Teaching plan 1 of high-quality mathematics open class in junior middle school
(A) the creation of situations, the introduction of new courses
Without tools, please divide a corner made of paper into two equal corners. What can you do?
What should I do if I change the paper in front of me into an angle that can't be folded, such as a board or a steel plate?
Design purpose: to gather students' thinking and create a good teaching atmosphere for the development of new courses.
(B) explore cooperation and exchange of new knowledge
(Activity 1) Explore the principle of angular bisector. The specific process is as follows:
Play the video material of Obama's visit to China-draw an umbrella-observe its cross section, so that students can clearly understand the corner relationship-draw the bisector; And use the geometric drawing board to dynamically demonstrate the opening and closing of the umbrella, so that students can intuitively feel the relationship between the umbrella surface and the main pole-let students design and make an angle bisector; And use the knowledge learned before to find the theoretical basis and explain the principle of making this instrument.
Design purpose: to perceive with examples in life. Taking the recent events as the introduction and the most common things as the carrier, let students feel that there is mathematics everywhere in their lives and appreciate the value of mathematics. Among them, the design and production of the bisector can cultivate students' creativity and sense of accomplishment and their interest in learning mathematics. Let the students finish Activity 2 easily.
(Activity 2) Through the above exploration, can you sum up the general method of using a ruler to make the bisector of a known angle? Do it yourself, and then exchange operating experience with your partner.
Complete this activity in groups, let teachers participate in student activities, find problems in time, give inspiration and guidance, and make comments more targeted.
The discussion results show that: according to the students' narration, the teacher demonstrated the method of making the known bisector with multimedia courseware;
Known: ao B.
Ask:? The bisector of AOB.
Exercise:
(1) Make an arc with O as the center and appropriate length as the radius, so that OA and OB intersect at m and n respectively.
(2) Take m and n as the center respectively, and the length greater than 1/2MN as the radius. Where are the two arcs? AOB internal intersection C.
(3) Ray OC, which is what you want.
Design purpose: let students understand painting more intuitively and improve their interest in learning mathematics.
Discussion:
1. In the second step of the above method, delete? Longer than MN? Is this condition all right?
2. The intersection of the two arcs made in the second step must be in? In AOB?
The purpose of designing these two questions is to deepen the understanding of the angular bisector and cultivate a good study habit of mathematical rigor.
Summary of student discussion results:
1. remove Longer than MN? In this case, the two arcs may not intersect, so the bisector of the angle cannot be found.
2. If two arcs are drawn with m and n as the center and the length greater than MN as the radius, the intersection of the two arcs may be in? In AOB \u, maybe? What are we looking for outside AOB? The intersection point inside AOB, otherwise the light obtained by connecting the intersection point of two arcs with the vertex is not? The bisector of AOB.
The bisector of an angle is a ray. It is neither a line segment nor a straight line, so the two restrictions in the second step are indispensable.
The feasibility of this method can be proved by congruent triangles.
(Activity 3) Explore the nature of the angular bisector.
Thinking: It is known that an angle and its bisector plus auxiliary lines form a congruent triangles; Form an congruent right triangle. How many pairs of such triangles are there?
The purpose of this design is to deepen the understanding of congruence.
Junior high school mathematics excellent open class teaching plan II
I. teaching material analysis
This lesson is selected from the third quarter of chapter 11 of the eighth grade mathematics textbook published by New People's Education Press. It is taught on the basis of learning the concept of angle bisector in seventh grade and the proof of congruence of right triangle just learned. The nature of angular bisector opens up a new way to prove the equality of line segments or angles, simplifies the proof process, and is also the continuation of congruent triangles's knowledge, which lays the foundation for the study of the judgment theorem of angular bisector. Therefore, this section plays a connecting role in the mathematical knowledge system. At the same time, the arrangement of teaching materials is from shallow to deep, from easy to difficult, and the knowledge structure is reasonable, which conforms to students' psychological characteristics and cognitive laws.
Two. content of courses
The teaching content of this course includes the nature and preliminary application of angular bisector method and angular bisector method.
