Selected Mathematics Teaching Plans for Senior High School 1
First, the nature, status and role of teaching materials
Logarithmic function (the second lesson) is the content of the second lesson in the eighth section of chapter 2 of senior one mathematics (the first volume) published by People's Education Publishing House in 20__ _. This section involves the related knowledge of logarithmic function and is divided into three classes. The following is the second lesson to review and consolidate the images and properties of logarithmic function, so as to solve three kinds of logarithmic ratio problems, which is the continuation and development of what we have learned (exponential function, exponential ratio size, logarithmic function) and also reflects the fact that,
Second, the teaching objectives
According to the requirements of the syllabus and the position and function of this course, combined with the cognitive characteristics of senior one students, the teaching objectives are as follows:
Learning objectives:
1, review and consolidate the images and properties of logarithmic functions.
2. Compare the size of two numbers by using the properties of logarithmic function.
Ability goal:
1. Cultivate students' awareness of using graphics to solve problems, that is, the ability to combine numbers with shapes.
2. Students' ability to solve new problems by using the knowledge and experience they have learned.
3, explore methods, the ability to explain their views in an orderly manner.
Moral education goal:
Cultivate students' good personality qualities such as diligent thinking, independent thinking and cooperative communication.
Third, the focus and difficulty of the textbook
Logarithm plays a connecting role. The former is to review and consolidate the image and properties of logarithmic function, and the latter is to embody and apply the mathematical thought and method of ratio problem in exponent again, which lays the foundation for solving logarithmic equation and logarithmic inequality. Therefore, the focus of this lesson is to compare the size of two numbers by using the image properties of logarithmic functions.
Teaching will focus on the following two links:
1, using students' experience after previewing, resources are shared and complemented.
2, through appropriate practice, strengthen the mastery of problem-solving methods and understanding of principles.
On the other hand, students have a certain understanding of the knowledge in the textbook after preview, but it is challenging for students to explore independently in groups and supplement the third analogy problem-the same reason but different bottom types. So determine the difficulty of this lesson: the logarithm ratio of the same truth with different bases.
Teaching will break through the teaching difficulties in the following three aspects:
1. Teachers should adjust their roles, make students the masters of learning, and teachers should play a guiding role in it.
2. When exploring new problems in group cooperation, we should pay attention to student-student cooperation and teacher-student interaction, encourage students with language in time, and enhance their confidence in participating in the discussion.
3. Multimedia-assisted teaching is adopted in this course, which saves time, speeds up the progress of the course and enhances the intuition.
Fourthly, the analysis of students' learning situation.
Advantages: After several years of mathematics study, senior one students have a certain mathematical literacy, and have a certain application ability and awareness of the knowledge they have learned or the mathematical thinking methods they have used. As far as this course is concerned, the images and properties of logarithmic functions have just been learned. This course is the application of knowledge. As far as mathematical ability is concerned, the ideas and methods to solve the problem of exponential ratio can be used for reference. In addition, the ability to combine numbers and shapes and the ability to summarize are special.
Difficulties that students may encounter: From the teaching content of this lesson, the logarithmic ratio of the third kind is a supplementary content outside the textbook, and there is no preview experience. It is challenging for students to complete the construction of problem-solving ideas quickly through cooperative inquiry in class. From the perspective of students' ability, the ability to explore methods and explain ideas in an orderly manner needs to be strengthened, and the understanding of the relationship between knowledge is still insufficient.
Characteristics of teaching methods of verbs (abbreviation of verb)
The new curriculum emphasizes that teachers should adjust their roles and change the traditional educational methods. In terms of educational methods, we should take students as the center, let students become the masters of learning and let teachers play a guiding role. Based on this, this course follows this principle and focuses on the teaching methods of question inquiry and inspiration. Starting from previewing and exchanging experiences, exploring new problems, and then reviewing and summarizing after the topic, we should take students as the center, reflect students' dominant position everywhere, let students talk more, analyze more, think more and summarize more, guide students to explain their views in their own language, strengthen understanding, solve problems in student-student cooperation and teacher-student interaction, and lay a foundation for improving students' ability to analyze and solve problems. This course adopts multimedia-assisted teaching, which saves time, speeds up the progress of the course and enhances the intuition.
An analysis of the teaching process of intransitive verbs
1, the courseware shows the learning objectives of this lesson.
Design intention: to clarify the task and stimulate interest.
2. Review the old knowledge (the form has been filled out to review the images and properties of logarithmic functions).
Design intention: review the knowledge and methods learned, build a platform for students, form the connection and framework between knowledge, and lay the foundation for the next application.
3. Experience exchange after rehearsal
1) Logarithmic ratio with the same base
2) Logarithmic ratios of different cardinality and true values.
Take the textbook example as an example, exchange ideas on solving problems, summarize the general methods of this analogy example after the problem, and then strengthen understanding and consolidation through practice.
Design Intention: Through students' preview, summarize the method and the types of questions to which it applies, and explain their own learning experience in an orderly way. The teacher only needs to play a guiding role, guiding students to rise from the surface of the topic to the essence of the topic, so as to find an effective way to solve the problem.
4. Cooperative exploration-logarithmic ratio of homomorphism.
Take Example 3 as an example. Students will explore the problem-solving methods in groups. It is expected that there are two ways: one is to convert this type into a heterogeneous type with the same bottom by using the formula of changing the bottom, and solve this problem by using the method summarized before. The second is to explore the images of different logarithmic functions in the same rectangular coordinate system by using the size relationship of specific logarithms, so as to solve this kind of ratio problem.
Design intention: This part is the difficulty of this lesson. Give full play to students' initiative, cultivate students' awareness of active learning, and provide a good opportunity to exercise students' abilities in all aspects, accumulate experience and methods for future inquiry learning, and fully embody the teaching concept that "it is better to teach people to fish than to teach them to fish". In addition, the solution of mathematical problems is only half, and it is more important to look back after solving problems, that is, to reflect. Without reflection, they will miss an important and beneficial aspect of solving the problem. Therefore, after solving this problem, let students reflect and understand that the key to using nature to solve problems is to have a picture in their minds and promote "number" with "shape".
5. Summary
Summarize the harvest of this class through the students' independent summary. Teachers can guide and summarize from three aspects: what they have learned, mathematical ideas and mathematical methods.
Step 6 think about the problem
Taking 20__ college entrance examination questions as an example, let students apply what they have learned and enhance their interest in mathematics learning.
7. Homework
Include two aspects:
1, do your homework
2. Preview homework before the next class
Seven, teaching effect analysis
From the teaching example of this class, this method of previewing the textbook content first and then exchanging the learning results in class is very effective, which can not only complete the teaching task well, but also give full play to the students' initiative. In the process of independent inquiry, students discuss in groups, and I participate in group discussion. For capable groups, after exploring a method, I can encourage more method exploration. For groups with weak ability, I can give appropriate hints to make students move, gain something in class and enhance their self-confidence. In addition, the students' summary answers may be slow. I will listen patiently, encourage them in time, and give them smiles and verbal encouragement. The effect is very good. The summary link is my teaching attempt to summarize the methods of senior one students themselves. Because students have only trained for half a semester, they can only reach the level of summing up knowledge. In the future training, they will also add the summary content of mathematical thinking methods, so that these mathematical terms will make students no longer feel abstract, but become concrete, operable and concrete problem-solving tools.
Selected Text 2 of Mathematics Teaching Plan for Senior One.
Teaching objectives:
(1) Understand the representation of a set;
(2) Being able to correctly choose natural language, graphic language and assembly language (enumeration or description) to describe different specific problems and feel the significance and function of assembly language;
Teaching emphasis: master the representation method of set;
Teaching difficulties: choose the appropriate expression;
Teaching process:
First, review review:
1. Definition of sets and elements; Three characteristics of elements; The relationship between elements and sets; Commonly used number sets and their representations.
