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1、二分法教案及教案说明（Dichotomy teaching plans and lesson plans）Topic: the approximate solution for the 3.1.2 equationTancheng, Linyi, Shandong, America and Australia school Yang MingTeaching target:Knowledge and skills - through the concept of specific examples to understand dichotomy and applicable condition
2、s, understand the dichotomy is the equation approximation method used, will use specific dichotomy to solve the approximate solution of the equation, experience between function and equation of contact and its application in practical problems in experience program to solve the problem of ideology.T
3、he approximate solution - use a calculator for dichotomy equation for the process and methods, to enable students to fully experience the approximation method, approximation idea and program to deal with the problem of thinking and its significance, and preparing for the learning algorithm for the n
4、ext step.Emotions, attitudes, values - through inquiry, experience, presentation and communication, develop good learning qualities and enhance awareness of cooperation. By understanding the process of mathematical approximation, we feel the relative unity of precision and approximationTeaching emph
5、asis:Key point: by using dichotomy to find the approximate solution of the equation, we can understand the relation between the zero point of the function and the root of the equation, and initially form the consciousness of dealing with the problem with the function viewDifficulty - the proper use
6、of information technology tools, and the use of dichotomy to find the approximate solution of an equation of a given degree of accuracyTeaching methods:Problem guided learning and mathematical inquiry: the principles and steps of guiding students to explore the dichotomy through the problems, and th
7、e teaching method based on the interaction between teachers and students. And supplemented by multimedia teaching methods to create problem scenarios, students based on questions.Teaching procedure and link design:Teaching process and operation design:Teaching linkTeaching process and contentTeacher
8、-student interactionSituation creation and self study perception1, the game: suppose lucky 52 scene, let students do guess the price of a game.2, the actual problem: there are 15 points to the United States from Shanghai San Francisco submarine cable fault happens now a contact, the need for timely
9、repair as soon as possible in order to conclude that the failure occurs, you can find a simple and easy method?Generally, at least check the number of contacts3. Mathematical problems:Question 1: can you work out the solutions of the following equations?Question 2: if you cant ask, can you determine
10、 the general scope of the solution?Question 3: do you have any ways to further narrow down the scope of the solution?1, teachers choose two students guess the price.2, teachers encourage students to explore and exchange, and understand the ideas and methods of solving problems.3, the teacher introdu
11、ces the definition of dichotomy in real life and points out its scope of application.4, students in the exercise book to solve the equation, found the problem, the teacher pointed out: simple equation by deformation formulas or seeking exact solutions, most complex equations no exact solutions, expl
12、ore penetrate the history of mathematics and leads to the problem of target.ComprehensionExample: approximate solution of the equation (error is not more than 0.1).Analysis: first of all, use the function property or draw a function image with the computer and calculator, determine the interval of t
13、he function zero point, then use the dichotomy to solve the problem graduallyExploring communication issues:Question 1. How do you determine the approximate range of the zeros of the function?Question 2. How do you further narrow the zero?Question 3 what can be achieved by using this method to meet
14、the requirements of accuracy?Question 4. Can you sum up the general steps of solving the approximate solution of the equation by dichotomy?Note: 1, the first step to determine the approximate interval of zero where the available functions, can use a calculator or computer, but as an endpoint for int
15、eger interval, usually can determine a length 1 interval;The 2 suggested list styles are as follows:frequencyTake aTake B|a-b|OneTwo point five-0.084Two point fiveThreeZero point fiveTwoTwo point seven fiveZero point five one twoTwo point fiveTwo point seven fiveZero point two fiveThreeTwo point six
16、 two fiveZero point two one fiveTwo point fiveTwo point six two fiveZero point one two fiveFourTwo point five six two fiveZero point zero six sixTwo point fiveTwo point five six two fiveZero point zero six threeThe advantage of such a list is that the number of steps is clear and the interval length
17、 is less than the accuracy,The relation between the function image and the root of the equation has been preliminarily understood. It has a certain idea of combination of figures and shapes, which provides an intuitive understanding of the function value symbols near the zeros of functions. But the
18、students for understanding between function and equation of contact is still relatively weak, the use of the application, image and character of function of the computer is skilled enough, these are for students in function and equation, we find that the function value function approximation zero ha
19、s caused some difficulties.Therefore, according to the requirements of the teaching materials and the actual situation of the students, I set the teaching objective of the course as follows:Knowledge and skills - through the concept of specific examples to understand dichotomy and applicable conditi
20、ons, understand the dichotomy is the equation approximation method used, will use specific dichotomy to solve the approximate solution of the equation, experience between function and equation of contact and its application in practical problems in experience program to solve the problem of ideology
21、.The approximate solution - use a calculator for dichotomy equation for the process and methods, to enable students to fully experience the approximation method, approximation idea and program to deal with the problem of thinking and its significance, and preparing for the learning algorithm for the
22、 next step.Emotions, attitudes, values - through inquiry, experience, presentation and communication, develop good learning qualities and enhance awareness of cooperation. By understanding the process of mathematical approximation, we feel the relative unity of precision and approximationThree, the
23、content of this course, the status of roleThe dichotomy is mainly about function knowledge, whose theory is based on the existence of the zero of function (theorem). This lesson is a natural extension of the last section of the study of the root of the equation and the zero of the function.Algorithm
24、 is a computer age the most important mathematical thinking methods, new will serve as a new arrangement of the contents of the course in mathematics teaching in compulsory 3, dichotomy is a prelude to mathematics teaching and compulsory 3, Kai is an important content of thoughts, ideas and penetrat
25、ion approximate approximation algorithm.Four, and other knowledge and other disciplines and ApplicationsDichotomy is not only a common method for finding approximate solutions of a single equation, but also helps us solve some related problems, such as inequality, the distribution and the maximum of
26、 the root of a two equation. It is also intrinsically linked to the preferred method. In physics, logic, statistics, computer science and life practice as long as it is and find relevant, can reflect the important role of it, such as finding lines, water pipes, pipe pipe line fault and experimental
27、design, data query and so on.Five 、 teaching diagnosis analysisThe thought of method of dichotomy is simple and easy to understand, the required mathematical knowledge is less, the algorithm flow is relatively simple, and the use of calculators and multimedia assisted teaching, intuitive, students a
28、lso have relevant experience in life, it is easy to be understood and mastered by students. But the dichotomy cannot be used to solve equation even root approximation accuracy, and the concept of interval length are different but related, these are easy to be misunderstood miscalculation.Six, teachi
29、ng methods and characteristicsThis class is used to issue guidance, mathematical inquiry teaching mode: the problem of guidance and interaction between teachers and students, supplemented by multimedia teaching means, the students create problems, the principle and procedure of dichotomy.The main fe
30、atures of this course are as follows:1, the teaching method reflects the student-centered teaching philosophy.2, create a situation close to student life, stimulate interest, let students experience mathematical ideas in activitiesAt the start of the lesson, the teacher from the student guess commod
31、ity prices and solve the practical problems in present the topic and to create situations, not only have a strong appeal to students, students can experience the dichotomy in the process of speculation that.3, pay attention to cooperation and exchange, pay attention to the inquiry processEach questi
32、on in this class is produced in the communication between teachers and students. It is solved in the process of student cooperation and inquiry, which enables students to experience the whole process of learning and cultivate the students thinking ability.4, the proper use of information technology
33、to help students explore the essence of MathematicsIn this lesson, the calculator has been calculated several times and gradually reduced the scope of the real solution. The determination of accuracy is very natural. It breaks through the difficulties in teaching and improves the validity of the inq
34、uiry activity. With the help of Geometers Sketchpad, the range of the real solution is gradually reduced, and it is intuitive and realistic, which is beneficial for students to observe the approximate range of function zeros. The whole courseware is made of PowerPoint, and the painting is lively. It
35、 fully embodies the organic integration of information technology and mathematics curriculum.Seven. Expected effect analysisThe function and equation of knowledge as the foundation, through exploring the class discussion, the students to actively participate in the practice of mathematics, and the u
36、se of multimedia technology, a large amount of information and presents a vivid demonstration, can improve students learning interest and activate students thinking, deepen the understanding of knowledge, grasp the essence of the dichotomy to complete the teaching goal.However, some students may be
37、distracted by activities and discussions in class, thus affecting their deeper understanding and mastery of knowledge. Therefore, attention should be paid to organization and coordination in teaching. In addition, although the use of scientific calculators, the solution of an equation is also time-consuming, students prone to errors in computing and impatience.?One