition of Plane Cartesian Coordinate System and Related Concepts
1. Introduce the formation of plane rectangular coordinate system.
2. Introduce the concept of plane rectangular coordinate system, four quadrants, and emphasize that the points on the coordinate axis are not in any quadrant.
3. Establish an appropriate rectangular coordinate system on the grid paper and evaluate each other within the group.
Design intent
1, cultivate students' language expression ability.
2, writing exercises, deepen the impression, cultivate students' serious study habits, evaluate each other in groups, and enhance their ability to identify.
3, from shallow to deep, from slow to fast, emphasize key points, cater to students' cognitive characteristics, and take care of students at different levels.
Second, determine the coordinates of known points.
1. Introduce the definition and representation of coordinates, emphasizing that coordinates are ordered number pairs.
2. Give concrete examples of points in different positions in the coordinate plane, practice speaking coordinates and emphasize the representation of points on the coordinate axis.
Example 1. Write the coordinates of points A, B, C, D and E in the diagram.
A(2，3)B(3，2)C(-2， 1)D(-4，-3)E( 1，-2)
Example 2: Draw points A (2,4), B (5,2), C (-3.5,0), D (-3.5,2) and E (0 0,3) in a plane rectangular coordinate system.
Design intent
1, from shallow to deep, from slow to fast, emphasizing key points, catering to students' cognitive characteristics and taking care of students at different levels.
2, from looking directly at the screen, collective answering questions, to personal behavior, give each student the opportunity to think independently. Help each other in the group, give low-level students a chance to learn again, evaluate each other in the group, strengthen understanding and experience the combination of numbers and shapes initially.
Thirdly, explore the coordinate characteristics of special location points.
1, explore the symbolic characteristics of point coordinates in quadrant.
2. Explore the coordinate characteristics of points on the coordinate axis.
The design intention is to consider students' cognitive characteristics, use multimedia images to display intuitively, and reduce the difficulty. This link aims to consolidate the writing coordinates, sum up the rules and focus on experience, and stimulate students' enthusiasm by answering questions; Take the group as a unit, supplement and modify each other, and enhance the awareness of cooperation and exchange; Through regular exploration, students' observation ability, summary ability and language expression ability are cultivated.
(3) Group discussion to consolidate new knowledge.
The design intention is to cultivate students' observation ability, summary ability and language expression ability through regular exploration.
(four) to consolidate, deepen and improve the application.
1, as shown in the figure, the coordinate of point A is (b).
A.(3，2)B.(3，3)C.(3，-3)d .(3，-3)
2. As shown in the figure, the point with negative abscissa and ordinate is (c).
A.a. point B.B. point C.C. point D.D.
3. As shown in the figure, the point with the coordinate of (-2,2) is (D).
A.a. point B.B. point C.C. point D.D.
4. if the coordinate of point m is (a, b) and A >；; 0, b<0, and point m is in quadrant (d).
A. 1 B.2 C.3 D.4
5. Point A (-3,2) is in the _ _ second quadrant, and point B (3,2) is in the _ _ fourth quadrant.
Point C (3 3,2) is in the _ _ _ first quadrant, and point D (-3,2) is in the _ _ _ third quadrant.
Point e (0 0,2) is on the positive semi-axis of _y, and point f (2 2,0) is on the positive semi-axis of _ x.
6. known point M(a, b)
When a>0, b>0 and M are in the _ _ _ _ quadrant;
When a _ _
When a _ _ >；; 0____ _ _ _ & lt0__ _, m is in the fourth quadrant;
When a<0, b<0 and M are in the third quadrant.
7. Determine which quadrant or axis the following points are located in? Then trace the following points in the coordinate system.
A(-5，2)，B(3，-2)，C(0，4)，D(-6，0)E( 1，8)，F(0，0)，G(5，0)，H(-6，-4)K(0，-3)
Review and consolidate the design intent, and face all. The purpose is to use knowledge flexibly, increase the connection between knowledge, comprehensively consider problems and deepen the understanding of knowledge, which is comprehensive and helps to encourage students to consider problems flexibly and comprehensively.
(5) Learning summary and independent evaluation.
1, guide students to learn from the understanding of knowledge, the experience and feelings in the process of knowledge acquisition, the experience in the process of problem solving and the experience in mathematical thinking methods, and carry out exchanges.
2. Encourage students to reflect and evaluate teachers' teaching, peers and their own learning behavior, or question this class, tell the existing doubts and talk about their different views.
(6) Transfer
1, see lesson plan "Consolidating new knowledge through after-class exercises"
2. Exercise 6. 1: Question 3, Question 5
Reflection after class
On the basis of the last lesson, students can correctly establish the plane rectangular coordinate system and further consolidate their knowledge of the plane rectangular coordinate system according to the correct coordinates. The teaching effect is good, students can actively participate in teaching activities, but other students are still not interested in learning. Teachers should give individual guidance and education.