China normal university printing plate eighth grade first volume mathematics courseware 1. square root
Teaching objectives
Knowledge and skills
Understand the meaning of square root, arithmetic square root and square root of a number, and use the root sign to represent the square root and arithmetic square root of a number. You can find the square root of a number with a calculator.
Process and method
Knowing that roots and powers are reciprocal operations, we use this reciprocal operation relationship to find some arithmetic square roots of non-negative numbers.
Emotions, attitudes and values
Through learning, the knowledge of empirical mathematics comes from practice, which is generated and developed for the needs of life or production.
Important and difficult
focus
The concepts of square root and arithmetic square root.
difficulty
Difference and connection between square root and arithmetic square root.
teaching process
First, create situations and introduce new lessons.
Students, it was successfully launched on June 65438 10:00+07:38, 2065438. Its flying speed is higher than the first cosmic speed v, but lower than the second cosmic speed v2, v 1, v2, which meets the requirements of v 12=gR and v22=2gR.
Multimedia display of the questions raised in the guide map of teaching materials, (? )2=25。
Second, teacher-student interaction, exploring new knowledge
1。 Find the square root by square operation
Teachers' activities
Example at the end of self-study textbook P2 1. What is a square root? On what basis do we find the square root of 25?
Student activities
After the group discussion, the representative spoke.
Teachers' activities
The teacher wrote the concept of square root on the blackboard, emphasizing that "who" is the square root of "who". A positive number has two square roots, the two square roots are in opposite directions, and a negative number has no square root. On this basis, complete the example 1, and pay attention to the standardization of the language when students use square operation to find the square root of a number.
2。 arithmetic square root
Teachers' activities
The positive square root of a positive number is called the arithmetic square root of a, marked as a, the square root of a positive number is marked as a, the square root of 0 is 0, and the arithmetic square root of 0 is 0.
Student activities
Complete Example 2.
Teachers' activities
The teacher emphasized the square root with square operation, the square root with mathematical symbols and the arithmetic square root with.
3。 Find the square root of arithmetic with a calculator
Student activities
Operate with a calculator.
Teachers' activities
Teachers emphasize: correct operating procedures and accuracy.
Third, practice and consolidate new knowledge in class.
1。 Look for the following values:
( 1) 1。 96; (2)—49; (3) 5 1 16; (4)(— 15)2。
answer
( 1) 1。 96 means 1. The arithmetic square root of 96, ∫ 1. 42= 1。 96,∴ 1。 96= 1。 4。
(2)-49 represents the reciprocal of the arithmetic square root of 49, ∫72 = 49, ∴-49 =-7.
(3) 5 1 16 represents the square root of 5 1 16, ∫ 5116 = 8116, (.
(4) (- 15) 2 represents the arithmetic square root of (-15) 2 = 225, ∫ 152 = 225, ∴ (-15) 2 =/kloc-
2。 Find the arithmetic square root of the following numbers:
( 1) 1 144; (2)(— 100)2; (3)( 25)2。
answer
The arithmetic square root of (1)∫( 1 12)2 = 1 144, ∴ 1 144 is/kloc-0.
(2) The arithmetic square root of ∫ (-100) 2 =1002 and ∴ (- 100) 2 is100, that is, (-100) 2.
(3) ∵ 25 represents the square root of 25, (5) 2 = 25,
The square root of ∴25 is 5. ∴( 25)2=( 5)2=25,
∵52=25,∵( 25)2=( 5)2=25。
∫52 = 25, the arithmetic square root of∴ (25) 2 is 5,
That is, (25) 2 = 5.
Fourth, analyze typical cases in detail and expand new knowledge.
Example 1
The three sides of a triangle are A, B and C, A-2+| B-3 | = 0, and C is an even number. Find the perimeter of △ABC.
analyse
A-2 stands for the arithmetic square root of A-2, so A-2 is ≥ 0, that is, A-2 is ≥ 0, while | b-3 | is ≥ 0. If the sum of non-negative numbers is 0, they are 0 respectively, so that A and B can be obtained, and then they can be solved by trilateral relations.
answer
The circumference of △ABC is 7 or 9.
A represents the arithmetic square root of a, which has double nonnegativity. If the sum of non-negative numbers is 0, then every non-negative number is 0.
Sixth, teacher-student interaction, classroom summary
What did you learn in this class? What did you get? What's the confusion? And communicate with peers, on the basis of students' exchange of speeches, the teacher summarizes.
1。 Concept, representation and reading of square root and arithmetic square root.
2。 (1) A positive number has two square roots, and the two square roots are in opposite directions;
(2) There is only one square root of 0, which is 0;
(3) Negative numbers have no square root.
3。 0 is both the square root of 0 and the arithmetic square root of 0.
4。 The concept of square root.
Teaching reflection
There are many concepts in this class. Starting from "Ten Days of Flying", introduce new lessons and grasp students. From the square area of 25, find its side length, teach square root and arithmetic square root. The interaction between teachers and students in the whole class takes students as the main body, taking into account the particularity of concept class, and presents a model of teacher guidance, student expression, teacher guidance and student understanding.
Square root is calculated by square operation, and square root or arithmetic square root is expressed by or in time. The double non-negativity of typical cases to A may make students with learning difficulties have learning difficulties, and teachers should pay due attention to it.