Lecture notes of "Square Root" 1
This lesson is arranged on the basis of the previous study of power operation, which is the premise of learning arithmetic square root in the next class, and is the preparatory knowledge of learning real numbers, which is helpful to understand the concept of n-th square root, pave the way for learning square root and provide knowledge accumulation.
In the content arrangement of this lesson, the square root and its concept are introduced with examples. In the second half, a method to find the square root of a number is found on the basis of comparing the square root and the square root, and the concept learned is consolidated by two examples, in which the number selected is relatively simple and the solution process is detailed, which shows that the design purpose is not to focus on calculation, but to consolidate the concept. Therefore, the focus and difficulty of this lesson is the concept of square root. The key to breaking through the difficulty is to grasp the essential characteristics of the concept of square root and show it step by step from different angles.
The new curriculum standard clearly points out that the mathematics curriculum in compulsory education should start from the characteristics of mathematics itself, from the psychological laws of students learning mathematics and their existing knowledge and experience, so that students can experience a learning process of practice, thinking, exploration, communication, explanation and application, and at the same time gain an understanding of mathematics, so that they can make progress and development in many aspects such as thinking ability, emotional attitude and values. Therefore, the three-dimensional teaching objectives of this class are:
1, knowledge and ability goal: make students understand the concepts of square root and square root, and read and write the formula about square root correctly.
2. Process and Method Objective: Let students experience the process of inducing the concept of square root from practical examples and understand the essence of the concept.
3. Emotional attitude and values goal: let students experience that mathematics is closely related to life, and experience the role and value of mathematics to life from life, so that everyone can learn useful mathematics.
Second, oral teaching methods
Although students have studied power operation before, they will forget it to varying degrees because of the long interval, and even some concepts have lost their impression. At the same time, in order to realize the integration of old and new teaching methods and learning methods, combined with the characteristics of this lesson, I adopted the following teaching methods:
(1) Situational teaching method: The purpose is to let students "walk into the classroom" as soon as possible, to stimulate students' interest and arouse students' thinking.
(2) Contrastive teaching method: that is, compare the old and new knowledge, the concepts of quadratic and square root, and the calculation process for teaching. Even if the essence of the concept is mastered, the knowledge structure of students is improved, thus reducing the learning difficulty of students.
(3) Experience exchange method: Even if students learn to communicate and cooperate with others on the basis of independent practice and thinking, they can enjoy the experience.
Third, theoretical study.
Speaking of learning the law, there is a document that says: when American teachers teach students to draw apples, they are given a bag of apples, so that they can draw all kinds of apples in life, their own apples, not the teachers' apples. It can be seen that students are the masters of learning, so we should return the process to students and pay equal attention to both the process and the result. The new curriculum also emphasizes that students should study actively and individually under the guidance of teachers. On this basis, students' learning methods are defined as group communication and cooperation method and autonomous learning method. This can not only form a learning atmosphere of intra-group cooperation and inter-group competition, but also build a platform for students to show their personal charm.
Fourth, talk about procedures.
In terms of design ideas, I have designed four links: (1) situational introduction and finding problems. (2) The concept of cooperation, communication and understanding. (3) Self-study and self-improvement. (4) Comprehensive training, highlighting key points.
(A) situational import, found the problem
First of all, I use multimedia to play the problem situation, which is three questions:
(1) The side length of a square desktop is 3 feet. How many square feet is the area of this desktop?
(2) Given that the area of a square is 9cm2, find its side length.
(3) If the area of a square exhibition hall is 50 square meters, find its side length.
The first two questions are easy to answer directly, while the third question will confuse students' thinking, cause them to think and guide them in the square root.
(B) cooperation and exchange, understanding the concept
This link is the key link of the whole class. First, I designed the following exercises:
1, fill in the blanks: (1)32= (), (-3) 2 = (), (2)2= (), (-2) 2 = () 02 = ().
(2)()2=9,()2=4,()2=0
(3) If x2=9, what is X? What about x2=? X2=0？
(4) Is there a number whose square is equal to a negative number?
Step 2 think about it
If x2=a and x is the square root of a, think about the result in question 1 and complete the following blanks:
There are () square roots of (1) positive numbers and they are () each other.
(2)0 has () square roots, which is ()
(3) Negative _ _ _ _ _ square root (fill in "Yes" or "No")
Through comparative communication and independent inquiry, students can easily complete the above two questions and have a deeper understanding of the nature of square root and its relationship with square. In order to highlight the key points, this conclusion is also the content of the blackboard book.
(3) Self-study and self-improvement.
This link mainly involves some odds and ends, and the difficulty is not too great. It can be carried out through students' self-study and teachers' guidance. This is done in two steps:
Step 1: Ask students to learn the middle part of the text by themselves and complete the following questions:
give it a try
(1) The positive square root of the positive number A is indicated by the symbol ().
(2) The negative square root of the positive number A is represented by the symbol ().
(3) In x2 = a, x is called _ _, and 2 is called _ _ _ _ _ _; In, 2 is called _ _ _ _ _, and A is called _ _ _ _ _.
(4) Read _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(5) Can A be a negative number in _ _ _ _ _ _ _?
Step 2: The teacher sums up on the blackboard.
Thus, the teaching of reading and memory square root is well completed, and students can feel the two non-negative characteristics of a sum in the formula, which is beneficial to the teaching of arithmetic square root.
(D) comprehensive training, highlighting the key points
1. Read the bottom of page 122 and fill in the blanks:
(1) In the formula x2=a(a≥0), it is known that finding a from x is an operation of _ _ _ _ _ _.
As we all know, it is found that x is a _ _ _ _ _ _ _ operation.
The sum of squares and the square root are _ _ _ _ _ _ _.
Through the above study, how to find the square root of a number? How do you verify the results you get?
