Teaching material analysis.
Status and Function: This lesson is the third lesson in Chapter 24, Book 2, Grade 9, People's Education Press. It is the basis for students to learn the different positional relationships between two circles on the plane after mastering the positional relationships between points and circles and between straight lines and circles. It is also the basis for students to apply the knowledge of circle in senior high school and continue to learn the positional relationship between plane and ball, and between ball and ball. Therefore, the content of this lesson is very important and plays a connecting role in knowledge.
Second, the teaching objectives
Knowledge and skills objectives:
1. Explore and understand the positional relationship between circles.
2. Explore the quantitative relationship between the center distance of two circles and the radius of two circles in the positional relationship between circles.
3. Be able to use the positional relationship and quantitative relationship between circles to solve problems.
Process and method:
Students experience the process of exploring the positional relationship between circles and cultivate the ability of observation, analysis, induction and generalization; Learn the mathematical ideas of "analogy", "classified discussion" and "combination of numbers and shapes"; Improve the ability to use knowledge and skills to solve problems and cultivate application awareness.
Emotional attitude goal:
After operation, experiment, verification and other mathematical activities, students can experience the viewpoint of movement change, the variable is the dialectical materialism viewpoint of qualitative change, and feel the beauty in mathematics.
Teaching emphases and difficulties:
Teaching emphasis: explore and understand the positional relationship between circles.
Difficulties in teaching: To explore the quantitative relationship between the center distance of two circles and the radius of two circles in the positional relationship between circles.
Analysis of Three Teaching Methods and Learning Methods
1. In class, based on the new curriculum concept that everyone learns useful mathematics and everyone gets valuable mathematics, we introduce new lessons from graphic examples in life and demonstrate the positional relationship between circles with animation. Through the learning process of exploration, discussion, observation, summary and reuse, it is very consistent with the cognitive characteristics of students of this age to explore and master knowledge step by step.
2. Do not engage in rigid teaching and lectures, but pay attention to intuitive perception and operational understanding. Starting from the reality that students are familiar with, let students look at and think about the main characteristics of graphics and the basic nature of graphic changes, and learn to identify different graphics with the positional relationship between circles;
3. Give proper teaching reasoning in the classroom, so as to make the knowledge from shallow to deep; From irregular to regular; The mathematical learning process from intuitive knowledge to rational knowledge can cultivate students' rational reasoning ability, enhance students' rigorous thinking ability and cultivate students' appropriate mathematical literacy.
Four teaching program design
1. Create situations and stimulate interest.
2. Ask questions and guide the inquiry.
3. Animation demonstration, exploring new knowledge
4. Summary, overall feeling
5. Apply new knowledge, expand and improve
6. Arrange homework to consolidate and deepen.
Five teaching processes
1. Create situations and stimulate interest.
Design intention: guide students to appreciate pictures, stimulate students' interest in exploring the positional relationship between two circles, and introduce topics to be studied. (Courseware demonstration)
2. Ask questions and guide the inquiry.
Query 1: The geometric features of the positional relationship between a straight line and a circle are described by common points. Please guess, how many types can the positional relationship between circles be divided into according to their common points?
Hands-on operation; Draw two ⊙O 1 and ⊙O2 with different radii on two transparent sheets prepared in advance, and stack them together, fix one and move the other. How many different positional relationships can you find between ⊙O 1 and ⊙O2? How much do two circles have in common in each positional relationship?
Design intention: Let students do experiments by themselves and participate in math activities.
3. Animation demonstration, exploring new knowledge
Design intention: Let students observe the change of the position relationship between two circles and the change of the number of common points from the viewpoint of movement change, and learn to study the position relationship between two circles by analogy and classified discussion.
Learn for practice.
1.2008 The positional relationship between the two circles in the cycling logo of Beijing Olympic Games is _ _ _
2. There are many positional relationships between the two circles in the picture. Please find out that the location relationship that is not found is _ _
Please point out the relationship between the circle and the circle contained in the picture in your life (the picture is on the courseware).
Design intention: It is to let students learn to express problems in mathematical language, realize that mathematics comes from life, serves life, and enhances application consciousness.
Question2: The quantitative factors that affect the positional relationship between a straight line and a circle are the radius and the distance from the center of the circle to the straight line. What are the quantitative factors that affect the positional relationship between a circle and a circle?
Inquiry 2 is the key content of this lesson. In teaching, students can explore the quantitative relationship between the center distance (D) of two circles and the radius (R and R) of two circles in different positions through the animation demonstration of courseware. (Watch the courseware animation)
Design Intention: With multimedia animation demonstration, students can intuitively observe the positional relationship between circles, and students can easily explore the positional relationship between two circles from the perspective of quantitative relationship, break through difficulties and experience the mathematical thought of combining numbers with shapes.
4. Summary, overall feeling
Ask the students to summarize themselves through the previous teaching and fill in the following table:
The positional relationship between circles
Relationship between intersection point d and r, r of position relation graph
(R & gtr)
d & gtR+r
d=R-r
Design intention: Summarize the knowledge points in the form of tables, through which it is easy to see the classification of the positional relationship between circles, experience the idea of combining numbers with shapes and the method of judging the positional relationship between two circles, so that students can form a clear, systematic and complete knowledge network.
5. Apply new knowledge, expand and improve
Example 1: As shown in the figure, the radius ⊙0 is 5cm, the point P is a little outside ⊙0, and OP=8cm.
Find: (1) What is the radius of the small circle P with P as the center and circumscribed by ⊙P and ⊙O?
(2) What is the radius of the great circle P with p as the center and inscribed with ⊙P and ⊙O?
Exercise: The radii of circle O 1 and circle O2 are 3cm and 4cm respectively. What is the positional relationship between two circles in the following situations?
( 1)o 1o 2 = 8cm(2)o 1o 2 = 7cm。
(3)o 1o 2 = 5cm(4)o 1o 2 = 1cm。
(5) O1O2 = 0.5cm (6) O1coincides with O2.
Design intention: Use the positional relationship between two circles and the quantitative relationship between center distance and radius to solve the problem. Cultivate students' ability to apply knowledge.
6. Summarize and assign homework
1) Question: What new knowledge and methods have we learned by reviewing the inquiry process of this lesson?
2) Homework: A: Textbook exercises 1, 4, 6.
B: Inquiry after class: How many circles are tangent to circle O 1 (radius 2) and circle O2 (radius 1) and have a radius of 3?
Design intention: By summarizing and reviewing the contents of this section, help students learn to summarize and reflect, and cultivate scientific cognitive habits. Homework arrangement pays attention to stratification, so that inquiry can be extended to extracurricular activities.
6. Teaching evaluation
1. In the design of this lesson, I introduced a new lesson from graphic examples in my life, and showed the positional relationship between circles intuitively and vividly by means of animation demonstration. Let the students draw a conclusion through exploration, discussion, observation and summary.
2. Classifying and listing the positional relationship between circles in the form of a table not only embodies the idea of classification, but also embodies the idea of combining numbers with shapes; The process of mathematics learning from shallow to deep, from intuitive knowledge to rational knowledge, enables students to truly understand and master basic mathematics knowledge and skills, ideas and methods, and gain rich experience in mathematics activities.
3. Through the completion of homework after class, we can further understand students' understanding and mastery of the relationship between circles. Teachers make corresponding feedback and adjustment according to these evaluation results, adjust and design the teaching content of the next class or the next stage, and achieve the best teaching effect as much as possible.