Design of eighth grade mathematics teaching plan of Beijing Normal University Edition
First, the teaching objectives
(A) imparting knowledge points
1. Master the judgment methods of triangle similarity 2 and 3.
2. similar triangles's judgment methods 2 and 3 will be used for judgment, proof and calculation.
(2) Ability training requirements
1. By doing it yourself, summarize similar triangles's judgment methods 2 and 3, and cultivate students' hands-on operation ability and induction and generalization ability.
2. Use similar triangles's judgment methods 2 and 3 to judge and cultivate students' flexible application ability.
(C) emotional and values requirements
1. By exploring similar triangles's judgment methods 2 and 3, mathematical activities are full of exploration and creativity.
2. Through the exploration of judgment methods, develop the flexibility of students' thinking, further cultivate their logical reasoning ability and understand the classification thought.
Second, the difficulties in teaching
Teaching emphasis: the derivation process of similar triangles's judgment methods 2 and 3, mastering judgment methods 2 and 3 and using them flexibly. Teaching difficulty: derivation and application of judgment method.
Third, the teaching process design
(A) the creation of situations, the introduction of new courses
screen sheet
There are four pairs of similar triangles. They are △AEF∽△DEC, △AFB∽△ACD, △AEB∽△CED, △AEF∽△EBA. The reason why they are similar is that they all use similar triangles's 1 judgment method.
[T] Now we have two methods to judge the similarity of two triangles, one is the definition, and the other is the judgment method 1. Besides, is there any other way to judge the similarity of two triangles? This problem is what we need to study in this class.
(B) new curriculum teaching
[T] similar triangles's judgment method 1 only from the perspective, we only consider it from the side below. When studying congruent triangles's judgment method, we only use edge to judge, that is, SSS axiom. Can we guess the method of judging the similarity of triangles only by edges by analogy?
Three sides correspond to the similarity of two triangles in proportion.
[T] Let's check it out.
1. similar triangles's judgment method 2: Similarity of three sides corresponding to two proportional triangles.
screen sheet
Each group takes the same K value, and different groups take different K values, okay?
in good health
[T] What's your conclusion after your personal experience?
[Health] What is the conclusion? A=？ Answer? ,? B=？ b？ ,? C=？ c？
△ABC∽△A？ b？ c？ , on the grounds that:
? A=？ Answer? ,? B=？ b？ ,? C=？ c？
According to similar triangles's definition: △ABC∽△A? b？ c？ .
[T] Did other students come to the same conclusion?
Same [raw].
After discussion, we have mastered a method to judge similar triangles, that is, two triangles with corresponding proportions on three sides are similar.
2. similar triangles's judgment method 3.
[Comment] We only consider the first two judgment methods from the angle or side, and then consider them from two aspects. We should compare congruent triangles's judgment methods. Among the congruence judgment methods, there are ASA, SAS and AAS, among which we don't need to consider ASA and AAS because we already have the judgment method of 1 and 3. Let's verify SAS, guess first and then verify.
Two triangles with corresponding proportional sides and equal included angles are similar.
Ok, let's deduce it ourselves. Please look at the slide.
Please follow the above steps and adopt different grouping methods and take different values.
[Health] According to the requirements of △ABC and △A? b？ c？ Medium, right? B=？ b？ ,? C=？ c？ So according to the judgment method 1, △ABC∽△A? b？ c？ .
Do you agree?
Agreed.
[T] Well, we have explored a method to judge similar triangles, that is, two triangles with equal angles and corresponding proportions are similar.
Think about it.
107
[T] Let's verify SSA, that is, two sides are proportional and one diagonal is equal. Are these two triangles similar?
SSA is not valid in congruent triangles's judgment. It can also be deduced according to the above verification process. The following are triangles drawn by Xiao Ming and Xiao Ying respectively that meet the requirements. What conclusions can be drawn from this?
It can be concluded from the above figure that there are two triangles with corresponding proportions, one of which has the same diagonal.
Do it
In these two lessons, we learned the general similar triangles's judgment method. Please summarize several methods.
There are four ways of life.
The first type: two triangles with equal corresponding angles and proportional corresponding sides are similar, that is, the definition method.
The second method: decision method 1.
