(1) Master the geometric characteristics of the circle, and master the standard equation and general equation of the circle;

(2) According to the given equation of straight line and circle, the positional relationship between straight line and circle can be judged;

(3) Some simple problems can be solved by equations of straight lines and circles;

(4) Understand the idea of dealing with geometric problems by algebraic methods.

2 teaching material analysis

"The positional relationship between straight line and circle" is an important content in the chapter of circle and equation. It is the three positional relationships between straight lines and circles that students learned in plane geometry in junior high school. On the basis of studying the equation of straight line and circle in the previous sections, the positional relationship between straight line and circle is further studied from the algebraic point of view by using coordinate method, which paves the way for the subsequent study of the positional relationship between straight line and conic curve. Therefore, this lesson plays a connecting role in this chapter and even the whole senior high school geometry.

3 Analysis of academic status quo

Senior one students are active in thinking and eager for knowledge. Junior high school students have learned that there are three kinds of positional relationships between straight lines and circles. Students all know that the positional relationship between a straight line and a circle can be studied by comparing the distance between the center of the circle and the radius of the circle. They have just learned the knowledge of straight line equation, circle equation and the distance from point to straight line, and have certain ability to study geometric objects with equation and coordinate thought.

4 Analysis of teaching objectives

4. 1 teaching objectives

Knowledge and skill goal: according to the equation of straight line and circle, judge the position relationship between straight line and circle with algebra and geometry.

Methods and process objectives: Based on practical problems, the positional relationship between straight line and circle is abstracted and solved by analytical method. Finally, the general methods of solving problems are summarized to improve students' experience in mathematics activities.

Emotion, attitude and values: Through the process of mathematization of life problems and algebra of mathematical problems, students can feel that mathematics comes from life and realize the useful value of mathematics in real life.

4.2 Teaching Emphasis and Difficulties

Emphasis: master the algebraic method and geometric method to judge the position relationship between straight line and circle, and summarize the advantages and disadvantages of the two methods by solving problems.

Difficulties: Turn practical problems into mathematical problems and establish corresponding mathematical models to solve them.

5 Analysis of teaching methods

5. 1 Teaching Method

In order to fully mobilize students' learning enthusiasm and break through difficulties, multimedia courseware and geometry sketchpad software are appropriately used to assist teaching in this course, and the inquiry activities are deepened with interlocking questions, so that students can actively challenge and solve problems and form a teaching method of group cooperation, modeling, method inquiry and induction.

5.2 Analysis of learning methods

(1) preview the study plan before class, review the knowledge points used in this class, and learn new things by reviewing the past;

(2) Junior high school students have learned the positional relationship between straight lines and circles from the perspective of "shape". This section highlights the essence of "Algebra of Geometric Problems", which should be used well when learning.

(3) When solving problems, let students judge the positional relationship between straight lines and circles from the angles of algebra and geometry, and realize the superiority of geometric methods.

6 Teaching process design

The whole teaching process is linked and driven by problems, and * * * is divided into six links: scene setting and bedding; Cut into the theme and raise the topic; Explore research and solve problems; Apply new knowledge to deepen understanding; Summarize the methods of improvement and formation; Homework after class, consolidate and improve.

Background: There is a desolate cape in California, USA, which is called Cape Onda by the locals. The sea near it is harsh and often foggy. Strong waves erode Cape Onda all day, and there are rocks around it that only emerge from the water at low tide, so the sea area is called "the devil's chin". Many ships lost their lives here because they hit the rocks, but the most serious accident occurred in 1923 9. Seven brand-new American destroyers and 23 sailors died here, which was the worst maritime disaster in the history of the US Navy. These disasters may be avoided if the distribution of reefs and the route of ships can be predicted in advance.

7 Teaching reflection

Based on the students' original cognitive basis, the teaching of this class has prepared a tutoring plan, which requires students to review their old knowledge before class. In the classroom, students are guided by independent inquiry and cooperative communication, so that students can experience the formation and application of mathematical knowledge and deepen their understanding of what they have learned, thus breaking through difficulties. The whole classroom is a dynamic generation process of imagination, eye movement observation, hands-on operation, practical verification and consolidation of application, so that students can master it. " Infiltrating the combination of numbers and shapes, equations and special to general mathematical thinking methods, they have cultivated their mathematical core literacy such as intuitive imagination, mathematical abstraction, mathematical modeling and mathematical operation.