Ninth grade mathematics probability teaching plan (teaching goal)
1, knowledge and skills
(1) Understand the concepts of random events, inevitable events and impossible events;
(2) Correctly understand the significance of the frequency of event A;
(3) Understand the concept and significance of probability correctly, and make clear the difference and connection between the frequency fn(A) of event A and the probability P(A) of event A. 。
The ninth grade mathematics probability teaching plan (process and method)
(1) discovery method teaching, through obtaining data in coin and dice throwing experiments, summarizing experimental results, discovering laws, truly learning through exploration and improving through exploration;
(2) through real life? Flip a coin? ,? Fair competition? ,、? Did you win the lottery? Explore this kind of problem, perceive the method of applying mathematical knowledge to solve mathematical problems, and understand the mathematical method of logical reasoning.
1, emotional attitudes and values
(1) Through students' hands-on, brains and personal experiments, students can understand knowledge and realize the connection between mathematical knowledge and the real world;
(2) Cultivate students' dialectical materialism and enhance their scientific consciousness.
2 Analysis of academic status quo
Students have been exposed to simple probability problems in junior high school, so they are no strangers in teaching. The key is to guide students to master and break through the definition of probability and the difference and connection with frequency, explain the difficulties in real life with probability knowledge, and how to turn specific problems into abstract concepts.
Ninth grade mathematics probability teaching plan (emphasis and difficulty)
Teaching emphasis: event classification; The definition of probability and its difference and connection with frequency;
Teaching difficulty: understanding the statistical law of random events.
Ninth grade mathematics probability teaching plan (teaching process)
Activity 1 Introduction (1), creating a situation.
1, using mathematical stories? A mathematician = 10 teachers? Stimulate students' interest in learning, make students feel that probability is really useful around them, and stimulate students' desire to continue learning.
2. Use rich examples of daily life: for example, what time will you get up tomorrow? How many people are waiting at the bus stop at 7: 20? 12: 10 How many people eat in the school cafeteria? Can I win the lottery by buying this welfare lottery? Wait a minute. The results of these questions are uncertain and accidental, so it is difficult to give accurate answers.
Activity 2 Teaching (2) Exploring new knowledge
1, inevitable event, impossible event, random event
Exploration 1: Investigate the following events. Do these events occur and what are their characteristics?
(1) The earth keeps turning;
(2) firewood combustion generates energy;
(3) At normal temperature, the stone is weathered;
(4) Someone shoots once and hits the target;
(5) Flip a coin and the head appears;
(6) Snow melts at standard atmospheric pressure and below 0℃.
Inquiry 2: Combining the above events, give the general meanings of inevitable events, impossible events and random events (students give, correct, teachers guide and standardize).
Under condition S, the inevitable event is called the inevitable event relative to condition S; Relative to condition S, an event that must not happen is called an impossible event; Relative to condition S, events that may or may not occur are called random events.
Question 3: Can you give more examples of random events, inevitable events and impossible events in real life?
Give full play to students' opinions and let more students have the opportunity to show.
2. frequency and probability of event a.
The size of objects is often measured by mass and volume, and the level of learning is often measured by examination results. For random events, how likely it is to happen, we also hope to reflect it with a quantity-probability.
Exploration 1: Is this game fair? (See the courseware), guide the students to compare the possibility of event A and event B.
Question 2: Flip a coin to see which side the coin will face up when it lands.
(1) Ask the students to experiment in groups and make statistics. Each group reports the results and analyzes the reasons for the poor performance of different groups.
(2) Computer simulation experiment;
(3) The results of a large number of repeated coin toss experiments made by five mathematicians in history.
Frequency and times: repeat the test for n times under the same condition S, and observe whether an event A appears, and call the frequency nA of the event A in the n tests as the frequency of the event A; Let the ratio fn(A)=nA/n of the occurrence of event A be the frequency of the occurrence of event A. ..
Question 3: The above experiments show that it is unpredictable whether there is a random event A in each experiment, but after a large number of repeated experiments, with the increase of the number of experiments, the frequency of the occurrence of event A presents a certain regularity. How is this regularity reflected?
The frequency of event A is relatively stable, swinging around a constant.
Probability: Because the frequency fn(A) of random event A tends to be stable in a large number of repeated experiments and swings around a certain constant, we can use this constant to measure the possibility of event A, and call this constant the probability of event A, and write it as P(A).
Inquiry 4: What is the probability of heads up in the coin toss experiment mentioned above? What is the probability of rape germination in the above experiment?
Question 5: In practical problems, the probability of random event A is often unknown (for example, the probability of shooting a target under certain conditions). How do you get the probability of event A?
Through a large number of repeated experiments, the stable value of the frequency of event A, that is, probability, is obtained.
Question 6: Under the same conditions, must the frequency fn(A) of event A in two consecutive experiments be equal? Is the probability P(A) of event A occurring in two consecutive experiments necessarily equal?
The frequency is random. If the experiment is repeated for the same number of times, the frequency of event A may be different. Probability is a definite number, which exists objectively and has nothing to do with every experiment.
Question 7: What are the probabilities of inevitable events and impossible events? What are the ranges of frequency and probability?
Question 8: Can you tell the difference and connection between frequency and probability?
The (1) frequency itself is random and cannot be determined before testing. Repeat the experiment for the same number of times to get events with different frequencies;
(2) The probability is a definite number, which has nothing to do with every experiment. It is a quantity used to measure the possibility of an event;
(3) Frequency is an approximate value of probability, and with the increase of test times, frequency will be closer to probability.
3. Knowledge application: students' practice is the mainstay, and teachers guide and evaluate (see courseware).
Activity 3 Activity (3) Summary and improvement
Knowledge: 1, random events, definite events, impossible events and other concepts;
2. Definition of frequency and probability, and their differences and connections.
Methods: Observe the experiment, summarize the general conclusions and analyze the phenomena in life.
Activity 4 Exercise (4) Self-evaluation
Practice in class (see courseware)
3. 1. 1 Probability of random events
Class design class record
3. 1. 1 Probability of random events