Excellent teaching plan design
First, the teaching objectives
1, knowledge goal: master the three elements of number axis and draw number axis.
2. Ability goal: to be able to represent known numbers on the number axis, to say the numbers represented by points on the number axis, and to know that rational numbers can be represented by points on the number axis;
3. Emotional goal: Infiltrate the idea of combining numbers and shapes into students.
Second, the difficulties in teaching
Teaching emphasis: three elements of the number axis and expressing rational numbers with points on the number axis.
Teaching difficulties: the corresponding relationship between rational numbers and points on the number axis.
Third, teaching methods.
Heuristic teaching is mainly used to guide students to explore, observe, compare and communicate independently.
Fourth, the teaching process
(A) create a situation to activate thinking
1. Students watch the related background video of Zhongxiang No.2 Middle School.
Intention: attract students' attention and stimulate their pride.
2. Contact with reality and ask questions.
Question 1: 75 meters south of the gate of Zhongxiang No.2 Middle School is Zhongxiang Statistics Bureau, 100 meters is China Construction Bank, 75 meters north of her is Haiyun Art School, and 200 meters is Zhong Bai Warehouse. Please draw this scene.
Teacher-student activities: students think and solve problems, and students represent drawing and demonstrating.
Students ask questions after drawing:
1. What geometry does the road represent? (straight line)
2. What are the expressions in the relevant places in the text? (Point on a straight line)
3. What does the school gate do? (Datum point, reference object)
4. How do you determine the position of each point in the question? (direction and distance)
Design intention: The "three elements" are directional, and the practical problems are represented by geometric symbols such as straight lines, points, directions and distances. This is the first mathematical abstraction of practical problems.
Question 2: In the above question, "South" and "North" have opposite meanings. We know that positive and negative numbers can represent two quantities with opposite meanings. Can you directly use numbers to express the relative position relationship between these geographical locations and the school gate?
Teacher-student activities:
Students think and answer the solution. Students draw pictures on their behalf.
Students ask questions after drawing:
What does 1.0 stand for?
2. What is the practical significance of the symbols of numbers?
3. What does-75 mean? What does 100 mean?
Design intention: continue to take the three elements as the guide, use numbers to represent points, realize secondary abstraction, and provide an intuitive basis for defining the concept of number axis.
Question 3: A common thermometer in life, can you describe its structure?
Design intention: With the help of common tools in life, explain the function of positive and negative numbers, guide students to express with three elements, and provide an intuitive basis for defining the concept of number axis.
Question 4: Can you talk about the similarities between the above two examples?
Design intention: further clarify the meaning of "three elements", understand the thinking methods of "using points to represent numbers" and "using numbers to represent points", and provide another intuitive basis for defining the concept of number axis.
(B) independent learning, exploring new knowledge
Student activities: self-study textbook page 8, with the following questions:
1. What kind of straight line is the number axis? What conditions does it have?
2. How to draw a number axis?
3. According to the experience of the above examples, what role does the "origin" play?
4. How to understand "choose the appropriate length as the unit length"?
Teacher-student activities:
After students learn by themselves, please draw a number axis on the blackboard on their behalf and explain the general steps of drawing a number axis.
Design intention: Make clear the steps of drawing the number axis, make the three elements of the number axis leave a deeper impression on students' minds, and get the definition of the number axis at the same time.
At this point, students have been able to draw several coordinate axes, and teachers and students have the same induction and summary (blackboard writing)
① Definition of number axis.
② Three elements of number axis.
Exercise: (Media Presentation)
1. Determine whether the following figure is a number axis.
2. Oral answer: the number represented by each point on the number axis.
3. Draw the following points on the number axis: 1.5, -2, -2.5, 2, 2.5, 0,-1.5.
(3) Group cooperation, exchange and exhibition
Question: Look at the points on the number axis. What did you find?
On which side of the origin is the point representing 3 on the number axis? How many unit lengths is the distance from the origin? On which side of the origin is the point representing -2? How many unit lengths is the distance from the origin? Let a be a positive number, and discuss the points representing a and -a in the same way.