2. What are the elements of the set {1, 2}, {( 1, 2)}, {(2, 1)} and {2, 1} respectively? What does it matter?
Second, the new curriculum teaching
(1). Representation of set
We can use natural language and graphic language to describe a set, but this will bring us a lot of inconvenience. In addition, enumeration and description are often used to represent a collection.
(1) enumeration: The method of enumerating the elements in a collection one by one and enclosing them in curly braces is called enumeration.
Such as: {1, 2, 3, 4, 5}, {_ _ 2, 3 _+2, 5y3-_ _, __2+y2}, …;
Note: 1. The elements in the collection are out of order, so there is no need to test when using enumeration to represent the collection.
Consider the order of the elements.
2. Separate each element with a comma;
3. Elements cannot be duplicated;
4. Elements in a set can be counted, points, algebraic expressions, etc.
5. For the set containing more elements, when expressed by enumeration, ellipsis can only be used after the laws between elements are clearly displayed, because the set of natural numbers n is expressed by enumeration as follows.
Example 1. (textbook example 1) The following sets are enumerated:
(1) The set of all natural numbers less than 10;
(2) The set of all real roots of equation __2=__;
(3) A set consisting of all prime numbers from 1 to 20;
(4) A set of solutions of equations.
Thinking 2: (Textbook P4 Thinking Questions) Get the definition of descriptive method:
(2) Description: describes the common attributes of the elements in the collection and is written in curly braces.
Specific methods: write down the general symbols and value (or variation) ranges of the elements in this set with curly braces, then draw a vertical line, and write down the * * * same characteristics of the elements in this set after the vertical line.
Universal format:
For example: {_ | _-3 > 2}, {(_ _, y)|y=__2+ 1}, {_ | right triangle}, ...;
Description:
1. The last paragraph of textbook P5;
2. The descriptive representation of a set should pay attention to the representative elements of the set, such as {(_ _, y)|y= __2+3__+2} and {y|y= __2+3__+2}, which are two different sets. As long as it does not cause misunderstanding, the representative elements of the set can also be omitted, such as {_ _ _.
Discrimination: The {} here already contains the meaning of "all", so there is no need to write {all integers}. It is also wrong to write {real number set} and {R} below.
Example 2. (Textbook Example 2) Try to express the following sets by listing and describing respectively:
The set of all real roots of (1) equation _ _ 2-2 = 0;
(2) A set consisting of all integers greater than 10 and less than 20;
(3) The solution of the equation.
Thinking 3: (P6 thinking in textbook)
Note: Enumeration and description have their own advantages, and it is necessary to decide which representation to adopt according to specific problems. It should be noted that enumeration is not suitable when there are many elements or infinite elements in a general collection.
(2). Classroom exercises:
1. Exercise 2 of the textbook P6;
2. Represent the set in an appropriate way: all odd numbers greater than 0.
3. Let A = {_ | ∈ z, __∈N}, then its element is.
4. The known set a = {_ |-3
Summarize:
Starting with examples, this lesson introduces common representations of sets, including enumeration and description.
Task:
1. Exercise 1. 1, question 3.4;
2. Preview the basic relationship between sets after class.
Selected Mathematics Teaching Plans for Senior One 3
Teaching objectives:
1. Understand the necessity and importance of stratified sampling in combination with actual problem scenarios;
2. Learn to extract samples from the population by stratified sampling;
3. Simple random sampling, systematic sampling and stratified sampling methods, and reveal their relationships.
Teaching focus:
Understand the method of stratified sampling through examples.
Teaching difficulties:
Steps of stratified sampling.
Teaching process:
First, the problem situation
1. Review the concepts, characteristics and application scope of simple random sampling and systematic sampling.
2. Example: A school has students' names in senior one, senior two and senior three. In order to understand the vision of the whole school, how to choose a capacity of.
