Positive and negative numbers teaching plan (1) teaching content: the first chapter of rational numbers (1. 1) in the seventh grade of People's Education Press.
Teaching objectives:
In familiar life situations, positive numbers and negative numbers can be used to represent quantities with opposite meanings in life, while if you can write and read negative numbers, you will use negative numbers to represent some quantities in daily life.
Make students experience the process of mathematicization and symbolization and realize the necessity of negative numbers.
Feel the close relationship between positive and negative numbers and life, and enjoy the fun of creative learning.
Teaching emphasis: understand the meaning of negative numbers, and learn to use positive numbers and negative numbers to represent quantities with opposite meanings in daily life.
Difficulties in teaching: Understand the meaning of negative numbers, and understand positive numbers, negative numbers and "0" through descriptive definitions.
Teaching process:
Feel the quantity in the opposite direction first and experience the process of negative number generation.
1, recall those numbers learned in primary school: natural numbers, fractional presentation information: look at the generation process of numbers and the necessity of learning negative numbers in reality.
2. Introduce the concept of negative numbers.
3. Add positive and negative numbers.
(1) These numbers are very special. All signed. They are a "new number". -9, -4.5 and so on. Are all negative numbers; +7 and +988 are both positive numbers. Can you read? Please read it to everyone. Note that "-"is a negative sign and "+"is a positive sign.
(2) Read it to your partner.
(3) Write two more negative numbers you know recently and read them out.
Let's go into the world of positive numbers and negative numbers and learn more about them. (blackboard writing topic)
Second, with the help of intuition in real life situations, we can enrich our understanding of positive and negative numbers.
What is the use of 1 and negative numbers? Use positive or negative numbers to represent the following quantities. (1 Go east for 200m, which is indicated by+200m; Then walk 200 meters west.
2. Talk about the determination of negative numbers in practical problems.
(1.) indicates the altitude.
(2) Explain the meaning of positive and negative numbers in temperature.
(3) Do Exercise 3
3. How to understand the quantity with opposite meaning?
Third, understanding 0
1, 0 is neither positive nor negative. 0 is the boundary between positive and negative numbers.
2,0 only means no?
1). The number of gold coins in an empty can;
2) The temperature is 0℃;
3). The height of sea level;
4). Standard water level;
5). Benchmark of height comparison;
6.) the dividing point between positive and negative numbers;
3. Summary
0 is neither positive nor negative; 0 is the boundary between positive and negative numbers.
0 is an integer, 0 is an even number and 0 is the smallest natural number.
Fourth, inquiry activities (show courseware):
1. Inquiry activity 1: Things are two opposite directions. If -4m means that the object moves 4m to the west, what does +2m mean? Objects stay in their original positions. Why?
If 28 counts as 0, 27 can count as-1. Guess if 27 counts as 0, 28 should count as 0.
2. Inquiry activity 2: A building has 20 floors above ground and 5 floors underground. If positive numbers and negative numbers are used to indicate the floor number of each floor of this building, the highest floor on the ground is expressed as, and the lowest floor underground is expressed as, someone takes the elevator from the lowest floor underground to the sixth floor on the ground, and the elevator runs one floor.
3. Inquiry Activity 3: Use positive numbers and negative numbers to represent quantities with opposite meanings, of which the correct one is ().
A. According to the statistics of the major retail businesses of the 20xx Fortune 500, the annual income of Rong Da Company is below $2,532,065,438+0,000, the profit is-654,38+0,952,000 and the loss is $654,38+0,952,000.
B. If +9.6 means 9.6m above sea level, then-19.2m means-19.2m below sea level.
C, income 30 yuan and 2 meters is the opposite amount.
D The temperature is -4℃ in the morning and 4℃ higher at noon, so the temperature at noon is +4℃. Income and expenditure are opposite quantities.
F, if the income increase 18 yuan is recorded as+18 yuan, then -50 yuan means that the expenditure decreases by 50 yuan.
5. Inquiry Activity 4: If a number is represented by letters, what kind of number might A be? Must it be a positive number?
A: Not necessarily. A can be positive, negative or 0.
Exploration and reflection on verb (abbreviation of verb);
1, for example 1: One month, Xiaoming gained -2kg, Xiaohua lost-1kg, and Xiao Qiang's weight did not change. Write down their weight gain this month;
2. Example 2-1 small integers are arranged as follows.
The first, second, third and fourth columns.
-2 -3 -4 -5
-9 -8 -7 -6
- 10 - 1 1 - 12 - 13
- 17 - 16 - 15 - 14
............
In the numbers above, observe their laws. What column will the answer number-100 be in?
3. Example 3
The changes of the total import and export volume of countries under 20xx compared with the previous year are as follows: the United States decreased by 6.4%, Germany increased by 1.3%, France decreased by 2.4%, Britain decreased by 3.5%, Italy increased by 0.2% and China increased by 7.5%. Write the growth rate of total import and export of these countries as 20xx.
Thinking: negative and positive, increasing -2 means decreasing 2; Growth-1, what do you mean? When will the growth be zero?
Application and improvement of intransitive verb
1. There is a batch of canned food, the standard quality is 500g per can, and samples from 10 can are taken for testing. The results are as follows. (Unit: gram)
Quality 497 501503 498 496 495 500 499 501505.
The quality error is as follows:
If the label of cans is marked "mass: 500g", are there any unqualified cans?
Seven, classroom exercises
1, the correct number in the following statement is ()
1), the number with positive sign is positive, and the number with negative sign is negative.
2) Any positive number starting with "-"is negative.
30, 0 is the smallest positive number,
4) Numbers greater than 0 are positive numbers.
5) The letter A is both positive and negative.
A.0 B. 1 C.2. D.3
judge
(1)0 is an integer ()
(2) Natural numbers must be integers ()
3)0 must be a positive integer ()
(4) Integer must be a natural number ()
3. Explain the meaning of the following words:
① Temperature rise +3℃ ② Temperature drop +3℃
③ Income +4.25 Yuan ④ Expenditure -4.2 yuan
4. What does the sentence "Xiaoming's score in this math exam dropped by -20 points" mean?
5. What is the practical significance of1)+5m, -6m and 0m?
(2) A cement factory plans to produce cement 1 0,000 t per month, and the actual production in 1 month is 950t, the production in February is 1 0,000 t, and the production in March is 1 654,38+0,000 t.. What are the positive and negative numbers of tonnage exceeding the planned monthly quota?
Eight, class summary:
1. positive number: among the previously learned numbers, numbers other than 0 are called positive numbers; Such as: +5,+0.23,8818.
2. Negative numbers: numbers with a "-"sign in front of positive numbers are called negative numbers; For example: -5, -0.54,
3,0 is neither positive nor negative.
The "+"and "-"signs in front of a number are called its symbols.
5. In the same problem, positive numbers and negative numbers are used to represent quantities with opposite meanings.
Attached book:
Positive and negative numbers
Positive number > 0> negative number
+is neither a positive number-
A plus sign is not a minus sign.
Reflection after class:
This lesson is to let students understand the meaning of positive and negative numbers in real situations, and will use positive and negative numbers to describe the quantities with opposite meanings in daily life.
1, exercises close to real life, to promote students' effective use of what they have learned, such as "analyzing quality problems and temperature problems." "Survey Weight" makes students realize that mathematics comes from life and is applied to life, so that students can feel the function and intimacy of mathematics.
2. This course can use information technology to create situations and stimulate students' interest in learning. String the three key words of temperature, revenue and expenditure and altitude with a relatively complete thing. In this way, students will be more interested in what they have learned.
3. This course can also use information technology to understand the relative meaning of quantity. For example, show photos of Mount Everest and Turpan Basin. Compared with the sea level, one is high and the other is low. These are relative quantities. With these images, it is more conducive to students' understanding of relative meaning.
4. Integrate various learning methods to promote effective teaching.
Guiding students to explore and learn independently, giving students enough time to try and exchange methods, and allowing students to analyze and solve problems from different angles, so as to realize the exchange of ideas among students, brainstorm, find answers and solve problems, which embodies the diversification and individualization of students' thinking in solving mathematical problems. In addition, in classroom teaching, we should strive to achieve: teacher-student interaction, student-student interaction, classroom communication, and study together.
