What analysis do teachers have when preparing collective teaching design?

Instructional design of the meaning and representation of set

First, the teaching objectives

Knowledge and skills

Knowing the commonly used number sets and their special symbols, I can express mathematical objects in set language and understand the relationship between elements and geometry.

Process and method

By abstracting the process of summarizing the same characteristics of a set from the examples of the set, we can perceive the meaning of the set and improve the ability of induction and summary.

Emotional attitudes and values

In the process of learning to express sets by enumeration, we should enhance our ability to understand things and initially improve our rigorous learning spirit of seeking truth from facts and rigorous scientific attitude.

Second, the difficulties in teaching

focus

The meaning and representation of a set.

difficulty

Represent a set by description.

Third, the teaching process

(A) the introduction of new courses

Teacher: Students, let's play a game before class. Now introduce our family members or our school from the number one.

Health: Free to answer.

Teacher: OK, just now the students said, "My parents and I are in my family", "I come from No.38 Middle School" and "My class is Grade One (1). There are 45 students in the class, including 23 boys and 22 girls. That's just like what the students said: "family", "school" and "class". Today we will learn this new representation set.

Design intention: Use playing cards that students are interested in in in life, connect what they want to learn in class, and turn abstract things into things they can actually understand, which will increase students' interest in learning and reduce the difficulty of accepting new knowledge. )

(2) Explore new knowledge

1. Explore the meaning of set

Teacher-student activities: Teachers and students discuss the generation of the meaning of set together.

In fact, in life, we will encounter all kinds of things. In order to facilitate the discussion, we need to classify the things discussed in a certain range according to certain standards. After classification, we will use some terms to describe it, such as "group", "complete works" and "collection".

Generally speaking, all definite and different objects in a certain range constitute a set. Each object in a collection is called an element in the collection, or simply a meta.

Teacher: OK, I know what set means. Now the teacher will test everyone.

Please observe the elements in the collection Capital of Asian Countries and see what elements it has.

After students freely answer, guide students to expand-find that new york and Paris are not in the collection, and emphasize the certainty of elements.

Please write a set of letters in the book to emphasize the differences between elements.

Query 1: Our class changes seats every week. Has the collection of all students in our class changed?

Health: No change.

Explain that as long as the elements that make up the two groups are the same, we say that the two groups are equal-teacher's summary

Specifically, for natural number set, the set of positive integers is N* or n, the set of integers is z, the set of rational numbers is q, and the set of real numbers is R. 。

2. The relationship between elements and sets

Generally, capital Latin letters A, B, C … are used to represent sets, and lowercase Latin letters A, B, C … are used to represent sets.

If a is an element of set A, it is said that A belongs to set A, marked as A ∈ A; If A is not an element of set A, say A does not belong to set A, remember? If A is used to represent the set of "all girls in our class", then xx belongs to A and xxx does not.

3. Representation method of set

enumeration method

The collection of "municipalities directly under the Central Government of China" is expressed as

{Beijing, Tianjin, Shanghai, Chongqing}

The method of enumerating the elements of a set one by one and enclosing them in curly braces is called enumeration.

Note: There are not too many or omitted curly braces, and elements are separated by ",".

Grouping: a group of boys and a group of girls discuss the competition in groups, and the loser is responsible for mobilizing the whole school to do Yushu.

Raise funds in the earthquake-stricken areas.

Discuss in groups: Then collect some students' answers and analyze them.

Example 1. Use enumerations to represent the following collections:

① the set of all natural numbers less than 10;

② The set of all real roots of equation x2=x;

③ The set of all prime numbers in1~ 20.

Solution: ① {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

②{0, 1}.

③{2,3,5,7, 1 1, 13, 17, 19}.

Thinking: You can express the inequality x ‐ 7.

No, because the elements in this set are inexhaustible. But we can describe these elements by their * * * same characteristics.

Description method

The method of representing a set with the * * * same characteristics of the elements contained in the set is called description.

The specific method is as follows: first, write out the general symbols and value (or change) ranges representing the elements of this set with curly braces,

Draw another vertical line and write down the * * * characteristics of the elements in this set after the vertical line.

Note: The symbol and value range of elements are the same as * * *.

Example 2. Try to express the following sets by enumerating and describing respectively:

(1) The set of all real roots of equation x2‐2=0;

② The set of all integers greater than 10 and less than 20.

Solution: ① Description is {x∈R|x2‐2=0}.

Expressed as {8202} s by enumeration.

② Represented by descriptive method as {x ∈ z | 10.

Through example 2, let students find that when describing a set, if you look at the relationship from the context, the values of the elements are different.

If the range is definite, you can omit the range and write only its elements.

(3) deepen understanding

Thinking: When enumerating and describing collections, try to compare their characteristics and applicable objects.

Example 1, inequality 2x-3 >；; 5-piece solution

Solution: 2x-3 & gt；; 5 available x>4, so the inequality 2x-3 >；; The solution set of 5 is {x | x >；; 4，x∈R}

Here {x | x>4 and x ∈ r} can be abbreviated as {x | x & gt4}.

The solution set of example 1 has infinite elements. Generally speaking, a set with finite elements is called a finite set, and a set with infinite elements is called an infinite pole.

We call a set without elements an empty set, remember? .

(4) Consolidate and improve

1. Use enumeration to represent the following collections.

(1) {x | x+1= 0} (2) {x | x is the positive divisor of 12.

2. Describe the following sets.

(1) set of odd numbers

(2) Positive even set

(5) Summarize the homework

Summary: Teachers and students review the main contents of this lesson together and ask students to answer questions:

1. What is a setting?

2. what are the characteristics of 2.set?

Homework: Do Exercise 2.4 after class.