Design intention: Summarize the characteristics of different points on the number axis by the method from special to general, and cultivate students' abstract generalization ability.
(d) induction, reflection and improvement
Teachers and students review the main contents of this lesson and answer the following questions:
1. What is a number axis?
2. What do you mean by the "three elements" of the number axis?
3. Drawing of several axes.
Design intention: to sort out the content of this lesson and master the "three elements" of the number axis, the core of this lesson.
(5) Target detection design
1. The following statement is true ()
A. All points on the number axis represent integers.
B. The points representing 4 and -4 on the number axis are on both sides of the origin, and the distance from the origin is equal to 4 unit lengths.
C. the number axis includes two elements: the origin and the positive direction.
D. Points on the number axis can only represent positive numbers and zeros.
2. Draw a number axis, mark all the integers between -5 and +5 on the number axis, and list all the integers whose distance to the origin is less than 3.
3. Draw the number axis, which means that there are _ _ _ _ _ points on the left side of the origin when observing the number axis among the following rational points. 4. On the number axis, point A stands for -4. If the origin o moves 1.5 units in the negative direction, then the number represented by point A on the new number axis is _ _ _ _ _ _ _.
Five, blackboard writing
The definition of 1. number axis.
2. Three elements of the number axis (figure).
3. Drawing of several axes.
4. nature
Sixth, after-class reflection
Attachment: list of activities
Activity 1: Draw a picture.
Seventy-five meters to the south of Zhongxiang No.2 Middle School is Zhongxiang Municipal Bureau of Statistics, 100 meters is China Construction Bank, 75 meters to the north is Haiyun Art School, and 200 meters is Zhong Bai Warehouse. Please draw this scene.
Thinking: How to concisely express the relative position relationship between these geographical locations and school gates with numbers?
Activity 2: Reading.
Read the P8 page of the textbook with the following questions:
1. What kind of straight line is the number axis?
Definition: A straight line is defined as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Three elements of the number axis: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
2. What are the steps to draw a number axis?
3. What does "Origin" do? __________
4. How to understand "choose the appropriate length as the unit length"?
Exercise:
Draw a number axis.
2. Represent the following rational numbers on the axis you draw: 1.5, -2, -2.5, 2, 2.5, 0,-1.5.
Activity 3: Discussion.
Group discussion: observe the points on the axis you draw. What did you find?
Induction: Generally speaking, if a is a positive number, the number axis indicates that the number A is on the _ _ _ side of the origin, and the distance from the origin is _ _ _ unit lengths; The point representing the number -a is on the _ _ side of the origin, and the distance from the origin is _ _ unit lengths.
Exercise:
1. The point representing -3 on the number axis is on the _ _ _ _ side of the origin, and the distance from the origin is _ _ _ _ _ _; The point representing 6 is on the _ _ _ _ side of the origin, and the distance from the origin is _ _ _ _ _ _; The distance between two points is _ _ _ _ _ unit length.
2. The number represented by a point 5 units away from the origin is _ _ _ _ _ _ _ _.
3. On the number axis, move the point representing 3 along the negative direction of the number axis for 5 unit lengths to reach point B, then the number represented by point B is _ _ _ _ _ _ _.
Attachment: Target detection
1. The following statement is true ()
A. All points on the number axis represent integers.
B the points representing 4 and -4 on the number axis are on both sides of the origin, and the distance from the origin is equal to 4 unit lengths.
C. the number axis includes two elements: the origin and the positive direction.
D. Points on the number axis can only represent positive numbers and zeros.
2. Draw a number axis and mark all the integers between -5 and +5 on the number axis. Lists all integers whose distance from the origin is less than 3.
3. Draw several axes and observe them. There are _ _ _ _ _ points to the left of the origin.
4. On the number axis, point A stands for -4. If the origin o moves 1.5 units in the negative direction, then the number represented by point A on the new number axis is _ _ _ _ _ _ _.
Reference of excellent teachers' teaching plans
First, the analysis of teaching content
1.2 rational number1.2 axis. This section is a very important content in junior high school mathematics. From the perspective of knowledge, the number axis is an important tool for mathematics learning and research. It is mainly used to understand the concept of absolute value, deduce the operation rules of rational numbers and solve inequalities. It is also the basis of learning rectangular coordinate system. In terms of thinking methods, the number axis is the starting point of the combination of numbers and shapes, and the combination of numbers and shapes is an important thinking method for students to understand and learn mathematics well. Measuring temperature with a thermometer is common in daily life, which lays a certain foundation for learning the concept of number axis. It is the main learning method of this lesson to get the concept of number axis through the analogy of problem situations. At the same time, the number axis can display the classification of numbers intuitively, which is the basis for students to understand the classification idea.
Second, the analysis of students' learning situation
(1) In terms of knowledge mastery, grade seven students have just learned the positive and negative numbers in rational numbers, and their understanding of the concept of positive and negative numbers is not necessarily profound. Many students forget knowledge easily, so we should speak it comprehensively and systematically.
(2) Knowledge barriers for students to learn this lesson. It is difficult for students to understand the concept and three elements of the number axis, which easily leads to the phenomenon of drawing falling apart, so teachers should make a simple and clear analysis in teaching;
(3) Due to the understanding ability, thinking characteristics and physiological characteristics of seventh-grade students, students are active, easily distracted, and love to express their opinions, hoping to get praise from teachers. We should grasp this physiological and psychological characteristic of students in teaching, on the one hand, we should use intuitive and vivid images to arouse students' interest and keep their attention focused on the classroom all the time; On the other hand, we should create conditions and opportunities for students to express their opinions and give full play to their initiative.
Third, the design ideas
It is an important principle for us to study new problems from students' existing knowledge and experience. When I was in primary school, I learned to represent numbers by points on the light. To this end, we can guide students to think: how to improve the ray to represent rational numbers? Taking thermometer as a model, the concept of number axis is introduced. In teaching, we should carefully analyze the three elements of the number axis, so that students can rise from intuitive understanding to rational understanding. Straight line and number axis are very abstract mathematical concepts. Of course, beginners should not talk too much, but it is feasible to properly guide students to engage in abstract thinking activities. For example, ask students: Can you draw a point corresponding to one billionth on the number axis? Whether it exists or not.
Fourth, teaching objectives.
Knowledge and skills
1, master the three elements of the number axis and draw the number axis correctly.
2. Can represent the known number on the number axis, and can tell the number represented by the known point on the number axis.
(2) Process and method
1, so as to cultivate students to abstract practical problems into mathematical problems and gradually form the meaning of applied mathematics.
Knowledge.
2. Infiltrate the thinking method of combining numbers and shapes into students.
(3) Emotion, attitude and values
1, let students understand that mathematics comes from practice and in turn serves the dialectical materialist of practice.
Concept of righteousness.
2. By drawing a number of axes, students are educated in the beauty of graphics, and at the same time, due to the combination of numbers and shapes, students will get
Enjoy the beauty of harmony.
V. Teaching Emphasis and Difficulties
1, the key point: correctly master the drawing method of the number axis, and use the points on the number axis to represent rational numbers.
2. Difficulties: the correspondence between rational numbers and points on the number axis.
Sixth, teaching suggestions.
1, analysis of key and difficult points
This section focuses on a preliminary understanding of the thinking method of combining numbers with shapes, correctly mastering the drawing method of the number axis, expressing rational numbers with points on the number axis, and comparing the size of rational numbers. The difficulty lies in correctly understanding the corresponding relationship between rational numbers and points on the number axis. The concept of number axis contains two contents. One is the three elements of the number axis: the origin, the positive direction and the unit length are indispensable, and the other is to stipulate these three elements. In addition, it needs to be clear that all rational numbers can be represented by points on the number axis, but not all numbers represented by points on the number axis are rational numbers. Through learning, students can master the method of solving problems with the number axis, laying a foundation for making full use of the tool of "number axis" in the future.
