1. Teaching plan of the first volume of senior three mathematics.
1. teaching material analysis and processing function are one of the important contents of high school mathematics, and the basic knowledge of function is widely used in mathematics and many other disciplines; Functions are closely related to algebraic expressions, equations and inequalities. Function is an important basic knowledge for further learning mathematics; The concept of function is the concrete embodiment of the viewpoint of movement change and unity of opposites in mathematics; The concept of function and the mathematical thinking method it reflects have penetrated into all fields of mathematics.
To understand the essence of the concept of function, we should first understand the concept of function described by set and corresponding language through comparison with the definition of junior high school, connection with other knowledge and continuous application. Secondly, through basic elementary functions, students should be guided to repeatedly and spirally rely on specific functions to understand the essence of functions in subsequent studies.
The focus of teaching is the concept of function, and the difficulty is the understanding of the essence of function concept.
Current situation of students
In the first chapter, students learned the concept of set, and at the same time, they learned elementary function, inverse proportional function and quadratic function in junior high school. Then how to use the concept of set knowledge understanding function to combine the original knowledge background, activity experience and understanding into today's classroom, how to effectively activate students' interest in learning, let students actively participate in learning activities, achieve the purpose of understanding knowledge, mastering methods and improving their ability, and make students obtain beneficial and effective learning experience and emotional experience.
Second, the analysis of three-dimensional teaching objectives
1, knowledge and skills (key and difficult points)
(1), through examples, students can further understand that function is an important mathematical model to describe the dependence between variables. On this basis, learn to describe functions with sets and corresponding languages, and understand the role of correspondence in describing the concept of functions. Students can not only complete the study of this section of knowledge, but also review the previous content better and connect before and after.
(2) Knowing that the three elements that make up a function are indispensable, we can find the domain and value domain of a simple function, and judge whether the two functions are in phase, and so on.
(3), master the representation of the domain, such as interval form.
(4) Understand the concept of mapping.
2. Process and method
The concept of function and its related knowledge points are abstract and difficult to understand. The following questions should be paid attention to in learning:
(1) First of all, through multimedia examples, let students discuss in groups, explore and discover knowledge by means of conjecture, observation, analysis, induction, analogy and generalization, find out similarities and differences, realize students' dominant position in teaching, and cultivate students' innovative consciousness.
(2), for all students, according to the requirements of the syllabus.
(3) Strengthen the guidance of learning methods, not only let students learn the knowledge points in this section, but also let students learn actively.
3. Emotional attitudes and values
(1), through multimedia examples, students discuss in groups, give their own conclusions and opinions, and cooperate with the teacher's auxiliary explanation to cultivate students' practical ability and bold innovation consciousness.
(2) Let students discuss and draw conclusions by themselves, and cultivate students' self-help ability and group unity ability.
Third, teaching equipment.
Multimedia ppt courseware
Fourth, the teaching process
Teaching content, teachers' activities, students' activities design intention
The introduction of the topic "Function" (which takes one minute) is accompanied by simple music, and the application of function is widely introduced from simple examples to guide students to pay attention to function. Listening to melodious music in learning allows students to start from being close to students' lives and pay full attention to what the teacher says, which is in line with students' cognitive characteristics. Let students enter the functional world while appreciating the beauty and harmony of nature, which embodies the concept of the new curriculum standard: from knowledge to life.
Knowledge review: review the definition and nature of junior middle school functions from the knowledge of functions learned in junior middle school (it takes two minutes), simply review the nature, definition and simple drawing of linear function, quadratic function, proportional function and inverse proportional function, listen carefully to the teacher to review junior middle school knowledge, find similarities and differences, and guide students to explore and seek knowledge on the basis of junior middle school knowledge. That is to review what has been learned and pave the way for what is about to be learned.
Thinking and discussion: Introduce the main content of this lesson through the questions given (four minutes). Give students two simple questions to think about. The content of junior high school can't give the correct answer. It is necessary to understand the function from a new height, combine the knowledge reviewed by the teacher, think about the questions given by the teacher and discuss them in groups. Start with simple questions, step by step, lead to the main knowledge of this section, review the collective feelings of the previous section and apply them.
New knowledge explanation: conceptually explain the knowledge in this section (it takes three minutes), and explain the knowledge of functions in detail, including definition domain and value domain. Go back to the beginning of the question, take notes, listen attentively, explain the concept of function, and then explain the knowledge back to the question and solve it.
Answer the questions (it takes five minutes) and guide the students to solve the first two questions by themselves, and then give the final answer in the same interaction. Answer the initial question by discussing with the teacher, sum up the concept of better grasping the function, and better grasp the knowledge by asking questions.
Function interval (takes five minutes) introduces the representation method of function domain. In this paper, a concise method is used to express the function domain or value domain, and another method is introduced on the basis of set representation.
Pay attention to the main points (spend three minutes) simply review the new content, put forward the difficult points, let students remember to answer questions and concepts, give the key points and difficulties, and remind students to pay attention to the content and knowledge points.
Exercises (take ten minutes) give exercises, analyze the meaning of the questions, and simply answer them on the manuscript paper. Make clear the important and difficult points by practicing answering questions, remember what you don't understand, and students will contact each other further after class.
Mapping (it takes two minutes) explains the meaning of mapping from the concept, so that the image and the original image can learn more knowledge on the basis of new knowledge, and the learning of mapping will better pave the way for future knowledge content.
Summary (five minutes) Briefly describe the knowledge points in this section, focusing on the coherence and summary of knowledge before and after taking notes, so that students can better understand the knowledge points.
Teaching evaluation of verbs (abbreviation of verb)
In order to make students understand the background of the concept of function, enrich their perceptual knowledge of function and gain experience in understanding the objective world, this lesson adopts the method of "highlighting the theme, step by step, and applying it repeatedly", and investigates different aspects of the problem from the superficial to the deep on different occasions. This course adopts the problem-based teaching method, and gradually deepens, so that students can gradually understand the concept of function, so as to accurately understand the concept of function. The three correspondences in the introduction to function are related to the content of learning function in junior high school, and play a connecting role. These three correspondences are not only the growing point of function knowledge, but also highlight the essence of function, which lays the foundation for learning function from inside mathematics.
In terms of cultivating students' ability, this course has also been designed as a whole. Through exploration and thinking, students' practical ability, observation ability and judgment ability are cultivated. Cultivate students' dialectical thinking ability by revealing the internal relations between things; Cultivate students' ability of analysis, solution and communication through solving practical problems; Through case teaching, cultivate students' innovative consciousness and inquiry ability.
Although the concept of function is abstract and difficult to understand, students can basically understand the essence of the concept of function through this teaching design, which meets the requirements of curriculum standards and embodies the teaching concept of curriculum reform.
2. Teaching plan of the first volume of senior three mathematics.
Teaching objectives 1. Understand the meaning of formula, so that students can use formula to solve simple practical problems;
2. Initially cultivate students' ability of observation, analysis and generalization;
3. Through the teaching of this course, students can initially understand that formulas come from practice and react to practice.
Teaching suggestion
First, the focus and difficulty of teaching
Key points: Understand and apply the formula through concrete examples.
Difficulties: Find the relationship between quantity from practical problems and abstract it into concrete formulas, and pay attention to the inductive thinking method embodied in it.
Second, analysis of key points and difficulties
People abstract many commonly used and basic quantitative relations from some practical problems, which are often written into formulas for application. For example, the area formulas of trapezoid and circle in this lesson. When applying these formulas, we must first understand the meaning of the letters in the formula and the quantitative relationship between these letters, and then we can use the formula to find the required unknowns from the known numbers. The concrete calculation is to find the value of algebraic expression. Some formulas can be deduced by operation; Some formulas can be summed up mathematically from some data (such as data tables) that reflect the quantitative relationship through experiments. Solving some problems with these abstract general formulas will bring us a lot of convenience in understanding and transforming the world.
Third, knowledge structure.
At the beginning of this section, some commonly used formulas are summarized, and then examples are given to illustrate the direct application of formulas, the derivation of formulas before application, and some practical problems are solved through observation and induction. The whole article runs through the dialectical thought from general to special, and then from special to general.
Four. Suggestions on teaching methods
1. For a given formula that can be directly applied, the teacher creates a situation under the premise of giving specific examples to guide students to clearly understand the meaning of each letter and number in the formula and the corresponding relationship between these numbers. On the basis of concrete examples, students participate in excavating the ideas contained therein, make clear that the application of formulas is universal, and realize the flexible application of formulas.
2. In the teaching process, students should realize that there is no ready-made formula to solve problems, which requires students to try to explore the relationship between quantity and quantity themselves, and derive new formulas on the basis of existing formulas through analysis and concrete operation.
3. When solving practical problems, students should observe which quantities are constant and which quantities are changing, make clear the corresponding change law between quantities, list formulas according to the laws, and then solve problems further according to the formulas. This cognitive process from special to general and then from general to special is helpful to improve students' ability to analyze and solve problems.
