Explain the knowledge teaching plan
square root
I. Knowledge structure
Second, the teaching focus and difficulty analysis
This section focuses on the concepts of square root and arithmetic square root. Square root is the basis of square root operation and the preparatory knowledge for introducing irrational numbers. A correct understanding of the concept of square root is helpful to the understanding of symbolic representation, and it is the premise of correct square root operation, which directly affects the learning of square root. The teaching of arithmetic roots is not only the focus of this chapter, but also the focus of mathematics learning in the future. The radical operation to be learned later is, in the final analysis, the operation of arithmetic roots, and non-arithmetic roots should also be transformed into arithmetic roots.
The difficulty of this section is the difference between square root and arithmetic square root. First of all, these two concepts are easily confused, and the meanings of their symbols are not easy for students to distinguish. In teaching, we should master the positive terms of the arithmetic square root formula, explain the meanings of their respective symbols, and distinguish the differences between the two expressions. The square root operation not only has a limited number of times, but also has two results, which are very different from the previous number operation, and it is difficult for students to really understand.
Three. Suggestions on teaching methods
1. has a special to general induction, and the square root is the inverse of the square. After obtaining the concept of square root, let students observe the square relationship of specific numbers, analyze characteristics and summarize the general law of square root, which is helpful for students to understand the source of knowledge and the inductive thought of mathematics.
2. The root sign and the square are opposite. Logarithm has some restrictions relative to other operations, which is the difference and connection between open operation and arithmetic square root. Because this is the difficulty of this section, on the basis of defining the square root, we will compare and explain the arithmetic square root, and list the differences between them in concept, nature, operation and symbol. To make the analogy between knowledge points easy for students to remember.
3. The main contents of this section are square root and arithmetic square root. Pay attention to the simplicity of numbers, and the key is to let students understand the concepts. In addition, pay attention to the strict specification of language when describing words.
Four. Definition of square root
If the square of a number is equal to a, then this number is called the square root of a, also called the quadratic root.
Students use a calculator to find the square root.
I. Knowledge structure:
2. Analysis of teaching emphases and difficulties:
The teaching emphasis is the process of finding the square root of a positive number with a calculator. Calculator is often used to find the square root of a number in real life and other disciplines, which is also one of the basic skills of students.
Teaching difficulty: Finding the square root of a positive number accurately with a calculator. Because the second function key is used in the square root operation, it is easy for students to miss this operation, so the function of this key should be emphasized in the teaching process.
Three. Suggestions on teaching methods:
When explaining to students how to find the square root of a number with a calculator, the explanation speed is slower. First, students should find the key operation before explaining the next step. In particular, we should emphasize the role of the second function key, so that students can understand the necessity of the second function key when solving problems. In addition, students should be taught to practice by themselves in class and be familiar with the function of each key and the steps of solving it.
Cubic root concept
If the cube of a number X is equal to A, that is, the cube of X is equal to A (X 3 = A), then this number X is called the cube root of A, also called the cube root. It is pronounced "cube root number a", where a is called root number and 3 is called root index. (a is not equal to 0)
The operation of finding the cube root of a number is called root extraction.
All real numbers have one and only one cubic root.
The cube root of a positive number is positive, the cube root of a negative number is negative, and the cube root of 0 is 0.
The nature of the cube root:
(1) Positive numbers have a positive cube root.
(2) Negative numbers have negative cubic roots.
(3) The cube root of 0 is 0.
How does the cube root compare with other figures?
Cube these two numbers.
Similarities and differences between square root and cubic root.
Among the square roots, a positive number has two square roots, the two square roots are in opposite directions, and a positive number has only one positive cube root; In the square root, negative numbers have no square root, while negative numbers have negative cubic roots; The only similarity between square root and cube root is the square root of 0, and the cube root is itself.
Summary:
Any book has a cube root, the cube root of positive numbers is positive, the cube root of negative numbers is negative, and the cube root of 0 is 0.