Teaching plan for generating integer random numbers in senior two mathematics.

1, knowledge and skills:

(1) Understand the concept of random numbers and master the method of generating random numbers with calculators or computers to find random numbers;

(2) Probability can be estimated by simulation.

2, process and method:

(1) Through the exploration of specific probability problems in real life, we can perceive the method of applying mathematics to solve problems, experience the connection between mathematical knowledge and the real world, and cultivate the ability of logical reasoning;

(2) Through the simulation experiment, I feel the method of applying mathematics to solve problems, and consciously develop the good habit of using my hands and brains.

3, emotional attitudes and values:

Experience the importance of mathematics and the application of information technology in mathematics through the design of simulation method; Experience the fun of doing mathematics through hands-on simulation and brain thinking; Cultivate the team spirit of cooperation and communication through cooperative experiments.

Second, the key points and difficulties:

Key points: random number generation;

Difficulty: using random test to find probability.

Third, the teaching process

(1) Introduction:

Historically, it takes too much time to repeat the experiment to find the probability of a coin flip. Is there any other way to replace the experiment?

We can use random simulation experiments instead of a large number of repeated experiments to save time.

This section mainly introduces the generation of random numbers. The purpose is to replace complex hands-on experiments with random simulation experiments in order to obtain the frequency and probability of random events.

(2), random number generation method:

1。 Random numbers are generated by experiments (such as touching the ball or drawing lots)

Example: Generate a random integer between 1-25.

(1) Put 25 balls of the same size and shape into a bag and mix well.

(2) Draw a ball from it, and the number on the ball is a random number.

2。 A random number generated by a calculator or computer

Because the random number generated by calculator or computer is generated according to a certain algorithm, it has periodicity (long period), which is similar to random number, but not true random number, and is called pseudo-random number.

The method of simulation test with calculator or computer is random simulation method or Monte Carlo method.

(3) How to generate random numbers with a calculator?

Example 1: Generate random numbers with integer values between 1 and 25.

Solution: The specific operation is as follows:

Step 1: mode-mode-1-0-

Step 2: 25-shift-ran #-+-0. 5—=

Step 3: Every time you press = in the future, a random number will be generated, and the integer value will be 1 to 25.

Working principle: Step 1, press the MODE key three times continuously, and then press 1 to make the calculator enter the mode of determining decimal places, where 0 means that the decimal places are 0, that is, the displayed calculation results are rounded integers;

The second step is to put the generated 0 into the calculator. 000~0。 The random number between 999 is amplified by 25 times to generate 0. 000—24。 975, plus 0. After 5, you get 0. 5~25。 475; Then the random integer between 1 and 25 can be obtained randomly by rounding in the first step.

Summary:

Integer random numbers in any interval can be generated by expansion and translation transformation.

That is to say, to generate a random integer of [M, N], the operation is as follows:

Step 1: OnModeModeModeMode 10

Step 2: n-m+ 1 Shiftran #+m-0. 5 =

Step 3: Every time you press = in the future, a random number with an integer value from m to n will be generated.

Tips:

(1) The operation sequence of the first step and the second step can be interchanged;

(2) If a random integer has been generated once, the first step can be omitted by doing similar operations;

(3) Restore the number of the calculator to MODE 3 1.

Exercise: Design an experiment, use a calculator to simulate coin toss for 20 times, and count the frequency and times of human head.

Solution: (1) specifies that 0 means the reverse side is facing up, and 1 means the front side is facing up.

(2) Use a calculator to generate a random number 0, 1. The operation process is as follows:

Mode mode 10 shift operation # =

(3) Press = every time until a random number 20 is generated, counting to the number n of 1.

④ frequency f=n/20

How accurate is the probability of this frequency estimation? Is the error large?

(4) How to generate random numbers by computer?

Every software with statistical function has random function. Take Excel software as an example, open Excel software and perform the following steps:

(1) Select a cell in the table, such as A 1, type = rand between (0, 1) in the menu = after, and press enter to generate 0 or 1.

(2) select cell A 1, press Ctrl+C to copy the cell, then select cell A2~A 1000 to paste it, and press ctrl+v.

(3) Select box C 1 and enter = frequency (A1:A1000,0) after menu =. 5), press Enter.

(4) Select box D 1, type1-c11000 after = in the menu, and press Enter.

At the same time, we can draw a frequency line chart, which tells us more intuitively that the frequency fluctuates up and down around the probability.

The weather forecast says that the probability of rain every day in the next three days is 40%. What is the probability that it will rain on exactly two of these three days?

Analysis: What are the possible results of the test?

Use and non-use represent rain and no rain on a certain day respectively, and the test results are as follows.

(Down, Down, Down), (Down, Down, No), (Down, No, Down), (No, Down, Down),

(no, no, get down), (no, get down, no), (get down, no, no), (no, no, no)

* * * There are eight possible results, which are obviously not equal probability, so we can't use the classical probability formula, so we have to use the random simulation method to find the frequency, which is approximately regarded as probability.

Solution: (1) Design probability model

Computers (calculators) are used to generate random numbers (integer values) between 0 and 9. It is agreed that 0, 1, 2, 3 means rain, and 4, 5, 6, 7, 8, 9 means no rain, so the probability of rain is 40%. Simulation of three-day rain: three random numbers are generated continuously as a group as the simulation result of three days.

(2) Conduct simulation test.

For example, 30 groups of random numbers are generated, which is equivalent to 30 experiments.

(3) Statistical test results

In this set of numbers, if there are exactly two numbers in 0, 1, 2 and 3, it means that it rains exactly two days out of three days. If such tests are counted, the frequency of rain in just two days in 30 statistical tests is f=n/30.

Summary:

(1) The random simulation method can only get the approximate value of the frequency or probability of exactly two rains in 30 experiments, but can't get the probability. After learning binomial distribution, we can calculate the probability that it will rain on exactly two of the three days. 288。

(2) For the probability problem that satisfies the finiteness but does not satisfy the equal possibility, the random simulation method can be adopted.

(3) random function RANDBETWEEN(a, b) generates random numbers with integer values from integer a to integer b. ..

Exercise:

. Try to design an experiment, use a calculator or computer to simulate dice throwing, and estimate a little probability.

Analysis:

( 1)。 It is stipulated that 1 means that 1 point appears, and 2 means that it appears at 2 o'clock. . . 6 means to appear at 6 o'clock.

(2)。 Use a calculator or computer to generate n random numbers between 1 and 6.

(3)。 Count the number n of 1 and calculate the approximate value n/N of probability.

(5), class summary:

Random numbers have a wide range of applications, which can help us arrange and simulate some experiments, so that we can do a lot of repeated experiments instead of ourselves. Through the study of this lesson, we should master the method of generating random numbers and the steps of random simulation test:

(1) design probability model

(2) Conduct simulation test.

(3) Statistical test results

(6), homework