Junior high school mathematics teaching design case 1
inverse proportion function
First, teaching material analysis:
The image and properties of inverse proportional function are the review and comparison of the image and properties of positive proportional function, and also the basis for learning quadratic function in the future. The study of this course is a process for students to re-recognize the image and essence of functions. Because it is the first time for junior two students to contact hyperbola, we should pay attention to guiding students to master the characteristics of inverse proportional function images in teaching, so that students can have an intuitive understanding of inverse proportional function.
Second, the analysis of teaching objectives
According to the second curriculum reform? Take students as the main body, enliven the classroom atmosphere and fully mobilize students to participate in the teaching process? The spirit of. In teaching design, I imagine that by using multimedia courseware to create situations, while mastering the knowledge about inverse proportional function, I can stimulate students' interest in learning and desire to explore, and guide students to actively participate in and explore.
Therefore, the teaching goal is determined as: 1. By mastering the concept of inverse proportional function, we can get the analytical formula of inverse proportional function according to the known conditions. Learn to draw the image of inverse proportional function by tracing points; Master the characteristics of the image and the function properties obtained from the function image. 2. Guide students to explore, think and imagine independently in the teaching process, and cultivate students' comprehensive ability of observation, analysis and induction. 3. Cultivate students' spirit of active participation and exploration through learning.
Third, the analysis of teaching priorities and difficulties
The focus of this lesson is to master the definition, image characteristics and properties of inverse proportional function;
The difficulty lies in how to grasp the characteristics and draw the inverse proportional function image accurately.
In order to highlight key points and break through difficulties. I designed and made a multimedia courseware that can dynamically demonstrate function images. Let students operate by themselves, actively participate in and actively explore the properties of functions, and help students intuitively understand the properties of inverse proportional functions.
Fourth, teaching methods.
In view of the characteristics of teaching materials and the age characteristics, psychological characteristics and cognitive level of junior two students, the problem-based teaching method is envisaged.
By asking questions step by step, students are inspired to think deeply, explore actively and acquire knowledge actively. At the same time, pay attention to the connection with students' existing knowledge, reduce the difficulty for students to accept new concepts, and give them enough time to explore independently. Through the guidance of teachers, stimulate and mobilize the enthusiasm of students, let students have more activities and observations in class, take the initiative to participate in the whole teaching activities, and organize students to participate? Discuss, discuss, communicate and summarize? In the process of learning activities, at the same time, in teaching, we also make full use of multimedia teaching to inspire students through activities such as demonstration, operation, observation and practice between teachers and students, so that each student can start, move his mouth, move his eyes and use his brain, and cultivate students' intuitive thinking ability.
V. Guidance on learning methods
This course is based on students. Study? Let students do more and observe more, and help them form an analysis.
Comparative inductive thinking method. Ask the students to compare and discuss. Doing middle school? Improve students' ability to actively acquire new knowledge by using what they have learned. Therefore, in the classroom, we should actively guide students to participate in and cooperate with each other to organize teaching, so that students can truly become the main body of teaching, experience the fun of participation, the joy of success, and perceive the wonders of mathematics.
Sixth, the teaching process.
(1) Review the introduction of the analytic formula of inverse function.
Exercise 1: Write the relationship between the following questions:
(1) The relationship between the perimeter c and the side length a of a square.
(2) In the track and field competition of the sports meeting, the average speed of athlete Xiao Wang is 8m/s, and the relationship between the distance S he runs and the time T he takes.
(3) When the area of a rectangle is 10, the relationship between its length x and width y.
(4) Master Wang wants to produce 100 parts. What is the relationship between his work efficiency X and his working hours T?
Question 1: Please judge which of these relations we wrote are proportional functions.
1 is mainly to review the definition of direct proportional function, and lay a foundation for students to give the definition of inverse proportional function by comparison.
Question 2: Then please take a closer look. Are there any similarities between the other two functions?
The analytical expression of inverse proportional function is derived through question 2, and students are required to compare the judgment of positive proportional function.
The definition of inverse proportional function is not only helpful to review and consolidate old knowledge, but also to cultivate students' comparative inquiry ability.
Example 1: It is known that the variable y is inversely proportional to x, and when x=2, y=9.
(1) Write the resolution function between y and x.
(2) Find the value of y when x=3.5.
(3) When y=5, find the value of x.