Two triangles with equal angles are similar.
The third type: judgment method 2.
Three sides correspond to the similarity of two triangles in proportion.
The fourth method: decision method 3.
Two triangles with equal included angles and corresponding proportional sides are similar.
[Comment] From these four methods, it can be seen that the first judgment method is more troublesome and needs to study three diagonal lines and three opposite sides, while the latter method only needs to study three opposite sides or angles at most, so the definition method is generally not adopted. If the known condition only involves angle, the second judgment method is adopted; If the known condition only involves edges, the third judgment method is used; If there are both corners and edges, you can consider the fourth method.
Discuss it
As shown in the figure, △ABC and △A? b？ c？ Is it similar? What are your judgment methods?
[Biology] Solution: △ABC∽△A? b？ c？ .
The judgment methods are.
1. Similarity of three sides corresponding to two proportional triangles.
2. Two triangles with equal corresponding angles are similar.
3. The two sides are proportional and the included angle is equal.
4. Define the method.
(3) Consolidate application and expand research.
Are the two triangles in each group similar? Why?
Solution: (1)△ABC∽△DEF
∵
? △ABC∽△DEF
(2) In △ABC
AB=2，AC=6
∵? A=？ A
? △ABC∽△AEF
(d) Consolidating and promoting migration.
Determine △ABC and △A according to the following conditions? b？ c？ Are they similar and explain why.
( 1)? A= 120？ , AB=7 cm, AC= 14 cm,
? Answer? = 120? ，A？ b？ =3 cm，A？ c？ =6 cm,
AB = 4 cm, BC=6 cm, AC=8 cm,
Answer? b？ = 12 cm，B？ c？ = 18 cm，A？ c？ =24 cm。 Solution:
Again? A=？ Answer?
? △ABC∽△A？ b？ c？ The two sides are proportional and the included angle is equal, and the two triangles are similar. )
(2)
? △ABC∽△A？ b？ c？ (Three sides are proportional and two triangles are similar)
(5) Review contacts and form a structure.
This lesson mainly discusses similar triangles's other two judgment methods, that is, the similarity of triangles whose three sides are in direct proportion and whose two angles are equal, so as to cultivate everyone's spirit of exploration and make students understand that mathematical activities are full of exploration and innovation. The purpose of learning is to use what you have learned to solve problems. Here, we can prove it by judging.
Eighth grade mathematics teaching plan
First, the purpose of making a plan
In order to make students learn the basic knowledge of algebra and geometry well, have the basic skills necessary for every citizen in contemporary society to adapt to daily life, participate in social production and further study, further cultivate students' computing ability, develop students' thinking ability and spatial concept, enable students to solve practical problems with what they have learned, and gradually form a sense of mathematical innovation, the teaching plan of this subject is specially formulated.
Second, the content analysis of teaching materials
The contents of this semester's mathematics textbooks include: chapter 1, Axisymmetry in life, chapter 2, Pythagorean theorem, chapter 3, real numbers, chapter 4, preliminary understanding of probability, chapter 5, plane Cartesian coordinate system, chapter 6, linear function, and chapter 7, binary linear equations.
The first chapter "Axisymmetry in Life" mainly studies the properties and applications of axisymmetric graphics. Its emphasis is on the properties of axisymmetric graphics.
The second chapter "Pythagorean Theorem" is mainly about the exploration and application of Pythagorean Theorem. Among them, the application of Pythagorean theorem is the focus of this chapter.
The third chapter "Real Numbers" mainly talks about the concepts and solutions of square roots and cubic roots, and the concepts and operations of real numbers. Although the content of this chapter is not much, it occupies a very important position in junior high school mathematics. The teaching emphasis of this chapter is the concept and solution of square root and arithmetic square root, and the teaching difficulty is the understanding of the two concepts of arithmetic square root and real number.
The fourth chapter, "Preliminary Understanding of Probability", is mainly to understand probability through the size of possibility and make a simple probability calculation. Probability calculation is the focus of this chapter.
The fifth chapter "Plane Cartesian Coordinate System" mainly focuses on the determination of the midpoint in the plane Cartesian coordinate system, and the coordinates of some points will be obtained.
The main content of the sixth chapter "linear function" is to introduce the concept of function, as well as the image and expression of linear function, and learn to solve some practical problems with linear function. The image expression of linear function is the focus and difficulty of this chapter.
Chapter 7 "Binary linear equations" requires learning to solve binary linear equations, and using binary linear equations to solve some practical problems.
Three. Student analysis:
There are 44 students in Class * * * in Grade 2 (3). According to the statistics of last semester, the number of people who passed the exam was 50, and the number of outstanding people was 50. Many students in this class have poor grades, so it is difficult to improve their grades. Judging from the results of the unified examination at the end of last semester, it is best to get a zero score and a difference. These students are in the same class. Good students ask their teachers to speak more profoundly, while poor students ask them to speak more simply. There are no relatively concentrated fractions in a class, and the number of people in each fraction is almost the same from a few points to more points, which brings unfavorable factors to teaching.
Four. Teaching objectives
Chapter 1: Axisymmetry in life 1. In rich realistic situations, we have experienced mathematical activities such as appreciation and design of folded paper-cut graphics, and further developed the concept of space. 2. Understand the symmetry axis through rich life examples, explore its basic properties, and understand the nature that the line segments connected by corresponding points are vertically bisected by the symmetry axis. Explore and understand the axial symmetry of basic graphics and its related properties. 4. Be able to make a simple plane figure after axial symmetry as required; Explore the axial symmetry relationship of simple figures and point out the axis of symmetry. Appreciate the axial symmetry graphics in real life, design some patterns by using axial symmetry, and experience the wide application and rich cultural value of axial symmetry in real life.
Chapter 2 Pythagorean Theorem 1 By exploring Pythagorean Theorem and the condition that a triangle is a right triangle, we can develop reasonable reasoning ability and understand the idea of combining numbers with shapes. Master Pythagorean Theorem, understand the method of verifying Pythagorean Theorem with puzzles, and use Pythagorean Theorem to solve some practical problems. Master the condition of judging a triangle as a right triangle, and use it to solve some practical problems. Understand the history and application of Pythagorean theorem through examples, and understand its cultural value.
Chapter 3: Real number 1 lets students experience the process of expanding the number system and explore the properties and operation rules of real numbers; With the help of calculators, we engage in activities to explore mathematical laws, develop students' abstract generalization ability, and further cultivate students' awareness and ability of independent thinking and cooperative communication in activities. Combined with the specific situation, let students understand the significance of estimation, master estimation methods, and develop students' sense of numbers and estimation ability. Understand the real numbers of square roots and cubic roots and their related concepts; Will be represented by the root sign, and will find the square root and cube root of the number; Able to perform simple operations on real numbers. 4. Real number operation can be used to solve simple practical problems, improve students' application consciousness, develop students' problem-solving ability, and realize the application value of mathematics.
The fourth chapter is about probability 1 experience? Guess, verify, collect experimental data and analyze experimental results? Activity flow. 2 understand the possibility of inevitable events, impossible events and uncertain events, and understand the possibility of events and the fairness of the rules of the game; Understand the meaning of probability, realize that probability is a mathematical model to describe uncertain phenomena, and develop the concept of randomness. 3 can simply calculate the probability of two events and design a simple probability model that meets the requirements. 4 further understanding of mathematics is around us, and cultivate the consciousness and ability to use mathematics.
The fifth chapter, Plane Cartesian Coordinate System 1 is engaged in observing, analyzing, abstracting and summarizing the phenomenon of determining position in the real world, and has experienced the process of exploring the relationship between the change of graphic coordinates and the change of graphic shapes, further developing students' thinking ability, consciousness, image and mathematical application ability of combining numbers and shapes. Understand and draw the plane rectangular coordinate system; In a given rectangular coordinate system, the position of a point is tracked according to the coordinates, and its coordinates are written from the position of the point. 3. Can establish an appropriate rectangular coordinate system on the grid paper to describe the position of the object; The position of the object can be determined flexibly in various ways according to the specific situation. 4 In the same rectangular coordinate system, feel the change of the coordinates of points after the change of graphics and define the change of graphics after the change of the coordinates of points.
