4-4 synchronous lesson preparation teaching plan for senior high school mathematics elective course

As a tireless people's teacher, we usually need to use teaching plans to assist teaching, which can make teaching more scientific. Let's refer to how the lesson plan is written! The following is my teaching plan for preparing lessons for senior high school math elective 4-4 synchronously for your reference, hoping to help friends in need.

Senior high school mathematics elective 4-4 synchronous lesson preparation teaching plan 1 1. Teaching objectives:

Knowledge and skills: Understand the conditions of linear parametric equation and the meaning of parameters.

Process and method: According to the geometric conditions of a straight line, the parameter equation and the meaning of the parameters can be written.

Emotion, attitude and values: cultivate innovative consciousness through the creative process of observation, exploration and discovery.

Double Difficulties: Teaching Emphasis: Definition and Method of Curve Parameter Equation

Teaching difficulty: choose appropriate parameters to write the parametric equation of the curve.

Third, teaching methods: heuristic and induced discovery teaching.

Fourth, the teaching process

(a), review the introduction:

1. Write the standard formula of circular equation and the corresponding parameter equation.

Circular parametric equation (as parameter)

(2) The cyclic parameter equation is (as a parameter)

2. Write the elliptic parameter equation.

3. Review the concept of direction vector. Question: Given a point and inclination of a straight line, how can we express the parametric equation of the straight line?

(2), explain the new lesson:

1. Question: The inclination of the straight line L is, passing through point P (2 2,3). How to describe the position of any point on the straight line L?

If it is known that the straight line l passes through two

The fixed point q (1, 1), p (4 4,3),

So how to describe any point on the straight line L

Where is the location?

2. Teachers guide students to derive the parameter equation of straight line;

(1) passes through a straight line with a fixed point inclination of.

parameter equation

(is a parameter)

Analysis of the parametric equation of a straight line: Let M(x, y) be any point on a straight line, and the geometric meaning of the parameter T refers to the displacement from point P to point M, which can be expressed by the number of directed line segments. Signed it.

(2) The parameter equation of a straight line passing through two fixed points Q and P (where) is

. Where the point M(X, y) is any point on a straight line. The geometric meaning of the parameter here is obviously different from T in the parametric equation (1), which reflects the ratio of the number of directed segments of the moving point m, when m is the midpoint; When sum, m is the outer bifurcation point; At that time, point m and point q coincided.

(3) The application of linear parametric equation strengthens the understanding.

1, for example:

Students practice and the teacher can comment on the questions. Reflection induction method: 1, the solution method of linear parameter equation; 2. Find the intersection point with linear parameter equation.

2. Consolidate and guide:

Supplement: 1. If the straight line is tangent to the circle, the inclination of the straight line is (a).

A. or b or c or d or

2. (Coordinate system and parameter equation are selected as questions) If the straight line is perpendicular to the straight line (as a parameter), then.

Solution: The linearized constant equation is,

The slope of the straight line is,

Convert a straight line (as a parameter) into an ordinary equation,

The slope of the straight line is,

Then, from the necessary and sufficient condition that two straight lines are perpendicular, …

(4) Summary: (1) Solve the linear parameter equation; (2) Characteristics of linear parametric equation; (3) Pay attention to the meaning of the parameters according to the known conditions and the geometric properties of the graph.

(5), homework:

Supplement: Let the parameter equation of the straight line be (t is the parameter) and the equation of the straight line be y=3x+4, then the distance from it is _ _ _ _ _ _ _ _.

The small question of the location of the test center transforms the parameter equation into a constant equation, the distance between two parallel lines, and the basic question.

Analysis: Since the constant equation of a straight line is, the distance between it and it is.

Five, teaching reflection:

High school mathematics elective 4-4 synchronous lesson preparation teaching plan 2 teaching purpose;

Knowledge goal:

Understand the method of describing the position of space midpoint in cylindrical coordinate system and spherical coordinate system.

Ability goal:

Understand the conversion formula between cylindrical coordinates, spherical coordinates and rectangular coordinates.

Moral education goal:

Cultivate innovative consciousness through observing, exploring and discovering the creative process.

Teaching focus:

Differences and relations between experience and spatial point position drawing in rectangular coordinate system.

Teaching difficulties:

Use them in simple mathematical applications.

Teaching type:

New teaching

Teaching mode:

Enlightening, inducing and discovering teaching.

Teaching AIDS:

Multimedia and physical projectors

Teaching process:

First, review the introduction:

Situation: We use three data to determine the position of the satellite, namely the distance, longitude and latitude from the satellite to the center of the earth.

Q: How to locate a point in space? What are the methods?

Student review

A method of depicting the position of a point in a spatial rectangular coordinate system]

Significance of polar coordinates and reciprocity principle between polar coordinates and rectangular coordinates

Second, explain the new lesson:

1, spherical coordinate system

Let p be any point in space, the projection on the oxy plane is Q, connect OP, let |OP|=, the angle between OP and OZ axis is Q, the projection of P on the oxy plane is Q, and the minimum positive angle when the Ox axis rotates counterclockwise to OQ is 0. The position of point P can be represented by an ordered array. We call the coordinate system that establishes the above correspondence a spherical coordinate system (or a spatial polar coordinate system).

An ordered array is called the spherical coordinates of point P, where ≥0, 0≤≤0, and 0 ≤ < 2.

The transformation relationship between rectangular coordinates and spherical coordinates of space point P is as follows:

2. Cylindrical coordinate system

Let p be an arbitrary point in space, and the projection on the oxy plane is Q, and use (ρ, θ) (ρ≥ 0, 0 ≤ θ.

Polar coordinates on the plane oxy, the position of point P can be represented by an ordered array (ρ, θ, z), and the coordinate system that establishes the above corresponding relationship is called cylindrical coordinate system.

The ordered array (ρ, θ, z) is called the cylindrical coordinate of point P, where ρ ≥ 0, 0 ≤ θ.

The transformation relationship between rectangular coordinates (x, y, z) and cylindrical coordinates (ρ, θ, z) of space point P is:

3. Mathematical application

Example 1 Establish an appropriate spherical coordinate system to represent the vertices of a cube with a side length of 1.

Variant training

Establish an appropriate cylindrical coordinate system to represent the vertices of a cube with a side length of 1

Example 2. Convert the spherical coordinates of point m into rectangular coordinates.

Variant training

1. Converts the rectangular coordinates of point m into spherical coordinates.

2. Convert the cylindrical coordinates of point m into rectangular coordinates.

3. What is the spherical coordinate of the point > 0 in the rectangular coordinate system?

Example 3. What is the graph composed of points whose spherical coordinates satisfy the equation r=3? The equation is transformed into a rectangular coordinate equation.

Variant training

What is a graph composed of points satisfying equation =2?

Example 4. When the cylindrical coordinate of point M is known as the spherical coordinate of point N, find the length of line segment MN.

Thinking:

In the spherical coordinate system, what is the volume of the graph represented by the set?

Third, consolidate and practice.

Conclusion: The following points have been learned in this lesson:

1. Functions and rules of spherical coordinate system;

2. The role and rules of cylindrical coordinate system.

5. Homework after class: textbook P 15, page 12, page 13, page 14, page 15, page 16.

Reflection after class: This section combines plane rectangular coordinates and polar coordinates to facilitate students' understanding. But I use it less in the future and may soon forget it. Students' memories need to be recalled regularly.