Teaching objectives

1. The structural features of prism, pyramid, cylinder, cone, frustum, frustum and sphere will be summarized in language.

2. Space objects can be classified according to their geometric characteristics.

3. Improve students' observation ability; Cultivate students' spatial imagination and abstract tolerance.

Emphasis and difficulty in teaching

Teaching emphasis: let students feel a large number of space objects and models, and summarize the structural characteristics of columns, cones, platforms and balls.

Teaching difficulties: generalization of structural characteristics of column, cone, platform and ball.

teaching process

1. scene import

Teachers ask questions, guide students to observe, give examples and communicate with each other, put forward what they have learned in this lesson and show the topics.

2. Show the target and check the preview

3. Cooperative exploration, exchange and exhibition

(1) Guide the students to observe the geometric objects of the prism and the pictures of the prism, and tell them what their respective characteristics are. What are their similarities and differences?

(2) Organize students to discuss in groups, and one student in each group will publish the results of the group discussion. On this basis, the main structural characteristics of the prism are obtained. There are two parallel faces; Other faces are parallelograms; The public sides of every two adjacent quadrangles are parallel to each other. Summarize the concept of prism.

(3) Question: Please list the prisms around you and classify them.

(4) In a similar way, let students think, discuss and summarize the structural characteristics of pyramids and truncated cones, and draw related concepts, classifications and representations.

(5) Let students observe the cylinder and demonstrate the physical model, and summarize the cylinder and related concepts and the representation of the cylinder.

(6) Guide students to think about the structural characteristics of cones, frustums and spheres in a similar way, as well as related concepts and representations, and guide students to think, discuss and summarize with the help of physical model demonstration.

(7) The teacher pointed out that cylinders and prisms are called cylinders, frustums and frustums are called frustums, and cones and pyramids are called cones.

4. Questioning the defense, solving problems and dispelling doubts, developing thinking, teachers asking questions and making students think.

(1) Is the geometry with two faces parallel to each other followed by a parallelogram a prism (give a counterexample)?

(2) Can any two planes of the prism be used as the bottom surface of the prism?

(3) Cylinders can be rotated by rectangles, cones can be rotated by right triangles, and frustums can be rotated by what figures? How to rotate?

(4) What is the relationship between prism and pyramid? What about frustum, cylinder and cone?

(5) Is the geometry around one side of a right triangle necessarily a cone?

5. Typical examples

Example: Judge whether the following statement is correct.

(1) A geometric figure with one face being a polygon and the other face being a triangle is a pyramid.

If two faces are parallel to each other and the other face is trapezoidal, then this geometry is a prism.

Answer AB

6. Classroom test:

Textbook P8, Exercise 1.1Group A1.

Summarize and sort out

What did the students learn?

2. Examples of teaching plans in the first volume of senior three mathematics.

Teaching objectives

Further familiar with the content of sine and cosine theorem, can skillfully use cosine theorem and sine theorem to solve related problems, such as judging the shape of triangle and proving triangle identity in triangle.

Emphasis and difficulty in teaching

Teaching emphasis: ingenious application of theorem.

Teaching difficulties: apply sine and cosine theorems to transform the corner relationship.

teaching process

First, review preparation:

1. Write sine theorem, cosine theorem, inference and other formulas.

2. Discuss the triangle type solved by each formula.

Second, teach new lessons:

1. On the solution of teaching triangle;

① Example 1: In △ABC, the following conditions are known to solve triangles.

Two groups of exercises → Discussion: Why does the number of solutions change?

② Analyze and solve with the following figure (when A is an acute angle).

② Exercise: In △ABC, the following conditions are known to judge the solution of triangle.

2. Flexible application of sine theorem and cosine theorem in teaching;

① Example 2: In △ABC, it is known that sinA∶sinB∶sinC=6∶5∶4, and the cosine of the angle is found.

Analysis: How do known conditions transform? → Introduce the parameter k, set three sides, and use cosine theorem to find the angle.

② Example 3: In ABC, it is known that a=7, b= 10 and c=6, and the type of triangle is judged.

Analysis: What knowledge can be used to distinguish triangles? → Find the cosine of the angle and judge by the symbol.

③ Example 4: Given △ABC, try to judge the shape of △ABC.

Analysis: How to turn an edge in an angular relationship into an angle? → Rethink: How to Turn Keratosis into Edge?

3. Summary: Discussion on triangular solution; Judging the type of triangle; How to make the corner relationship mutual?

3. Examples of teaching plans in the first volume of senior three mathematics.

First, the teaching objectives

1, knowledge and skills

(1) Understand the concept of logarithm and the relationship between logarithm and exponent;

(2) Ability to convert exponential and logarithmic expressions;

(3) Understand the nature of logarithm, master the above knowledge, and cultivate the ability of analogy, analysis and induction;

2. Process and method

3. Emotional attitudes and values

(1) Through the study of this section, experience the rigor of mathematics, cultivate good thinking habits of careful observation and careful analysis, and constantly explore the spirit of new knowledge;

(2) the cognitive process of perception from concrete to abstract, from special to general, from perceptual to rational;

(3) Experience the scientific function, symbolic function and tool function of mathematics, and cultivate intuitive observation.

Good mathematical thinking quality of exploration, discovery and scientific demonstration,

Second, the focus and difficulty of teaching

Teaching focus

The definition of (1) logarithm;

(2) mutual conversion between exponential expression and logarithmic expression;

Teaching difficulties

Understand the concept of (1) logarithm;

(2) Understanding of logarithmic properties;

Third, the teaching process:

Fourth, summary:

The concept of 1, logarithm

Generally speaking, if the function ax=n(a0 and a≠ 1), then the number X is called the logarithm with the base of n, and it is denoted as x=logan, where A is called the base of the logarithm and N is called the real number.

