Theoretical support
The introduction of negative numbers is an important expansion of the range of logarithms, which is a practical need and also the need to learn the follow-up teaching content. The structure of numbers in students' minds needs to be greatly adjusted (in fact, it is a process of knowledge adaptation). Negative numbers are more abstract to students than previous numbers, so this concept cannot be established at once. In order to accept this new number, the original structure of the number must be sorted out, and the example of introducing passbook is for this purpose.
Mathematics Curriculum Standard points out: "Mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. "This lesson is based on students' learning positive numbers, that is, positive integers, positive fractions, zeros and the operations of these numbers. According to the age characteristics and psychological characteristics of grade seven students, students have a strong perceptual cognitive foundation and are very interested in some specific practical activities. They are lively, quick-thinking and expressive, but their thinking is not comprehensive.
"Mathematics Curriculum Standard" points out: "Students' mathematics learning content should be realistic, meaningful and challenging". The main reason for negative numbers is that the original numbers are not enough (numbers cannot be expressed correctly and concisely), and the negative numbers in books or pictures are just to make students feel and experience this. It is the teaching difficulty of this course to make students accept that there are two opposite meanings in life and production. Therefore, we can give more examples in this respect in teaching, and the examples should be in line with 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).
"Mathematics Curriculum Standard" points out: "The evaluation of students' mathematics learning should not only pay attention to the results of students' learning, but also pay attention to the changes and development of students in the learning process; We should not only pay attention to students' mathematics learning level, but also pay attention to their emotions and attitudes in mathematics practice. "Therefore, the teaching design of this course 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, encouraged to discuss and communicate, and teachers should give appropriate guidance.
Teaching objectives
Knowledge and skills: 1. Understand how positive and negative numbers are generated;
2. Know what is positive and what is negative;
3. Understand the meaning of the quantity represented by the number 0.
Mathematical thinking: a symbolic method of understanding mathematical symbols and corresponding ideas and expressing quantities with opposite meanings with positive and negative numbers.
Problem solving: positive numbers and negative numbers will be used to represent quantities with opposite meanings.
Emotional attitude: through the cooperation between teachers and students, linking with reality, stimulate students' enthusiasm for learning mathematics well.
Emphasis and difficulty in teaching
1. key: know what positive and negative numbers are and understand the meaning of the quantity represented by the number 0.
2. Difficulties: quantitative elements with opposite meanings.
Class arrangement
One class hour
Teaching design
Extension before class
Fill in the blanks with basic knowledge and answer.
1. Which of the following numbers are positive and which are negative?
-3,0,-0.45,+ 12 1,4,-67,π.
2. Fill in the blanks:
(1) If the length of bicycle batten is 2 cm longer than the standard length, it will be marked as +2 cm, and if it is shorter than the standard length, it will be marked as1.5cm..
(2) If saving 16 tons of water is recorded as+16 tons, then wasting 6 tons of water is recorded as.
(3) If walking 5000m to the south is-5000m, then walking 8000m to the north is.
(4) If the income 15 yuan is recorded as+15 yuan, the expenditure is recorded as 20 yuan.
[Answer] 1. Positive numbers:+12 1, 4, π; ? Negative numbers: -3, -0.45, -67.
2. (1)-1.5cm.
②-6 tons.
(3)+8000m。
(4)-20 yuan.
[Design Description] Preview is not only helpful for students to learn new lessons by themselves before the teacher gives a lecture, but also helps students to improve the efficiency of attending classes and change passive learning into active learning.
Classroom investigation
First, introduce the new course:
Teacher: Students, today we are Grade 7 students, and I am your math teacher. Let me introduce myself to you first. My name is XXX, my height is1.59m, my weight is 50.5kg, and I am 33 years old. Our class is Class 7 (2), with 50 students, including 27 boys, accounting for 54% of the class.
Question: What data appeared in the teacher's introduction just now? Can you classify these figures?
Student activities: thinking and communication
Teacher: In fact, there are two main categories of numbers learned before, namely integers and fractions (including decimals).
[Design Description] This problem situation created in the teaching process comes from real life. Students have a deep understanding, which can stimulate students' interest in learning mathematics and is also of great significance to improve students' mathematical literacy and consciousness. First of all, let's review the types of numbers we learned in primary school and summarize the integers and fractions we have learned. Then, we cite some quantities with opposite meanings in real life, explaining that in order to express quantities with opposite meanings, we need to introduce negative numbers. This emphasizes the rigor of mathematics, but for students, mathematics is more boring. In order to review the numbers learned in primary school and stimulate students' interest in learning, create the following question situations, which are as close to students' reality as possible.
Second, explore new knowledge.
1. Question: In life, we will encounter the following figures. Please observe the figures used to show the goods, think about the similarities and differences with the data you have learned before, and then communicate. (you can also display the temperature map in the weather forecast, the topographic map showing the terrain, the record page of deposit and withdrawal in the salary card, etc.). ).
After the students exchange.
The teacher concluded: In the previous study, we found that the numbers we had learned were not enough, and a new number with "-"appeared.
2. Reveal the topic, organize the concept and write on the blackboard.
Subject: Positive and Negative Numbers
[Design Description] Grade seven students are cheerful and lively, especially sensitive to new things and easy to accept, which can increase their enthusiasm for exploring new knowledge. The above situations and examples make students realize that there is mathematics everywhere in their lives. Through examples, students can get a lot of perceptual materials, which makes them feel the necessity of learning negative numbers and lays the foundation for correctly establishing quantities with opposite meanings.
3. Arrange students to study by themselves:
Question: 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?
Teacher-student communication.
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.
[Design Description] These questions are the main knowledge of this lesson. Teachers should explain clearly 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.
Activity: Ask students to cite a large number of examples in life to illustrate positive and negative numbers.
4. Emphasize the meaning of the number 0:
The number 0 not only means no, but also a quantity. For example, 0℃ means no, which is also an exact temperature, and 0 meters above sea level means the average altitude, and so on.
Let the students give examples to deepen their understanding.
Third, form new knowledge.
(1) Fill in the blanks:
If the drop of 5 meters is -5 meters, then record the rise of 8 meters, and record it without rising or falling.
On the basis of reading and understanding positive and negative numbers, students can try to solve simple fill-in-the-blank problems with concepts first. This can easily attract students' intentional attention and actively standardize the writing format.
[Reference Answer]+8m, 0m.
(2) When the temperature is -3℃ in the morning and rises by 2℃ at noon, the temperature at noon is _ _ _ _ _ _ _ _
[Reference Answer]-1.
(3) Please give the practical meaning of +5 and -5? .
[Reference Answer] The answer is not unique.
Design Description: On the basis of students' full understanding of "positive and negative numbers", through independent inquiry, they can further understand the practical significance of "positive and negative numbers" and the matters needing attention when expressing them.
Fourth, consolidate new knowledge:
(1) The following statement is true (? )
"Black" and "white" are quantities with opposite meanings.
"Fast" and "slow" are quantities with opposite meanings.
C "Go 4.5 meters north" and "Go 8 meters south" are quantities with opposite meanings.
D. "+15m" means going east15m.
[reference answer] C.
(2) The statement of "0" is correct ()
10 is the boundary between positive and negative numbers; ○20℃ is the determined temperature; 30 is a positive number; 40 is a natural number; ○5 There is no number that is neither correct nor irresponsible; 60 is not a negative number.
A.3？ B. 4 C. 5 D. 2
Friendly reminder 0 is the smallest natural number.
[reference answer] B.
(3) One day, Xiaohua was walking on an east-west expressway. He started from home. If he records 350 meters eastward as +350 meters, what does he mean by going back 280 meters? At this time, he stopped to have a rest. Where is his family's resting place? How far is it from home? How many meters did Xiaohua walk?
[Reference Answer] Walked 280 meters to the west; East; 70 meters; 630 meters.
Pointing method: the combination of numbers and shapes is to understand the mathematical characteristics of the research object and find the mathematical thought to solve the problem according to the relationship between numbers and shapes. Usually, when applying the combination of number and shape to solve problems, we often focus on the function of "shape" on "number", that is, we often use the intuition of graphics to solve some mathematical problems. For the cognitive level of junior one students, the combination of numbers and shapes can more intuitively reflect the relationship between numbers.
