The meaning and expression of set 1 lecture notes, a compulsory course of mathematics in senior one.
Teaching material analysis: The concept of set and its basic theory, called set theory, are the important foundation of modern mathematics. On the one hand, many important branches of mathematics are based on set theory. On the other hand, set theory and its mathematical thought have been applied in more and more fields.
Two. Target analysis:
Teaching emphases and difficulties
Key point: the meaning and representation of set.
Difficulties: the proper choice of representatives.
Teaching objectives
Length knowledge and skills
(1) Understand the meaning of set and the relationship between elements and set through examples;
(2) Know the commonly used number sets and their special signs;
(3) Understand the certainty, mutual dissimilarity and disorder of elements in the set;
(4) Being able to express related mathematical objects in assembly language;
2. Process and method
(1) Let students experience the process of abstracting and summarizing the same characteristics of a set from the examples of the set, and feel the meaning of the set.
(2) Ask students to summarize what they have learned in this section.
3. Emotions, attitudes and values
Let students feel the necessity of learning assembly and enhance their enthusiasm for learning.
Three. Analysis of teaching methods
1. teaching method: students can read textbooks, study independently, think, communicate, discuss and summarize, so as to better accomplish the teaching objectives of this course.
2. Teaching means: use projector to assist teaching in teaching.
Four. process analysis
(A) create a scene to reveal the theme
1. The teacher asks first: (1) Introduce his family, his old school and his current class.
(2) Question: Do you like it? Family? 、? School? 、? Class? Wait, what are the same characteristics?
Guide students to communicate with each other. At the same time, teachers evaluate students' activities.
2. Activities: (1) List examples of collections in life;
(2) Analyze and summarize the same characteristics of each case.
This leads to the content to be studied in this section.
Design intention: not only stimulate students' strong interest in learning, but also pave the way for new knowledge.
(2) Explore new knowledge and construct concepts.
1. Teachers use multimedia devices to show students the following seven examples:
( 1) 1? All prime numbers within 20;
(2) four great inventions of ancient china;
(3) All permanent members of the Security Council;
(4) all squares;
(5) All overpasses completed before September 2004 in Hainan Province;
(6) To all points with the same distance on both sides of an angle;
(7) All senior one students enrolled in Guoxing Middle School in September 2004.
2. Teachers organize students to discuss in groups: What are the similarities and differences between these seven examples?
3. Each group chooses a classmate to publish the discussion results of the group. On this basis, teachers and students summed up the characteristics of seven examples and gave the significance of setting them.
Generally speaking, the sum of some specific objects is called a set. Every object in a set is called an element of this set.
The teacher pointed out the capital letters a, b, c, d,? Represents that elements usually use lowercase letters. Express delivery.
Design intention: let students feel the concept of set through examples, stimulate their interest in learning and cultivate the spirit of being willing to seek.
(3) Questioning defense and developing thinking.
1. The teacher guides the students to read the relevant contents in the textbook and thinks: What are the characteristics of the elements in the set? Pay attention to individual counseling and answer students' questions, so that students can clearly understand the three characteristics of set elements, namely certainty, mutual difference and disorder. As long as the elements that make up two sets are the same, we call them equal.
2. Teachers' organizations guide students to think about the following questions:
Determine whether all the following elements form a set and explain why:
(1) is an even number greater than 3 and less than 1 1;
(2) Small rivers in China.
Let students fully express their solutions.
3. Ask students to give some examples that can form a set and some examples that can't form a set, and explain the reasons. Teachers give timely evaluation to students' learning activities.
4. The teacher asks questions to make students think.
(1) If a stands for high? (3) The collection of the whole class is used to indicate that a classmate in Class 3 of Grade 1 is a classmate in Class 4 of Grade 1, so what is the relationship between them and the collection A? This leads students to conclude that there are two relationships between elements and sets: attribution and non-attribution.
If it is an element of set a, it belongs to set a and is recorded as.
If it is not an element of set a, it is said that it does not belong to set a, and it is recorded as.
(2) if it is represented by a? All permanent members of the Security Council? What is the relationship between China, Japan and Set A? Please use mathematical symbols to represent them respectively.
(3) Let the students finish the exercise on page 6 of the textbook 1.
5. Teachers guide students to recall the process of developing several groups, and then read the cross contents in the textbook, write the marks of several commonly used groups, and ask students to complete the question1.1a.
6. Teachers guide students to read the relevant content in the textbook, and think and discuss the following questions:
(1) How many representations can a set * * * have?
(2) Try to compare natural language. What are the characteristics of enumeration and description in representing collections? What is the applicable object?
(3) How to choose an appropriate set representation according to the problem?
Make students understand the advantages and disadvantages of the three expressions, the necessity of their existence and the applicable objects.
Design intention: Make clear the three characteristics of set elements, so that students can understand the advantages and disadvantages of the three representations, thus breaking through the difficulties.
Consolidate and deepen, feedback and correct
Teachers' projection learning;
(1) Describe the set in natural language {1, 3,5,7,9};
(2) Use case method to represent the set.
(3) Try to choose an appropriate method to represent the following set: Exercise 2 on page 6 of the textbook.
Design intention: to enable students to consolidate new knowledge in time and realize the necessity and applicable objects of the three expressions.
(5) Summarize the assignment.
Summary: In the interaction between teachers and students, let students understand or experience the following questions:
1. What have we learned in this lesson?
2. What do you think is the significance of learning assembly?
3. What should I pay attention to when choosing the representation of a set?
Design intention: Through review, we can have a clear understanding of the occurrence and development process of the concept, and review the three characteristics of the set elements and the three manifestations of the set.
Homework:
1. Written homework after class: exercise 1. 1A Group 4 13 pages.
2. How many relationships are there between elements and sets? How to express it? Similarly, how many relationships are there between sets? How to express it? Students are required to preview their textbooks.
Analysis of verb (abbreviation of verb) on the blackboard
The meaning and expression of PPT set
definition
Example 1
Example 2
work arrangement
Read "1. Summary of knowledge points of compulsory mathematics collection in senior one.
2. High school mathematics compulsory key knowledge points.