The teaching goal is 1, and the knowledge of integers and fractions (including decimals) learned in the first two sections is sorted out to master the concepts of positive and negative numbers;

2, can distinguish two quantities with different meanings, and will use symbols to represent positive and negative numbers;

3. An important reason for experiencing the development of mathematics is the actual needs of life, which stimulates students' interest in learning mathematics.

Teaching difficulties correctly distinguish two quantities with different meanings.

Two opposite quantities of knowledge focus.

Design concept of teaching process (teacher-student activities)

Set the situation

At the beginning of the introductory class, the teacher should briefly explain the figures we have learned in the first two sections through concrete examples, and ask the students to think: health.

Are these "previously learned numbers" enough in life? The following example

For reference only.

Teacher: Today, we are Grade 7 students, and I am your math teacher. Let me introduce myself to you first. My name is XX, my height is 1.73m, my weight is 58.5kg, and I am 40 years old. Our class is Class 7 (13), with 60 students, including 22 boys, accounting for the total number of the class.

Question 1: How many figures appeared in the teacher's introduction just now? What is the difference? Can you classify these numbers according to the number classification method you have learned before?

Student activities: thinking and communication

Teacher: In fact, there are two main categories of numbers learned before, namely integers and fractions (including decimals).

Question 2: Are only integers and fractions enough in life?

Please read a book (observe what numbers are used in the pictures in front of this section, so that students can feel the necessity of introducing negative numbers), think and discuss, and then communicate.

(You can also display the temperature map in the weather forecast, the topographic map of the terrain, the record page of deposit and withdrawal in the salary card, etc. )

After the students exchanged ideas, the teacher concluded that the previous numbers were not enough, and sometimes a new number with a "-"in front was needed. Let's review the types of numbers learned in primary school and summarize the integers and fractions we have learned. Then, some quantities with opposite meanings in real life are given, which shows that in order to express quantities with opposite meanings, we need to introduce negative numbers and emphasize the rigor of mathematics.

Secret, but for students, more.

I feel that math is boring. In order to review the numbers learned in primary school and stimulate students' interest in learning.

Interesting, so create the following question situations and try to be close to the students' reality.

This question can stimulate students' desire to explore. Autonomous reading is an important way to cultivate students' autonomous learning and should be paid attention to.

The above situations and examples make students realize that there is mathematics everywhere in their lives. Through examples, students can obtain a large number of perceptual materials, laying the foundation for correctly establishing quantities with opposite meanings.

parsing problem

Quest for new knowledge Question 3: What should be the name of the new number with "one" in front of it? Why attract negative numbers? Usually in daily life, what quantities do we use positive and negative numbers to represent respectively?

These questions must be made clear to students.

Teachers can use multimedia to show these questions, and let students read books and teach themselves with these questions, and then communicate with teachers and students.

This stage is mainly to let students learn to express positive and negative numbers.

Key points: positive numbers and negative numbers represent quantities with opposite meanings in practical problems, and quantities with opposite meanings contain two elements: one is opposite meanings, such as east and west, income and expenditure; Second, they are all of the same kind. These questions are the main knowledge of this lesson. Teachers should make it clear to students, pay attention to the accuracy and standardization of language, and be willing to take the time to let students fully express their ideas.

After the above discussion and communication, students have a preliminary understanding of why negative numbers should be attracted and how to express two opposite quantities with positive numbers and negative numbers. Teachers can ask students to cite similar examples in real life to deepen their understanding of the concepts of positive and negative numbers and broaden their thinking.

Question 4: Please give examples of positive and negative numbers.

Question 5: How to understand "positive integer", "negative integer", "positive fraction" and "negative fraction"? Please give an example.

Whether you can give examples is the embodiment of students' mastery of knowledge, and it can further help students understand the necessity of quoting negative numbers.

Subject: 1.2. 1 rational number.

The teaching goal is 1, master the concept of rational numbers, classify rational numbers according to certain standards, and cultivate the ability of classification;

2. Understand the correlation between classification standards and classification results, and preliminarily understand the meaning of "set";

3. Empirical classification is a common method to deal with problems in mathematics.

Difficulties in teaching correctly understand the classification standards and classify them according to certain standards.

Knowledge lies in correctly understanding the concept of rational numbers.

Design concept of teaching process (teacher-student activities)

In the first two periods of exploring new knowledge, we have learned many different types of numbers. Through the study of the last two lessons, we know that the current figures contain negative numbers. Now please feel free to write 3 numbers on the draft paper (and please write 3 numbers on the blackboard).

