The teaching goal of the ninth grade mathematics courseware 1;
1. Prove the property theorem, judgment theorem and related conclusions of rectangle by synthesis method.
2. Mainly use the property theorem and judgment theorem of rectangle to solve the problem.
3. Through the process of exploring, guessing and proving the nature theorem and judgment theorem of rectangle, the necessity of proof is further manifested, and the ability of rational reasoning and deductive reasoning is further developed.
Teaching focus:
1. Prove the property theorem, judgment theorem and related conclusions of rectangle by synthesis method.
2. Mainly use the property theorem and judgment theorem of rectangle to solve the problem.
Teaching difficulties:
Solving problems by using the property theorem and judgment theorem of rectangle
Teaching methods:
1. Read the textbook, review what the students have learned before, and get the property theorem and judgment theorem of the rectangle in groups.
2. The teaching of this course is based on the guiding scheme, through group discussion, student analysis (explanation) and teacher guidance and inspiration.
Teaching aid preparation:
Triangle? Multimedia booth
Analysis of learning situation:
Grade 9 students have certain abilities of self-study, asking questions, analyzing and solving problems, and summarizing, and have their own unique learning methods and unique opinions on problems. They are more willing to show themselves to other students in class, so as to gain a great sense of accomplishment and establish their image among their classmates. The shortcomings are incomplete understanding, incomplete analysis and single method. And it is through cooperation and communication that the correct conclusion can be drawn.
Students have explored the properties and judgment methods of special parallelograms (rectangles, diamonds and squares) in Grade Two, and solved simple problems with them. The first three sections of this chapter prove and master the property theorem and judgment theorem of parallelogram and its application. Through the process of proving the triangle midline theorem, students have been able to study the related properties and judgment theorems of special parallelograms from the angles of sides, angles and diagonals, which laid the foundation for learning this lesson.
Teaching process:
(A) Ming Biao's profile
1. The learning objectives of this lesson are: (teachers read or project)
(1) synthesis method can be used to prove the property theorem, judgment theorem and related conclusions of rectangles.
(2) Using the property theorem and judgment theorem of rectangle to solve problems.
2. Students read page 73 of the guidance plan and think about the math problem that Xiaohong and Liang Xiao are arguing about. Who do you agree with? Can you explain your reasons? (Group discussion allowed)
Do you need this condition "∠A=300"? After this lesson, we can solve this problem smoothly.
(2) Self-study, cooperation and exchange, and demonstration.
Activity 1:
1. In the second day of junior high school, we have explored a special parallelogram. Please read the content on page 95 of the textbook, and combine the related contents of the special parallelogram learned in the previous two years to independently complete the first two questions in the "textbook guide" section on page 73 of the Learning Plan Guide. And answer the following questions:
① What is a rectangle?
② What are the properties of rectangle?
(3) How many methods are there to judge a rectangle?
④ Prove that "parallelograms with equal diagonals are rectangles".
2. Communicate the completion in groups to solve the problems in self-study.
On the basis of reviewing the relevant conclusions of rectangle, this part explores the nature of rectangle and the proof process of judgment theorem, and further experiences the necessity of proof.
(Question preset)
(1), according to the proposition, write the known and verified in geometric symbol language.
(2) The proof method to prove that "parallelograms with equal diagonals are rectangles".
3. The group showed the second question and the fourth supplementary question in the "Introduction to Textbooks" section.
4. Teachers emphasize the standard writing of geometric symbol language, and students supplement and summarize various proof methods of the two questions.
Activity 2:
5.① Students independently complete the third and fourth questions in the "Guide to Teaching Materials" on page 73 of the "Guide to Learning Plan".
② It is inferred that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse.
③ Completion of group communication.
6. Is the inverse proposition of this inference true or false?
① Students narrate the inverse proposition.
② Complete the debate design on page 74 of the Learning Guidance Scheme.
③ Completion of group communication.
(3) Record the harvest and find the problems.
1. independently complete the harvest and problems on page 74 of the guidance plan.
2, group communication problems, * * * enjoy the harvest.
(4) Typical analysis and consolidation training.
1, complete the independent evaluation. & lt this link is done independently >
2. 74 pages of exhibition theme design. & lt independent thinking, group communication, classroom demonstration >
3. Supplement: Quadrilateral ABCD is the plan of rectangular desktop made by carpenter. Now there is only one ruler that can measure the length. How to verify that the plane figure of this quadrilateral desktop is rectangular?
(5) Contact with senior high school entrance examination
As shown in the figure, in △ABC, AB=AC, D is the midpoint of BC, and the quadrilateral ABDE is parallel four.
Excellent Mathematics Courseware for Grade 9 2 I. Brief Introduction of Contents
Topic of this lesson: Through a series of inquiry activities, guide students to sum up two complete square formulas from the calculation results.
Key information:
1, based on the teaching materials and according to the mathematics curriculum standards, to guide students to experience and participate in the scientific inquiry process. Firstly, the relationship between the two multiplication polynomials on the left side of the equal sign and the three terms on the right side of the equal sign is proposed. Students discover problems independently, make assumptions and guesses about possible answers, and draw correct conclusions through repeated tests. Students acquire knowledge, skills, methods, attitudes, especially innovative spirit and practical ability through activities such as collecting and processing information, expressing and communicating.