5. In the teaching of this class, there are still many shortcomings, such as how to better arrange time and apply knowledge to practice. ""When communicating, how to choose individual communication and collective communication? How can the teacher's evaluation be more in place? "I think these are the directions of my future efforts.
Teaching objectives of "positive and negative teaching plans" (2)
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
Design concept (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 examples are 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, my height is 1.73m, my weight is 58.5kg, and I am 40 years old. 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: thinking and communication
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, citing some quantities with opposite meanings in real life, it shows that in order to express quantities with opposite meanings, it is necessary to introduce negative numbers, which emphasizes the rigor of mathematics, but for students, mathematics is boring. In order to review the numbers learned in primary school and stimulate students' interest in learning, we create the following question situations. 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
Course summary
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. Positive numbers are numbers other than 0 (or "+"before them), and negative numbers are "-"before ` numbers other than 0.
Exercise1.1.1.1.2,4,5 (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.
Comments on this lesson (classroom design concept, actual teaching effect and improvement ideas)
Closely connect with real life and create learning situations. This lesson is the first lesson of rational numbers. The introduction of negative numbers is an important extension of the range of logarithms, and the structure of numbers in students' minds needs to be greatly adjusted (in fact, it is a process of knowledge adaptation), and 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, 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 number in the examples or pictures in the book is to let 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.
"Positive and negative lesson plans" Chapter III I. Knowledge and skills
Further consolidate the concepts of positive and negative numbers; Understand that in the same problem, the quantities represented by positive numbers and negative numbers have the same meaning.
Two. Process and method
By analogy, positive numbers and negative numbers are used to represent quantities with opposite meanings around them, and then they are found to have the same characteristics.
Three. Emotional attitudes and values
Encourage students to think positively and stimulate their interest in learning.
Emphasis, Difficulties and Keys in Teaching
1. key point: correctly understand the concepts of positive and negative numbers, and be able to use positive and negative numbers to represent quantities with opposite meanings in life.
2. Difficulties: the comprehensive application of the concepts of positive and negative numbers.
3. Key points: Through the further analysis of examples, students can realize that positive numbers and negative numbers can be used to represent quantities with opposite meanings in real life.
training/teaching aid
projector
teaching process
Fourth, review the introduction of questioning class
1. What is a positive number? What is a negative number? For example, are there any numbers that are neither positive nor negative?
2. If a positive number means a profit of 50,000 yuan, what does-8,000 yuan mean?
Verb (abbreviation for verb) newly granted
Example 1. In a month, Xiaoming gained 2 Jin, Xiaohua lost 1 Jin, and Xiao Qiang's weight remained unchanged. Write down their weight gain this month.
2.20xx The changes in the total import and export volume of countries below XX over the previous year are as follows:
The United States decreased by 6.4%, Germany increased by 1.3%, France decreased by 2.4%, Britain decreased by 3.5%, Italy increased by 0.2% and China increased by 7.5%.
Write the growth rate of total import and export of these countries as 20xx.
Analysis: add a negative sign before the number to indicate the number with the opposite meaning to the original number. Negative and negative are only relative, increasing-1 means decreasing1; An increase of -6.4% means a decrease of 6.4%, so under what circumstances is the growth rate zero? When it was the same as last year, the growth rate was 0.
Solution: 1 Xiaoming gained 2 Jin this month, Xiaohua gained-1 Jin, and Xiao Qiang gained 0 Jin.
The growth rate of the total import and export volume of the six countries in 2.20xx is as follows:
USA -6.4%, German 1.3%, French -2.4%, British -3.5%, Italian-0.2% and China-7.5%.
Induction: In the same question, positive numbers and negative numbers have opposite meanings. For example, a profit of-2,000 yuan means a loss of 2,000 yuan; -3 meters forward means 3 meters backward; Waste-14 yuan means saving 14 yuan; Going south -7 meters means going north-7 meters, so making a profit of 2,000 yuan and making a profit of-2,000 yuan have opposite meanings.
Sixth, consolidate practice.
