One: Speaking of teaching materials

The scalar product of plane vector is the product of two vectors, and the coordinate representation of plane vector transforms the operation between vectors into the operation between numbers. Starting from the coordinate representation of plane vector, the product of plane vector and its algorithm, this section introduces the coordinate representation of the product of plane vector, the distance formula between two points in plane, and the necessary and sufficient conditions for the vertical coordinate representation of vector. It provides a good method to solve the problem of vertical line and triangle angle. This part is also one of the important contents of the whole chapter.

Secondly, talk about learning objectives and requirements.

Through the study of this section, students should master.

(1): coordinate representation of plane vector product.

(2): the distance formula between two points on the plane.

(3): Necessary and sufficient condition of vector ordinate.

And their simple applications, the above three points are also the focus of this lesson. The difficulty of this lesson is the necessary and sufficient condition and flexible application of the ordinate representation of vectors.

Three: Oral Teaching Method

In the teaching process, I mainly adopted the following teaching methods:

(1) heuristic teaching method

Because it is relatively easy to deduce the key coordinate expression in this class, I am going to let students deduce the coordinate expression of two vector quantity products themselves in this class, and then guide students to find several important conclusions: for example, the formula for calculating modulus, the formula for the distance between two points on the plane, and the necessary and sufficient conditions for the vertical vector coordinate expression.

(2) Explanatory teaching methods

Mainly to clarify the concept and relieve students' doubts in concept understanding; When explaining examples, demonstrate the problem-solving process!

The main means of assisting teaching (powerpoint)

(3) discussion method

Mainly through the mutual communication between students, deepen the understanding of difficult problems, improve students' self-study ability and the ability to discover, analyze, solve problems and innovate.

Four: methods of speaking and learning

Students are the main body of the classroom, and all teaching activities should be carried out around students, so as to stimulate students' interest in learning, enhance communication with students in the classroom, and achieve the purpose of finding and solving problems in time. Through intensive lectures and more practice, students' enthusiasm for autonomous learning can be fully mobilized. For example, let the students deduce the coordinate formula of the product of two vectors themselves, and guide the students to deduce four important conclusions! And in specific problems, let students establish the idea of equations and solve problems better!

Five: Talking about the teaching process

I'm going to take this course like this:

First of all, ask the question: what quantities do we need to know to calculate the product of two non-zero vectors?

Continue to ask questions: If you know the coordinates of two non-zero vectors, can you use the coordinates of these two vectors to represent the quantitative product of these two vectors?

Guide students to derive the coordinate expression formula of plane vector product. On the basis of this formula, students can also be guided to draw the following important conclusions:

Calculation formula of (1) module

(2) The distance formula between two points on the plane.

(3) Coordinate representation of cosine of included angle between two vectors.

(4) Necessary and sufficient conditions for vertical scalar representation of two vectors.

The second part is the explanation of examples, through which students can be more familiar with the formula and apply it.

Example 1 is the example 1 on page 22 of this book. This problem is a coordinate formula that directly uses the product of plane vectors. The purpose is to make students familiar with this formula, and on the basis of this problem, find the included angle between these two vectors. The purpose is to familiarize students with the coordinate expression of cosine of the included angle between two vectors. Example 2 is a direct proof of straightness. Although simple, it embodies an important proof method. This method should be mastered by students. This example is actually an application of the necessary and sufficient conditions of the vertical coordinate expressions of two vectors: whether the quantitative product of two vectors is zero is one of the important methods to judge whether the corresponding two straight lines are vertical.

Example 3 is slightly modified on the basis of Example 2. The purpose is to let students use formulas to solve problems and let them have the idea of establishing equations here.

Combined with practice, students can skillfully use formulas and master what they have learned today.

Then the learning summary (completed by the students)

Final homework!