1. High school mathematics courseware
First, the teaching objectives
1. Knowledge and skills
(1) Enhance students' intuitive perception through physical operation.
(2) Space objects can be classified according to their geometric characteristics.
(3) Summarize the structural features of prism, pyramid, cylinder, cone, frustum, frustum and sphere in language.
(4) The classification of geometry, column, cone and platform will be indicated.
2. Process and method
(1) Let students intuitively feel the space objects, and summarize the geometric structure characteristics of cylinders, cones, platforms and spheres from the objects.
(2) Let students observe, discuss, summarize and summarize what they have learned.
3. Emotional attitudes and values
(1) Let students feel that space geometry exists around real life, and improve their learning enthusiasm and observation ability.
(2) Cultivate students' spatial imagination and abstract tolerance.
Second, the focus and difficulty of teaching
Key points: let students feel a large number of space objects and models, and summarize the structural characteristics of columns, cones, platforms and balls.
Difficulties: generalization of structural characteristics of columns, cones, platforms and spheres.
Third, teaching tools.
(1) Learning methods: observation, thinking, communication, discussion and summary.
(2) Physical model and projector
Fourth, teaching ideas
(A) create a scene to reveal the theme
1. The teacher asked: There are many distinctive buildings around our lives. Can you give some examples? What are the geometric features of these buildings? Guide students to recall, give examples and communicate with each other. Teachers evaluate students' activities in time.
2. The mentioned buildings are basically composed of these geometric bodies (space objects showing the structural characteristics of cylinders, cones, platforms and spheres), which you can observe. Are these space objects classified according to some standard? This is what we want to learn.
(2) Explore new knowledge
1. Guide students to observe objects, think, communicate and discuss, classify objects, and distinguish prisms, cylinders and pyramids.
2. Observing the geometric objects of the prism, what are the characteristics of the picture of the projection prism? What are their similarities and differences?
3. Organize students to discuss in groups, and each group chooses a student to publish the results of the group discussion. On this basis, the main structural characteristics of the prism are obtained.
(1) has two parallel faces;
(2) All other faces are parallelograms;
(3) The public sides of every two adjacent upper quadrangles are parallel to each other. Summarize the concept of prism.
4. Teachers and students combine the graphics * * * to get the related concepts of prism and the representation of prism.
5. Question: What are the main differences between these prisms? Can prisms be classified in different ways? Please list the objects around you that have studied geometric features, and tell the geometric features that make up these objects? What basic geometric figures are they made of?
6. 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.
7. Let the students observe the cylinder and demonstrate how to get the cylinder through the physical model, so as to sum up the concept of the horn and related concepts and the representation of the cylinder.
8. Guide students to think about the structural characteristics of cones, frustums and spheres in a similar way, as well as related concepts and expressions, and guide students to think, discuss and summarize with the help of physical model demonstration.
9. The teacher pointed out that cylinders and prisms are collectively called cylinders, frustums and frustums are collectively called platforms, and cones and pyramids are collectively called cones.
10. In the real world, most of the objects we see are composed of columns, cones, platforms, balls and other objects with geometric structural characteristics. Please list the objects around you that have studied geometric features, and tell the geometric features that make up these objects? What basic geometric figures are they made of?
(3) Questioning the defense, solving problems and dispelling doubts, developing thinking, teachers asking questions and making students think.
1. Is a geometric figure with two faces parallel to each other and the others all parallelograms a prism?
2. Can any two planes of the prism be used as the bottom surface of the prism?
3. Textbook P8, Exercise 1.1Group A1.
4. Cylinder can be rotated by rectangle, cone can be rotated by right triangle, and frustum can be rotated by what figure? How to rotate?
5. What is the relationship between prism and pyramid? What about frustum, cylinder and cone?
Verb (abbreviation of verb) consolidates and deepens.
Exercise: textbook P7 Exercise 1, 2( 1)(2)
Textbook P8 Exercise 1. 1 Questions 2, 3 and 4
Sixth, induction and finishing
What did the students learn?
Seven. distribute
2. High school mathematics courseware
First, the teaching objectives
Knowledge and skills:
Understand the concepts of arbitrary angle (including positive angle, negative angle and zero angle) and interval angle.
Process and method:
Can establish a rectangular coordinate system to discuss any angle, can judge the quadrant angle, and can write a set with the same angle at the end; Master the writing of interval angle group.
Emotional attitudes and values:
1 to improve students' reasoning ability;
2. Cultivate students' awareness of application.
Second, the teaching emphasis and difficulty:
Teaching focus:
Understanding the concept of arbitrary angle; Writing of interval angle set.
Teaching difficulties:
A representation of a set with the same angle on the edge of the terminal; Writing of interval angle set.
Third, the teaching process
(A) the introduction of new courses
Definition of retrospective angle
The first definition of (1) angle is that a graph composed of two rays with a common endpoint is called an angle.
The second definition of angle is that an angle can be regarded as a graph formed by a ray rotating from one position to another around an endpoint on a plane.
Teach new courses
1, related concepts of angle:
Definition of (1) angle:
An angle can be regarded as a graph formed by a ray rotating from one position to another around an endpoint on a plane.
(2) Name of angle:
note:
(1) "angle α" or "∠ α" can be simplified to "α" without causing confusion;
(2) If α is a zero-degree angle α = 0, the terminal edge of the zero-degree angle coincides with the initial edge;
⑶ The concept of angle has been extended to include positive angle, negative angle and zero angle.
Please tell me what the angles of α, β and γ are?
2, the concept of quadrant angle:
Definition: If the vertex of an angle coincides with the origin, and the starting edge of the angle coincides with the non-negative semi-axis of the X axis, then in which quadrant is the final edge of the angle (except the endpoint), we say that the angle is a quadrant.
3. High school mathematics courseware
Teaching objectives:
1. Understand the basic logical structure of the flow chart selection structure.
2. Be able to recognize and understand the function of simple block diagram.
3. Can use three basic logical structures to design flow charts to solve simple problems.
Teaching methods:
1. Through imitation, operation and exploration, experience the process of expressing and solving problems in the design flow chart, and deepen the perception of the flow chart.
2. In the process of solving specific problems, master the drawing method of basic flow chart and three basic logical structures of flow chart.
Teaching process:
First, the problem situation
1. Situation:
According to the regulations of a railway passenger transport department, the cost of checked baggage between A and B is as follows
Where (unit: xx) is the weight of luggage.
2. Try to give an algorithm for calculating the cost (unit: xx yuan) and draw a flow chart.
Second, student activities.
Students discuss and the teacher guides the students to express.
Third, structural mathematics.
1. The concept of selection structure:
The structure that judges first according to the conditions and then decides which operation to perform is called the selection structure.
Inside the dotted box is a selection structure, which contains a judgment box, which is executed when the condition is true (or called "true"), otherwise it is executed.
2. Description:
(1) Some problems need to be analyzed, compared and judged according to given conditions, and different operations should be carried out according to different situations. The realization of this kind of problem needs to choose the design of the structure;
(2) Selection structure is also called branch structure or selection structure. The judgment must be made according to the specified conditions first, and then one of the two branch paths is determined by the judgment result;
(3) In the selection structure shown above, only one of and cannot be executed, but one of the two boxes can be empty, that is, no operation can be performed;
(4) The shape of the flowchart box should be standardized, and the judgment box must be drawn as a diamond, with an entry point and two exit points.
3. Thinking: In the algorithm shown in the figure on page 7 of the textbook, which step is judged?
4. High school mathematics courseware
Teaching purpose: to master the standard equation of circle and solve related problems.
Teaching emphasis: the standard equation of circle and its related application
Teaching difficulty: flexible application of standard equation
Teaching process:
First, introduce a new lesson and explore the standard equation.
Second, master knowledge and consolidate practice.
1. Say the equation of the circle below.
The radius of (1) center (3, -2) is 5; (2) The radius of the center (0,3) is 3.
3. Indicate the center and radius of the following circle.
⑴(x-2)2+(y+3)2=3
⑵x2+y2=2
⑶x2+y2-6x+4y+ 12=0
3. Judge the positional relationship between 3x-4y- 10=0 and x2+y2=4.
The center of the circle is (1, 3), which is tangent to 3x-4y-7=0. Find the equation of this circle.
Third, extend and improve, for example.
For example, 1, the equation with the center at y=-2x passes through p(2,-1) and is tangent to x-y= 1 (highlighting the mathematical method of undetermined coefficient).
Exercise:
1, a circle passes through (-2, 1) and (2,3), and its center is on the X axis. Find its equation.
2. Find the equation of the circle passing through A (-10,0), B (10/0,0) and C (0 0,4).
Example 2: A circular arch bridge with a span of 20 meters and an arch height of 4 meters. During construction, add a pillar every 4 meters to find the length of A2P2.
Example 3, the point M(x0, y0) is on x2+y2=r2, and the tangent equation of circle passing through m is found (multiple solutions to one problem, training thinking).
Fourth, summarize exercise P77 1, 2, 3, 4
Verb (abbreviation of verb) operates P8 1 1, 2, 3, 4.
5. High school mathematics courseware
First, teaching material analysis:
The concept of set and its basic theory, called set theory, is an important foundation of modern mathematics. On the one hand, many important branches of mathematics are based on set theory. On the other hand, set theory and its mathematical thought have been applied in more and more fields.
Two. Target analysis:
Teaching emphases and difficulties
Key point: the meaning and representation of set.
Difficulties: the proper choice of representatives.
Teaching objectives
1. Knowledge and skills
(1) Understand the meaning of set and the relationship between elements and set through examples;
(2) Know the commonly used number sets and their special signs;
(3) Understand the certainty, mutual dissimilarity and disorder of elements in the set;
(4) Being able to express related mathematical objects in assembly language;
2. Process and method
(1) Let students experience the process of abstracting and summarizing the same characteristics of a set from the examples of the set, and feel the meaning of the set.
(2) Ask students to summarize what they have learned in this section.
3. Emotions, attitudes and values
Let students feel the necessity of learning assembly and enhance their enthusiasm for learning.
Three. Analysis of teaching methods
1. Teaching method: Students can learn, think, communicate, discuss and summarize independently by reading textbooks, so as to better accomplish the teaching objectives of this course.
2. Teaching method: Use projector to assist teaching in teaching.
Four. process analysis
(A) create a scene to reveal the theme
1. The teacher first asked:
(1) Tell me about your family, your old school and your current class.
(2) Question: What are the characteristics of "family", "school" and "class"?
Guide students to communicate with each other. At the same time, teachers evaluate students' activities.
2. Activities:
(1) list examples of life sets;
(2) Analyze and summarize the same characteristics of each case.
This leads to the content to be studied in this section.
Design intention: not only stimulate students' strong interest in learning, but also pave the way for new knowledge.
(2) Explore new knowledge and construct concepts.
1. Teachers use multimedia devices to show students the following seven examples:
All prime numbers in (1) 1-20;
(2) four great inventions of ancient china;
(3) All permanent members of the Security Council;
(4) All squares;
(5) All overpasses completed before September 2004 in Hainan Province;
(6) To all points with the same distance on both sides of an angle;
(7) All senior one students enrolled in Guoxing Middle School in September 2004.
2. Teachers organize students to discuss in groups: What are the similarities and differences between these seven examples?
3. Choose a student from each group to publish the results of the group discussion. On this basis, teachers and students summed up the characteristics of seven examples and gave the meaning of the set. Generally speaking, the sum of some specific objects is called a set. Every object in a set is called an element of this set.
The teacher pointed out that sets are usually represented by uppercase letters A, B, C and D, and elements are usually represented by lowercase letters A, B, C and D. 。
Design intention: let students feel the concept of set through examples, stimulate their interest in learning and cultivate the spirit of being willing to seek.
(3) Questioning defense and developing thinking.
1. The teacher guides the students to read the relevant contents in the textbook and thinks: What are the characteristics of the elements in the set? And pay attention to individual counseling, answer students' questions, and let students know the three characteristics of set elements, namely certainty, mutual difference and disorder. As long as the elements that make up two sets are the same, we call them equal.
2. Teachers' organizations guide students to think about the following questions:
Determine whether all the following elements form a set and explain why:
(1) is an even number greater than 3 and less than 1 1;
(2) Small rivers in China. Let students fully express their solutions.
3. Ask students to give some examples that can form a set and examples that can't form a set, and explain the reasons. Teachers give timely evaluation to students' learning activities.
4. The teacher asks questions to make students think.
B is (1). If A represents the collection of all the students in Grade Three, and A represents a classmate in Grade Three and a classmate in Grade Four, what is the relationship between A and B respectively? This leads students to come to the conclusion that there are two relationships between elements and sets: attribution and non-attribution.
If a is an element of set a, it is said that a belongs to set a.
If a is not an element of set a, it is said that a does not belong to set a.
(2) If A is used to represent the set of "all permanent members of the Security Council", what is the relationship between China and Japan and set A? Please use mathematical symbols to represent them respectively.
(3) Let the students finish the exercise on page 6 of the textbook 1.
5. Teachers guide students to recall the process of developing several groups, and then read the cross contents in the textbook, write the marks of several commonly used groups, and ask students to complete the question1.1a.
6. Teachers guide students to read the relevant content in the textbook, and think and discuss the following questions:
(1) How many representations can a set * * * have?
(2) Try to compare natural language. What are the characteristics of enumeration and description when representing collections? What is the applicable object?
(3) How to choose an appropriate set representation according to the problem?
Make students understand the advantages and disadvantages of the three expressions, the necessity of their existence and the applicable objects.
Design intention: Make clear the three characteristics of set elements, so that students can understand the advantages and disadvantages of the three representations, thus breaking through the difficulties.
Consolidate and deepen, feedback and correct
Teacher projection learning
(1) Describe the set in natural language {1, 3,5,7,9};
(2) Set A is represented by an example.
(3) Try to choose an appropriate method to represent the following set: Exercise 2 on page 6 of the textbook.
Design intention: to enable students to consolidate new knowledge in time and realize the necessity and applicable objects of the three expressions.
(5) Summarize the assignment.
1. Summary: In the interaction between teachers and students, let students understand or experience the following questions:
What knowledge have we learned in this class?
2. What do you think is the significance of learning assembly?
3. What should I pay attention to when choosing the representation of a set?
Design intention: Through review, we can have a clear understanding of the occurrence and development process of the concept, and review the three characteristics of the set elements and the three manifestations of the set.
Homework:
1. Written homework after class: exercise 1. 1A Group 4 13 pages.
2. How many relationships are there between elements and sets? How to express it? Similarly, how many relationships are there between sets? How to express it? Students are required to preview their textbooks.