I. Content analysis

Summary and review are divided into two parts. The first part summarizes the concepts of positive and negative numbers, rational numbers, antonyms and absolute values, as well as the operation methods and laws of addition, subtraction, multiplication and division of rational numbers, thus giving the general outline of the whole chapter. The second part questions the new contents and methods of this chapter. Through these questions, students can be inspired to think and actively construct new knowledge.

Second, the schedule:

The requirement of section and review is to systematize the content of this chapter, so as to further consolidate and deepen the understanding of the learning content. The main content of this chapter can be summarized as the concept of rational number and the operation of rational number. Therefore, the general review arrangement for the second class in this chapter is as follows (except for quizzes):

The first lesson reviews the meaning of rational number and its related concepts;

The second class reviews the operation of rational numbers.

Third, the determination of teaching methods:

Review the concepts involved in the chapter of rational numbers, test the students' knowledge mastery, and make a scientific summary and induction.

Fourth, the teaching arrangement:

first kind

First, the teaching objectives:

1. Knowledge and skills:

Understand eight important concepts: rational number, number axis, reciprocal, absolute value, reciprocal, scientific counting method, divisor and effective number.

Enable students to improve their ability to distinguish concepts and correctly use concepts to solve problems.

③ Can correctly compare the sizes of two rational numbers.

2. Process and method

In the teaching process, we should use the number axis to know and understand the related concepts of rational numbers, and string these concepts together with the help of the number axis to form a system to describe the characteristics of rational numbers. Besides,

3. Emotional attitudes and values

While applying the concept of rational numbers, we should also pay attention to correcting possible misunderstandings, so that students can learn to find and correct mistakes in their studies.

Second, the teaching focus:

Understanding and application of eight concepts of rational number: rational number, number axis, reciprocal, absolute value, reciprocal, scientific counting method, divisor and effective number.

Third, the teaching difficulties:

Understanding and application of the concept of absolute value.

Fourth, the teaching process:

Knowledge carding and consolidation exercises:

1, positive numbers and negative numbers: numbers with "-"in front of positive numbers are called negative numbers; Give the concept of negative number, and then give some judgment questions and application questions to let students understand the concept of negative number and its application in production and life.

[Basic exercises]

1. Judgment

1)a must be a positive number;

2)-a must be a negative number;

3)-(-a) must be greater than 0;

2. Adding -20% actually means.

3.B-3 means.

2. Classification of rational numbers: (Let students master two classification methods of rational numbers by summarizing the following contents)

[Basic exercise]:

1. Fill the following figures in the corresponding brackets:

1,-0. 1,-789,25,0,-20,-3. 14,-590,6/7

Positive integer set {0}; Positive rational number set {};

Negative rational number set {};

Natural number set {}; Positive score set {0};

Negative diversity {}.

2. The price of an edible oil fluctuates with the change of market economy, and the increase is recorded as positive, then the meaning of -5.8 yuan is; If the original price of this oil is 76 yuan, then the current price is.

3. Number axis: a straight line that defines the origin, positive direction and unit length.

-3 –2 – 1 0 1 2 3

1) The number on the right is always greater than the number on the left.

2) Positive numbers are all greater than 0, and negative numbers are all less than 0; Positive numbers are greater than all negative numbers;

3) All rational numbers can be represented by points on the number axis.

[Basic exercises]

1. The figure shows the number axis drawn by four students, of which the correct one is ().

2. A negative integer greater than -3 is _ _ _ _ _ _; ② It is known that m is an integer and -4.

3. Point A on the axis represents -4. If the origin o moves 1 unit in the negative direction, then the number represented by point A on the new number axis is ().

A.-5，B.-4 C.-3 D.-2

4. Inverse number: Only two numbers with different signs, one of which is the inverse of the other. (give the definition of inverse number and the conclusion that needs attention. )

The inverse of 1) number A is -a(a is an arbitrary rational number);

2) The antipodal of 0 is 0. 3) If A and B are antipodal, then a+b=0.

[Basic exercises]

The reciprocal of 1 -5 Yes; The inverse of -(-8); The reciprocal of 0 is; The inverse of a is;

The number represented by 2-a must be ()

A. negative number B. positive number

C. positive or negative number D. positive or negative number or 0

The reciprocal of a number is the smallest positive integer, so this number is ()

Answer. – 1 b . 1 C . 1d . 0

4① Two opposite numbers are located on both sides of the origin on the number axis ()

(2) As long as the signs are different, these two numbers are opposites ()

5. Reciprocal: Two numbers whose product is 1 are reciprocal. (Give the concept and main conclusion of reciprocal)

The reciprocal of 1)a is (a ≠ 0);

2)0 has no reciprocal;

3) If A and B are reciprocal, ab= 1.

4) The reciprocal itself is _ _ _ _ _.

6. Absolute value: The absolute value of a number A is the distance between the point representing the number A on the number axis and the origin. Let students pay attention to understand the definition of absolute value and its non-negative characteristics. )

1) The absolute value of the number A is ︱ A ︱;

If a > 0, then ︱a︱=；;

2) if a < 0, then ︱ a ︱a︱=；;

If a =0, then a =;

3) For any rational number A, there is always ︱a︱≥0.

[Basic exercises]

The absolute value of 1 -2 means that its distance from the origin is one unit.

2. The number whose absolute value is equal to its opposite number must be ()

A. negative number B. positive number C. negative number or zero D. positive number or zero

calculate

7. Comparison of rational numbers: (Summary of comparison methods of rational numbers).

1) can be compared through the number axis: two numbers on the number axis, the number on the right is always greater than the number on the left;

Positive numbers are all greater than 0, and negative numbers are all less than 0; Positive numbers are greater than all negative numbers;

2) Two negative numbers, the larger one has the smaller absolute value.

That is, if a < 0, b < 0, ︱ a ︱ b ︱, then a < b.

8. Scientific notation, divisor and significant number (give the definitions of scientific notation, divisor and significant number, etc. )

1). Write a number greater than 10 in the form of a× 10n, where a is a number with only one integer bit (i.e. 1 ≤ A)

2). An approximate number, from the first non-zero number on the left to the exact number, all numbers are called the significant digits of this number.

[Basic exercises]

1. There are as many as 28 million bacteria in the abdomen of a fly. Can you express them with scientific symbols?

2. How many integers are there in1.03x106?

3.3.0× 10n(n is a positive integer) How many integers are there?

4. Where is the approximate value obtained by rounding below accurate, and how many significant digits are there?

( 1) 43.8 (2) 0.03086 (3) 24,000 (4)6× 104 (5)6.0× 104.

(2) class summary:

Several problems that should be paid attention to

1. Two classifications of rational numbers are often used, and attention should be paid to their differences;

2. The three elements of the number axis are indispensable, and rational numbers can be compared intuitively by using the number axis;

Antiquities refer to two numbers with different symbols. The distance between two points representing a pair of opposites on the number axis is equal to the origin, and their sum is 0; Reciprocal refers to two numbers whose product is 1;

4. The absolute value of a number is always non-negative, and the absolute value of the number A is the distance from the point representing the number A on the number axis to the origin;

(3) Transfer: