Knowledge and skills

Understand the concepts of square root and arithmetic square root, and understand that negative numbers have no meaning of square root and non-negative square root.

Process and method

Knowing that square root and square are a pair of reciprocal operations, we can use the concept of square root to find the square root of some numbers, which can be expressed by a root sign, and we can find the square root and its approximate value with a scientific calculator.

Emotions, attitudes and values

Experience the dialectical relationship between square and square root, feel the objective existence of square root in the real world, and enhance the application consciousness of mathematical knowledge.

The teaching focuses on understanding that square root and square are a pair of reciprocal operations, and the concept of square root will be used to find the square root of some numbers, which can be expressed by a root sign.

Teaching difficulties will use the concept of square root to find the square root of some numbers, which can be expressed by the root sign.

Teaching aid preparation small blackboard scientific calculator

teaching process

First, import

1. Through the study in grade seven, I believe all the students have a deeper understanding of the course of mathematics. This semester, we will study the math knowledge of Grade 8 together, and this semester's knowledge will be more interesting.

2. blackboard writing: real number 1. 1 square root

Second, new funding.

(A) to explore new knowledge

1, discussion: Is there a square with an area of 8 square centimeters? If so, what is its side length? A few students who are ahead of their studies may be able to solve the problem. How long is this side? Have you seen it before?

2. Introduce the concept of "irrational number": an infinitely circulating decimal, such as (2. 12 ...), is called irrational number.

3. What other irrational numbers can you cite? Is 1/3 an irrational number?

4. Rational numbers and irrational numbers are collectively called real numbers.

(2) knowledge induction:

1, blackboard writing: 1. 1 square root

2. Teacher Li's family decorated the kitchen, laying 10.8 square meters of floor tiles, and using 120 square bricks. Can you calculate the side length of the tile used? (0.3m)

3. how to calculate? The area of each floor tile is10.8120 = 0.09m2..

Since 0.32=0.09, the side length of a square with an area of 0.09 square meters is 0.3 meters.

Step 4 practice:

Because () =400, the side length of a square with an area of 400 square centimeters is () centimeters.

In practical problems, we often find that the square of a number is equal to a given number. For example, if a number A is known and R is needed to make r2=a, then we call R the square root of A ... (also called quadratic root).

For example, 22=4, then 2 is the square root of 4; 62=36, so 6 is the square root of 36.

6. Say: What is the square root of 9, 16, 25, 49?

(3) Seeking new knowledge:

Is there any other number besides 2 for the square root of 1 and 4?

2. Students' inquiry: Because (-2)2=4, -2 is also the square root of 4.

Is there any other number besides 2 and -2 for the square root of 3.4? There are only two square roots of 4: 2 and -2. )

4. Conclusion: If R is the square root of a positive number, then A has only two square roots: R and-R. ..

5. We call the positive square root of A the arithmetic square root of A, and write it as "root number A";

Write the negative square root of a as-.

There is only one square root of 6.0: 0. The square root of 0 is written as =0.

7. Negative numbers have no square root.

8. Finding the square root of a non-negative number is called the square root.

(4) Consolidation exercises:

1, find the square roots of the following numbers respectively: 36, 25/9, 1.2 1.

(6 and -6, 5/3 and -5/3, 1. 1 and-1. 1) (can also be expressed by numbers)

2. Find the arithmetic square roots of the following numbers respectively: 100, 16/25, 0.49. ( 10,4/5,0.7)

Third, summary and improvement:

1 is a square with an area of 196 square centimeters. How long is its side?

2. Find the arithmetic square root: 8 1, 25/ 144, 0. 16.

Square Root Excellent Teaching Plan Design Part II Learning Objectives:

1. In practical problems, feel the significance of the existence of arithmetic square root and understand the concept of arithmetic square root. The arithmetic square root has double nonnegativity.

2, will use a calculator to find the arithmetic square root of a number; Explore the law between the expansion (or contraction) of square root and its arithmetic expansion (or contraction) with a calculator;

Learning focus: Understand the concept of arithmetic square root.

Learning difficulty: arithmetic square root has double nonnegativity.

Learning process:

First, study preparation

1, look at the third page of the textbook and get the equation x= from the meaning of the question, then X=,

The side length of this floor tile is meters.

2. Positive number A has two square roots, and the positive square root of positive number A is also called the arithmetic square root of A. ..

For example, the square root of 4 is the arithmetic square root called 4, which is recorded as =2.

The square root of 2 is called the arithmetic square root of 2.

3. What is the arithmetic square root of (1)16? What is the arithmetic square root of 5?

(2) What is the arithmetic square root of 0? How many arithmetic square roots does 0 have?

(3) Do 2, -5 and -6 have arithmetic square roots? Why?

4. Find the arithmetic square root of the following numbers according to the format of example 1 on page 4 of the textbook:

( 1)625(2)0.8 1; (3)6; (4) (5) (6)

Second, cooperative exploration:

1. Read page 5 of the textbook to find the arithmetic square root with a calculator, and find the following values with a calculator.

( 1) (2) (3)

2. Use a calculator to find the arithmetic square root of the following numbers.

a2000020020.020.0002

By observing the arithmetic square root, the change law of decimal point between the root sign and the arithmetic square root is summarized.

3. In, it means a number, it means a number, and the arithmetic square root has

Exercise: If a-5+ =0, the square root of is

Third, learn:

What did you learn in this class? What should I pay attention to? Do you have any doubts?