Let the students solve the problem independently (1), and then exchange the answers to the question (2) in groups to find the solution to the problem.
2. Examples 2 and 3 are the consolidation and expansion of the concept of square root. In Example 2, because students are not familiar with the representation of square root, they should be clear about the concept and addition and subtraction sign, while in Example 3, we should grasp the essence of the concept of square root and determine its square root according to the addition and subtraction sign or zero of a number. This part of the content can be carried out through exhibition board performance or booth display, so that students can complete it independently and should be given appropriate evaluation.
3. Finally, I designed an analysis problem: when doing the problem to find the square root of 4, Xiaoming said, "The square root of 4 is 2", Xiaohong said, "The square root of 4 is -2", Xiao Qiang said, "2 is the square root of 4" and Xiao Fang said, "-2 is the square root of 4". Are their statements correct?
Through this topic, students can have a deeper understanding on the basis of being familiar with the concept of square root, and at the same time, they can explain the phenomenon of two solutions to one problem that has never appeared in the previous five operations, so that students can understand the relationship between the whole and the parts and highlight the key points again.
(5) In the summary, I use the column "I want to say" to encourage students to participate in the summary, discover the students' small progress and improve their knowledge system.
(6) After-class exercises, taking care of students' differences and echoing each other, are divided into two categories:
1, required question: textbook exercise.
2, choose to do the problem: solve the problem in the introduction and explain the rationality of the answer.
"Square Root" Lecture Notes 2 I. Talking about Teaching Materials
"Arithmetic square root" is the first section of the real number in the sixth chapter of seventh grade mathematics (20 19 edition). The first lesson of this class-arithmetic square root, is the preparatory knowledge of learning real numbers, paving the way for learning square root and providing knowledge accumulation.
Second, talk about teaching objectives
Combined with the cognitive structure and psychological characteristics of grade seven students, I have set the following teaching objectives:
1, let students understand the concept of arithmetic square root, read and write the formula about arithmetic square root correctly, and find the arithmetic square root of complete square number by square operation.
2. Let students experience the process of summarizing the concept of arithmetic square root from practical examples and understand the essence of the concept.
Third, talk about the difficulties in teaching.
Teaching emphasis: the concept of arithmetic square root
Teaching difficulties: master the concept and nature of arithmetic square root, correctly calculate the arithmetic square root of complete square number, and solve problems by using double non-negativity
Fourth, talk about learning.
1, students' existing foundation: students have learned the operation of power last semester, which is helpful for the learning activities in this section.
2. Learning status: Students at this stage are particularly interested in new things or new content, but lack learning methods.
Verb (abbreviation of verb) oral teaching method and learning method
Teaching method: Although students have learned the power operation before, they will forget it to varying degrees because of the long interval, and even some concepts have lost their impression. At the same time, in order to realize the integration of old and new teaching methods and learning methods, combined with the characteristics of this lesson, I adopted the following teaching methods:
(1) Situational Teaching Method:
(2) Contrastive teaching method: The concept and calculation process of quadratic and arithmetic square root are compared, which reduces the learning difficulty of students.
Learning methods: group communication and cooperation method and autonomous learning method. Give the process back to the students, so that the process and the result are equally important.
Six, teaching procedures:
The main process of this lesson is:
Preview new knowledge, stimulate interest → explore new knowledge, cooperate and exchange → consolidate practice and strengthen understanding.
(A) preview new knowledge and stimulate the introduction of interest
The concept of arithmetic square root is introduced from the canvas problem: if the square of a positive number is equal to A, that is, 2 = A, then this positive number X is called the arithmetic square root of A. The purpose of this design is to introduce the concept of arithmetic square root by filling in a table and comparing it with the square of a positive number, to communicate the relationship between them and to cultivate students' reverse thinking ability.
(B) Explore cooperation and exchange of new knowledge
This link is the key link of the whole class, guiding students to explore the concept and properties of arithmetic square root, and on this basis, mastering the expression method of arithmetic square root of A and the limit of square root of A.
(3) Consolidate practice and strengthen understanding.
Because students are not familiar with the expression of arithmetic square root, they should try to standardize their writing. The practice of reading and memorizing the arithmetic square root allows students to understand the meaning expressed in each place () through concrete examples, operate it by themselves, and then summarize it, so as to enjoy the experience and improve students' language expression ability.
In concluding this lesson, we will focus on the following issues:
1, what is a nonnegative arithmetic square root?
2. What is the rule of the arithmetic square root of positive numbers and 0?
3. How to find the arithmetic square root of a number? How to express the arithmetic square root of positive number a?
(4) Blackboard design
arithmetic square root
Problems and tables of projecting text canvas
1, the concept example of arithmetic square root 1 student
2. Representation of arithmetic square root Example 2 Executive Board
3, the nature of the arithmetic square root Example 3
Seven. Design description:
1 1, guiding ideology:
According to the position and function of students' existing foundation and teaching materials, students should pay attention to the cultivation of mathematical thinking methods and good study habits while learning knowledge and skills in teaching.
2. Heuristic teaching and emotional teaching are adopted in teaching methods and learning methods to create problem situations, guide students to think positively, stimulate students' interest, adjust their learning emotions, and let students find problems in the comparison of the natural laws of power and arithmetic square root; Improve the ability to solve problems and cultivate good study habits in practice and training. At the same time, media-assisted teaching is adopted to increase teaching density and improve teaching efficiency.
3. About the design of teaching program
In the design of the teaching plan, the teaching principle of teacher-oriented and student-centered is fully embodied, and the following points are highlighted:
(1) for all students, heuristic and inquiry teaching.
② Attach importance to students' participation in the process of knowledge formation, and enhance students' confidence in learning mathematics.
(3) Let students master methods and use them flexibly while acquiring knowledge.