Content parsing:
By making full use of real prototypes, teaching materials cultivate students' ability to build mathematical models in practical problems. The bisector of an angle is the basic drawing method in geometric drawing. The nature of the bisector is the continuation of congruent triangles's knowledge, and it is also an important basis for proving that two angles are equal or two line segments are equal in the future. Therefore, this section plays a connecting role in the mathematical knowledge system.
Third, the teaching objectives
Basic knowledge: understand the principle of ruler drawing and the nature of angle bisector.
2. Basic skills
(1) will draw the bisector of the angle with a ruler.
(2) congruent triangles will be used to prove the nature of the angular bisector.
(3) Simple geometric problems can be solved by using the bisector property theorem of angles.
3. Mathematical thinking method: from special to general.
4. Basic activity experience: experience the activity experience of verifying the correctness of geometric propositions from the process of operation, measurement, guess and verification.
Target resolution:
By letting students experience the process of hands-on operation, cooperation and communication, and independent inquiry, we can cultivate students' ability to solve problems with mathematical knowledge and mathematical modeling ability, understand the application of angular bisector in production and life, cultivate students' interest in exploring problems, enhance their confidence in solving problems, gain successful experience in solving problems, and stimulate students' enthusiasm for applying mathematics.
Fourthly, the analysis of learning situation.
The students who have just entered the second grade of junior high school have strong observation, operation and guessing ability, but their sense of induction and application of mathematics is weak, and their thinking lacks universality, agility and flexibility, which needs further guidance in classroom teaching. According to the students' cognitive characteristics and acceptance level, I set the teaching focus of the first class as: mastering the ruler drawing method of the angular bisector, understanding the nature of the angular bisector and applying it initially. The difficulty lies in exploring the essence of angular bisector.
Ways to break through teaching difficulties;
(1) Use multimedia to dynamically show the essential content of the properties of the angular bisector, and deepen the impression in students' minds, so as to correctly use the property theorem; (2) Through comparative teaching, let students choose simple problem-solving methods; (3) Creating inspiring question situations through multimedia, so that students can learn in a positive thinking state.
Verb (abbreviation of verb) teaching method and learning method
I insist on taking this course. Dialectical unity of teaching and learning, knowledge and ability? And then what? Let every student get all-round development? Principles, using the methods of guiding exploration and discovery, active inquiry and teaching, to guide students to learn independently, cooperatively and exploringly, and to guide students? Hands-on operation, cooperation and communication, independent exploration? Encourage students to think more, speak more and practice more, adhere to multi-directional communication between teachers and students, and strive to achieve the optimal combination of teaching methods and learning methods.
Teaching AIDS: According to the actual teaching needs of this class, I choose multimedia PPT courseware and geometry sketchpad software to teach, and dynamically display the relevant teaching contents, so that students can observe intuitively and leave a clear impression, so as to find constant changes. This attracts students' attention, stimulates students' interest in learning mathematics, and is conducive to students' understanding and mastery of knowledge points.
Teaching process design of intransitive verbs
Activity 1. Create a scene
[Teaching content 1]
There are many math problems in life:
Xiao Ming lives on the first floor of a residential building, just at point P on the bisector of the corner formed by a heating and natural gas pipeline. Starting from point P, two pipelines will be built, which are connected to the heating and natural gas pipelines respectively.
Question 1: How to build the shortest pipeline?
Question 2: What is the relationship between the lengths of two new pipelines? Draw it and have a look
[Integration point 1] Use multimedia to render the atmosphere and stimulate emotions.
Teachers use multimedia display to guide students into actual problem situations, and use information technology not only to vividly display problems, but also to make students feel life as if they were there. Students begin to draw pictures, guess and say the observed conclusions. Guide students to understand that there are many unknown properties of the angular bisector that we need to solve, and write the questions on the blackboard.
[Design Intention] According to the new curriculum concept, teachers should creatively use teaching materials as the first example of this course, starting from students' lives, stimulate students' interest in learning, cultivate students' awareness of using mathematical knowledge to solve practical problems, review the concept of the distance from point to straight line, and make a good knowledge reserve for subsequent learning.
Activity 2. Explore the experience
[Teaching Content 2]
To study the properties of the bisector of an angle, it is necessary to draw the bisector of the angle. Workers often draw a bisector of an angle with a simple tool as shown in the figure. Show the model of the instrument and introduce its characteristics (two opposite sides are equal). Put point A at the vertex of the angle, put AB and AD along both sides of the angle, and draw a ray AE through AC. AE is? Budd bisector
Teachers continue to guide, show the experimental process with multimedia, students dictate, and prove AE with triangle congruence method. Budd bisector
【 Design Intention 】 Help students experience being divorced from production and life, abstract mathematical models, and actively use what they have learned to solve problems.
From the above exploration, we can get the method of making the bisector of known angle.
[Teaching Content 3]
When a simple bisector is placed on both sides of a corner, both sides of the bisector are equal. How to draw from the perspective of geometric drawing? BC=DC, how to draw from the perspective of geometric drawing?
Teachers ask questions, students communicate in groups, summarize the bisector of the angle, and prove the bisector of the angle orally.
【 Design Intention 】 According to the drawing process, we get inspiration from the experimental operation, clarify the basic ideas and methods of geometric drawing, and communicate and summarize them between teachers and students.
Teachers first demonstrate drawing on the blackboard, and then demonstrate the drawing process and method with multimedia to deepen the impression and emphasize the standardization of ruler drawing.
Using the bisector of the triangle congruence proof angle, we can further clarify the topic and conclusion of the proposition and be familiar with the geometric proof process.
[Teaching Content 4]
Make a right angle? AOB bisector OC, extend OC reversely to get straight line CD. Please tell the position relationship between straight line CD and AB, and then make a 45? Angle.
Students think independently and find that the straight line AB is perpendicular to the CD.
【 Design Intention 】 By making a bisector at a special angle, students can master the method of making a point on a straight line perpendicular to a known straight line and making a special angle, thus cultivating students' divergent thinking.
[Teaching Content 5]
Let the students cut a corner with paper, fold the paper in half so that the two sides of the corner overlap, then fold the folded paper into a straight triangle (so that the first crease is the hypotenuse), then unfold it and observe the three creases formed by the two folds.
Question 1: What is the relationship between the first crease and the corner? Why?
Question 2: What is the relationship between the two creases formed by secondary folding and the two sides of the corner, and what is the relationship between their lengths?
Students began to cut paper and fold, and the teacher demonstrated the folding process with multimedia. After observing and thinking, students communicate in class: the first crease is the bisector of the angle, and the second crease is the distance from the point on the bisector of the angle to that point, both of which are equal in length.
【 Design intention 】 To cultivate students' hands-on operation ability and observation ability, and pave the way for further revealing the essence of the bisector.
[Teaching Content 6]
As shown in the figure: Draw the angle formed by origami and three creases in turn. Ask the students to discuss and communicate in groups, then verify the conclusion with geometry sketchpad software and explain the obtained properties in written language. (The points on the bisector of an angle are equidistant from both sides of the angle. )
[Integration point 2] Make use of the advantages of multimedia intuition to break through the teaching difficulties.
Write what is known, verify the analysis, and then write the proof process. The teacher summed up and emphasized the conditions and functions of the theorem.
The teacher narrates the conclusion in written language, guides the students to write what they know, proves it with graphic requirements, writes the proof process after analysis, and shows it with physical projection.
After the proof, the teacher emphasized that the proved proposition can be used as a theorem, and emphasized the steps of proving the written proposition.
[Design intent] Experience and practice? Guess what? Proof? The process of induction conforms to the cognitive law of students, especially the verification of conclusions. Information technology shows its irreplaceability here, which is more conducive to students' intuitive experience rising to rational thinking.
Activity 3. Cooperation and communication
[Teaching Content 7]
Judge true and false, and explain the reasons:
(1) as shown in figure 1, p is on ray oc, PE? OA，PF？ OB, then PE=PF.