Through the study of the example 1, students can master how to find the analytical formula of inverse proportional function according to the known conditions. exist
In the process of solving problems, guide students to use the analytical formula used in finding the positive proportional function? Undetermined coefficient method? Set the inverse proportional function to, and then substitute the corresponding values of x and y to find out the determination of k, and the resolution function is determined.
Classroom exercise: It is known that X is inversely proportional to Y. According to the following conditions, the functional relationship between Y and X can be found.
( 1)x=2，y=3 (2)x=，y=
Through this question, we can give students a simple feedback on how to find the analytical formula of inverse proportional function according to the known conditions.
(2) Inquiry learning 1 function image drawing.
Question 3: How to draw the image of the proportional function?
Review the drawing method of the image of the direct proportional function through question 3, which is mainly divided into three steps: listing, drawing points and connecting lines, laying a foundation for learning the drawing method of the image of the inverse proportional function.
Question 4: How to draw the image of inverse proportional function?
In the teaching process, students can be guided to imitate the drawing method of proportional function images.
The envisaged teaching design is:
(1) Guide the students to draw the image of proportional function by using the method they have learned, discuss and try in groups, and draw the image of function sum by using list method, dot drawing method and connection method;
(2) Teachers' patrol guidance, reflecting some students' typical mistakes in function images with physical projectors, and finding out the mistakes with students and analyzing the reasons;
(3) Then the teacher demonstrates the steps of drawing inverse proportional function images on the blackboard, showing the correct function images and guiding students to observe their image characteristics (hyperbola has two branches).
The second grade students first came into contact with hyperbola, a special function image. Imagine that students may make mistakes in the following links:
(1) in? List? This link
Students can get zero when they get points. Here, students can be guided to draw the conclusion that X cannot be zero by combining algebraic methods. It may also be due to improper selection of points, resulting in incomplete and asymmetric function images. Students should be instructed here that when listing, the value of independent variable X can be selected as a number with equal absolute value and opposite sign, and the corresponding function values with equal absolute value and opposite sign can be obtained accordingly, which can simplify the calculation procedure and facilitate finding points on the coordinate plane.
2 in? Connect? This link
The connection line between points drawn by students may have endpoints and cannot be connected with smooth lines. So it is particularly important to emphasize here that when connecting the selected points, it should be? Smooth curve? And lay a foundation for learning the image of quadratic function in the future. In order to make the function image clear and obvious, students can be guided to choose the value of independent variable X and the corresponding function value Y as much as possible, so as to get more on the coordinate plane. Point? Draw a curve.
So as to guide students to draw correct function images.
(3) The image intersects with the X axis or the Y axis.
Here I think we can bury a foreshadowing, leave a suspense for students, and lay the foundation for learning the properties of functions later.
It should be noted that learning with multimedia courseware can attract students' attention and arouse their interest in further study. However, although multimedia demonstration is fast and accurate, I think that in the process of students learning to draw inverse proportional function images for the first time, teachers should seriously demonstrate every step of drawing images on the blackboard. After all, multimedia can't replace our usual teacher writing on the blackboard.
Consolidation exercise: draw a picture of the sum of functions
Through consolidation exercises, let students redraw the function image and correct some problems in the first drawing. Teachers use the courseware of function images to verify the accuracy of the function images drawn by students with the function images displayed on the screen.
(C) Inquiry learning 2 function image attributes
1, the distribution of images
Question 5: Please recall the distribution of the proportional function.
The main purpose of asking question 5 is to consolidate review and lay a foundation for guiding students to learn the distribution of inverse proportional function images.
Question 6: Looking at the image just drawn, we find that the image of the inverse proportional function has two branches, so what is its distribution?
Design in this link:
(1) Guide students to compare the distribution of the images of the direct proportional function, inspire them to actively explore the distribution of the inverse proportional function, and give students time to fully consider;
(2) Make full use of the advantages of multimedia in teaching, use the courseware of function images, try to input several values of k at will, and observe the different distribution of function images and the dynamic evolution process of function images. Focus different functional images on one screen, which is convenient for students to compare and explore. Through observation and comparison, students have an intuitive understanding of the relationship between the distribution of inverse proportional function images and k;
(3) Organize group discussion and summarize a property of inverse proportional function: when k >; 0, the two branches of the function image are in the first quadrant and the third quadrant respectively; When k < 0, the two branches of the function image are in the second and fourth quadrants respectively.