3. Teaching plan of the first volume of senior three mathematics.
First, the analysis of teaching content
The definition of conic curve reflects the essential attribute of conic curve, which is highly abstract after countless practices. When XX is properly used to solve problems, simplicity can control complexity in many cases. Therefore, after learning the definitions, standard equations and geometric properties of ellipse, hyperbola and parabola, we should emphasize the definition again and learn to skillfully use the definition of conic curve to solve problems. "
Second, the analysis of students' learning situation
Students in our class are very active and active in classroom teaching activities, but their computing ability is poor, their reasoning ability is weak, and their mathematical language expression ability is also slightly insufficient.
Third, the design ideas
Because this part of knowledge is abstract, if we leave perceptual knowledge, it is easy for students to get into trouble and reduce their enthusiasm for learning. In teaching, with the help of multimedia animation, students are guided to find and solve problems actively, actively participate in teaching, find and acquire new knowledge in a relaxed and pleasant environment, and improve teaching efficiency.
Fourth, teaching objectives.
1. Deeply understand and master the definition of conic curve, and can flexibly apply XX to solve problems; Master the concepts and solutions of focus coordinates, vertex coordinates, focal length, eccentricity, directrix equation, asymptote and focal radius. Can combine the basic knowledge of plane geometry to solve conic equation.
2. Through practice, strengthen the understanding of the definition of conic curve and improve the ability of analyzing and solving problems; Through the continuous extension of questions and careful questioning, guide students to learn the general methods of solving problems.
3. Stimulate the interest in learning mathematics with the help of multimedia-assisted teaching.
Five, the teaching focus and difficulty:
Teaching focus
1. Understand the definition of conic.
2. Using the definition of conic curve to find the "maximum"
3. "Definition method" to find the trajectory equation
Teaching difficulties:
Clever use of quadratic curve XX to solve problems
4. Teaching plan of the first volume of senior three mathematics.
First, the basic concept of unit teaching content (1) algorithm
(2) The basic structure of the algorithm: sequence, condition and cycle structure.
(3) Basic statements of the algorithm: input, output, assignment, condition and loop statements.
Second, the analysis of unit teaching content
Algorithm is an important part of mathematics and its application and an important foundation of computational science. With the rapid development of modern information technology, algorithms play an increasingly important role in the development of science and technology and society, and are increasingly integrated into many aspects of social life. The idea of algorithm has become the mathematical literacy that modern people should have. China's ancient mathematics, in particular, contains rich algorithmic ideas. In this module, students will experience the function of program block diagram in solving problems on the basis of their preliminary feelings about algorithm thought in middle school education and the analysis of specific mathematical examples; Through imitation, operation and exploration, learn to design program block diagram to express the process of solving problems; Understand the basic idea, importance and effectiveness of the algorithm, develop thinking and expression ability, and improve logical thinking ability.
Third, the unit teaching schedule:
1, the basic concept of the algorithm 3 class hours
2, the program block diagram and the basic structure of the algorithm 5 class hours
3. Basic statement of algorithm 2 class hours
Fourthly, the analysis of unit teaching objectives.
1, by analyzing the process and steps of solving specific problems, we can understand the idea and significance of the algorithm.
2. Through imitation, operation and exploration, experience the process of expressing and solving problems by designing program block diagram. Understand the three basic logical structures of program block diagram in solving specific problems: sequence, condition and cycle structure.
3. Through the process of transforming the program block diagram of specific problems into program statements, I understand several basic algorithm statements: input, output, boundary value, condition and loop statements, and further understand the basic idea of the algorithm.
4. By reading the algorithm cases in China's ancient mathematics, we can understand the contribution of China's ancient mathematics to the development of world mathematics.
5. Analysis of key points and difficulties in unit teaching.
1, key points
(1) Understand the meaning of the algorithm.
(2) Master the basic structure of the algorithm.
(3) Able to use algorithmic statements to solve simple practical problems.
2. Difficulties
(1) program block diagram
(2) Variables and assignment
(3) circular structure
(4) Algorithm design
Sixth, the whole teaching method of unit.
This chapter adopts heuristic teaching, supplemented by observation, discovery, practice and explanation. The reason why these methods are adopted is that students' logical ability is not very strong. Only through careful understanding of examples and certain exercises can they master these knowledge.
Seven, the unit capacity expansion mode and characteristics
1, extended mode
Natural language → program block diagram → algorithm statement
2. Features
(1) spirals up, step by step.