2. Knowledge structure
With the number axis, number and shape have been preliminarily combined, which is beneficial to the study of mathematical problems. The combination of numbers and shapes is an important way of thinking to understand and learn mathematics well. The main points of this lesson are as follows:
The straight line that defines the origin, positive direction and unit length is called the number axis.
Unit length in the positive direction of the origin of three elements
Apply a combination of numbers and shapes
Seven, learn to guide.
1. Teaching method: According to the principle of taking teachers as the leading factor and students as the main body, the teaching method of "stimulating interest-using hands and brains-enlightening and inducing-feedback and correction" runs through all the time.
2. Students' learning methods: hand drawing and counting axes, brain summarizing the three elements of counting axes, and hand and brain doing exercises.
Eight, class arrangement
1 class hour
Nine, prepare teaching AIDS and learning tools
Computer, projector, triangle board
X. Design of teacher-student interaction activities
Teach a new lesson
(Display projection 1)
Question 1: Three thermometers. A thermometer has two scales above 0, one thermometer has five scales below 0, and the other thermometer has one scale below 0.
Teacher: What are the temperatures indicated by the three thermometers?
Health: 2℃, -5℃, 0℃.
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)
Teacher: Can we use similar graphs to represent rational numbers?
Teacher: This figure representing numbers is what we are going to learn today-number axis (blackboard writing subject).
Teacher: Similar to a thermometer, we can also draw a scale on a straight line and mark the reading.
Numbers, using points on a straight line to represent positive numbers, negative numbers and zeros. The specific method is as follows
(talking and drawing):
1. Draw a horizontal straight line, and take any point on this straight line as the origin (generally take a moderate position, if the required numbers are positive, it can also be left), and use this point to represent 0 (equivalent to 0℃ on the thermometer);
2. If the direction of the origin to the right on the straight line is positive (the direction indicated by the arrow), then the direction of the origin to the left is negative (equivalent to positive above 0℃ and negative below 0℃ on the thermometer);
3. Choose the appropriate length as the unit length. On a straight line, from the origin to the right, take a point every other length unit, which is expressed as 1, 2, 3, … From the origin to the left, take a point every other length unit, which is expressed as-1, -2, -3, …
The teacher asked: Can we use this straight line to represent any rational number? (You can list several figures)
Let the students observe the drawn straight line and think about the following questions:
(Display Projection 2)
(1) What number does the origin represent?
(2) What number does the right side of the origin represent? What number does the left side of the origin represent?
(3) Where is the point representing +2? Where is the point representing-1?
(4) What number does point A, whose origin is 0.5 unit length to the right, represent?
What number does point B with the origin of 65438+ 0.5 unit length to the left represent?
Students think about what to draw on a horizontal straight line according to the teacher's drawing steps. Then summarize the definition of number axis.
Teacher: On this basis, the definition of number axis is given, that is, specifying origin, positive direction and simplex.
The straight line of bit length is called the number axis.
Then ask the students: On the number axis, a point P is known to represent the number -5. If the origin on the number axis is not selected in the original position, but re-selected in another position, is the number corresponding to P still -5? What if the unit length changes? What if the positive direction of the line changes?
Through the above problems, it is pointed out that the three elements of the number axis-origin, positive direction and unit length are indispensable.
Teaching methods show that the formation of knowledge is a process from perceptual knowledge to rational knowledge through "observation-analogy-thinking-generalization-expression", so that students can understand mathematical thoughts and thinking methods in the process of acquiring knowledge and consciously train their ability of induction, generalization and oral expression.
Teachers and students draw the number axis synchronously, students summarize the three elements of the number axis, teachers show the projection and students practice with their hands and brains.
Try to give feedback and consolidate the exercise.
(Show Projection 3). Draw a number axis to represent the following rational numbers:
1、 1.5,-2.2,-2.5,,,0.
2. Write the numbers represented by points A, B, C, D and E on the number axis:
Please answer the following questions:
(Display Projection 4)
(1) Some people say that a straight line is a number axis, right? Why?