2. Changes in image
Question 7: What has happened to the image of the proportional function?
The main purpose of asking question 7 is to consolidate review and lay a foundation for guiding students to learn the changes of inverse proportional function images.
Question 8: Does the image of inverse proportional function also have this property?
The teaching design of this link is:
(1) Review the image of inverse proportional function sum, and through actual observation;
(2) Select the pair value according to the analytical formula, and compare the change of function value when x takes different values;
(3) Computer demonstration and student group discussion, asking students to give conclusions. That is, this problem must be discussed in two situations, that is, when k>0, when the independent variable X increases gradually, the value of Y decreases gradually; When k < 0, when the independent variable x increases gradually, the value of y also increases gradually.
(4) Teachers should affirm students' conclusions, and at the same time, they can ask: Do students have anything to add? If not, for example: when k>0 compares the values of Y in the third quadrant x=-2 and the first quadrant x=2, does the above property still hold? The student's answer should be: no, then the teacher asked the students to make a summary: it must be limited in each quadrant before the above properties can be established.
Question 9: When the two branches of the function image extend infinitely, do they intersect with the X axis and the Y axis? Why?
In this link, students can be guided to analyze the analytical formula of inverse proportional function by algebraic method, and the denominator cannot be zero, so x cannot be zero. By k? 0, y must not be zero, thus verifying the image of inverse proportional function. When two branches extend infinitely, they can approach the X axis and the Y axis infinitely, but they will never intersect. Then he stressed that attention should be paid to accuracy when drawing.
(4) redundant thinking
1, the image of the inverse proportional function is in the first and third quadrants, and find the value range of a.
2、
(1) When m is a value, y is a proportional function of x.
(2) when m is a value, y is an inverse proportional function of x.
(5) Summary:
Case 2 of junior high school mathematics teaching design
The first lesson of exploring Pythagorean theorem
I. teaching material analysis
(A) the status of teaching materials
This lesson is the first lesson of Exploring Pythagorean Theorem, a junior high school textbook for nine-year compulsory education. Pythagorean theorem is one of several important theorems in geometry, which reveals the quantitative relationship between three sides in a right triangle. It has played an important role in the development of mathematics and has a wide range of functions in the world at present. Through the study of Pythagorean theorem, students can have a further understanding and understanding of right triangle on the original basis.
(B) Teaching objectives
Knowledge and ability: master Pythagorean theorem and use Pythagorean theorem to solve some simple practical problems.
Process and method: Through the process of exploring and verifying Pythagorean theorem, we can understand the method of verifying Pythagorean theorem by puzzles, cultivate students' reasonable reasoning consciousness, the habit of active exploration, and feel the combination of numbers and shapes and the thought from special to general.
Emotional attitude and values: inspire students' patriotic enthusiasm, let students experience a sense of accomplishment in trying to draw conclusions, experience mathematics full of exploration and creation, and experience the beauty of mathematics, so as to understand and like mathematics.
(3) Teaching emphasis: Experience the process of exploring and verifying Pythagorean theorem, and use it to solve some simple practical problems.
Teaching difficulty: using area method (puzzle method) to discover Pythagorean theorem.
Ways to highlight key points and break through difficulties: give full play to students' main role, and let students explore, understand and comprehend through hands-on experiments.
Second, the analysis of teaching methods and learning methods:
Analysis of learning situation: Grade 7 students have already possessed certain abilities of observation, induction, guessing and reasoning. They have learned some calculation methods of geometric figure area (including cutting and splicing) in primary school, but their awareness and ability to solve problems by using area method and cutting and splicing ideas are not enough. In addition, students generally study and participate in classroom activities more actively, but their ability of cooperation and communication needs to be strengthened.
Analysis of teaching methods: combining the characteristics of seventh-grade students and this textbook, adopt it in teaching? Problem situation-modeling-explanation and application-expansion and consolidation? Mode, choose guided exploration method. Turn the teaching process into a process of students' personal observation, bold guess, independent exploration, cooperation and exchange, and induction.
Analysis of learning methods: under the guidance of teachers' organization, students adopt the discussion learning mode of independent inquiry and cooperative communication, so that students can truly become the masters of learning.
Third, the teaching process design 1. Create a situation and ask question 2. Experimental operation, model construction 3. Return to life and apply new knowledge.
4. Expand knowledge, consolidate and deepen. 5. Feel the harvest and assign homework.
(A) the creation of questioning situations
(1) Picture Appreciation Pythagorean Theorem Digital Diagram 1955 Greece issued the international mathematical commemorative stamp "Beautiful Pythagorean Tree" in 2002. The design intention is to appreciate the beauty of mathematics and feel the cultural value of Pythagorean theorem through graphics.
(2) A fire broke out on the third floor of a building. Firefighters came to put out the fire and learned that each floor was 3 meters high. The fireman is holding a 6.5-meter ladder. If the distance between the bottom of the ladder and the wall base is 2.5 meters, can firefighters enter the third floor to put out the fire?
Design intention: The introduction of new curriculum with practical problems as the breakthrough point reflects that mathematics comes from real life and people's needs, and also reflects the process of knowledge generation, and the process of solving problems is also one? Math? Procedure, which will lead to the following link.
Second, the construction of experimental operation model
1. isosceles right triangle (several squares)
2. Ordinary right triangle (cut and fill)
Question 1: What is the relationship between the areas of squares I, II and III for isosceles right triangle?
Design intention: This will help students to participate in exploration, cultivate language expression ability and experience the idea of combining numbers with shapes.
Question 2: Do the areas of squares I, II and III have the same relationship for a general right triangle? (Digging and filling method is the difficulty of this section, organize students to cooperate and exchange. )
Design intention: It is not only conducive to breaking through difficulties, but also lays a foundation for inductive conclusion, so that students' ability to analyze and solve problems can be improved invisibly.
The Pythagorean theorem is summarized through the above experiments.
Design Intention: Through cooperation and communication, students summed up the rudiment of Pythagorean Theorem, cultivated students' abstract generalization ability, and at the same time played the main role and experienced the cognitive law from special to general.
3. Return to life and apply new knowledge
Let students solve problems in the opening scene, call first and then respond, enhance students' awareness of learning and using mathematics, and increase the fun and confidence of applying what they have learned.
Fourth, the expansion, consolidation and deepening of knowledge
Basic questions, situational questions and inquiry questions.
Design intention: Give a group of topics, divide them into three gradients, practice from the shallow to the deep, take care of students' individual differences, pay attention to students' personality development and sublimate the application of knowledge.
Basic question: The right side of a right triangle is 3, the hypotenuse is 5, and the other right side is X. How many mathematical questions can you ask according to the conditions? Can you solve the problem raised?
Design intention: This question is based on double bases. By creating situations, students exercise divergent thinking.
Situation: Xiaoming's mother bought a 29-inch (74 cm) TV set. Xiao Ming measured the TV screen and found that the screen was only 58 cm long and 46 cm wide. He thinks that the salesman must have made a mistake. Do you agree with him?
Design intention: to increase students' common sense of life, and also to show that mathematics comes from life and is used in life.
Question: Can a wooden box with a length of 50 cm, a width of 40 cm and a height of 30 cm be put in? Why? Try to explain what you learned today.
Design intention: It is relatively difficult to explore the problem, but teachers use the teaching mode to cooperate and communicate with students, expand students' thinking and develop their spatial imagination.
Verb (abbreviation for verb) Feel the harvest homework: What did you gain in this class?
Homework: 1, textbook exercise 2. 1 2, collect information about the proof of Pythagorean theorem.
Exploration of Pythagorean Theorem in Blackboard Design
If the two right angles of a right triangle are A and B and the hypotenuse is C, then
Design description:: 1. The exploration theorem uses the area method to create a harmonious and relaxed situation for students, so that students can experience the combination of numbers and shapes, from special to general thinking methods.
2. Let all students participate and pay attention to the evaluation of student activities. First, the degree of students' participation in activities; Second, students' thinking level and expression level in activities.
Junior high school mathematics teaching design case 3
pythagorean theorem
1. teaching material analysis: Pythagorean theorem is a very important property of right triangle, which students learn on the basis of mastering the related properties of right triangle. It reveals the quantitative relationship among the three sides of a triangle, which can solve the calculation problem in a right triangle and is one of the main bases for solving a right triangle. It is of great use in real life.
When compiling teaching materials, we should pay attention to cultivating students' hands-on operation ability and problem analysis ability, and make students get a more intuitive impression through practical analysis, puzzles and other activities; Understanding Pythagorean Theorem through contact and comparison is beneficial to correct application.
