As a nameless and selfless educator, it is necessary to carry out meticulous preparation of the lecture notes, which will help the success of teaching and improve the quality of teaching. Then write the lecture notes need to pay attention to what problems? The following is my compilation of the seventh grade next book "Explore the conditions of parallelism of two straight lines" lecture notes sample, welcome to read, I hope you can enjoy.
7th grade next book "Explore the conditions of parallelism of two straight lines" said draft 1First, say the analysis of the teaching materials
"Explore the conditions of parallelism of two straight lines" is the first lesson of the second chapter of the second section of the seventh grade book of the North Normal University edition, the students in the intuitive understanding of the angle, the parallel lines and perpendicular, and accumulated a preliminary experience of mathematical activities, this section will further explore the facts about parallel lines, the textbook by setting up the process of observation, operation, summary and other exploratory activities, to explore the conditions of judgment, in the intuitive understanding of the basis, training students to make simple reasoning to deepen the understanding of the parallel lines, and further develop the spatial concepts of the students, the section in the knowledge, mathematical thinking, the development of the students' ability are very important.
Second, the teaching objectives
According to the idea of the arrangement of the content of the textbook, combined with the cognitive characteristics of the first-year students, I formulated the following educational and teaching objectives:
Knowledge Objectives:
1) to experience the process of exploring the conditions of parallelism of the two straight lines, to experience the process of exploring the conditions of parallelism of the straight lines, to master the the conclusion of using the equality of congruent angles to determine the parallelism of straight lines, and be able to solve some problems.
2) Identify the congruent angles formed by the "three lines and eight angles", and use a triangle ruler to draw a parallel line to a known point outside the line.
Ability Objectives:
To experience observation, manipulation, imagination, reasoning, communication and other activities, to experience the use of manipulation, induction to obtain mathematical conclusions, and to further develop spatial imagination, reasoning ability and the ability to express themselves in an organized manner.
Emotional Objectives:
To enable students to actively participate in the exploration and exchange of mathematical activities, to experience the close connection between mathematics and real life, to stimulate students' desire for knowledge, and to feel the importance of cooperation with others.
Third, the teaching focus, difficult points
According to the new standards, in the study of teaching materials on the basis of I determined:
Key: master the conditions of the two straight lines parallel to be able to correctly recognize the congruent angle, the interior angle, the same side of the interior angle in the figure of the position.
Difficulties: the process of determining the parallelism of two straight lines
The basis for this are:
(1) From the point of view of the body of knowledge, it is the study of angles, parallel lines and perpendicular lines of mathematical activities, on the basis of the exploration, the initial understanding of the reasoning and argumentation, and the gradual cultivation of the students' ability to think and the development of students' spatial concepts.
(2) From the point of view of the cognitive process of students, the main hands-on practice, independent exploration, cooperative exchange.
Fourth, the teaching method, learning method
For the age of the first year students and psychological characteristics, as well as their level of knowledge, this lesson I "hands-on, independent exploration, cooperative learning, summarization, application of the practice" method, so that students are always in the active learning state of learning. The students are always in the active learning state of learning, so that students have ample opportunity to think, with the help of teaching aids, multimedia presentations, so that students in practice thinking, in the process of thinking of summarizing the process of cultivating their spatial concepts, reasoning ability and the ability to express themselves in an organized manner.
Teaching method: operation method, observation method, discussion method, multimedia teaching.
Learning method: hands-on operation, observation and conjecture, independent investigation, cooperation and communication, summarization.
Teacher preparation: triangle board, protractor, three even wooden bars, pegs, multimedia courseware.
Student preparation: triangle board, protractor, three uniform wooden strips, pegs.
V. Teaching process:
(a) Review and review, situational introduction
First of all, review the definition of parallel lines and the conditions for determining the parallelism of two straight lines (the parallelism of the passages) learned in the last semester. And let the students talk about parallel lines in daily life . Recognition, through the students' own recollection can avoid the traditional teaching of a question-and-answer approach, but also can be active in the students' thinking, to prepare for the study of the new lesson.
I also make full use of the examples in the book to ask two students to personally do the small carpenter demonstration, ask questions to introduce the new lesson. Through the creation of scenarios to stimulate students' interest in learning, but also let the students realize that math and real life have a close connection.
(2) hands-on, cooperative inquiry:
The first link: break through the difficult, cooperative exploration of the concept of congruent angles. The concept of congruent angles is the difficulty of this lesson, but also the difficulty of the chapter, in order to break through the difficulty, I set up the following questions:
1, ∠1, ∠5 of the side of the line where the straight line is which line?
2. Which is the common **** line? (The common **** line is the third straight line)
3. ∠1 and ∠5 can be seen as the angles of which two lines intercepted by the third straight line?
4. What are the similarities in position between ∠1 and ∠5? Emphasize the positional relationships.
Emphasize the two words "together". "together": on the same side of the intercepted line, "two together" on the same side of the intercepted line. In order to facilitate the understanding of congruent angles, I also made up a catchphrase: look at the three lines, find the truncation line, and then the position of the fine distinction. By finding other congruent angles, we can develop students' observation skills and deepen their understanding of congruent angles. In this I also designed an exercise to consolidate the concept of congruent angles
5, with the same method to recognize: interior angles, congruent interior angles.
