Peng kexiang
I. Status of this chapter:
Chapter 5 "Determination of Position" is the main content of Section 3 "Graphics and Coordinates". "Graph and coordinate" is one of the four important components of "space and graph" (graph cognition, graph and transformation, graph and coordinate, graph and proof), and it is an important carrier for developing students' spatial concept. As the development of the first and second phases of "Graphics and Position", this chapter not only presents the contents of "various methods to determine the position and plane rectangular coordinate system", but also enables students to further understand the mathematical connotation of graphic translation and axial symmetry from the perspective of coordinates. At the same time, it is also an important basis for the sixth chapter "Linear Function" in this book.
Two. The teaching objectives of this chapter are:
1. Knowledge and skill objectives:
(1) There are many methods to determine the position of an object, and different methods can be flexibly used to determine the position of an object;
(2) Understand the concept of rectangular coordinate system, and trace the position of a point or write its coordinates according to its position in a given rectangular coordinate system;
(3) An appropriate rectangular coordinate system can be established on the grid paper to describe the position of the object;
(4) We can know the characteristics of some special point coordinates, and we can calculate the coordinates of some special points according to these characteristics;
(5) In the same coordinate system, feel the change of coordinates of points after the change of graphics and the change of graphics after the change of coordinates.
2. Process and method objectives:
(1) Let the students choose the appropriate method to represent the position of the object by feeling the examples;
(2) Through association and imitation, the method of establishing plane rectangular coordinate system is preliminarily realized;
(3) By drawing, we can understand the graphic changes caused by the coordinate changes of points.
3. Emotions, attitudes and values:
(1) By constructing a plane rectangular coordinate system, the combination of numbers and shapes in a wider range is formed, so that students can experience that mathematics comes from life and serves life at the same time;
(2) Cultivate students' study habits of observation, analysis, inquiry and cooperation, and experience the changes of things; (3) By discussing the relationship between the change of graphic coordinates and the change of graphic shapes, we can cultivate students' awareness of the combination of numbers and shapes, their thinking ability in images and their mathematical application ability, and form students' good mathematical outlook.
3. Teaching ideas of this chapter:
In this chapter, according to the arrangement of "general" and "special", first let students feel the rich realistic background of location determination through colorful and diverse ways. Then, based on very practical background materials, let students systematically learn the relevant contents of the plane rectangular coordinate system; Finally, through the interesting topic of "changing fish", the change of graphic coordinates is skillfully linked with the change of graphic shape.
This chapter attempts to present relevant contents with realistic themes, and presents the content of "finding coordinates from points, determining the position of points by coordinates, and establishing a simple plane rectangular coordinate system" with interesting and challenging questions, trying to reflect the connection between the plane rectangular coordinate system and the real world; Through "changing fish", there are a lot of graphic transformations in real life, such as various picture processing on TV screen. For all kinds of methods to determine the location, this chapter presents the common positioning methods in real life to each student through various themes (such as "monsters eat peas", "finding seats in cinemas" and "determining the location of cities on maps"). ), including the positioning method that embodies the idea of polar coordinates and the positioning method that embodies the idea of rectangular coordinates.
This way of presentation, first, allows students to understand the coordinate thought and its origin in relatively relaxed and interesting activities, and further develops students' reasonable reasoning ability and rich emotional attitude (especially their interest in learning mathematics); The second is to master the basic methods of determining position and the basic knowledge and methods of plane rectangular coordinate system in a large number of practical applications.
Four. The emphases and difficulties of this chapter:
1. The focus of this chapter is to establish a rectangular coordinate system and determine the position of the object.
2. Difficulties in this chapter:
(1) Establish a rectangular coordinate system and determine the position of the object;
(2) Understand the relationship between the change of coordinates of each point after the change of graphics and the change of graphics after the change of coordinates of each point.
Verb (abbreviation of verb) Teaching suggestions in this chapter:
1. Pay attention to using students' real life and personal experience to determine the position of objects and improve students' mathematical application ability;
2. Pay attention to demonstration experiments, such as using computer to dynamically demonstrate the relationship between position determination and coordinate transformation, as well as the relationship between translation, rotation and axial symmetry.
The allocation of class hours for intransitive verbs in this chapter;
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classes
A heavier point
difficulty
1. Determine the location
2
Determine the position of an object on a plane
Master several ways and methods to determine the position of objects.
2. Plane rectangular coordinate system
three
Understand the plane rectangular coordinate system and determine the way and expression of point coordinates.
Establishment of digital model of plane rectangular coordinate system and one-to-one correspondence between points on coordinate plane and ordered real number pairs.
3. The changing "fish"
2
The relationship between the coordinate changes of points on a graph and the graphic changes.
The relationship between the coordinate changes of points on a graph and the graphic changes.
Review and thinking
1
Method of determining position in plane rectangular coordinate system
The relationship between the change of coordinates of points after the change of graphics and the change of graphics after the change of coordinates of points.
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Seven. Several issues that need to be discussed collectively in this chapter:
1. Increase or decrease of each category;
2. Specific operations to implement key and difficult contents;
3. Other issues.