(2) Are the following axes drawn correctly? If not, point out what is wrong.
The teaching method shows that the purpose of this group of exercises is to consolidate the concept of number axis.
XI。 abstract
This lesson requires students to master the three elements of the number axis and draw it correctly. Remind students here that all rational numbers can be represented by points on the number axis, and vice versa, that is, not all points on the number axis represent rational numbers. As for which points on the number axis cannot represent rational numbers, this problem will be studied later.
Twelve. Exercise after class 1.2 Question 2
Thirteen, teaching reflection
1, the number axis is an important medium for number-shape conversion and combination. The prototype of situational design comes from real life and is easy for students to experience and accept. Through observation, thinking and hands-on operation, students can experience and appreciate the formation process of number axis, which can deepen their understanding of the concept of number axis and cultivate their ability of abstract generalization, which also reflects 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. Attach importance 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.
Model essay on the design of famous teacher's teaching plan
First, the teaching objectives
Knowledge and skills
Knowing the concept of number axis, rational numbers can be accurately represented by points on the number axis.
Process and method
Through observation and practical operation, we can understand the corresponding relationship between rational numbers and points on the number axis, and realize the idea of combining numbers with shapes.
Emotions, attitudes and values
In the process of combining numbers with shapes, we can experience the fun of mathematics learning.
Second, the difficulties in teaching
Teaching focus
The three elements of the number axis represent rational numbers with points on the number axis.
Teaching difficulties
The thinking method of combining numbers and shapes.
Third, the teaching process
(A) the introduction of new courses
Ask a question: through the example of the meaning of numbers on a thermometer, it is concluded that there is also an axis in mathematics that can be used to represent numbers like a thermometer, which is the number axis we are studying today.
(2) Explore new knowledge
Student activities: group discussion, showing the relationship between poplars, willows and bus stop signs on the east-west road in the form of painting;
Question 1: In the above questions, "east" and "west", "left" and "right" all have opposite meanings. We know that positive and negative numbers can represent quantities with opposite meanings. Then, how to use numbers to represent the relative positions of these trees, telephone poles and bus stop signs?
Student activity: Ask questions after painting a picture.
Question 2: What does "0" stand for? What is the practical significance of the symbols of numbers? Answer the thermometer.
The teacher gave a definition: in mathematics, numbers can be represented by points on a straight line, which is called the number axis, and it meets the following conditions: take any point to represent the number 0, representing the origin; Usually, the right (or up) on a straight line is the positive direction, and the left (or down) from the origin is the negative direction; Select the appropriate length as the unit length.
Question 3: How to understand the three elements of the number axis?
Both teachers and students sum up that the "origin" is the "benchmark" of the number axis, which means 0 and is the dividing point between positive and negative numbers. The positive direction is artificially specified, and the appropriate unit length should be selected according to the actual problem.
(3) Classroom exercises
As shown in the figure, write the numbers represented by points A, B, C, D and E on the number axis.
(4) Summarize the homework
Question: What did you get today?
Guide the students to review: the three elements of the number axis, and use the number axis to represent the number.
Homework after class:
Practice the second question after class; Thinking: What are the characteristics of two points with the same distance from the origin?
Articles related to the excellent teaching plan design of mathematics in the seventh grade of junior high school;
1. Model essay on teaching plan design for junior high school math teachers
2. Five high-quality model essays of Algebraic Formula, the first volume of mathematics in the seventh grade.
3. Excellent teaching plan design template for junior high school mathematics
4. The complete set of teaching plans in the second volume of seventh grade mathematics published by People's Education Press.
5. Excellent number axis teaching plan model template of junior high school mathematics
6. People's Education Edition seventh grade mathematics teaching plan book.
7. The seventh grade mathematics "Algebraic" teaching plan design encyclopedia.
8. Fan Wenxuan's five rational numbers, the first volume of junior one mathematics.
9. The first volume of the seventh grade mathematics "Geometry" excellent teaching plan model article 5.
10. Five high-quality model essays on real numbers in the second volume of the seventh grade of junior high school.