The second link: independent investigation, cooperation and exchange of the relationship between the location of the line a,b and the size of ∠1, ∠2. At this time, I let students take out the three prepared wooden strips to fix the wooden strips b,c to rotate the wooden strips a according to the requirements, in the process of rotation, observe the graphics, and answer the following three questions:
1. Observe the change of ∠1 and its relationship with the size of ∠2.
2. What changes do you notice in the positional relationship between the wooden bar b and the wooden bar a?
3. When is wooden bar b parallel to wooden bar a?
Have students work with the questions!
As this part is the focus of this lesson, I give students enough time to independently operate, observe, and find out the conclusion through their own multiple operations, and then communicate in the group to express their views, and finally choose a representative to speak and draw conclusions. Through the operation, students can accumulate experience in mathematical activities and establish spatial concepts. Through exchanges, students with different levels of knowledge strengthen their communication, their personalities are promoted, and they develop the spirit of cooperation with others and the ability to express themselves in an organized way. The purpose of my setting 3 questions is to guide students to connect the abstract quantitative relationship with the intuitive positional relationship, which reduces the difficulty. The students who answered the questions were recognized in time, so that the students could experience the success . Joy, but also stimulate students' interest in learning math.
Let the students again with the previous three wooden bar operation, observation and communication, to draw conclusions. What kind of angle is a congruent angle? As students are just exposed to geometric knowledge, logical thinking ability is relatively weak, so I pay attention to guide students to summarize the conclusions obtained.
The third link: summarize the theorem. Guiding students to use their own language to summarize the conclusions of the last two parts of the focus of this lesson: congruent angles are equal, two straight lines are parallel, which both the development of the students' reasoning ability and to strengthen the students' ability to express themselves in a structured manner.
(C) application and consolidation, gradually improve:
This part of the design of the five exercises from shallow to deep, compare, test you, I can do, I'm the best, expanding thinking. These problems I explained by letting the students themselves, I give appropriate comments and guidance. This not only improves student participation, but also experiences the value of the students themselves!
(D) self-evaluation, review and summarize
Let students communicate with each other in this lesson what to gain? This cultivates both the ability to generalize and develop students' divergent thinking. I appreciate the results of student learning at the same time, the students said the content of the summary into a point to summarize.
1. The concept of congruent angles
2. Congruent angles are equal and two lines are parallel.
(E) homework assignment, expanding thinking
Part A is the consolidation of basic knowledge, while Part B is to improve the ability. This not only consolidates the students' foundation, but also expands their thinking. It also focuses on the development of all students! This is also the idea of the new curriculum reform.
(VI) Board Design:
Explore the conditions for two lines to be parallel
1. Recognize the three lines and eight angles
Congruent angles
Interior angles
Interior angles on the same side
2. Explore the conditions for two lines to be parallel
Congruent angles are equal, and the two lines are parallel
The geometric language is: ∵ ∠1 = ∠2 (known)
∴a‖b (congruent angles are equal, two straight lines are parallel)
3Exercises to explain
Six, say the teaching effect evaluation
Through the teaching of this lesson, I think that the students in the participation of the students to stimulate their own interest and desire to learn, and its participation in the ability to work together will be somewhat Improvement, independent construction of their own logical thinking ability, for the next step in learning to lay a good foundation
My speech is over, thank you!
First, the analysis of learning
(1) Textbook analysis: this lesson is the second section of Chapter 5, the first lesson, the relationship between the location of two straight lines in the plane is the study of "space and graphics" of the basic problem. These content students in the first two semesters have been exposed to, this lesson in the students' existing knowledge and experience on the basis of continuing to explore the two straight lines in the plane parallel to the positional relationship between the axiom of parallelism and its inference. Therefore, this lesson plays a role in the material.
(2) analysis of the situation: students have learned before this straight line, line segments and rays, on the line has been a preliminary understanding, which for the successful completion of the teaching task of this lesson laid the foundation, but for the understanding of the concept of parallel, students may have certain difficulties, so the teaching should be simple to understand, in-depth analysis.
Second, the objectives of the analysis:
1, through some examples in life to experience the concept of parallel lines (knowledge and skills)
2, understand the positional relationship between the two straight lines in the same plane, through the students to observe, manipulate, discuss and other mathematical group activities, so that the students feel that mathematics is actually full of infinite exploratory and creative. (Process and Method)
3. In the process of exploring the axiom of parallelism and its corollaries, students experience understanding problems from a mathematical point of view, and develop strategies and methods for solving problems. (Emotional attitude and value)
3. According to the above analysis of the teaching materials and objectives, so I will summarize the teaching focus and difficulties of this lesson as follows:
Focus: Students explore this process of parallel axioms through observation, drawing and discussion, **** with.
As the abstract thinking ability of seventh-grade students is still in the early stages, and have never been exposed to the idea of inverse
Difficulties: is that the students themselves independently of the parallel axiomatic reasoning clearly reasoning this problem.
Four, teaching and learning method analysis
I will be summarized as a 4-word key: move, explore, enjoy, seepage.