2. Draw conclusions with standard mathematical language, so that students can feel the rigor of science and inspire their learning attitudes and methods.
Second, the learner analysis:
1, the basic knowledge and skills that should be possessed before learning this course:
(1) Definition of similar projects.
② Rules for merging similar projects
③ Polynomial multiplication polynomial rule.
2. Learners' level of what they will learn:
Before learning the complete square formula, students have been able to sort out the correct form of the formula. The purpose of this lesson is to let students summarize the application methods of formulas from the relationship between the left and right forms of equal signs.
Three. Teaching/learning objectives and corresponding curriculum standards;
Teaching objectives:
1, by exploring the process of complete square formula, the sense of symbol and thrust ability are further developed.
2. A complete square formula can be derived, and simple calculation can be made by using the formula.
(b) Knowledge and skills: Understanding is reasonable through the process of abstracting symbols from specific situations.
Numbers, real numbers, algebraic expressions, defensive cities, inequalities, functions; Master the necessary calculation (including estimation) skills; Explore the quantitative relations and changing laws in specific problems, and describe them with algebraic expressions, guarding cities, inequalities, functions, etc.
(4) Problem solving: being able to find and put forward mathematical problems in combination with specific situations; Try to learn from different people.
Seek solutions to problems from different angles, and effectively solve problems, and try to evaluate the differences between different methods; Through the reflection on the process of solving problems, we can gain experience in solving problems.
(5) Emotion and attitude: Dare to face the difficulties in mathematics activities and have the ability to overcome them independently.
And have the confidence to learn math well. And respect and understand the opinions of others; Can benefit from communication.
Fourth, educational ideas and teaching methods:
1. Teachers are the organizers, promoters and collaborators of students' learning: students are the masters of learning, learning actively and individually under the guidance of teachers, experiencing with their own bodies and feeling with their own hearts.
Teaching is a process of communication, positive interaction and common development between teachers and students. When students get lost
Wait, the teacher does not tell the direction easily, but instructs him how to distinguish the direction; When a student is afraid of climbing, the teacher does not drag him away, but arouses his inner spiritual motivation and encourages him to keep climbing.
2. Adopt the mode of "problem scenario-inquiry communication-summary-intensive training"
Start teaching.
3. Teaching evaluation methods:
(1) Pay attention to students' initiative in observation, summary and training through classroom observation.
Dynamic participation and awareness of cooperation and exchange, timely encourage, strengthen, guide and correct.
(2) Give students more opportunities to relax naturally by judging and giving examples.
Revealing the thinking process and giving feedback on the mastery of knowledge and skills will help teachers diagnose the situation in time and investigate teaching.
(3) Through after-class interviews and homework analysis, timely check and fill gaps to ensure the expected results.
Teaching effect.
Verb (abbreviation of verb) Teaching media: multimedia. Teaching and activity process:
The teaching process is designed as follows:
< 1 >, ask questions.
[Introduction] Students, we have learned the rule of polynomial multiplication and the rule of merging similar items. By operating the following four small questions, can you sum up the relationship between the result and the two monomials in the polynomial?
(2m+3n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-2m-3n)2=____________，
(2m-3n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-2m+3n)2=____________ .
< 2 >, analyze the problem
1, [student answers] group discussion.
(2m+3n)2= 4m2+ 12mn+9n2，(-2m-3n)2= 4m2+ 12mn+9n2，
(2m-3n)2= 4m2- 12mn+9n2，(-2m+3n)2= 4m2- 12mn+9n2 .
(1) The characteristics of the original formula.
(2) The item number characteristics of the results.
(3) The characteristics of trinomial coefficients (especially the characteristics of symbols).
(4) The relationship between three terms and two monomials in the original polynomial.
2. [Student answers] Summarize the language description of the complete square formula:
The square of the sum of two numbers is equal to the sum of their squares, plus twice their product;
The square of the difference between two numbers is equal to the sum of their squares minus twice their product.
3. [Student's solution] Mathematical expression of complete square formula:
(a+b)2 = a2+2ab+B2；
(a-b)2=a2-2ab+b2。
(3) Using formulas to solve problems
1, oral answer: (the form of rushing to answer, active classroom atmosphere, stimulate students' enthusiasm for learning)
(m+n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _，(m-n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _，
(-m+n)2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _，(-m-n)2=______________，
(a+3)2=______________，(-c+5)2=______________，
(-7-a)2=______________，(0.5-a)2=______________。
2. Judges:
()① (a-2b)2= a2-2ab+b2
()② (2m+n)2= 2m2+4mn+n2
()③ (-n-3m)2= n2-6mn+9m2
()④ (5a+0.2b)2= 25a2+5ab+0.4b2
()⑤ (5a-0.2b)2= 5a2-5ab+0.04b2
()⑥ (-a-2b)2=(a+2b)2
()⑦ (2a-4b)2=(4a-2b)2
()⑧ (-5m+n)2=(-n+5m)2