What are the cases of junior middle school mathematics teaching design?

If teachers want to teach well, they must write good lesson plans. Carefully formulating a plan is the prerequisite for successful lectures and an effective way for teachers to improve their professional quality. The following is the information about the junior high school mathematics teaching design case I shared with you. I hope you like it!

Junior high school mathematics teaching design case 1

Inverse proportional function

1. Textbook analysis:

The image and properties of inversely proportional functions are a review and comparison of the images and properties of directly proportional functions, and are also the basis for learning quadratic functions in the future. The learning in this class is a process for students to re-understand the images and properties of functions. Since it is the first time for second grade students to come into contact with the image of a function such as a hyperbola, attention should be paid to guiding students to grasp the characteristics of the image of an inverse proportional function during teaching. Let students have an image and intuitive understanding of inverse proportional functions.

2. Analysis of teaching objectives

According to the second phase of curriculum reform, students should be the main body, the classroom atmosphere should be activated, and students should be fully mobilized to participate in the teaching process. In terms of teaching design, I envision creating situations through the use of multimedia courseware, stimulating students’ interest in learning and desire to explore while mastering knowledge about inverse proportional functions, and guiding students to actively participate and actively explore.

Therefore, the teaching objectives are determined as follows: 1. Master the concept of inverse proportional function, and be able to find the analytical formula of inverse proportional function based on known conditions; learn to use the point drawing method to draw the image of inverse proportional function; master the image The characteristics of and the function properties obtained from the function graph. 2. Guide students to explore, think and imagine independently during the teaching process, thereby cultivating students' comprehensive abilities of observation, analysis and induction. 3. Cultivate students’ spirit of active participation and courage to explore through learning.

3. Analysis of teaching key points and difficulties

The focus of this class is to master the definition of inverse proportional functions, image characteristics and properties of functions;

What are the difficulties? Grasp the features and accurately draw the graph of the inverse proportional function.

In order to highlight key points and break through difficulties. I designed and produced multimedia courseware that can dynamically demonstrate function images. Let students operate with their own hands, actively participate in and actively explore the properties of functions, and help students intuitively understand the properties of inverse proportional functions.

IV. Teaching Methods

In view of the characteristics of the teaching materials and the age characteristics, psychological characteristics and cognitive level of the second grade students, it is envisaged to adopt the problem teaching method

and comparison The teaching method uses layer-by-layer questioning to inspire students to think deeply, actively explore, and actively acquire knowledge. At the same time, pay attention to the connection with students' existing knowledge, reduce students' difficulties in accepting new concepts, and give students sufficient time to explore independently. Through the guidance of teachers, we inspire and mobilize students' enthusiasm, allow students to engage in more activities and observations in class, actively participate in the entire teaching activities, and organize students to participate in the learning activity process of "exploration", "discussion", "exchange" and "summary", and at the same time, In teaching, we also make full use of multimedia teaching to inspire students through demonstrations, operations, observations, exercises and other joint activities between teachers and students, so that each student can use their hands, mouth, eyes and brain to cultivate students' intuitive thinking ability.

5. Study Method Guidance

This class is based on students’ learning and requires students to do more hands-on work and observe more, which can help students form analysis, analysis, and analysis.

Thinking methods of comparison and induction. Let students "learn by doing" through comparison and discussion, and improve students' ability to use the knowledge they have learned to actively acquire new knowledge. Therefore, teaching should be organized in the classroom by actively guiding students to actively participate, cooperate and communicate, so that students can truly become the main body of teaching, experience the fun of participation, the joy of success, and perceive the wonder of mathematics.

VI. Teaching process

(1) Review the introduction of analytical expressions of inverse functions

Exercise 1: Write the relational expressions of the following questions:

(1) The relationship between the perimeter C of a square and the length a of one side of it

(2) In the track and field competition of the sports meeting, the average speed of athlete Xiao Wang is 8 meters/second , the relationship between the distance s he ran and the time t he took

(3) When the area of ??the rectangle is 10, the relationship between its length x and width y

(4) Master Wang wants to produce 100 parts, the relationship between his work efficiency x and working time t

Question 1: Please judge which of the relationship expressions we have written are Direct proportional function?

Question 1 is mainly to review the definition of direct proportional function and lay the foundation for students to use the method of comparison to give the definition of inverse proportional function.

Question 2: Then please take a closer look. Are there any similarities between the other two functional expressions?

Use question 2 to derive the analytical expression of the inverse proportional function. Ask students to compare the definitions of direct proportional functions

to give the definition of inverse proportional functions. This not only helps to review and consolidate old knowledge, but also cultivates students' comparison and inquiry abilities.

