People's education printing plate seventh grade mathematics first volume teaching plan 1
Subject: 1. 1 positive and negative numbers
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 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 Grade 7 students, and I am your math teacher. Let me introduce myself to you first. My name is XXX, 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.
People's education printing plate seventh grade mathematics first volume teaching plan 2
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 law
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.
People's education printing plate seventh grade mathematics first volume teaching plan 3
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.
Because the geometric meaning of the concept of absolute value is a typical transformation from number to shape.
It is difficult for students to accept the model for the first time. Configure this observation and thinking to prepare for establishing the concept of absolute value.
Cooperation and communication
Explore the example of law 1 and find the absolute value of the following number, and find the absolute value of rational number a.
What are the rules? 、
-3,5,0,+58,0.6
Group discussion and cooperative learning are required.
Teachers guide students to use the meaning of absolute value to find the answer first, then observe the characteristics of the original number and its absolute value, and combine the meaning of the inverse number to finally sum up the law of finding the absolute value (see textbook 15).
Consolidation exercise: textbook 15 page exercise.
Among them, the answer to the question 1 is written directly according to the law, which is the basic training for finding the absolute value; The second problem is to distinguish the concept of reciprocal and absolute value, which requires students' analytical judgment ability. Pay attention to the thoroughness of thinking and let students understand the difference between different statements. The law of finding the absolute value of a number can be regarded as an absolute value summary.
Look at an application, so arrange this example.
Students do what they can, and teachers are only organizers in the teaching process. Based on this concept, this discussion is designed.
Guide the students to look at the pictures on page 16 of the textbook and answer the related questions:
Arrange from low to high 14 temperature;
The number 14 is represented by points on the number axis;
Observe and think: observe the positions of these points on the number axis and think about their relationship with temperature. Do you think two rational numbers can be compared?
How should I compare the sizes of two numbers?
After the students exchanged ideas, the teacher concluded:
14 The order of numbers from left to right is the order of temperature from low to high:
Rational numbers are represented on the number axis, and the order from left to right is from small to large, that is, the number on the left is smaller than the number on the right.
In the above 14 number, select two numbers to compare, and then select two numbers to try. By comparison, we can sum up the comparison rules of rational numbers.
Imagination exercise: imagine that there is a number axis in your mind, and there are two points on the axis, which represent the numbers-100 and -90 respectively. Realize the distance between these two points and the origin (that is, their absolute values) and the relationship between the sizes of these two numbers.
Students are required to have clear graphics in their minds, so that students can realize that all the laws of mathematics come from life and each law has its rationality.
The number in the second point of the size comparison method is difficult for students to master. It is necessary to combine the meaning of absolute value with the number on the number axis, configure imagination exercises, and strengthen the imagination of logarithm and shape.
Classroom exercise example 2, compare the following figures (textbook page 65438 +07)
The process of comparing sizes should be carried out in strict accordance with the rules and pay attention to the writing format.
Exercise:/kloc-exercise on page 0/8
Summary and homework
How to find the absolute value of a number and how to compare the sizes of rational numbers?
The assignment for this lesson is 1, and the required questions are: teaching production book 19 page exercise 1, 2, 4, 5, 6, 10.
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 reasons for scenario creation are as follows: ① It reflects the close connection between mathematical knowledge and real life, so that students can learn.
Obtaining mathematical experience in these familiar daily life situations not only deepens the understanding of absolute value, but also feels learning.
The necessity of learning the concept of absolute value and stimulating learning interest. ② The concept of absolute value of numbers in textbooks is based on geometric meaning.
Meaning to define (its essence is to interpret numbers as forms, which is a difficult point), and then get it through practice and seek rationality.
The law of absolute value of numbers, if the concept of absolute value is given directly, the taste of instilling knowledge is very strong and too abstract.
It is not easy for students to accept.
2. The law of absolute value of a number is actually a direct application of the concept of absolute value, and it also embodies the mathematical idea of classification, so it is very concise and is the focus of teaching directly through examples 1; From the perspective of knowledge development and students' ability training, teachers should pay more attention to the process of students' autonomous learning and inquiry, pay attention to students' thinking, do a good job in teaching organization and guidance, and leave enough space for students.
3. The comparison rule of rational number size is a direct induction of the law of size, among which item (2) is difficult for students to understand and teach.
The meaning and stipulation of absolute value should be combined: "Rational numbers are expressed on the number axis, and the order from left to right is from small to large."
"Grand order" helps students to build a model combining numbers and shapes, that is, "the farther the point to the left on the number axis is from the origin, the smaller the number represented". So I set up imagination exercises.
4. The content of this lesson includes the concept of absolute value, the solution of absolute value of numbers, the comparison law of rational numbers, and teaching.
There is a lot of learning content, which may be difficult for students to accept. It is suggested that the comparison of rational numbers be moved to the next class.
Subject: 1.3. 1 addition of rational numbers (1)
Teaching objective 1 Understand the significance of rational number addition in the realistic background.
2. Experience the process of exploring the law of addition of rational numbers and understand the law of addition of rational numbers.
3, can actively participate in exploring rational number addition.
Activities, and learn to communicate and cooperate with others.
4. Be able to add rational numbers skillfully.
Operation, and can solve simple practical problems.
5. Appropriate infiltration of the idea of classified discussion in teaching.
Addition of Two Different Symbols in Teaching Difficulties
Determination of knowledge key and symbol
Design concept of teaching process (teacher-student activities)
Set the situation
Introduce a practical example of project evaluation, and use positive and negative figures to express the quantity;
In a football match, if the number of goals is positive, the number of goals conceded is calculated.
Is negative, and their sum is called goal difference. If the red team scored 4 goals and lost 2 goals, what is the winning number of the red team? What about the number of goals scored by the blue team?
Teacher: How to add similar rational numbers? this is
What we discussed in this class.
(Show the topic)
Let students feel that the number of addition operations in practical problems may exceed the range of positive numbers and realize the necessity of learning rational number addition.
Sex stimulates students' interest in exploring new knowledge.
parsing problem
Explore new knowledge if the team concedes two goals in the first half of the game, the next game
Three goals were conceded at half-time, so how many winning goals was it? The formula should be
How to go public? If the team scored two goals in the first half and lost three goals in the second half, how to list the formula and seek the winning goal?
(Students think and answer)
Thinking: Please think about it, this team is ok in this game.
What else can happen? Can you list the formulas? Communicate with peers.
After the students communicate with each other, the teacher further guides the students to classify two rational numbers into three situations: two numbers with the same symbol are added, two numbers with different symbols are added, and one number is added to zero.
2. Discuss the addition of rational numbers with the help of the number axis. Idaho (short for Idaho)
When an object moves from left to right, we specify that the left movement is negative, the right movement is positive, the right movement is 5m, and the left movement is 5m, which is-5 m.
(1) (group cooperation) The situation of adding several rational numbers we have obtained is expressed by the direction of movement on the number axis, and the results show its significance.
(2) Exchange reports. (Learning group's report results, the coordinate axis is displayed by the physical projector, and the formula is written on the blackboard by the teacher. )
(3) What should we pay attention to when adding rational numbers? (Symbol, absolute value) Can you sum it up in your own language?
(4) On the basis of students' induction, the teacher shows the addition rule of rational numbers.
Rational number addition rule:
1, two numbers with the same sign are added, the same sign is taken, and the absolute values are added.
2. Add two numbers with different signs with unequal absolute values, take the sign of the addend with larger absolute value, subtract the one with smaller absolute value from the one with larger absolute value, and add the two numbers with opposite numbers to get 0.
3, a number is the same. Add it up, it's still this number. Re-create the football match situation, on the one hand, it echoes and is closely related to the topic, on the other hand, it allows students to
In this case, I feel several different situations of adding rational numbers, and can classify them, infiltrating the idea of classification discussion.
It is estimated that students can get (+)+(+), (+)+( 1), (1)+(+), (1) ten (-), 0+(+), 0+ (1.
, but can't be classified as different with the same number.
There are three kinds of quantity, so teachers are needed here, which reflects the guiding role of teachers.
① Assume that the origin 0 is the starting point of the first movement and the second movement.
The starting point is the end of the first movement. ② If students can't participate in the inquiry well in the study group, they can also refer to "Inquiry" on page 2 1 in the textbook.
③ Let students feel the "mathematical model"
(4) Learn to make friends with peers.
Flow and benefit from communication. Cultivate students' language expression ability
Ability and inductive ability, maybe learn.
Life is not rigorous enough, but it doesn't matter. It is important that you can express your findings in your own language.
The law of
Solve the problem, solve the problem.
Example 1 calculation:
( 1)(-3)+(-9); (2)(-5)+ 13;
(3)0 ten (-7); (4)(-4.7)+3.9.
Teacher, act it out and let the students say the rules on which each step is based.
Ask the students to compare, what are the similarities and differences between the addition of rational numbers and the addition learned in primary school? (For example, the addition calculation of rational numbers should pay attention to the sign, and the sum is not necessarily greater than the addend, and so on. )
In the football round robin, the red team beat the yellow team 4: 1 0, the yellow team beat the blue team, and the blue team beat the red team10. Count the goal difference of each team.
Let the students read, understand the meaning of the problem and think about the solution. Then the students dictate and the teacher writes on the blackboard.
Student activities: Let students talk about examples of rational number addition in life. Note: (1) First determine what kind of addition is used to determine the symbol, and finally calculate the absolute position. (2) Teaching teachers fully embodies the process of examples and requires students to pass in the middle when they first start learning.
The process is complete. (3) It embodies the idea of reduction. (4) Here are two additional questions, if students can skillfully use the rules for calculation.
Broaden students' horizons and let them learn.
Students realize the close relationship between mathematics and life.
Classroom exercises exercise on page 23 of the textbook.
Summary and homework
Class Summary What have you gained from this class? Students, summarize it yourself.
The homework for this class must be done: read pages 20~22, question 3 1, question 1.3, question 1, question 12, question 13.
Comments on this lesson (classroom design concept, actual teaching effect and improvement ideas)
1, in the design of this lesson, pay attention to guide students to participate in the process of exploring and summarizing the law of rational number addition (in their own language).
2. Pay attention to the infiltration of mathematical thinking methods. The infiltration of mathematical thinking methods can not be immediate, nor can it be understood and mastered by students overnight. So this lesson is mainly to let students feel the general methods of studying mathematical problems (classification, analysis, induction, reduction, etc.). For example, when exploring the law of addition, we consciously divide various situations into three categories (same number, different number, one number plus 0). When applying this law, when the sign of sum is determined, the addition of rational numbers is transformed into the addition and subtraction of arithmetic.
3. Pay attention to students' cooperative learning methods, so that students can benefit from cooperation with others, learn to communicate and learn to listen.
Opinions and suggestions of others.
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