1, moving: through the multimedia animation scenarios, encourage students to do, draw, think, speak;
2, explore: stimulate students a strong desire to explore;
3, music: prompt students to learn, think, explore, and innovate;
4, seepage: continuous penetration of observation, conjecture, induction, analogy and other mathematical thinking and methods to the students, and strive to do so. and methods to the students, and strive to do "closely linked with the students' life practice", so that students try to "explain the reason".
V. Teaching process:
(1) create a situation to introduce the subject
show the straight bamboo, the tower, the flag of the picture, so that students can observe its characteristics.
Design intention: through the life of common graphic examples to let the students find their own **** the same point, the introduction of the subject of parallel lines and the concept of exercise of the students to self-discovery, summarize, the ability to express!
(2) cooperation and communication to explore new knowledge
1, establish a model
In the process of rotation of the wooden bar, there is no straight line a and straight line b do not intersect the position?
Design intent: once again through dynamic thinking to emphasize the characteristics of the two parallel lines without intersection between the two, to strengthen students' understanding and memory!
Then show students a rectangle, ask students a rectangle is not in the same plane of the two prongs of the line is intersecting, whether parallel?
Design intent: to emphasize that the parallel lines are in the same plane on the basis of the conditions of locking the establishment, to strengthen the impression of student awareness!
2, the concept of parallel lines and conclusions
In the process of rotation of the wooden bar there is a straight line a and straight line b do not intersect the position, then the line a and b parallel to each other (parallel), recorded as a ‖ b, read a parallel to b. Conclusion: in the same plane, the positional relationship between the two straight lines are only two kinds of intersecting and parallel.
2, the drawing of parallel lines: (1) put (2) leaning (3) push (4) painting
Hands-on:
3, over the straight line AB outside of a point P for the straight line AB parallel lines, see what you can make? How many can you make?
Design intent: through the above preliminary understanding of parallel lines and knowledge, immediately let the students hands-on, learning to use, and emphasize the normative nature of the drawing, on the basis of which the axiom of parallelism and inference.
The axiom of parallelism: through a point outside the line, there is only one line parallel to the line.
Corollary to the axiom of parallelism: if two lines are parallel to a third line, then these two lines are also parallel to each other.
That is to say: if b‖a,c‖a,then b‖c.
(3) Feedback practice to implement the new knowledge
1.Consolidation practice
Here are a few judgmental questions
(1) Two lines that do not intersect are called parallel lines. (Wrong)
(2) In the same plane, two lines that do not intersect must be parallel. (True)
(3) Through a point there is and only one line parallel to a known line. (Wrong)
(4) Three straight lines a, b, c in the same plane, if a‖b, b‖c, then a‖c.(Right)
Design intention: through the judgment question set "the same plane", "do not intersect", "a point outside the line". "a point outside the line" to visualize the basic knowledge of students, while strengthening students' understanding of the basic concepts and properties and thinking!
2, comprehensive use
Read the following statements, and draw the graph:
(1) point P is a point outside the line AB, the line CD passes through the point P, and is parallel to the line AB;
(2) the line AB, CD is intersecting straight lines, the point P is a point outside the line AB, CD, the straight line EF passes through the point P and is parallel to the line AB, and intersects the line CD intersects in E.
Design intent: through the students' own practical hands-on exercise students will knowledge into hands-on ability, so that students not only learn knowledge, but also to exercise their practical hands-on ability!
3, broaden the exploration
Through the Xiaohong for his mother to design a provision for three rows, and then change a variety of formations of the square dance queue, as a way to lead to the parallel, intersection of the relevant knowledge points.
Xiaohong's mother is a dance teacher, once almost to the June 1 Children's Day, need to choreograph a dance, the provisions of the three rows, and then change a variety of formations. Xiaohong heard, happy to say to his mother, "This is the math knowledge we have learned, let me to staff for you." Xiaohong used the knowledge we had just learned: the relationship between the positions of three straight lines in the plane to design four kinds of formations. Xiaohong's mom took a look and saw that it was a good idea to have a lot of variations in the formation.
Do you know how Little Red designed it?
Design intention: through a life example to apply the students to learn parallel lines, intersecting lines inside the two intersect and intersect at a point of mathematical knowledge, reflecting the mathematics from life, and can help us solve life problems awareness and ideas
Six, the assignment of the formation of skills
Considering that the student's Individual differences, so I will be the class after class homework is divided into mandatory questions and optional questions, mandatory questions is a feedback on the content of this class, optional questions is an extension of the knowledge of this class.
1, P19, question 8 (mandatory) 2, P41, question 12 (optional)
VII, teaching design notes
1, focusing on the cultivation of students' interest in geometry learning.
2, focusing on the "basic knowledge" understanding and "basic skills" mastery, focusing on the cultivation of students' creative ability.
3, focusing on teachers and students, student-student exchanges.
Board Design:
5.2.1 Parallel Lines
1, the definition of parallel lines: Example:
2, the drawing of parallel lines: Student Drawing Area:
3, Parallelism Axiom:
4, Parallelism Axiom Corollary: Classroom Summarization: