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1、第六章频率与概率主备材料（The sixth chapter is the main materials of frequency and probability）The sixth chapter is the main materials of frequency and probabilityThird mathematics group, third experimental middle school, Hejin, ShanxiThis chapter is based on the two methods of probability calculation - theoreti
2、cal calculation and experimental estimation. There is no theory of probability or probability theory although there, but its calculation is beyond the cognitive level of the students, the test simulation obtains the estimation by the students, to estimate the probability of random events, the relati
3、onship between the frequency and the probability to make the students understand the events, this chapter also introduces two kinds of calculation method of probability - tree and list method, and the relationship between the test frequency and probability theory, some theoretical basis for revealin
4、g the strengthening of statistical inference, probability and statistics, so we should start the study of this chapter in the specific activities, let the students experience focus on test frequency stability in probability theory.Section 6.1 frequency and probabilityI. clear tasks1, clear how to co
5、mplete a touch card test?2, the possibility of the emergence of a variety of circumstances, in the same case, how to seek probability?(directly using a tree or list method)3, the possibility of a variety of circumstances arise in different cases, how to seek probability? (you have to try to re - par
6、tition the parts and divide them into areas of the same size, so you can use the tree diagram or the table method to find the probabilities.)Emphasis: the probability of occurrence of a variety of situations must be the same when using a tree chart or a table method.Two, students problems1, for no r
7、eturn of the ball, the game will not seek probability.2, the actual problems will not be translated into mathematical problems.Mathematical understanding of the 3 question: Xiao Hong next time the probability of getting the car is essentially: Xiao Ming and Xiao Hong two dice and 7 points thrown pro
8、bability.Section 6.2 needle testI. Analysis of teaching materials:In this section, students are asked to realize that when the number of trials is large, the test frequency is stable to the theoretical probability, and the probability of an event is estimated accordingly. But the students have not y
9、et have this experience, test simulation obtains the estimation by means of probability theory only, this section relates to the theoretical calculation is beyond the cognitive level of the students, this section selects the history of the more famous needle test for the subject, trying to make stud
10、ents through personally test, statistical process to estimate the probability of complex events experience with test methods.The first question in the textbook, and guide students to think can use the list or tree for the needle parallel lines intersect with the probability of an attempt to arouse s
11、tudents cognitive conflict and produce test estimates of desire, and then through the do the estimation of the probability, therefore this lesson is basically a festival class. Summary of test activities and test data can be organized and completed by the students themselves, during the test, a cloc
12、kwise and line is difficult to judge whether the intersection, this can guide students to ignore the test, re needle, or that do not intersect the intersection, half meter etc.Two, teaching objectives:The probability of the occurrence of some complex random events can be estimated by experimental me
13、thods. Through experiments, statistics and other activities, students can further develop their awareness and ability in cooperation and communication.Three, teaching focus:The probability of the occurrence of some complex random events can be estimated by experimental methods.Four, teaching difficu
14、lties:By means of repeated experiments, the experimental frequency is stable to theoretical probability.Five, teaching methods:Group activities.Six, teaching ideas:1, raise new questions and introduce new courses.What is the premise of the probability of a random event calculated by a tree or column
15、 table in a?(the result of the test is equal to possible, and the result of the test must be limited.)B, a figure throwing needle, needle and nail with equal likelihood?2, group activitiesFrom a certain height of the pin after landing a nail tip or a cap. Which event is the most likely to occur?Acti
16、vities: group cooperation, communication, the whole class summary test data, each group 20 times to do the test.The statistical data (cap with frequency) painted line graph.The estimated probability of a cap is about 0.565.3, group activities (two)Throwing needle test:Activities: grouping, two group
17、s. Take a blank sheet of paper and draw a parallel line on it. The distance between them is about 2cm. In addition, a long 1cm needle is used to place a layer of soft material under the paper, so that the needle will not bounce when it falls on the paper. At least 100 trials were performed in each g
18、roup, and the number of intersecting and disjoint records was recorded respectively. Statistics the experimental data of the whole class and estimate the probability of the intersection of the needle and the parallel line.Seven, class reviewThe lesson from the history of the famous needle test of cr
19、eative activities, not only to the problem, but also good to mobilize the active participation of students, make the class fully integrated into the teaching situation to.In the teaching of needle throwing test and pin drawing test,The method of grouping can not only strengthen students cooperation
20、and communication, but also make good use of time, so as to quickly collect and sort out data and ensure the normal rhythm of teaching.Inadequate: after the completion of the two experimental activities, should also be combined with two activities to make a series of inductive rational summary, so t
21、hat students get a more complete understanding.Difficulty: contact extension 2, arranged here is too difficult.Doubt: the needle test, it should be a test to estimate pi.Eight, teaching postscript:The introduction of this lesson attracted the students so as to make the students devote themselves to
22、the study, and the group activities were enthusiastic and fruitful. In this lesson, the teacher fully displays the image of a leader and organizer, and tries to make the students subjective initiative through the guidance of the teacher, and embodies the purpose of serving the students. The whole cl
23、ass atmosphere is more active, students always maintain a happy mood, thirst for knowledge and self-confidence are relatively strong.The probability of the same 6.3 birthdayIn this section, the emphasis is to estimate the probability of some random event complex occurred by the test method, and simu
24、lation experiment was carried out using a calculator or computer, the estimated probability of some complex random events occur, thus forming a more comprehensive understanding of probability of occurrence of an event, the initial formation of the concept of random. This class is divided into two cl