2. Conversion between logarithm and exponent

ab=n？ Logan =b

3. The basic properties of logarithm

Negative numbers and zero have no logarithm; loga 1 = 0； Logaa= 1 logarithmic identity: alogan = n；; logaa=nn

Verb (abbreviation for verb) homework after class

Exercise after class 1, 2, 3, 4

4. Examples of teaching plans in the first volume of senior three mathematics.

Teaching objectives

(1) correctly understand the meaning of addition principle sum multiplication principle, and distinguish their conditions and conclusions;

(2) It can be combined with tree diagram to help understand the principle of addition principle sum multiplication;

(3) Correctly distinguish between addition principle and multiplication principle, which principle is related to classification and which principle is related to step by step;

(4) addition principle sum multiplication principle can be applied to solve some simple application problems and improve students' understanding and application ability of the two principles;

(5) Through the study of addition principle and the principle of multiplication, cultivate students' good habit of thinking and analyzing carefully.

Teaching suggestion

I. Knowledge structure

Second, analysis of key points and difficulties

This section focuses on addition principle and multiplication principle, but the difficulty is to accurately distinguish addition principle and multiplication principle.

The principle of addition principle sum multiplication is easy to understand and even self-evident. These two principles are the basis of learning to arrange and combine content, which runs through the whole content. On the one hand, they are the basis of deriving permutation and combination numbers; On the other hand, its conclusions and ideas have many direct applications in the method itself and problem solving.

These two principles answer the question of how many different ways to accomplish a thing. The difference lies in: the precondition of applying addition principle is that there are n schemes to do one thing, and any method in any scheme can be completed, that is, the methods to complete it are independent of each other; The premise of applying the principle of multiplication is that there are n steps to do a thing, and it can be completed by choosing any method in each step and completing each step in turn, that is to say, the steps to complete it are interdependent. To put it simply, if all the methods to accomplish one thing belong to the classification problem, the final result will be obtained every time, and addition principle will be used; If the method of completing a thing is a step-by-step problem, then the principle of multiplication should be used every time the result of this step is obtained.

Three. Suggestions on teaching methods

The teaching of two counting principles should be divided into three levels:

The first is the knowledge and understanding of the two counting principles. Ask students to understand the meaning of two counting principles and find out the difference between them. They should know when to use the addition counting principle and when to use the multiplication counting principle. (It is recommended to use one type).

The second is the application of two counting principles. Students can do exercises (two classes are recommended):

① How many 8-digit numbers can be formed by 0, 1, 2, ..., 9;

② How many 8-bit integers can 0, 1, 2 form, ..., 9;

(3) How many 4-digit integers can 0, 1, 2 form, ..., 9?

④ How many 4-digit integers with repeated numbers can be formed by using 0, 1, 2, ..., 9;

⑤ How many 4-digit odd numbers can 0, 1, 2 form?

⑥0, 1, 2 can form how many 4-digit integers with repeated two numbers, ..., 9 and so on.

Third, let students master the comprehensive application of two counting principles. This process should run through teaching. Every permutation and combination number formula and its properties must be deduced by two counting principles, and every permutation and combination problem can be solved directly by two principles. In addition, direct calculation method and indirect calculation method are the embodiment of these two principles. Teachers should guide students to carefully analyze the meaning of questions, classify them appropriately, step by step, and make good use of two basic counting principles.

5. Examples of teaching plans in the first volume of senior three mathematics.

Academic goal

(1) enables students to have a preliminary understanding of the concept of set, and to know the concept and notation of common number set.

(2) Let students understand the meaning of "belonging" relationship.

(3) Make students understand the meaning of finite set, infinite set and empty set.

Important and difficult

Teaching emphasis: the basic concept and expression method of set

Difficulties in teaching: Using two common representations of sets-enumeration method and description method to correctly represent some simple sets.

Teaching type: new teaching

Class schedule: 1 class hour

Teaching AIDS: multimedia, physical projector.

content analysis

Set is an important basic concept in middle school mathematics. In primary school mathematics, the initial concept of set is permeated. Junior high school further expresses some problems in set language, such as number set and solution set used in algebra. As for logic, it can be said that from the beginning of learning mathematics, it is inseparable from the mastery and application of logic knowledge. Basic knowledge of logic is also an indispensable tool for understanding and studying problems in daily life, study and work. These can help students understand the significance of learning this chapter, and they are also the basis of learning this chapter.

The reason why the set of preparatory knowledge and simple logic knowledge are arranged at the beginning of high school mathematics is because in high school mathematics, these knowledge are closely related to other contents and are the basis for learning, mastering and using mathematical language. For example, the concepts and properties of functions in the next chapter are inseparable from sets and logic.

This section introduces the concepts of set and the elements of set from the examples involved in algebra and geometry in junior high school, and illustrates the concept of set with examples. Then it introduces the common representation methods of sets, including enumeration method and description method, and gives an example of representing sets by drawing.

This lesson mainly studies the introduction of the whole chapter and the basic concepts of set. The introduction is to arouse students' interest in learning and let them know the significance of learning this chapter. The teaching focus of this lesson is the basic concept of set.

Set is a primitive and undefined concept in set theory. When we came into contact with the concept of set, we got a preliminary understanding of the concept mainly through examples. The sentence "Under normal circumstances, some specified objects will become a set together, also known as a set" given in the textbook is only a descriptive explanation of the concept of set.