Accordingly, the teaching objectives are as follows: 1. Understand and master Pythagorean theorem and its proof. 2. Be able to use Pythagorean theorem and its calculation flexibly. 3. Cultivate students' abilities of observation, comparison, analysis and reasoning. 4. By introducing the achievements of ancient Pythagoras characters in China, we can inspire students' thoughts and feelings of loving the motherland and its long culture, and cultivate their national pride and research spirit.
Second, teaching emphasis: proof and application of Pythagorean theorem.
Third, teaching difficulties: proof of Pythagorean theorem.
Fourth, teaching methods and learning methods: teaching methods and learning methods are embodied in the whole teaching process, and the teaching methods and learning methods of this course reflect the following characteristics:
Give priority to self-study counseling, give full play to the leading role of teachers, stimulate students' desire and interest in learning by various means, organize student activities, and let students actively participate in the whole learning process.
Effectively reflect students' dominant position, let students understand theorems through observation, analysis, discussion, operation and induction, improve their hands-on operation ability, and their ability to analyze and solve problems.
By demonstrating objects, students are guided to observe, operate, analyze and prove, so that students can gain a sense of success in acquiring new knowledge, thus stimulating their desire to learn new knowledge.
Verb (abbreviation of verb) teaching procedure: The teaching of this section is mainly reflected in students' hands-on and brain. According to students' cognitive rules and learning psychology, the teaching program is designed as follows:
(A) to create a new situation
1, the story is introduced. More than 3,000 years ago, a man named Shang Gao told the Duke of Zhou that if you fold a ruler into a right angle and connect the two ends, you will form a right triangle. If the hook is 3 and the rope is 4, then the rope is equal to 5. This has aroused students' interest in learning and stimulated their thirst for knowledge.
2. Do all right triangles have this property? Teachers should be good at arousing doubts and let students enter a state of being willing to learn.
3. Write it on the blackboard to show the learning objectives. (B) the initial perception and understanding of teaching materials
Teachers guide students to learn new knowledge through self-study, which embodies students' awareness of autonomous learning, exercises students' initiative to explore knowledge, and forms good self-study habits.
(3) Discussion and summary of questioning and problem solving: 1, teachers ask questions or students ask questions. How to prove Pythagorean theorem? Through self-study, students above the intermediate level can basically master it, which can stimulate students' desire to express themselves. 2. Teachers guide students to do puzzles and observe and analyze them as required;
(1) What are the characteristics of these two graphs? (2) Can you write down the areas of these two figures?
(3) How to use Pythagorean theorem? Are there any other forms?
At this time, the teacher organizes students to discuss in groups, arouses the enthusiasm of all students, achieves the effect of everyone's participation, and then communicates with the whole class. First of all, one group of representatives spoke and expounded their understanding of the problem, while the other groups made comments and supplements. Teachers give enlightening guidance in time, and finally teachers and students sum up each other, form a consensus and finally solve the problem.
(4) Consolidate practice and strengthen improvement.
1, show exercises, students answer in groups, and students summarize the law of solving problems. Combine static and dynamic in classroom teaching to avoid causing students fatigue.
2. Give an example of 1. Students try to solve the problem, and teachers and students evaluate it together, so as to deepen the understanding and application of the example. In order to further improve students' ability to use knowledge, we can take the form of mutual evaluation and discussion on practical problems, and teachers can take the form of classroom discussion to solve the representative problems in mutual evaluation and discussion, thus highlighting the teaching focus.
(5) Summarize practical feedback.
Guide students to summarize the main points of knowledge and sort out their learning ideas. Distribute self-feedback exercises, and students can complete them independently.
This course aims to create a pleasant and harmonious learning atmosphere, optimize teaching methods, improve classroom teaching efficiency with the help of multimedia, and establish an equal, democratic and harmonious relationship between teachers and students. Strengthen the cooperation between teachers and students, create a classroom atmosphere in which students dare to think, feel and ask questions, make all students lively in teaching activities, and cultivate their innovative spirit and practical ability in learning.
Guess you like:
1. Junior high school math teachers must read.
2. Six main points of junior high school mathematics learning methods
3. Efficient classroom design of junior high school mathematics
4. Junior high school students' mathematics learning plan
5. Junior high school mathematics learning methods