Second, student activities.
Can sampling be simple random sampling or systematic sampling? Why?
It is pointed out that simple random sampling or systematic sampling can not accurately reflect the objective reality because of the difference of students' eyesight in different grades. When sampling, we should not only ensure that every individual has an equal chance of being drawn, but also pay attention to the hierarchy of individuals in the whole group.
Because the ratio of sample size to the total number of individuals is 100: 2500 = 1: 25,
Therefore, the number of individuals extracted from each level is. That's 40, 32, 28.
Third, structural mathematics.
1, stratified sampling: when the population is known to be composed of several obviously different parts, in order to make the sample reflect the overall situation more objectively, the population is often divided into several distinct parts according to different characteristics, and then sampling is carried out according to the proportion of each part in the population. This kind of sampling is called stratified sampling, and the divided part is called "layer".
Description:
① In stratified sampling, because the ratio of the number of individuals extracted from each part to that part is equal to the ratio of the sample size to the total number of individuals, the possibility of each individual being extracted is equal;
(2) Stratified sampling makes full use of the information we have, making the sample representative, and different sampling methods can be adopted at each level according to the specific situation, so stratified sampling is widely used in practice.
Selected Mathematics Teaching Plans for Senior High School 4
Hello, judges and experts! Today, the content of my lecture is the fifth section of chapter 1 of Mathematics, a full-time textbook for senior high schools (compulsory) published by People's Education Press.
The following lectures are conducted from six aspects: teaching material analysis, analysis of teaching objectives, analysis of teaching emphases and difficulties, teaching methods and learning methods, classroom design and effect evaluation.
I. teaching material analysis
(A) the status and role of teaching materials
"One-dimensional quadratic inequality solution" is not only the extension and development of junior middle school one-dimensional quadratic inequality solution in knowledge, but also the application and consolidation of collective knowledge in this chapter, and also paves the way for the definition of functions and the teaching of value range in the next chapter, and plays the role of chain. At the same time, this part well reflects the internal relationship and mutual transformation of equation, inequality and function knowledge, and contains rich mathematical thinking methods such as number-shape induction, transformation and combination, which can better cultivate students' observation ability, generalization ability, inquiry ability and innovation consciousness.
(B) Teaching content
This section is divided into 2 class hours. In this lesson, we explore the solution set of quadratic inequality in one variable through the image of quadratic function. By reviewing the relationship of "three firsts", that is, the relationship between a linear function and a linear equation and a linear inequality; Find the relationship between "three quadratic" and the old belt, that is, the relationship between quadratic function and quadratic equation and quadratic inequality; Using the thinking mode of "painting, watching, speaking and using", we can get the solution set of quadratic inequality, taste the beauty of harmony in mathematics and experience the fun of success.
Second, the analysis of teaching objectives
According to the requirements of the syllabus, the characteristics of this textbook and the cognitive rules of senior one students, the teaching objectives of this course are determined as follows:
Knowledge goal-understanding the relationship of "three quadratic"; Master the method of solving sets by looking at pictures, and be familiar with the solution of quadratic inequality in one variable.
Ability goal-looking for solution sets by looking at images, cultivating students' transformation ability from form to number, from concrete to abstract, from special to general.
Emotional goal-create problem scenarios, stimulate students' passion for observation, analysis and exploration, and strengthen students' sense of participation and subjective role.
Third, the analysis of important and difficult points
One-dimensional quadratic inequality is one of the most basic inequalities in high school mathematics and an important tool to solve many mathematical problems. The focus of this lesson is: the solution of quadratic inequality in one variable.
We should grasp this key point. The key is to understand and master the method of using the image of quadratic function to determine the solution set of univariate quadratic inequality-image method. Its essence is to understand the solution of equation and the internal relationship between the solution set of inequality and the abscissa of the corresponding point on the image of function by using the thinking method of combining numbers and shapes. Because junior high school has not specially studied such problems, senior one students are unfamiliar with them and it is difficult to really master them. Therefore, the difficulty of this lesson is determined as: the relationship between "three quadratic". To break through this difficulty, let students sum up the relationship of "three firsts" and make a good preparation.
Fourthly, analyze the teaching methods and learning methods.
(1) Guidance on learning the law
The main aspect of teaching contradiction is students' learning. Learning is the center and learning is the purpose. Therefore, students should be constantly guided to learn to learn in teaching. This course is mainly to teach students the learning methods of "painting by hand, moving eyes, thinking with brain, speaking in words, being good at refining and studying hard", which increases the opportunities for students to participate independently, cooperate and communicate, teaches students the ways to acquire knowledge and the methods to think about problems, and makes students truly become the main body of teaching; Only in this way can students have new ideas in learning, new gains in thinking and new gains in practice, and students will gradually feel the beauty of mathematics and have a sense of accomplishment, thus improving their interest in learning mathematics. Only in this way can classroom teaching have the characteristics of the times and meet the needs of cultivating "innovative" talents under quality education.
(B) Analysis of teaching methods
The guiding ideology of this course design is: modern cognitive psychology-constructivism learning theory.
Constructivist learning theory holds that learning should be regarded as students' active constructive activities, and students should be related to a certain knowledge background, that is, the situation. Learning in the actual situation can make students assimilate and index the new knowledge they want to learn by using the existing knowledge and experience, so that the acquired knowledge is not only easy to keep, but also easy to migrate to unfamiliar problem situations.
This course adopts the teaching method of "inducing thinking and exploring", and takes the problem as the starting point to guide students to "draw, see, speak and use". Better explore the solution of unary quadratic inequality.
Selected Texts of Mathematics Teaching Plan for Senior One 5
First, the teaching objectives
1. knowledge and skills: master the basic skills of drawing three views and enrich students' spatial imagination.
2. Process and method: Through students' own personal practice, hand-drawing, experience the role of the three views.
3. Emotional attitude and values: improve students' spatial imagination and experience the role of the three views.
Second, teaching emphasis: drawing three views of simple geometry and simple assembly;
Difficulties: Identify the space geometry represented by three views.
Third, the guidance of learning the law: observation, hands-on practice, discussion and analogy.
Fourth, the teaching process
(A) the creation of scenarios to uncover the theme
Show the landscape map of Lushan Mountain —— "When viewed from the side of the mountain, the distance is different", which shows that the visual effect of the same object may be different from different angles. To truly reflect an object, you can look at it from multiple angles.
(2) Teaching new courses
1, central projection and parallel projection:
Central projection: the projection formed by light scattering from a point;
Parallel projection: projection formed by parallel beams of light.
Orthographic projection: In parallel projection, the projection line faces the projection plane.
2, three views:
Front view: light is projected from the front of the geometry to the back;
Side view: the projection of light from the left side to the right side of the geometry;
Top view: light is projected from the upper surface of the geometry to the lower surface.
Three views: the front view, side view and top view of the geometry are collectively called three views of the geometry.
Three-view drawing rules: long alignment, high alignment and equal width.
Long alignment: the front view and the top view have the same length and are aligned with each other;
Height: the front view and side view are equal in height and aligned with each other;
Equal width: the width of top view and side view is equal.
3. Draw three views of the cuboid:
Front view, side view and top view are orthogonal views of geometry from the front, left side and top respectively, and they are all plane graphics.
The three views of a cuboid are all rectangles, front and side views, side views and top views, and both top and front views have a side length.
4. Draw three views of cylinder and cone:
5. Inquiry: Draw three views of a triangular pyramid with a square bottom and congruent sides.
(3) Consolidate exercises
Textbook P 15 Exercise 1 2; P20 exercise1.2 [group a] 2.
(4) inductive arrangement
Ask the students to review and publish how to make three views of space geometry.
(5) Transfer
Textbook P20 Exercise 1 .2 [Group A]1.