Chapter VI Elementary Function 1 Through the abstract generalization process of concepts such as function elementary function, we can understand the model idea of function and further develop students' abstract thinking ability; Experience the exploration process of function images and their properties, and develop students' cooperative consciousness and ability in cooperative communication activities. Experience the process of solving practical problems by using linear functions and their images, and develop students' mathematical application ability; Through the identification and application of function image information, students' thinking ability in images is cultivated. 3. Understand the concept of function; Understand the related properties of linear functions and their images; Understand the relationship between equations and functions. 4. Can determine the function expression according to the given information; I can make a function image once and use it to solve simple practical problems.
Chapter 7: Binary linear equations 1 has experienced the process of abstracting binary linear equations from practical problems, realized the model idea of equations, developed students' ability to solve practical problems flexibly by using relevant knowledge, and cultivated a good sense of mathematical application. 2 understand the related concepts of binary linear equations, and you can solve simple binary linear equations; According to the quantitative relationship in specific problems, we can list binary linear equations, solve simple practical problems and test the rationality of the solutions. Understand the image solution of binary linear equations and the relationship between equations and functions. Understand the elimination thought of binary linear equations, so as to preliminarily understand the reduction thought of turning the unknown into the known and turning complex problems into simple problems.
Teaching measures and methods of verbs (abbreviation of verb)
1, theoretical learning:
Do a good job in learning educational theory, especially the latest educational theory, keep abreast of the information and trends of curriculum reform, change teaching concepts, form new curriculum teaching ideas, and establish modern scientific educational concepts. Listen to lectures, learn from other teachers and learn some excellent teaching methods and skills.
2. Make plans for each period:
In order to do a good job in teaching, under the guidance of the idea of curriculum reform, according to the school's work arrangement and the teaching tasks and contents of senior two mathematics, the semester teaching work is planned and arranged as a whole, and the progress of each unit and topic is planned in detail.
3. Prepare for each class.
Seriously study the syllabus and teaching materials, do a good job in the overall preparation of lessons at all stages of junior high school, be aware of the overall teaching situation and various units and topics, prepare students to learn and master knowledge, write lesson plans for each class, ensure a good class, and do a good job in after-class reflection and after-class summary, so as not to improve their teaching theory level and teaching practice ability.
4. Do a good job in classroom teaching.
Creating teaching situations and stimulating learning interest, Anse once said: Interest is the best teacher. ? Stimulating students' interest in learning is one of the important means to improve the quality of mathematics teaching. Combined with the teaching content, select some math problems closely related to the reality for students to solve. The teaching organization is reasonable and the language of teaching content is vivid. Do everything possible to make students love listening and listening, so as to improve the quality of classroom teaching in an all-round way. Establish study groups, implement intra-group assistance and inter-group competitions, and enhance students' learning confidence and self-study ability. Pay attention to the guidance of double basics and learning methods. Actively apply new teaching methods and advanced teaching means such as trial teaching method.
Step 5 correct homework
Correcting each student's homework carefully, the students' homework defects are known to both teachers and students. Give timely feedback to each student's homework modification and mastery, and correct it again, so that students have a better chance to consolidate.
6. Do a good job in extracurricular counseling
Caring for students in an all-round way is the sacred duty of teachers. After class, we can give students targeted guidance, answer students' difficulties in understanding textbooks and solving specific problems, guide extracurricular reading to teach students in accordance with their aptitude, and make gifted students as excellent as possible? Are you full? , further improve; Let poor students clear students' obstacles in time, enhance students' confidence, as far as possible? Can you eat? . Actively carry out extracurricular activities such as mathematics lectures and extracurricular interest groups. Fully mobilize students' enthusiasm for learning mathematics, broaden their knowledge horizons, develop their intelligence level and improve their ability to analyze and solve problems.
Teaching progress plan of intransitive verbs this semester
Chapter 1 "Axisymmetry in Life" 9 class hours
Chapter II Pythagorean Theorem 5 class hours
Chapter III Real Number 10 Class Hours
Chapter IV "Preliminary Understanding of Probability" 5 class hours
Chapter V Plane Cartesian Coordinate System. 8 class hours
Chapter 6 "Linear Function" 9 class hours
Chapter 7 "Binary Linear Equations" 9 class hours
Always review 2 class hours.