1. The eighth question on the fifth page of the textbook.
Hugging: an increase of -3.4% means a decrease of 3.4%, so in this year, the service exports of China and Italy increased, while those of the United States, Germany, Britain and Japan all decreased, with Italy increasing the most and Japan decreasing the most.
2. supplementary exercises.
If you go west10m, mark it as-10/0m. If a person walks 12 meters from A and then walks-15 meters, can you tell where this person is at the moment?
Solution: If you go west 10 meter, record it as-10 meter. Then this person goes east 12 meters, and then goes west-15 meters, which means that this person goes east from A by 65,438 meters.
Seven. Course summary
Through the study of this lesson, do you have a further understanding of the concepts of positive numbers and negative numbers? Please use positive and negative numbers to indicate the quantity with opposite numbers around you.
Eight, homework arrangement
Exercise 1. 1, questions 4, 5, 6 and 7 on page 5 of the textbook.
Nine, blackboard writing design
Positive and negative numbers
"Positive and Negative Teaching Plans" Chapter 4 Learning Objectives
1, understand that negative numbers are generated from actual needs;
2, can judge whether a number is positive or negative, and understand the meaning of the quantity represented by the number 0;
3. In practical problems, positive numbers and negative numbers are used to represent quantities with opposite meanings.
Important and difficult
Key point: The concepts of positive and negative numbers are quantities with opposite meanings.
Difficulties: Understand the concept of negative numbers and the meaning of the quantity represented by the number 0.
teaching process
A Review of Teacher-student Activity Time
First, the introduction of new courses.
Let me introduce myself to my classmates first. My family name is. You can call me teacher. I am meters tall and weigh kilograms. I am 10 years old this year, and my teaching experience is old. I will spend three years in junior high school with my classmates.
Some figures appeared in the teacher's introduction just now. What are they?
[Projection 1 ~ 3: Figure 1. 1- 1] Through counting and sorting, people have produced 1, 2, 3 and other integers. In order to express "none" and "vacancy", the number 0 is introduced; Measurement and distribution sometimes produce fractions and decimals without integer results. Therefore, figures come from people's actual production and living needs.
Are only integers and fractions enough in life?
Second, new funding.
1, self-study chapter, page 2, answer the following questions.
Numbers -3, 3, 2, -2, 0, 1.8%, -2.7%. What are the differences between these numbers and those learned before?
What is a positive number and what is a negative number?
Summary: Numbers greater than zero, such as 3, 2, and 2.7%, are called positive numbers, and numbers preceded by a negative sign "-",such as -3, -2, and 2.7%, are called negative numbers. If necessary, sometimes a plus sign is added before the positive number, such as +2, +0.5 and +65438.
In this way, a number consists of two parts, the+and-symbols in front of the number are called its symbols, and the latter part is called the absolute value of the number.
As shown in Figure -3.2, the symbol is "one", the absolute value is 3.2, and the symbol of the number 5 is "+",and the absolute value is 5.
2. Teach yourself page 23 and answer the following questions.
Numbers greater than zero are called positive numbers, and numbers preceded by a negative sign "-"are called negative numbers. What is 0?
What's the point of 0?
Summary: The number 0 is neither positive nor negative, it is the dividing line between positive and negative numbers.
The meaning of 0 is not only "nothing", but also a definite quantity.
3. Using positive numbers and negative numbers to represent quantities with opposite meanings: self-study textbook 34 pages.
What are the quantities with opposite meanings?
Please say what you know with opposite meaning.
What are the characteristics of "quantities with opposite meanings"?
Summary: first, the meaning is opposite, and second, it is quantitative, and it is the same kind.
Complete the exercise on 3 pages.
Step 4: Example
Teach yourself examples and complete the induction. Looking for a problem.
Complete the 4-page exercise
Third, classroom standard exercises
Exercise on page five of the textbook 1, 2, 3, 4, 7, 8.
Fourth, class summary.
1. What kinds of numbers have we learned so far?
2. What are positive numbers and negative numbers? Does zero just mean "nothing"?
3. Positive numbers and negative numbers originated from quantities representing two opposite meanings, and were later widely used in many aspects. Clear goals.