Lecture Notes on the Nature of Plane and Plane Parallelism in High School Mathematics

Respected examiners, hello, I am candidate X, and today I Speak a lesson The title of the book is "The Nature of Parallel Planes".

I will carry out my research from the aspects of textbook analysis, learning situation analysis, teaching process, etc Speak a lesson 。

1、 Talking about textbooks

First, let me talk about my understanding of the textbook. This lesson is selected from the second compulsory volume of People's Education A Edition. As the title says, it mainly explores the nature of parallel planes. The content of parallel relationship learned before laid a good foundation for the learning of this lesson; This lesson will pave the way for solving solid geometry problems.

2、 On learning emotion

Next, let's talk about the actual situation of students. The students already have the knowledge required for learning this lesson, and their logical reasoning ability is relatively mature. Teachers can fully mobilize students' initiative, but they need to guide the direction of thinking in a timely manner.

3、 On the Teaching Objectives

Based on the above analysis, I have formulated the following teaching objectives:

1. Grasp the property theorem of face parallelism, understand the mutual transformation between parallel relations, and can be used to solve simple problems.

2. Go through the process of exploring the property theorem of parallelism, and develop core literacy (intuitive imagination, logical reasoning).

3. Understand the preciseness of mathematics and establish a scientific attitude of seeking truth from facts.

4、 Talking about the key and difficult points of teaching

In the process of achieving the teaching objectives, the teaching focus is on the property theorem of parallelism, and the teaching difficulty is the exploration and proof of the theorem.

5、 On teaching and learning methods

Modern teaching theory believes that in the teaching process, students are the main body of learning, and teachers are the organizers, guides and collaborators of learning. All teaching activities must focus on the initiative and enthusiasm of students. According to this teaching concept, in combination with the content characteristics of this lesson and the age characteristics of students, I will adopt such teaching methods as question and answer method, exercise method, independent inquiry, etc.

6、 On the teaching process

Now let's focus on my design of teaching process.

（1） Import new lesson

In order to help students establish the connection between new and old knowledge and improve the knowledge system, at the beginning of the class, I intend to review the judgment theorem of parallelism between faces, emphasizing "two intersecting straight lines", to help students deepen their impression. Then, from the judgment to the nature, ask what conclusions can be deduced under the condition that the plane is parallel to the plane. Lead students to think and follow the trend to lead to the topic.

（2） Explain new knowledge

What conclusions can be drawn by introducing questions. "Dimension reduction" is one of the common ideas in solid geometry, and students are familiar with it. I will start from this idea and further guide the students' thinking direction. Question: If two planes are parallel, what is the position relationship between the line in one plane and the other? What is the positional relationship with a line in another plane? According to the fact that there is no common point between two planes, students can deduce that a line in one plane is parallel to the other plane, parallel to or different from the line in the other plane.

Parallelism is an important positional relationship that we focus on. The parallel of line and plane has been systematically studied before, so the question naturally arises here: When are two lines located in two parallel planes parallel? It has just been introduced that either parallel or different planes, so I will remind students to pay attention to the differences between parallel lines and lines in different planes. According to the fact that parallelism is a coplanar relationship, students can easily deduce that there is only one plane through two parallel lines located in two parallel planes, or the intersection line obtained by cutting two parallel planes with the third plane is parallel. It can be inferred that two parallel planes intersect the third plane at the same time, and the two intersection lines obtained are parallel. The above process can well develop core literacy such as intuitive imagination and logical reasoning while drawing conjectures.

Considering that the reasoning in the inquiry just now has paved the way for proof, I organize students to write a complete and standardized proof process. On this basis, I can standardize and emphasize details.

So far, we can sum up the property theorem of plane parallelism: two planes are parallel, and if the other plane intersects these two planes, then the two intersecting lines are parallel.

The above teaching activities can ensure that students can fully participate in the formation process of knowledge and more deeply understand the property theorem of parallelism, not only knowing its nature, but also knowing its reason.

Next, change the entry angle from "two parallel lines in two parallel planes" to "two parallel lines intersecting two parallel planes", and organize students to see what conclusions they have. Presupposition: students guess that the line segments of these two parallel lines cut by two parallel planes are equal.

（3） Classroom exercises

I intend to prove that "parallel line segments sandwiched between two parallel planes are equal" as a classroom exercise. On the one hand, it determines the correctness of the conjecture, and on the other hand, it consolidates the effect by applying the property theorem of parallelism.

（4） Summary homework

Considering that the nature of the parallel between the plane and the plane is the last new knowledge of the parallel between the spatial straight line and the plane in the textbook, and the judgment and nature of these parallel relations are connected with each other. In the class summary, I intend to sum up with students the mutual transformation relationship established by the judgment or nature of line parallel, line plane parallel, and plane parallel, and present it intuitively in the form of block diagram to help students form systematic cognition.

After class homework is first to complete the exercises on the book to further consolidate the content of this section; Next is thinking - if the straight line is not in two parallel planes, or the third plane does not intersect with these two planes, what conclusions can be drawn if the two planes are parallel?

7、 On blackboard design

My blackboard writing strives to be clean and clear, highlighting the key points. The following is my blackboard writing design: