The classical concept is also called traditional probability, and its definition was proposed by the French mathematician Laplace. If a random experiment contains a limited number of unit events, and the probability of each unit event occurring is equal, then the random experiment is called a Laplace trial, and the probability model under this condition is called a classical concept. Next is the 2020 high school mathematics classical outline lesson plan design I compiled for you. I hope you like it!
2020 high school mathematics classical outline lesson plan design 1
Teaching objectives: (1) Understand classical concepts and their probability calculation formulas,
(2) Be able to use enumeration methods to calculate the number of basic events contained in some random events and the probability of event occurrence.
Teaching focus: Understand the concept of classical concepts and use classical concepts to solve the probability of random events.
Teaching difficulties: How to judge whether an experiment is a classical concept, and distinguish between a The number of basic events included in a random event in the classical concept and the total number of basic events in the experiment.
Teaching process:
Introduction: Story introduction
Exploration 1
Experiment:
(1) The experiment of throwing a coin with uniform texture
(2) The experiment of throwing a dice with uniform texture< /p>
What are all the results of the above two experiments?
1. Basic event
1. Definition of basic event:
Randomized experiment Each result that may occur in is called a basic event
2. Characteristics of basic events:
(1) Any two basic events are mutually exclusive
< p> (2) Any event (except impossible events) can be expressed as the sum of basic events.Example 1. In the experiment of randomly picking out two different letters from the letters a, b, c, and d, how many basic events are there? What are they?
Exploration 2 : Can you find the same characteristics between the two experiments above and Example 1?
2. Classical profile
(1) All possible occurrences in the experiment There are only a limited number of basic events; (finiteness)
(2) Each basic event is equally likely to occur. (Equal possibility)
We call the probability model with these two characteristics a classical probability model, or classical profile for short.
Thinking: Determine whether the following test is a classical concept? Why?
(1). Pick any number from all integers
(2). If a point is randomly projected into a circle, it is equally likely that the point falls on any point within the circle.
(3). A shooter shoots at a bullseye. There are only a limited number of results of this test, such as hitting 10 rings, hitting 9 rings,...hitting 1 ring and hitting 0 rings (i.e. not hitting). .
(4). There are 5 playing cards of hearts 1, 2, 3 and spades 4, 5. Place the cards with their points down on the table. Now randomly draw one card from them.
2020 High School Mathematics Classical Concept Lesson Plan Design II
(1) Teaching Content
This lesson is selected from the "General High School Curriculum Standard Experimental Textbook" People's Education Version A compulsory course 3, Chapter 3, Section 2 "Classical Concepts", the teaching arrangement is 2 classes, and this class is the first class.
(2) Teaching objectives
1. Knowledge and skills:
(1) Understand the concepts and characteristics of basic events through experiments;
< p> (2) Through the analysis of specific examples, extract the two basic characteristics of the classical concept, and derive the probability calculation formula under the classical concept;(3) Be able to find some simple classical concepts A question of probability.
2. Process and methods: Experience the process of exploring classical concepts and experience mathematical thinking methods from special to general.
3. Emotion and value: Use examples with practical significance to stimulate students' interest in learning, and cultivate students' innovative ideas that are courageous to explore and good at discovery.
(3) Important and difficult points in teaching
Focus: Understand the concept of classical concepts and use classical concepts to solve the probability of random events.
Difficulty: How to judge whether an experiment is a classical concept and find out the total number of basic events in a classical concept and the number of basic events contained in a random event.
(4) Academic situation analysis
[Knowledge reserve]
Junior high school: Understand the relationship between frequency and probability, and be able to calculate the probability of some simple and other possible events. ;
High school: further study the meaning of probability and the basic properties of probability.
[Student Characteristics]
The students in my class are active in thinking, but they do not pay enough attention to basic concepts and do not have a deep understanding of knowledge. Good at discovering the similarities and differences in specific events, but there is still room for improvement from perceptual understanding to rational understanding.
(5) Teaching strategies
Starting from the examples around them, students can learn from the constant contradictions and conflicts through "teacher guidance", "group discussion", "independent inquiry" and so on. This way gradually formed the idea of ????finding problems and solving them.
(6) Teaching tools
Multimedia courseware, projector, coins, dice.
(7) Teaching process
[Scenario setting]
There is a good book that both students want to read. Student A proposes tossing a coin: A will see heads first, and tails B will see first. Student B proposes to roll the dice: if the number is less than three, A will see it first, and if it is above three, B will see it first. Are these two methods fair?
☆Processing: Quickly draw students’ attention into the classroom through life examples. The question of whether it is fair or not is essentially a matter of probability, which cuts into the topic of this class.
[Review the past and learn the new]
(1) Review the method of calculating probability in the previous lessons: repeat a large number of experiments.
(2) Conflicts caused by the shortcomings of the randomized trial method: We need to find another simpler and easier way to propose the necessity of establishing a probability model.
[Explore new knowledge]
1. Basic events
Thinking: Experiment 1: Toss a coin with a uniform texture and observe what possible outcomes?
Experiment 2: Throw a dice with uniform texture and observe the possible outcomes.
Definition: Each possible outcome in a trial is called a Basic events.
☆Processing: Based on the analysis of the two experiments, the concept of basic events is proposed. By analogy with the study of cells in biology, we transition to studying the necessity of basic events to establish probabilistic models.
Thinking: Roll a dice of uniform texture
(1) In a trial, will the two basic events "1 o'clock" and "2 o'clock" appear simultaneously< /p>
(2) What basic events are included in the random events "the number of occurrence points is less than 3" and "the number of occurrence points is greater than 3"?
Toss a coin of uniform texture
< p> (1) In an experiment, will the two basic events "heads up" and "tails up" appear at the same time(2) What basic events does the "inevitable event" include? < /p>
Characteristics of basic events: (1) Any two basic events are mutually exclusive;
(2) Any event (except impossible events) can be expressed as the sum of basic events .
☆Processing: Guide students to find the uniqueness in their personality and improve their ability to discover, summarize and summarize. The design of random events "occurrence points less than 3" and "occurrence points greater than 3" echoes the introduction in the classroom, and also lays the foundation for the subsequent calculation of the probability of random events.
2. Classical Overview
Thinking: From the perspective of basic events, what are the similarities between the above two experiments?
Classical Overview Characteristics of: (1) The number of all possible basic events that may occur in the experiment is limited;
(2) Each basic event is equally likely to occur.
☆Processing: Guide students to observe, analyze, and summarize the most common points between these two experiments, and cultivate their mathematical thinking ability from concrete to abstract, and from special to general. Clarify the perspective of thinking when asking questions, so that students' thinking can be directed to the essence of the concept and avoid unnecessary divergence.
Teacher-student interaction: Students and teachers each give some life examples and analyze whether they have the two characteristics of the classical concept.
(1) A point is randomly projected into a circle. If the point falls on any point within the circle, it is equally possible. Do you think this experiment can be described by a classical concept? Why?
(2) At the 2008 Beijing Olympics, Chinese athlete Zhang Juanjuan won the first Olympic gold medal in archery for our country with outstanding results. Do you think the target practice experiment can be described by classical concepts? Why?
Design intention: Let students more vividly and accurately grasp the two characteristics of classical concepts through examples around them, and break through how to judge a It is a teaching difficulty to test whether the test is a classical concept.
3. Solve the classical concept
Thinking: Under the classical concept, what is the probability of each basic event? How to calculate the probability of random events?
(1) Probability of basic events
Experiment 1: Coin toss
P ("heads up") = P ("tails up") =
< p> Experiment 2: Rolling diceP("1 point")=P("2 point")=P("3 point")=P("4 point")=P("5 Point")=P("6 point")=
Conclusion: In the classical concept, if the total number of basic events is n, then the probability of each basic event is
☆Processing: Ask "If you don't do experiments, how can you use the characteristics of classical concepts to calculate the probability?"
First, the students will be divided into groups to discuss how to calculate the probability of the basic event in the coin toss experiment and standardize the students' answers. , and at the same time point out the fairness of the "coin tossing plan" proposed by student A; then students analyze the process of solving the probability of basic events in the dice throwing experiment and draw general conclusions.
(2) Probability of random events
In the dice throwing experiment, event A is recorded as "the number of occurrence points is less than 3", and event B is "the number of occurrence points is greater than 3". How to solve P (A) and P(B)?
2020 High School Mathematics Classical Concept Lesson Plan Design 3
Teaching Background Analysis
(1) Teaching content of this class Function and status
The content of this lesson is the first lesson of the standard experimental textbook of the general high school curriculum People's Education A version 3 Chapter 3 Probability Section 2 Classical Concepts. The main content is the definition of classical concepts and its probability calculation formula.
From the perspective of teaching material knowledge arrangement, students have already learned the concept of random events and the definition of probability. They will use the frequency of random events to estimate probability. After learning classical concepts, students will also need to learn geometric concepts. , the knowledge of classical concepts plays a role in connecting the past and the future in the textbook. The classical concept is a special probability model. Since it was the main research object in the early days of the development of probability theory, and many of the initial results of probability were obtained from it, classical concepts occupy an important position in probability theory and are indispensable for learning probability.