25、asses.The first lesson is to let students focus on teaching how to review the previous understanding of the concept of probability, the probability method, then put forward the new problem: an estimated 6 people in the same probability 2 zodiac, let the students try to solve the map or list by using
26、 the method of tree, try to solve the method before the coin toss, dice, this needle test, when the students fully aware of previous methods can not solve, knowledge conflict, so, forcing the students to find a new way to solve the problem. The students then think of ways to collect data, collect an
27、d sort out the data, get the frequency, estimate the frequency, and then investigate and calculate the probabilities in the crowd known to the whole class. Then, the question of estimating the probability of 2 birthdays in 50 people is proposed, which allows students to fully experience the difficul
28、ties of collecting data and prepare for the next class of simulated tests.In the second class, the key is to let students understand the necessity of the simulation test. After the feasibility, they will learn to experiment on the computer, and go through the whole process of the problem simulation,
29、 simulation test, statistics, calculation frequency and estimation probability. In the process of changing the actual problem into the simulation experiment, the students step by step through the process of the problem of transformation, and form the strategy and method to solve the problem in the s
30、tudents consciousness. For example, some people say, you can use 12 series of numbers, the same size as the ball instead of 12 different animals, so that everyone in the zodiac corresponds to a ball 6, 2 people in the same year, it means that there are 2 Balls 6 balls of the same number, so 12, can
31、be put into a ball like this in the pocket, took out 1 balls in number, down the back; then pulled out 1 balls from it, write it down the number, put it back;. Sixth balls, 6 numbers, one trial, and many experiments to estimate the probability of 2 people having the same zodiac sign in 6.Question: (
32、1) do you think this statement makes sense?(2) why do you put it back every time you touch the ball?Then ask the question: can you think of any other way than to experiment with 12 balls of the same size?At this point, students may say that 12 cards with 1 to 12 cards can be used for testing. Then t
33、he teacher can demonstrate using computer generated random number to test, such as outstanding computer simulation test is convenient, collect data quickly, and the first class to collect data to estimate contrast probability method. In short, whether it is the problem of simulation into 12 differen
34、t balls, 12 different cards, as well as 12 different random numbers, the students personally experienced the process of problem reduction, experienced problem simulation, simulation test, statistics, calculation, estimation of frequency probability of the whole process of activities, this kind of ex
35、perience for students is the The imprint is engraved on my heart.The teaching method of computer simulation experiment is to use the random function rand (Excel) to generate random numbers to do the teaching of computer simulation experiment. Now I will talk about the specific method of the topic in
36、 the textbook. Such as the book has the same probability of two one of the 6 Zodiac do steps: first, open the Excel, put the mouse on the first cell, then the FX (or =) edit bar directly enter the following statement: =int (rand) (*12+1), drag the mouse to the F column you can generate 6 random inte
37、gers between 1 and 12, and then drag down several lines. Each produces six random integers for one test, and can be generated by a single simulation test in a A-F column,That is, a number of tests. When the number of each group can find two numbers at the same time, as the 6 people have two people t
38、he same probability of the Zodiac this event occurs, statistics, calculate the probability of its occurrence.Another example: if the input =int (rand) (*366+1) can generate a random number between 1 and 366, each generated 50 random numbers for a test, this can simulate the book 50 people have the s
39、ame probability of two birthday that a probability test. Friends can try to use Excel random function rand () to generate random numbers, this function is very easy to use.Teacher teaching postscript:1, in the teaching, the two students were divided into a group, direct operating experience of simul
40、ation, generate random numbers, statistics, calculation, data collection frequency class approximate probability of this series of activities, the relationship between the students simulation test, the frequency and probability of the computer has a more profound and more accurate understanding.2, t
41、he combination of mathematics teaching and information technology can help students dispel the mystery of computer simulation experiment and promote the accurate understanding of students mathematical problems. For example, the probability of the same two birthday in 50 this event if the students un
42、derstand the probability can be modeled by: generating a random number between 1 and 366, each generated 50 random numbers for a test, when each group number can be found there are two digital phase at the same time, the the incident, the statistics, and then calculate the probability of occurrence,
43、 will have the same probability to simulate 3 birthday in 50 the probability of an event. Therefore, by computer operation, students are more likely to understand the range of random numbers, the number of random numbers, and the conditions that correspond to the quantities in the real problem.For e
44、xample, 1 to 366 random integers -366 days;50 random numbers of -50 individuals were included as a group of subjects;2 numbers are the same, -2 birthdays are the same;3, this section should pay attention to teaching activities and students cognitive conflict, to organize the students, especially in
45、the computer room to operate, it is best to have a teacher counseling, so that students have sufficient time to establish the independent concept of probability.How many fish in the pond, 6.4First, the main knowledge of this lesson:1, combined with the situation, feel the rationality of statistical
46、inference.2, according to the relationship between frequency and probability, the design scheme estimates the actual problem.Two, this lesson is heavy and difficult:Let students understand the rationality of statistical inferenceWhy is the test frequency stable with theoretical probability?.Three, c
47、onfused1, classroom test, grouping, time limit, the number of tests is not many, some conclusions are inconsistent, and the actual error is large, let the students hard to think: test frequency stability in probability theory, the effect is not very good, the teacher number enough to justify frequen
48、cy stability, close to the theoretical probability. However, in actual estimates, how many fish are in the pond, which can only be estimated two times, is inconsistent with the former. The teacher explained it again, just to estimate it.How to deal with the above problems better?2, thinking of knowledge macThis section estimates the overall sample, the number of tests is not many, but the use of the testing frequency is close to the theoretical probability. This is inconsistent with the previous emphasis on the limited tes