Example 1: It is known that the variable y is inversely proportional to x, and when x=2, y=9

(1) Write the analytical expression of the function between y and x

(2) When x=3.5, find the value of y

(3) When y=5, find the value of x

By example The study of 1 enables students to master how to find the analytical expression of the inverse proportional function based on known conditions.

In the process of solving the problem, students are guided to use the "undetermined coefficient method" used in finding the analytical expression of the directly proportional function. First, suppose the inverse proportional function is, and then substitute the corresponding x and y values ??to find out. k, the value of k is determined, and the analytical formula of the function is determined.

Classroom exercise: It is known that x and y are inversely proportional. According to the following conditions, find the functional relationship between y and x

(1)x=2, y=3 (2)x= , y=

Through this question, we provide a simple feedback on students’ learning of how to find the analytical expression of the inverse proportional function based on known conditions.

(2) Exploring and learning 1? How to draw the graph of a function

Question 3: How to draw the graph of a proportional function?

Through question 3 Reviewing the drawing method of the graph of the directly proportional function is mainly divided into three steps: listing, drawing points, and connecting lines, which lays the foundation for learning the drawing method of the graph of the inverse proportional function.

Question 4: How to draw the image of an inverse proportional function?

In the teaching process, students can be guided to imitate the drawing method of the image of a directly proportional function.

The envisaged teaching design is:

(1) Guide students to apply the methods learned in drawing proportional function images, discuss and try them in groups, and use lists, drawing points, and connecting Draw the graph of the function sum using the line method;

(2) The teacher patrols and guides, uses a physical projector to reflect some typical mistakes that students make in function graphs, and works with the students to find out If there are errors, analyze the reasons;

(3) Then the teacher demonstrates the steps to draw the image of the inverse proportional function on the blackboard, displays the correct image of the function, and guides students to observe its image characteristics (a hyperbola has two branches).

This is the first time for second-year junior high school students to come into contact with a special function graph such as a hyperbola. It is assumed that students may make mistakes in the following links:

(1) In the "list" In this link

Students may take zero when picking points. Here, students can be guided to combine algebraic methods to find that x cannot be zero. It may also be due to improper point selection, resulting in incomplete and asymmetric function graphs.

Here, students should be guided when making lists. The value of the independent variable Convenient to find points in the coordinate plane.

(2) In the link of "Connecting Lines"

The lines drawn by students may have endpoints and cannot be connected with smooth lines. Therefore, it is particularly important to emphasize here that when connecting the selected points, it should be a "smooth curve" to lay the foundation for learning the image of the quadratic function in the future. In order to make the function image clear and obvious, students can be guided to select as many values ??of independent variables x and corresponding function values ??y as possible, so as to obtain more "points" in the coordinate plane and draw curves.

This guides students to draw correct function graphs.

(3) The image intersects the x-axis or y-axis

Here I think we can lay a foreshadowing, leave students with a suspense, and lay the foundation for learning the properties of functions later. Base.

It should be noted that using multimedia courseware to learn can attract students' attention and arouse students' interest in further learning. However, although the multimedia demonstration is fast and accurate, I think that when students first learn to draw the image of an inverse proportional function, the teacher should carefully demonstrate every step of drawing the image on the blackboard. After all, multimedia cannot be a substitute. Our teacher usually writes on the blackboard.

Consolidation exercises: Draw the graphs of functions and

Through consolidation exercises, students can draw the graphs of functions again and correct some problems that occurred when they first drew the graphs. The teacher uses the function graph courseware and uses the function graph displayed on the screen to verify the accuracy of the function graph drawn by the students.

(3) Exploration and Learning 2? Properties of function graphs

1. Distribution of the image

Question 5: Please recall the distribution of proportional functions What is the situation like?

The purpose of raising question 5 is mainly to consolidate the review and lay the foundation for guiding students to learn the distribution of inverse proportional function images.

Question 6: Observing the image just drawn, we find that the image of the inverse proportional function has two branches, so what is its distribution?

Here Design in the first link:

(1) Guide students to compare the distribution of images of directly proportional functions, inspire them to actively explore the distribution of inversely proportional functions, and give students time to fully consider;

(2) Make full use of the advantages of multimedia for teaching. Use the courseware of function images to try to input several k values ??arbitrarily, observe the different distributions of the function images, and observe the dynamic evolution process of the function images. Gather different function images on one screen to facilitate students' comparison and exploration. Through observation and comparison, students have an intuitive understanding of the relationship between the distribution of the image of the inverse proportional function and k;

(3) Organize group discussions to summarize a property of the inverse proportional function: when kgt; 0 , the two branches of the function graph are in the first and third quadrants respectively; when klt; 0, the two branches of the function graph are in the second and fourth quadrants respectively.