Fourth, self-test:

1, judge whether the following statement is correct:

①5 is the arithmetic square root of 25; () ②-6 is the arithmetic square root; ( )

③ The arithmetic square root of 0 is 0; () ④ 0.0 1 is the arithmetic square root of 0. 1; ( )

⑤ The side length of a square is the arithmetic square root of its area. ()

2. If =2.29 1, =7.246, then = ()

72.46 C.229. 1 D.724.6

3. Which of the following are meaningful and which are meaningless?

4. Find the arithmetic square root of the following numbers.

① 12 1 ②2.25 ③ ④(-3)2

5. Find the following values: 1234.

Thinking development:

1, the arithmetic square root of a number is equal to itself, and this number is.

2. If x= 16, the arithmetic square root of 5-x is.

3. If the square root of 4a+ 1 is 5, then the arithmetic square root of a is.

4. The square root of is equal to and the arithmetic square root is equal to.

5. If a-9+ =0, the square root of is

6. The square root of is equal to, and the arithmetic square root is.

7. Find the square root of xy arithmetic.

A little knowledge of mathematics-how to calculate the square root with a pen

China made brilliant achievements in ancient mathematics. As early as the first century BC, China's classic mathematical work "Nine Chapters Arithmetic" introduced the above writing methods for the first time in the history of mathematics in the world. According to historical records, it was not until the fifth century A.D. that Kaiping method spread abroad. This shows that China is far ahead in the study of ancient prescriptions in the world.

1. Divide the integer part of the square root into a section with two digits from the unit to the left, and separate it with apostrophes (vertically 1 1' 56), indicating how many digits there are in the square root;

2. According to the number in the first paragraph on the left, find the number at the highest square root (3 in vertical form);

3. Subtract the square of the highest digit from the number in the first paragraph, and write the number in the second paragraph to the right of their difference to form the first remainder (256 vertically);

4. Multiply the highest digit by 20 and try to divide by the first remainder, and the largest integer is the trial quotient (3×20 divided by 256, the largest integer is 4, that is, the trial quotient is 4);

5. Multiply the quotient by 20 times the highest digit of the quotient, and then multiply the quotient. If the product is less than or equal to the remainder, the quotient is the second digit of the square root; If the product is greater than the remainder, try again by subtracting the quotient ((20×3+4)×4=256 in vertical form, indicating that quotient 4 is the second place of the square root);

6. In the same way, continue to find other digits of the square root. As shown in Figure 2, the process of finding the square roots of 85264, 12.5 respectively. Give yourself an example!

Square Root Excellent Teaching Plan Design Part III Teaching Objectives:

1. Understand the concept of arithmetic square root, express the arithmetic square root of a positive number with a root sign, and understand the nonnegativity of the arithmetic square root.

2. Knowing that roots and powers are reciprocal operations, we use square operation to find some arithmetic square roots of non-negative numbers.

Teaching focus:

The concept of arithmetic square root.

Teaching difficulties:

According to the concept of arithmetic square root, correctly find the arithmetic square root of non-negative numbers.

teaching process

First, situational introduction

Please enjoy this part of the guide map and answer this question. Xiao Ou is very happy that the school will hold the Golden Autumn Art Competition. He wants to cut out a square canvas with an area of 25 and draw his own masterpiece to participate in the competition. What should be the side length of this square canvas? If the area of this canvas is. This problem is actually a problem of finding the square of positive numbers.

This requires the concept of square root, which is the main content of this chapter. In this lesson, we will first learn the concept of arithmetic square root.

Second, introduce new lessons:

1. Question: (the question on page 68 of the book)

How to calculate that the frame side length is equal to 5dm? (Students think and exchange solutions)

This problem is equivalent to finding the value of positive number x =25 in the expansion of the equation.

Generally speaking, if the square of a positive number X is equal to A, that is, =a, then this positive number X is called the arithmetic square root of A, and the arithmetic square root of A is recorded as, read as the root number A, and A is called the root number. Specifies that the arithmetic square root of 0 is 0.

That is, in the equation =a (x0), x =.

2. Try it: Can you tell the arithmetic square root of 144 according to the equation: = 144? And expressed by equation.

3. Think about it: What does the following formula mean? Can you work out their values?

Suggestion: when evaluating, write the relationship that should be satisfied according to the meaning of the arithmetic square root, and then write the corresponding value according to the notation of the arithmetic square root, such as the arithmetic square root of 25.

4. Example 1 Find the arithmetic square root of the following numbers:

( 1) 100; (2) 1; (3) ; (4)0.000 1

Third, practice.

P69 exercise 1, 2

Fourth, inquiry: (textbook page 69)

How to make a big square with an area of 2 from two small squares with an area of 1?

Method 1: the method in the textbook is omitted;

Method 2:

But there are other ways to encourage students to explore.

Question: What should be the side length of this big square?

The side length of a big square is the arithmetic square root of 2. How big is it? Can you work out its value?

Students are advised to observe the size of the graphic feeling. What is the length of the diagonal of the small square? We will discuss its approximation in the next class.

Verb (abbreviation of verb) summary:

1. What did you learn in this class?

2. What is the specific meaning of arithmetic square root?

3. How to find the arithmetic square root of a positive number

Six, homework:

P75 Sports 13. 1 activities 1, 2, 3.