(2) As shown in Figure 2, what is P? A point on the bisector OC of AOB, where E and F are on OA and OB respectively, then PE=PF.
(3) As shown in Figure 3, in? Take any point p from the bisector OC of AOB. If the distance from P to OA is 3cm, then the distance from P to OB is 3cm.
Using multimedia to show judgment questions, students can think independently, let students raise their hands to express their opinions, and the teacher will give affirmation and encouragement.
【 Design intention 】 Let students understand and consolidate the theorem of angular bisector through discrimination.
[Teaching Content 8]
Ask students to use what they have learned in this lesson to answer the questions in the cited examples before class:
Question: What is the relationship between the lengths of two pipes in the cited example? What is the reason?
Show the quoted situation again and ask the students to raise their hands to answer in the form of quick answer.
[Design Intention] Use the essence of learning to answer the questions in the cited examples before class, so that students can realize that life contains mathematical knowledge, which can solve problems in life, feel the value of mathematics, and let everyone learn useful mathematics. At the same time, use the form of quick answer to better activate the classroom atmosphere.
[Teaching Content 9]
Illustration
Example 1 As shown in the figure, in △ABC, AD is its angular bisector, BD=CD, DE? AB，DF？ AC, the vertical feet are e and F.
Proof: EB=FC.
Change 1: As shown in the figure, in △ABC,? C=90？ , AD is? The bisector of BAC, DE? AB in E, F in AC, BD=DF. Proof: CF=EB.
Variant 2: As shown in the figure, △ABC,? C=90？ , AD is? The bisector of BAC, DE? In e, AB, BC=8, BD=5, and find DE.
[Integration point 3] The application of multimedia has promoted the reform of classroom teaching methods and modes.
Teachers use multimedia to show questions, students observe pictures, think independently, discuss and communicate in groups, find out the idea of proof, and then encourage students to show their proof process through physical projection. The teacher commented on a changeable question with many solutions.
[Design Intention] The solution of this set of examples is an activity designed to highlight key points and break through difficulties. Students can use nature to solve mathematical problems, and use multimedia to color some edges to remind students to apply theorems directly instead of going to congruent triangles. At the same time, through information technology, it is convenient to carry out multi-solution and multi-variable research on a problem, which can better expand students' thinking of solving problems and form students' knowledge application ability. The simultaneous presentation of two variable questions meets the requirements of efficient classroom.
Cultivate students' awareness of cooperation and communication through observation, independent thinking and group discussion.
Example 2 is known: As shown in the figure, the bisectors BM and CN of △ABC intersect at point P, which proves that the distances from point P to AB, BC and CA are equal.
Let students think and analyze independently in a limited time, then exchange ideas about proof, and then show the general proof process through multimedia.
[Design Intention] Example 2 was independently completed and displayed within a limited time. By solving problems, students can better understand the essence of the angular bisector and achieve proficiency.
Activity 4. Evaluation and reflection
[Teaching content 10]
1. What have you gained from this class and what are your puzzles?
2. What thinking methods have you learned through this lesson?
The teacher asked the students to talk about the gains and experiences of this class. The students summarized, combed and exchanged the knowledge, skills and emotional experience gained in this class.
【 Design Intention 】 By guiding students to make independent induction, students' awareness of active participation is mobilized, and their ability of induction, generalization and expression is exercised.
Homework
[Teaching content 1 1]
Homework, required questions: question 65438 on page 22 of the textbook +0, 2 and 3; Choose to do the problem: question 6 on page 23 of the textbook
Teachers assign homework and students finish it independently.
[Design Intention] The purpose of setting required questions is to consolidate the content of this lesson, which is for all students and everyone must complete. Choosing a topic requires students to try their best to complete it according to their own actual situation, so that students with learning ability can improve and achieve? Different people get different development? The purpose.
Blackboard design:
(2) Time schedule:
It takes about 4 minutes to create the scene, explore the experience 13 minutes, cooperate and exchange 18 minutes, evaluate and reflect for 6 minutes and maneuver for 4 minutes.