Question 1: Observe the nine numbers on the blackboard and classify them.

Classification of students' thinking, discussion and communication.

Students may only give a rough classification, such as "positive number" and "negative number" or "zero". At this time the teacher should give guidance and encouragement.

For example,

For the number 5, you can ask: Are 5 and 5. 1 the same type? Can 5 represent 5 people, 5. 1 number of representatives? (No) So they are different types of numbers. The number 5 is an integer in a positive number, so we call it a "positive integer", while 5. 1 is not an integer, so it is called a "positive fraction, ... (Since decimals can be changed into fractions, both decimals and fractions are called fractions in the future).

Through teachers' guidance, encouragement and continuous improvement, and students' own induction, we finally summed up five different numbers we have learned, namely "positive integer, zero, negative integer, positive fraction and negative fraction".

According to the concepts of integer, fraction and rational number in the book.

Read books to understand the origin of rational number names.

"Collectively" means "collectively".

Try it: according to the above classification, can you make a classification table of rational numbers Can you tell me what the above criteria for rational number classification are? Classification (divided by integers and fractions) is a common method to solve problems in mathematics. This introduction is open and students are willing to participate.

When students try to classify themselves, it may be rough. Teachers give guidance and encouragement, and the types of classification numbers should be guided by the meaning expressed in words, so that students can understand them easily.

The rational number classification table should be displayed on the blackboard or the media, and the classification standard should guide students to experience it.

Practice 1, write three rational numbers at will, and tell what kind of numbers they are, and communicate with your partners.

2, the textbook page 65438 +00 exercises.

The concept of set appears in this exercise and can be explained to students as follows.

Put some numbers together to form a set of numbers, which is called "number set" for short. A number set consisting of all rational numbers is called a rational number set. Similarly, a number set composed of all integers is called an integer set, and a number set composed of all negative numbers is called a negative number set.

The number set is generally represented by circles or braces, because the numbers in the set are infinite, and only a few numbers are given in this question, so ellipsis should be added.

Thinking: Do the four sets in the above exercise add up to the set of all rational numbers?

Teachers can also say some figures for students to judge.

The concept of set needs no further expansion.

Innovative inquiry question 2: Rational numbers can be divided into positive numbers and negative numbers, right? Why?

When teaching, ask students to sum up the numbers they have learned, encourage students to sum them up, and give appropriate guidance through exchanges and discussions, and gradually get the following classification table.

The classification of rational numbers can determine whether teaching is needed according to the level of students.

Let the students understand that the classification results are different when the classification standards are different, so the classification standards should be clear, so that every elephant involved in the classification after classification belongs to a certain category, and can only belong to this category. In teaching, teachers can give some easy-to-understand examples to illustrate, either by age or by gender and region.

Summary and homework

Class summary Up to now, all the numbers we have learned are rational numbers (except pi). Rational numbers can be classified according to different standards, and the results of different standards are different.

The homework for this lesson is 1, and the required questions are: page 65438 of the textbook +08 exercise 1.2 question 1.

2. Teachers prepare themselves.

Comments on this lesson (classroom design concept, actual teaching effect and improvement ideas)

1, after introducing negative numbers, this lesson classifies the learned numbers according to certain standards and puts forward the outline of rational numbers.

Reading classification is a common means to solve mathematical problems. Through the study of this lesson, students can understand the idea of classification and go hand in hand.

Simple classification is the embodiment of mathematical ability, and teachers should pay enough attention to it in teaching. On classification standards and scores

The relationship between class grades and the determination of classification standards can be properly infiltrated into students. The concept of set is abstract, and it takes a long time for students to really accept it. Don't expand this lesson too much.

2. This course has the characteristics of openness, which provides students with more thinking space, can promote students to actively participate in learning and experience the formation process of knowledge personally, and can avoid the boredom caused by direct classification; At the same time, it also embodies the characteristics of cooperative learning, communication and inquiry, and has a good effect on the cultivation of students' classification ability.

3, two classification methods, should be based on the first method, the second method can be carried out according to the situation of students.

Subject: 1.2.2 number axis

The teaching goal is 1, master the concept of number axis, and understand the corresponding relationship between points on number axis and rational numbers;

2, the number axis will be drawn correctly, the given rational number will be represented by points on the number axis, and the rational number will be read according to the points on the number axis;

3. Feeling number and shape can be transformed into each other under certain conditions, and mathematics can be experienced in life.

The concept of number axis and the representation of rational numbers on the number axis are difficult points in teaching.