Learning classical concepts is helpful for understanding the concept of probability and calculating the probability of events; it lays the foundation for further learning of geometric concepts, distribution of random variables and other knowledge; it enables students to further understand random ideas and methods of studying probability, which can solve practical problems in life and cultivate students' awareness of applied mathematics.
(2) Analysis of students’ situation (the knowledge received by the objects being taught and the possible situation of knowing the teaching content)
1. Students’ cognitive basis:
< p> Students in junior high school have already had a preliminary understanding of random events, and can use list methods and tree diagrams to find the probabilities of other possible events. In the previous section on the probability of random events, we have mastered the method of estimating probability using frequency, that is, the statistical definition of probability. Understand the relationship and operations of events, especially the concept of mutually exclusive events, as well as the nature of probability and the addition formula of probability. These knowledge reserves lay the foundation for the conceptual understanding of basic events and the derivation of the probability formula of classical concepts in this lesson. Students are familiar with a large number of examples of random events in life in previous studies. The probabilities of simple random events such as tossing a coin or rolling a dice can be obtained.2. Cognitive difficulties of students:
I investigated the understanding of this part of knowledge by junior high school mathematics teachers and high school students, and found that students in junior high schools have learned and other possible events The probability of simple equally likely events can be calculated, but it is not modeled, so students only know what is happening but not why. According to past teaching experience, if there is no in-depth understanding of concepts and students still stay at the original cognitive level after learning classical concepts, then the fuzzy concepts will lead to calculation errors on complex problems.
Teaching objectives
1. Through comparative analysis of a large number of life examples, students can understand the characteristics of basic events and understand the concepts, characteristics and calculation formulas of classical concepts.
2. Students experience the process of abstracting mathematical models from life examples, which embodies the dialectical materialist perspective from concrete to abstract, and from specific to general; students can understand the world from a random perspective.
3. Through various interesting examples close to life, students understand that mathematics comes from life, and feel how to use mathematics to explain phenomena in the real world and solve problems in production and life.
Teaching Emphasis, Difficulties and Analysis
The focus of this lesson is to understand the two characteristics of classical concepts and their probability calculation formula through examples.
Since students have already learned the probability of equally possible events in junior high school, it is not difficult to understand and apply the probability calculation formula of classical concepts. Therefore, I think the difficulty of this lesson is the understanding of basic events. Conceptual understanding and an accurate understanding of two characteristics of classical concepts.
Teaching process
Since my question is relatively open-ended, I can only preset the process here. During the actual teaching process, corresponding adjustments must be made based on the students' answers.
1. Ask questions:
Question 1. What examples of random events can you give in life?
Examples that students may give for this question There are many, for example: tossing a coin with a uniform texture and it will come up heads; tossing a dice with a uniform texture and it will come up with 1 point; the car will hit a red light when it reaches the intersection; you will get a white piece from the Go jar; you will buy a lottery ticket. Win a prize; hit exactly 10 rings in a shooting; plant a seed and sprout just in time. etc.
If students have difficulty giving examples, the teacher can guide students to extract examples from a certain life scene, such as on the way to school, in sports competitions, playing cards, etc.
My design intention is to allow students to cite a large number of examples of random events from life, and then analyze and study them to summarize the characteristics of classical concepts. Giving students examples can stimulate students' curiosity and attract students to take the initiative to explore. On the other hand, it also allows students to realize that mathematics is a tool for solving practical problems.
Because the examples given by everyone must be used throughout, these examples should include examples of classical concepts, as well as typical examples that are not classical concepts. If students fail to give , after the students give examples, I will make appropriate supplements based on the students' examples. Must-have examples: tossing a coin, rolling dice, planting a seed, waiting time for train, throwing beans on a disk.
2. Analysis examples:
In this link, I want to let students first find the probability of these random events through their existing experience. Some students may use the statistical method learned in the previous section to estimate probability using frequencies. This method must be affirmed and students must be enlightened. The disadvantages of this method are that it is time-consuming and labor-intensive, and sometimes it is difficult due to limited conditions. operate. There are also students who will use the method of finding the probability of equally likely events in junior high school to find the probability of some random events. For this method, be sure first. My design intention is to allow students to connect with what they have learned previously and start from their existing cognitive foundation to experience new knowledge.
In the process of finding probabilities, students will find that the probabilities of some random events can be found out, but some cannot. For example:
Tossing a coin with a uniform texture and it comes up heads The probability of being on is 1/2;
Rolling a uniformly textured die and getting 1 is 1/6;
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