2. The change of the image

Question 7: What is the change of the image of the proportional function?

The main reason for raising question 7 is to consolidate the review and lay the foundation for guiding students to learn the changes in the graph of inverse proportional functions.

Question 8: Does the image of the inverse proportional function also have such properties?

The teaching design in this link is:

(1 )Review the image of the sum of inverse proportional functions through actual observation;

(2) Value the pair according to the analytical formula and compare the changes in the function value when x takes different values;

(3) Computer demonstration and student group discussion, asking students to give conclusions.

That is to say, this problem must be divided into two situations for discussion: when kgt; 0, when the independent variable x gradually increases, the value of y gradually decreases; when klt; 0, when the independent variable x gradually increases, the value of y The value also gradually increases.

(4) The teacher should affirm the conclusions made by the students, and at the same time ask: Is there anything the students need to add? If not, you can give an example: when kgt; 0, compare them respectively. When the third quadrant x=-2 and the value of y in the first quadrant x=2, do the above properties still hold? The student's answer should be: Not true. At this time, the teacher asked the students to make a summary: it must be limited to each quadrant for the above properties to be established.

Question 9: When the two branches of the function graph extend infinitely, does it intersect with the x-axis and y-axis? Why?

In this link, you can combine the students just now The error image drawn guides students to analyze the analytical expression of the inverse proportional function through algebra. Since the denominator cannot be zero, x cannot be zero. From k? 0, it is concluded that y must not be zero, thus verifying the image of the inverse proportional function. When the two branches extend infinitely, they can approach the x-axis and y-axis infinitely, but they will never intersect with the two axes. Immediately emphasize the importance of accuracy when drawing.

(4) Alternative thinking questions

1. The graph of the inverse proportional function is in the first and third quadrants. Find the value range of a

2. /p>

(1) When m has a certain value, y is a direct proportional function of x

(2) When m has a certain value, y is an inverse proportional function of x

(5) Summary:

Junior high school mathematics teaching design case 2

The first lesson of "Exploring the Pythagorean Theorem"

1. Analysis of teaching materials

(1) Status of textbooks

This lesson is the first lesson of Chapter 2, Section 1, "Exploring the Pythagorean Theorem", Beijing Normal University Edition of the Nine-Year Compulsory Education Junior High School Textbook, Beijing Normal University Edition. The theorem is one of several important theorems in geometry. It reveals the quantitative relationship between the three sides of a right triangle. It has played an important role in the development of mathematics and has a wide range of roles in the current world. By studying the Pythagorean Theorem, students can have a further understanding of right triangles based on the original knowledge.

(2) Teaching objectives

Knowledge and ability: Master the Pythagorean theorem, and be able to use the Pythagorean theorem to solve some simple practical problems.

Process and methods : Experience the process of exploring and verifying the Pythagorean Theorem, understand the method of using puzzles to verify the Pythagorean Theorem, develop students' awareness of reasonable reasoning and the habit of active inquiry, and experience the combination of numbers and shapes and the thought of moving from the specific to the general.

Emotional attitudes and values: Stimulate students' patriotic enthusiasm, let students experience the sense of accomplishment of reaching conclusions through their own efforts, experience mathematics full of exploration and creation, and experience the beauty of mathematics, so as to understand mathematics and like mathematics.

(3) Teaching focus: Experience the process of exploring and verifying the Pythagorean Theorem, and be able to use it to solve some simple practical problems.

Teaching difficulty: Use the area method (puzzle method) to discover the Pythagorean theorem.

Methods to highlight key points and break through difficulties: give full play to the main role of students, and let students explore through experiments, comprehend through exploration, and understand through comprehension.

2. Analysis of teaching and learning methods:

Analysis of academic situation: Seventh grade students already have certain abilities of observation, induction, conjecture and reasoning. They have learned some methods of calculating the area of ??geometric figures in primary school. (Including cutting and patching, splicing), but the awareness and ability to use the area method and cutting and patching thinking to solve problems are not enough. In addition, students are generally more motivated to learn and participate more actively in classroom activities, but their ability to cooperate and communicate needs to be strengthened.

Teaching method analysis: Combining the characteristics of seventh-grade students and the teaching materials of this section, the model of "problem situation--building model--explaining and applying---expanding and consolidating" is adopted in teaching. Choose guided exploration.

