The positional relationship between a straight line and a circle is based on the positional relationship between a research point and a circle, which paves the way for the positional relationship between the following circles and plays a connecting role. Continuation: The research and study on the positional relationship between line and circle is further developed on the basis of learning the positional relationship between point and circle. By analogizing the positional relationship between point and circle and combining the quantitative expression of the positional relationship between point and circle, the important teaching content of the positional relationship between line and circle is further studied. Enlightenment: The positional relationship between straight lines and circles is a lesson that paves the way for learning the positional relationship between circles, lays a good foundation for learning the positional relationship between circles, and is an important foundation and necessary skill for students to learn in the future. The application of the positional relationship between straight line and circle mainly lies in the mutual transformation between positional relationship and quantitative relationship, which embodies the thinking method of analogy classification, conjecture verification and induction.
Second, the analysis of learning situation
Students have learned the positional relationship between a straight line and a circle in junior high school, and the equation of a straight line and a circle in senior high school, and can solve simple geometric problems by coordinate method. All these are helpful for students to further learn the positional relationship between straight lines and circles. However, our students already have the ability of independent thinking and inquiry learning, but they lack the ability of spatial imagination and practical application.
Third, the teaching objectives
1. Knowledge and skills
Master the definition, judgment method and nature of three positional relationships between straight line and circle.
2. Process and method
Through the process of exploring the positional relationship between straight lines and circles, the ideas of analogy, classification and combination of numbers and shapes are infiltrated into students. Let students experience the process of discovering, asking, analyzing and solving problems, and cultivate students' independent exploration and innovation ability.
3. Form and values
By exploring the positional relationship between straight line and circle, students' ability to observe, analyze and find problems is cultivated. Let students feel the connection between mathematics and life and stimulate their curiosity and thirst for knowledge about mathematics.
Fourth, the focus of teaching
After exploring the positional relationship between straight line and circle, three positional relationships between straight line and circle are obtained. These three positional relationships are expressed by quantitative relationships.
Difficulties in teaching verbs (abbreviation of verb)
Judging the positional relationship between a straight line and a circle through the quantitative relationship.
Sixth, teaching strategies.
This lesson is a synthesis of straight lines and circles learned in the past, and it is also the basis for analyzing geometric thoughts in the future. Therefore, when arranging teaching, we should pay attention to infiltrating the idea of analogy and the combination of numbers and shapes, and adopt heuristic teaching methods to teach.
Seven. teaching process
1. Introduction
What are the positional relationships between straight lines and circles in plane geometry of junior and middle schools?
2. New knowledge and interpretation
① Play the teaching video of two methods to judge the relationship between straight line and circle in onion mathematics, and explain the knowledge of video teaching to let students have a certain understanding, and then summarize and strengthen their memory.
(2) Prepare examples to explain, one example and one variant training, so that students can learn to do problems and deepen their memory of knowledge points. A variant can make students draw inferences from others, learn to think and learn to solve problems.
3. Course summary
Step 4: Assign homework.
The topic of strengthening the foundation of the supporting workbook (optimization design).