(3) Instructional design:
This lesson has designed four links, which are interlocking and three combining points. It organically integrates information technology with teaching, fully mobilizes students' independent inquiry and cooperative communication, and teachers pay attention to timely guidance, so that students' dominant position and teachers' leading role can be fully reflected, achieving the fundamental purpose of developing thinking and improving ability, better realizing teaching objectives and better implementing the concept of curriculum standards.
Junior high school mathematics excellent open class teaching plan III
First, the teaching objectives
1. Understand the meaning of the square root of a number and an arithmetic square root;
2. To understand the meaning of the root sign, the root sign will be used to represent the square root and arithmetic square root of a number;
3. Improve students' logical thinking ability through the training in this section;
4. By learning that the operation of power sum root is reciprocal operation, we can understand the dialectical relationship of the unity of opposites between things and stimulate students' interest in exploring the mysteries of mathematics.
Second, the teaching focus and difficulties
Teaching emphasis: the concept and solution of square root and arithmetic square root.
Teaching difficulties: the connection and difference between square root and arithmetic square root.
Third, teaching methods.
Emphasize the combination with practice.
Fourth, teaching methods.
mixed-media
Teaching process of verbs (abbreviation of verb)
(1) ask questions
1. Given that the area of a square is 50 square meters, what should its side length be?
2. Given that the square of a number is equal to 1000, what is this number?
3. What is the side length of a cubic container with a volume of 0.1.25m3?
The common characteristics of these problems are: knowing the result of power, finding the value of base, how to solve these problems? This is what we will learn in this section. Let's do a little exercise: fill in the blanks.
1.( )2=9; 2.( )2 =0.25;
5.( )2=0.008 1.
When students finish this exercise, the most common mistake is to lose the negative solution, which should be corrected in teaching.
Introduce the concept of square root through practice.
(B) the concept of square root
If the square of a number is equal to a, then this number is called the square root (quadratic root) of a.
Expressed in mathematical language: If x2=a, then x is called the square root of a. 。
Know from practice: 3 is the square root of 9;
? 0.5 is the square root of 0.25;
The square root of 0 is 0;
? 0.09 is the square root of 0.008 1.
From this we can see that 3 and -3 are the square roots of 9, and the square root of 0 is 0. Let's look at such a question and fill in the blanks:
( )2=-4
After thinking, the students come to the conclusion that there is no answer to this question. Why? Because the squares of positive numbers, 0 and negative numbers are all nonnegative, it can be concluded that negative numbers have no square root. Let's sum up the nature of the square root (students can sum up and teachers can sort it out).
(3) the nature of the square root
1. Positive numbers have two square roots in opposite directions.
2.0 has a square root, which is 0 itself.
Negative numbers have no square root.
(4) Square root
The operation of finding the square root of a number is called square root operation.
It can be seen from practice that the square of 3 and -3 is 9, and the square root of 9 is 3 and -3. It can be seen that the square operation and the square root operation are reciprocal operations. According to this relationship, we can find the square root of a number by square operation. Different from other algorithms, it can only operate non-negative numbers, and the result of positive numbers is two.
(5) Representation method of square root
The positive square root of a positive number is represented by a symbol, a is called the root number, 2 is called the root index, and the negative square root of a positive number is represented by a symbol? - ? Say, the square root of a sum is, which is pronounced? Quadratic root number? , read as? A under the quadratic root sign? When the root sign is 2, this 2 is usually omitted, so the square root of a positive number can also be read as? Positive and negative root sign a? .
Exercise: 1 Use the correct symbol to represent the square root of the following numbers:
①26②247③0.2④3⑤
Solution: ① The square root of 26 is
② The square root of 247 is
③ The square root of 0.2 is
The square root of ④3 is
The square root of ⑤ is
Guess you like:
1. Three Experiences of High-quality Mathematics Course in Junior Middle School
2. What are the new curriculum teaching plans for junior high school mathematics?
3. What are the teaching plans for junior high school mathematics inquiry class?
4. Evaluation of junior high school mathematics open class
5. What are the junior high school mathematics teaching plans of Beijing Normal University Edition?