Transform the teaching process into a process of students' personal observation, bold guesses, independent inquiry, cooperation and communication, and summary.

Analysis of learning methods: Under the guidance of teachers, students adopt a seminar-style learning method of independent inquiry, cooperation and exchange, so that students truly become the masters of learning.

3. Teaching process design 1. Create situations and ask questions 2. Experimental operations and model construction 3. Return to life and apply new knowledge

4. Knowledge expansion, consolidation and deepening 5. Gain insights and assign homework

( 1) Create situations and ask questions

(1) Appreciate pictures of the Pythagorean theorem number shape diagram. In 1955, Greece issued a beautiful Pythagorean tree. A commemorative stamp for the International Mathematics Conference in 2002. The logo design intention: through graphics Appreciate, feel the beauty of mathematics, and feel the cultural value of the Pythagorean Theorem.

(2) There was a fire on the third floor of a building. Firefighters came to put out the fire. They learned that each floor was 3 meters high, and the firefighters took 6.5 For a meter-long ladder, if the distance between the bottom of the ladder and the base of the wall is 2.5 meters, can firefighters enter the third floor to put out the fire?

Design intention: Introduce new lessons based on practical problems, reflecting Mathematics comes from real life, arises from human needs, and also reflects the generation process of knowledge. The process of solving problems is also a "mathematical" process, which leads to the following links.

2. Experimental operations Model construction

1. Isosceles right triangle (number of grids)

2. General right triangle (cut and repair)

Question 1: For isosceles right triangle , what is the relationship between the areas of squares I, II, and III?

Design intention: This will help students participate in exploration, cultivate students' language expression ability, and experience the idea of ??combining numbers and shapes.

Question 2: For general right triangles, do the areas of squares I, II and III also have this relationship? (The cut and repair method is the difficulty of this section, organize students to cooperate and exchange)

Design intention: not only It is helpful to break through difficulties and lay the foundation for inductive conclusions, so that students' ability to analyze and solve problems can be virtually improved.

Through the above experiments, the Pythagorean Theorem can be summarized.

Design intention: Through cooperation and communication, students summarize the prototype of the Pythagorean theorem, cultivate students' abstraction and generalization abilities, and at the same time play the main role of students and experience the cognitive rules from special to general.

3. Return to life and apply new knowledge

Let students solve the problems in the opening scene, respond to each other, enhance students' awareness of learning and using mathematics, and increase their fun and confidence in applying what they have learned.

IV. Expansion, consolidation and deepening of knowledge

Basic questions, situational questions, exploratory questions.

Design intention: A set of questions is given, divided into three gradients, from shallow to deep. Practice, take care of students' individual differences, and pay attention to students' personality development. The application of knowledge is sublimated.

Basic questions: The length of one side of a right triangle is 3, the hypotenuse is 5, and the length of the other right side is For .

Situational question: Xiao Ming’s mother bought a 29-inch (74 cm) TV. After Xiao Ming measured the screen of the TV, he found that the screen was only 58 cm long and 46 cm wide. He felt that it must be The salesman made a mistake. Do you agree with his idea?

Design intention: to increase students' common sense of life, and also to show that mathematics comes from life and is used in life.

Exploration question: Make a wooden box with a length, width, and height of 50 cm, 40 cm, and 30 cm respectively. Can a 70 cm long wooden stick be put in it? Why? Try to learn today Explanation of past knowledge.

Design intention: The exploration questions are relatively difficult, but teachers use teaching models and students’ cooperation and communication methods to expand students’ thinking and develop spatial imagination abilities.

5. Assign homework for understanding and harvesting: What is your gain from this class?

Homework: 1. Textbook exercises 2.1　2. Collect information about the proof of the Pythagorean theorem.

Blackboard design exploration hook Stock theorem

If the two right-angled sides of a right triangle are a and b, and the hypotenuse is c, then

Design instructions: 1. Use the area method to explore the theorem and create a A harmonious and relaxed situation allows students to experience the combination of numbers and shapes and the thinking methods from special to general.

2. Let all students participate and pay attention to the evaluation of student activities. First, students’ performance in the activities The second is the level of thinking and expression shown by students in the activities.

Junior high school mathematics teaching design case three

Pythagorean theorem

1. Textbook analysis: The Pythagorean theorem is learned by students on the basis of mastering the relevant properties of right triangles. It is a very important property of right triangles and one of the most important theorems in geometry. It reveals that a triangle The quantitative relationship between the three sides can solve calculation problems in right triangles. It is one of the main basis for solving right triangles and is of great use in real life.

When compiling the teaching materials, attention is paid to cultivating students' hands-on operation ability and problem analysis ability. Through practical analysis, puzzles and other activities, students can obtain a more intuitive impression; through connections and comparisons, students can understand the Pythagorean Theorem, to facilitate correct use.

Based on this, the teaching objectives are formulated as follows: 1. Understand and master the Pythagorean Theorem and its proof. 2. Be able to flexibly use the Pythagorean Theorem and its calculations. 3. Cultivate students’ abilities of observation, comparison, analysis, and reasoning. 4. By introducing the achievements of ancient China in Pythagorean, inspire students to love the motherland and love the long culture of the motherland, and cultivate their national pride and research spirit.

2. Teaching focus: Proof and application of the Pythagorean Theorem.

3. Teaching difficulties: Proof of the Pythagorean Theorem.

IV. Teaching and learning methods: Teaching and learning methods are reflected in the entire teaching process. The teaching and learning methods of this course reflect the following characteristics:

Self-study Guidance is the main focus, giving full play to the leading role of teachers, using various means to stimulate students' desire and interest in learning, organizing student activities, and allowing students to actively participate in the entire learning process.

Effectively reflect students’ dominant position, allowing students to understand theorems through observation, analysis, discussion, operation, and induction, and improve students’ hands-on ability, as well as their ability to analyze and solve problems.

By demonstrating real objects, students are guided to observe, operate, analyze, and prove, so that students can feel the success of acquiring new knowledge, thereby stimulating students' desire to delve into new knowledge.

5. Teaching procedures: The teaching of this section is mainly reflected in students’ hands-on and brain-using aspects. According to students’ cognitive rules and learning psychology, the teaching procedures are designed as follows:

(1 )Create situations to introduce new ones from the past

1. Introduced by the story, more than 3,000 years ago, a man named Shang Gao said to Duke Zhou, fold a ruler into a right angle and connect the two ends to form a right triangle. , if the hook is 3 and the strand is 4, then the string is equal to 5. This arouses students' interest in learning and stimulates students' thirst for knowledge.

2. Do all right triangles have this property? Teachers should be good at provoking doubts so that students can enter a state of joy in learning.

3. Write the topic on the blackboard and provide learning objectives. (2) Preliminary perception and understanding of teaching materials

Teachers guide students to self-study teaching materials and understand new knowledge through self-study, which reflects students’ awareness of autonomous learning, trains students to actively explore knowledge, and develops good self-study habits.

(3) Questioning and problem solving Discussion summary: 1. Teachers set questions or students raise questions.

For example: How to prove the Pythagorean theorem? Through self-study, students at intermediate level and above can basically master it, which can stimulate students' desire to express themselves. 2. The teacher guides students to complete the puzzle as required, observe and analyze;

(1) What are the characteristics of these two figures? (2) Can you write the areas of these two figures?

(3) How to use the Pythagorean Theorem? Are there other forms?

At this time, the teacher organizes students to discuss in groups to mobilize the enthusiasm of all students to achieve the effect of everyone participating, and then the whole class comminicate. First, a representative of a certain group will speak to explain the group's understanding of the problem, and the other groups will make comments and supplements. The teacher gave inspiring advice in a timely manner. Finally, the teachers and students summarized and formed a consensus to finally solve the problem.

(4) Consolidate practice and strengthen improvement

1. Show exercises, students answer them in groups, and students summarize the problem-solving rules. Use a combination of movement and stillness in classroom teaching to avoid causing student fatigue.

2. Students will try to solve Example 1, and teachers and students will evaluate together to deepen their understanding and application of the examples. Consolidate exercises based on the reoccurrence of example questions to further improve students' ability to apply knowledge. Mutual evaluation and mutual discussion can be used to evaluate situations that arise during the exercises. For representative issues that arise during mutual evaluation and mutual discussion, teachers can take the form of whole-class Solve them in the form of discussion to highlight the key points of teaching.

(5) Summary and practice feedback

Guide students to summarize the key points of knowledge and sort out their learning ideas. Distribute self-feedback exercises for students to complete independently.

This course aims to create a pleasant and harmonious learning atmosphere, optimize teaching methods, use multimedia to improve classroom teaching efficiency, and establish an equal, democratic, and harmonious teacher-student relationship. Strengthen cooperation between teachers and students and create a classroom atmosphere where students dare to think, express and ask questions, so that all students can engage in lively and proactive teaching activities and cultivate their innovative spirit and practical ability in learning.