The teaching goal of the first volume of mathematics teaching plan in grade one of Jiangsu Education Press.
1. Understand the concept of set, and know the concept of common number set and its notation.
2. Understand the three characteristics of sets, judge the relationship between sets and elements, and use symbols correctly.
3. According to the characteristics of the elements in the set, express them with appropriate methods and accurate language, and realize the superiority of depicting objective things with mathematical abstract symbols.
Examination requirements
1. Understand the concept of common number set and its representation.
2. Understand the three characteristics of sets, judge the relationship between sets and elements, and use symbols correctly.
preschool education
The meaning of 1. set: form a set.
Elements in the (1) set and their representations:.
(2) Characteristics of elements in the set:
(3) the relationship between elements and sets:
(i) If A is an element of the set A, it is recorded as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(ii) If A is not an element of set A, it is recorded as _ _ _ _ or _ _ _ _ and read as "_ _ _ _ _ _ _ _ _".
Think about whether the elements that make up a set can only be numbers or points.
answer
2. Commonly used number sets and their symbols:
Generally speaking, the set of natural numbers is _ _ _ _ _ _ _ _ _, and the set of positive integers is _ _ _ _ _ _ _ _ or _ _ _ _ _ _ _ _ _,
Integer sets are recorded as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
3. Classification of sets:
According to the number of its elements:
(1) _ _ _ _ _ _ _ _ _ _ _ _ is called a finite set;
(2) _ _ _ _ _ _ _ _ _ _ _ _ _ _ is called an infinite set;
(3) _ _ _ _ _ _ _ _ _ _ is called an empty set, and it is recorded as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
4. Representation method of set:
(1) _ _ _ _ _ _ _ _ _ _ _ is called enumeration;
(2) _ _ _ _ _ _ _ _ _ _ _ _ is called description.
(3) _ _ _ _ _ _ _ _ is called Venn diagram.
Illustration
Example 1. Can each of the following objects form a set?
(1) All senior one students in senior one; (2) All points whose distance from the plane to the origin is equal to 2;
(3) The sum of all regular triangles; (4) Real number solution of the equation; (5) All real number solutions of inequality.
Example 2. Represent the following sets in an appropriate way.
① The set composed of all integers greater than 10 and less than 20 is recorded as;
(2) The set of points on a straight line is recorded as:
(3) The solution set of inequality is recorded as:
(4) The set of solutions of the equations is recorded as:
⑤ The point set of the first quadrant is recorded as:
⑥ The point set on the coordinate axis is recorded as.
Example 3. Given a set, if there is at most one element in it, find the range of the number.
Classroom detection
1. A set consisting of the following objects: ① a positive integer not exceeding 45; 2 bright colors; ③ Big cities in China; ④ The real number with the smallest absolute value; (5) Students in Grade 1 (2) of Senior High School who scored above 500 points, including _ _ _ _ _ _
2. 2a∈A and a2-a∈A are known. If a contains two elements, the following statement is correct.
①a takes all real numbers; ②a takes all real numbers except 0;
③a takes all real numbers except 3; ④a takes all real numbers except 0 and 3.
3. If the set is known, it is a set of real numbers x that meet the conditions.
Teaching reflection
The Meaning and Representation of 1. 1 Set (2)
Teaching objectives
1. Further deepen the understanding of the concept of set;
2. Seriously understand the characteristics of the elements in the set;
3. Master the representation method of set skillfully, and gradually cultivate the standardization of using mathematical symbols.
Examination requirements
3. Understand the concepts and symbols of common number sets.
4. By understanding the three characteristics of a set, we can judge the relationship between the set and elements and use symbols correctly.
preschool education
1. collection, then there are elements in the collection.
2. If the set is infinite, then.
3. If x2 ∈ {1, 0, x} is known, then the value of real number x 。
4. Set, then set =.
Illustration
Example 1. Observe the following three groups. Do they mean the same thing?
( 1) (2) (3)
Example 2. A set containing three real numbers can be expressed as or as, find.
Example 3, the value of a set, if, is known.
Classroom detection
1. Fill in the blanks with the appropriate symbols:
( 1) (2)
2. assemble, assemble, and then.
3. Represent the following sets through enumeration:
Teaching reflection
1.2 subset complement (1)
Teaching objectives
1. Understand the concepts of subset and proper subset, judge and prove the inclusion relation of two sets, and judge the equality relation of simple sets;
2. Through concept teaching, improve students' logical thinking ability and infiltrate the idea of equivalent transformation; The relativistic view of infiltration.
Examination requirements
1. It can judge who is a subset of two sets with subset relation, and then judge whether it is a proper subset.
2. Obviously, the determination of the inclusion relationship between two sets mainly depends on the relationship between their elements and sets.
preschool education
Concepts and symbols of 1. subset;
If any element in set A is an element in set B (), it is called.
Set A is a subset of set B, marked as _ _ _ _ _ _ _ or _ _ _ _ _ _, which can be read as "_ _ _ _ _ _" or "_ _ _ _ _ _ _ _ _", and can be expressed as: _ _ _ _ _ _ _.
2. The nature of the subset: 1A2③, then
Thinking: Can sum be established at the same time?
answer
3. proper subset's concepts and symbols:
If, at this time, the set is called the proper subset of the set, and it is recorded as _ _ _ _ _ _ _ or _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
4. The nature of proper subset:
(1) Any proper subset symbol is expressed as _ _ _ _ _ _ _ _ _ _ _.
② The transitive symbol of proper subset is _ _ _ _ _ _ _ _ _ _.
Illustration
For example 1, the following statement is true _ _ _ _ _ _ _
(1) If the set is a subset of the set, all elements in the set belong to;
(2) If the set is not a subset of the set, all the elements in the set do not belong to it;
(3) If a set is a subset of a set, there must be elements that do not belong to it;
(4) The empty set has no subset.
Example 2. Among the following six relationships, the correct one is _ _ _ _ _ _ _ _
( 1) ; (2) (3) (4) (5) (6)