(2) Before and after it is called comprehensive infiltration.
(3) three-in-one horizontal infiltration
(4) Flexible handling and multiple choices
Eight, unit teaching process analysis
Analysis of the teaching process of the basic concepts of 1. algorithm
Through the analysis of the process and steps of solving specific problems in life (drinking tea, for example, solving problems with binary linear equations), understand the idea of the algorithm, understand the meaning of the algorithm, and describe the algorithm in natural language.
2. Analysis of the teaching process of algorithm flow chart.
Through the imitation, operation and exploration of practical problems in life, through the design of flow charts to express and solve problems, we can understand the difference between algorithms and programming languages. In the process of solving specific problems, understand the three basic logical structures of flowchart: sequence, conditional branch and cycle, and express the algorithm with flowchart.
3. Analysis of the teaching process of basic algorithm sentences
Through the process of transforming the problem flow chart in real life into programming language, we have learned several basic algorithm statements: assignment statement, input statement, output statement, conditional statement and loop statement, and further understood the basic idea of the algorithm. The algorithm can be expressed by natural language, flow chart and basic algorithm statements.
4. By reading the algorithm cases in China's ancient mathematics, we can understand the contribution of China's ancient mathematics to the development of world mathematics.
Nine. Unit evaluation hypothesis
1. Pay attention to the evaluation of students' mathematics learning process.
Pay attention to whether students are interested in using set language to describe problems in mathematics and real life during the learning process of mathematical language; In the process of learning, can you appreciate the accuracy and conciseness of assembly language? Can you actively develop your ability to communicate in mathematical language?
2. Correctly evaluate students' basic knowledge and skills in mathematics.
Pay attention to students in this chapter (section) and later study, and let students concentrate on learning the preliminary knowledge of the algorithm, mainly including the basic structure, basic sentences and basic ideas of the algorithm. The idea of algorithm will run through the relevant parts of high school mathematics curriculum, and the algorithm will be further studied in other relevant parts.
5. The first volume of mathematics teaching plan for senior three.
I. Teaching objectives 1. Knowledge and skills
(1) Master the basic skills of drawing three views.
(2) Enrich students' spatial imagination
2. Process and method
Mainly through students' own personal practice and drawing, we can understand the role of the three views.
3. Emotional attitudes and values
(1) Improve students' spatial imagination.
(2) Experience the function of three views.
Second, the focus and difficulty of teaching
Point: Draw a simple assembly of three views.
Difficulties: Identify the space geometry represented by three views.
Third, learning methods and teaching tools.
1. Learning methods: observation, hands-on practice, discussion and analogy.
2. Teaching tools: physical model, triangle.
Fourth, teaching ideas
(A) the creation of scenarios to uncover the theme
"Viewing the peak from the ridge" means that the same object may have different visual effects from different angles. To truly reflect an object, you can look at it from multiple angles. In this lesson, we mainly study three views of space geometry.
In junior high school, we learned three views (front view, side view and top view) of cube, cuboid, cylinder, cone and sphere. Can you draw three views of space geometry?
(b) painting practice.
1. Put the ball and cuboid on the platform and ask the students to draw three views of them. Teachers will patrol, and students can exchange results and discuss after drawing.
2. Teachers guide students to draw three views of a simple assembly by analogy.
(1) Draw three views of the ball on the cuboid.
(2) Draw three views of the mineral water bottle (the object is placed on the desktop)
After painting, students can show their works, communicate with their classmates and sum up their painting experience.
Before making three views, you should carefully observe and understand its basic structural characteristics before drawing.
3. The mutual transformation between three views and geometry.
(1) Display pictures by projection (textbook P 10, figure 1.2-3)
Ask the students to think about the geometry represented by the three views in the picture.
(2) Can you draw three views of the truncated cone?
(3) What is the role of three views in understanding space geometry? What experience do you have?
Teachers patrol the guidance, answer students' learning difficulties, and then let students express their views on the above issues.
Please draw three views of space geometry represented by other objects in 1.2-4 and communicate with other students.
(3) Consolidate exercises
Textbook P 12 exercises 1, 2P 18 exercises 1.2A group 1
(4) inductive arrangement
Ask the students to review and publish how to make three views of space geometry.
Extracurricular exercises
1. Make a triangular pyramid model with quadrangular bottom and congruent sides, and draw its three views.
2. Make a prism model with similar top and bottom surfaces and congruent isosceles trapezoid sides, and draw its three views.