Knowledge focus

Design concept of teaching process (teacher-student activities)

Set the situation

Through examples and courseware demonstrations, this paper introduces how the project teacher obtains thermometer readings.

Question 1: Thermometer is an important tool for measuring temperature in our daily life. Can you read a thermometer? Would you please try to read the temperature displayed by the three thermometers in the picture?

(The multimedia shows three pictures, which are above zero, below zero and below zero.)

Question 2: On an east-west road, there is a bus stop. There are a willow tree and a poplar tree at 3m and 7.5m east of the bus stop, and a locust tree and a telephone pole at 3m and 4.8m west of the bus stop. Try to draw a picture to illustrate this situation.

(Group discussion, communication and cooperation, hands-on operation) Create problem situations to stimulate students' enthusiasm for learning and discover mathematics in life.

Points represent the perceptual knowledge of logarithm.

Rational understanding of point representing number.

Cooperation and communication

Exploring new teachers: What can we learn from the above two questions? Can you use points on a straight line to represent rational numbers?

Let the students operate on the basis of discussion and summarize on the basis of operation: What conditions must a straight line that can represent rational numbers meet?

Thus, the three elements of the number axis are obtained: the origin, the positive direction and the idea of combining numbers and shapes per unit length; Only the characteristics of the number axis are described, and the requirements of the number axis three are not particularly emphasized.

Learn mathematics from the game and play the game: the teacher prepares a rope to let eight students come up, adjust the position to equal distance, and stipulate that the fourth student is the origin and the positive direction is from west to east. Every student has an integer. Please remember, now please ask the students in the first row to issue the password in turn. When the password is a number, the student corresponding to the number should answer "to"; When the password is a classmate's name, the classmate should report his corresponding "number". If the third student is designated as the origin, can the game still be played? Students' game experience and understanding of the concept of number axis

Looking for patterns

Conclusion question 3:

1, can you give some practical examples of numbers represented by straight lines in real life?

2. If you are given some numbers, can you find their exact positions on the number axis accordingly? If you are given some points on the axis, can you read the numbers it represents?

3. Which numbers are on the left of the origin and which numbers are on the right of the origin, what rules will you find?

4. What is the distance from each count to the origin? What rules will you find from it?

(Group discussion, communication and induction)

Summarize the general conclusion, textbook number 12. These questions are the skills that need to be learned in this course. Teaching should focus on students' inquiry learning, and teachers can give students appropriate guidance in combination with textbooks.

Consolidation exercise

Textbook exercises 12 pages.

Summary and homework

Class summary Let students summarize:

1, three elements of number axis;

2. The work of number axis and the transformation method between number and point.

The assignment for this lesson is 1, and the required question is: Exercise 2 on page 18 of the textbook 1.2.

2, choose to do the problem: the teacher arranges it himself.

Comments on this lesson (classroom design concept, actual teaching effect and improvement ideas)

1, the number axis is an important medium for number-shape conversion and combination. The prototype of situational design comes from the reality of life and is easy for students to experience and accept. Through observation, thinking and hands-on operation, students can deepen their understanding of the concept of number axis, experience and appreciate the formation process of number axis, and cultivate their ability of abstract generalization, which also embodies the cognitive law from perceptual knowledge to rational knowledge to abstract generalization.

2. The teaching process highlights the main line from emotion to abstraction to generalization, and the teaching method embodies the mathematical thinking method of combining numbers and shapes from special to general.

3. Pay attention to students' knowledge and experience, give full play to students' subjective consciousness, let students actively participate in learning activities, guide students to feel the generation, development and change of knowledge in class, and cultivate students' independent exploration of learning methods.

Subject: 1.2.3 Countdown

The teaching goal is 1, master the concept of inverse number, and further understand the corresponding relationship between points and numbers on the number axis;

2. Cultivate inductive ability by summarizing the characteristics of the points represented by the reciprocal on the number axis;

3. Experience the idea of combining numbers with shapes.

Teaching difficulty: summarize the characteristics of the points represented by the opposite numbers on the number axis.

The concept of the opposite number of knowledge focus

Design concept of teaching process (teacher-student activities)

Set the situation

Introduce the topic 1: Please divide the following four numbers into two categories and explain why they are so classified.

4,-2,-5,+2

It is difficult to encourage students to have differences, as long as they can tell the truth, but teachers should guide them appropriately and gradually come to the conclusion that 5 and -5, +2 and -2 are distinctive points.

(Guide students to observe the distance from the origin)

Thinking conclusion: Thinking textbook page 13.

Try two other similar numbers.

Conclusion: Summary of page 13 of the textbook. Create situations in an open way, discuss with students and cultivate classification ability.

Cultivate students' ability of observation and induction, and infiltrate mathematical thinking.

Deepen the definition of theme refinement and give the definition of reciprocal.

Question 2: How to understand the meanings of the words "only different symbols" and "interaction" in the definition of opposites? What is the reciprocal of zero? Why?

Students think, discuss and communicate, and the teacher summarizes.

Law: Generally speaking, the reciprocal of the number A can be expressed as-A..

Thinking: What is the relationship between the two points representing the opposite number on the number axis and the origin?

Exercise: The first exercise on page 14 of the textbook is to experience the characteristics of symmetrical figures and prepare for the characteristics of opposites on the number axis.

Deepen the concept of reciprocal; "The inverse of zero is zero" is part of the definition of inverse.

Strengthen the geometric meaning of points represented by mutually opposite numbers on the number axis.

Give the law

Question 3: What do-(+5) and -(-5) mean respectively? Can you simplify them?

Student exchange.

The antonyms of +5 and -5 are -5 and +5, respectively.

Exercise: the second exercise on page 14 of the textbook, using the concept of reciprocal, obtains the method of finding the reciprocal of a number.

Summary and homework

Definition of class summary 1, reciprocal

2. Characteristics of points represented by mutually opposite numbers on the number axis.

3. How to find the inverse of a number? How to express the reciprocal of a number?

The assignment for this lesson is 1, and the required question is the third question on page 18 of the textbook.

2, choose to be the teacher's own arrangement.

Comments on this lesson (classroom design concept, actual teaching effect and improvement ideas)

1, the concept of inverse number is convenient to express the arithmetic rules of rational numbers, and also reveals the characteristics of two special numbers. These two special numbers have the same absolute value in quantity, and their sum is zero. When expressed on the number axis, the distance from the origin is in phase, and so on. So this teaching design is based on the idea of combining numbers with shapes.

2. Teaching attracts people with open questions and cultivates students' ability of classification and divergent thinking; Representing numbers on the number axis and observing their characteristics, while reviewing the knowledge of the number axis, infiltrating the mathematical method of combining numbers and shapes, and transforming numbers and shapes can also deepen the understanding of the concept of reciprocal; Question 2 can help students master the concept of reciprocal accurately; Question 3 actually gives a method to find the reciprocal of a number.

3. This teaching design embodies the teaching concept of the new curriculum. Under the guidance of teachers, students learn independently, explore independently, observe and summarize, attach importance to students' thinking process, and leave room for students to play.

Subject: 1.2.4 Absolute value

The teaching goal is 1, to master the concept of absolute value and the comparison rule of rational numbers.

2. Learn to calculate absolute values and compare the sizes of two or more rational numbers.

3. The concepts and rules of empirical mathematics come from real life and are permeated with the idea of combination and classification of numbers and shapes.

Comparison of two negative numbers in teaching difficulties

The concept of absolute value in knowledge set

Design concept of teaching process (teacher-student activities)

Set the situation

On Sunday, Mr. Huang started from school and drove to play. She first went 20 kilometers east to Zhujiajian Island Island, and then 30 kilometers west in the afternoon, and returned home (school, Zhujiajian Island Island and home are on the same line). If the rule is Dongzheng, ① use rational number to represent the distance between Miss Huang's two trips; (2) If the car consumes 0. 15 liter per kilometer, how many liters does the car consume on this day?

After the students thought, the teacher explained as follows:

Some problems in real life only focus on the specific value of quantity, but the opposite is true.

Meaning is irrelevant, that is, positive and negative are irrelevant. For example, we only care about the distance traveled by cars and the price of gasoline, but have nothing to do with the direction of travel;

Observe and think: draw a number axis, and the origin represents the school. Draw points on the axis representing Zhujiajian Island Island and Miss Huang's home. Look at the picture and tell the distance from Miss Huang's home to Zhujiajian Island Island School.

After the students answered, the teacher explained as follows:

The distance between a point representing a number on the number axis and the origin is only related to the length of the point from the origin, and has nothing to do with the positive or negative of the number it represents;

Generally speaking, the distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.

For example, the above question |20|=20, |- 10 | = 10. Obviously, in the example of |0|=0, the first question is a quantity with opposite meaning, with positive and negative numbers.

Numbers indicate that the answer to the latter question has nothing to do with symbols, which shows that there are some problems in real life. People only need to know their specific values without paying attention to their meanings, so as to prepare for introducing the concept of absolute value and make students feel better.

Test the connection between mathematics knowledge and real life.