Fifth, classroom feedback training.
1. Write three negative numbers as _ _ _ _ _ _ _ _ _ _ _.
[Reference Answer] The answer is not unique.
2. The following figures are known:-? , -,3. 14, +3065, 0,-239. Then a positive number has _ _ _ _ _ _ _ _ _ _ _ _; The negative number is _ _ _ _ _ _ _ _ _ _ _ _.
[Reference answer] Positive number: 3. 14,+3065; Negative number:-? ,- ,-239.
3. The diameter of a part on the drawing is mm, which means the standard size of this part? ____mm, the maximum processing requirements cannot exceed? Mm, the minimum can not be less than mm.
[Reference Answer] 10,? 10.05 , ? 9.95.
Pointing method is to use positive and negative numbers to represent quantities with opposite meanings, so it is necessary to first determine a standard record as 0, and then use positive and negative numbers to represent quantities with opposite meanings.
The practical significance of Xiao Wang's annual profit of-5,000 yuan when he goes out for business lies in:
[Reference Answer] The answer is not unique.
The positive and negative meanings of the opposite meaning of dialing methods are relative and interchangeable. For example, if the loss of 30,000 yuan is recorded as+30,000 yuan and the profit of 50,000 yuan is recorded as-50,000 yuan.
5. The following statement: ○ 1 Numbers without "-"sign are all positive numbers; ○20℃ means no temperature; ○3 Numbers without "+"sign are all negative numbers; ○4 There is no number that is neither correct nor irresponsible; ○5 A number is either positive or negative; ○6 The numbers learned in primary school mathematics can be regarded as positive numbers. Among them, the correct one is ().
A.0 B. 1 C.2 D.3
[reference answer] a.
Judging the number by dialing mode can be classified and discussed from three aspects: positive number, zero number and negative number, with special attention to 0, which is a special number.
6. Use positive numbers and negative numbers to represent the following quantities with opposite meanings.
(1) 200m east and 200m west;
(2) 3000 boxes of oranges were imported and 5000 boxes of oranges were exported;
(3) Turn 5 times clockwise and 3 times counterclockwise;
(4) 800 meters above sea level, 200 meters above sea level.
[reference answer] (1)+200m; 200 meters. (2)+3000 cases; -5,000 cases.
(3)+5 laps; -Three laps. (4)+800 meters; -200 meters.
7. The monthly profits recorded by the owner of a shopping mall in the first half of this year are as follows: the profits in June, February, March, April, May and June are130,000 yuan,120,000 yuan,150,000 yuan and1250,000 yuan respectively.
[Reference Answer]+1 ten thousand yuan; 00,000 yuan; -0.5 million yuan; +0.5 million yuan; -20,000 yuan; +20,000 yuan.
Promotion after class
First, after-class exercises and answers:
1. The place above sea level 100 meter is marked as altitude _ _ _ _ _ _ _, and the place 80 meters below sea level is marked as altitude? .
[Reference Answer]+100m, -80m.
2. Profit-What is the significance of 300 yuan? .
[Reference Answer] 300 yuan loses money.
3. If the year 1999 is recorded as+1999, then -2008 means.
[Reference Answer] 2008 BC.
4. When the elevator rises 68 meters, it is marked as +68 meters, then -6 meters means 0.0 meters.
The elevator drops 6 meters. 0 means neither rising nor falling.
5. The following statement is true ().
A.60 meters to the south means 60 meters to the west.
B. Saving 50 yuan and wasting -30 yuan are opposite quantities.
C. the number 0 means nothing.
D. the number 0 is neither positive nor negative.
[reference answer] d
6. The time difference between Paris and Beijing is -7 hours (a positive number means that the same moment is several hours earlier than Beijing time). If Beijing time is July 2nd 14: 00, then Paris time is ().
A. July 2 1? B. At 7: 00 on 2 July
C 7: 00 on July 7 1 5: 00 on July 2.
[reference answer] b