Title: 1. 1 positive and negative numbers
Teaching objectives
1, sort out the knowledge of integers and fractions (including decimals) learned in the previous two sections, and master the concepts of positive numbers 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.
Teaching process (teacher-student activities)
Set the situation
At the beginning of the introduction of the project, the teacher should briefly explain the figures we learned in the first two periods through specific 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 seventh grade students. I am your math teacher. Let me introduce myself to you first. My name is XX, and my height is 1. 73 meters, weighing 58. 5 kg, 40 years old this year. Our class is Class 7 (13), and there are 60 students, including 22 boys, accounting for 37% of the total 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:
Think, communicate
Teacher: Actually, there are two main categories of numbers I have 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 present these questions, so that students can 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, it's all quantity, and it's all 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.
Classroom exercises exercise on page 5 of the textbook.
Summary and homework
The classroom summary revolves around the following two points, in the form of teacher-student communication:
1 0 Because there are quantities with opposite meanings in practical problems, it is necessary to introduce negative numbers, so the range of numbers is expanded;
2. A positive number is a number other than 0 (or the "+"before it), and a negative number is a number other than 0 before it.
Exercise on page 7 of the homework textbook for this lesson 1. 1No。 1, 2, 4, 5 (The third question is the thinking question for next class.
Homework can be set with mandatory questions and multiple-choice questions, reflecting the hierarchy of requirements and meeting the needs of different students. The educational explanation of this lesson (classroom design concept, actual teaching effect and improvement ideas) is closely linked with real life and creates learning situations. This lesson is the first lesson of rational numbers. Attracting negative numbers is an important expansion of the range of logarithms. The structure of numbers in students' minds needs to be greatly adjusted (in fact, it is a process of adapting to knowledge), and negative numbers are more abstract to students than previous numbers, so this concept can not be established at once. In order to accept this new number, it is necessary to sort out the structure of the original number, and the example of lucky is for this purpose.
Negative numbers are mainly caused by insufficient original numbers (numbers cannot be expressed correctly and concisely). The negative numbers in the examples or pictures in the book are just to make students feel and experience this. It is difficult for students to accept that there are two quantities with opposite meanings in life and production. We can give more examples in this respect in teaching, and the examples should conform to the age and thinking characteristics of students. When students accept this fact, it is logical to introduce negative numbers (in order to distinguish these two opposite quantities).
This teaching design highlights the close connection between mathematics and real life, makes students realize the application value of mathematics, and embodies the teaching concept of students' independent learning and cooperative communication. The pictures and examples in the book are common facts in life and production, which are easily accepted by students. Therefore, students should be allowed to read and study independently, discussion and communication should be encouraged, and teachers should also give appropriate guidance.