Outline of the People's Education Edition of the first volume of mathematics in the first day of junior high school
(1) positive and negative numbers
1. positive number: a number greater than 0.
2. Negative number: a number less than 0.
3.0 neither positive nor negative.
4. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
(2) rational number
1. rational number: a number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. It is written in decimal form, and the numbers after the decimal point are infinite. Such as: π)
2. Integer: positive integer, 0, negative integer, collectively referred to as integer.
3. Score: positive score and negative score.
(3) Number axis
1. Number axis: Numbers are represented by points on a straight line, which is called number axis. Draw a straight line and take any point on the straight line to represent the number 0. This zero point is called the origin, which specifies that the right or upward direction of the straight line is positive; Select the appropriate length as the unit length, so as to take points on the number axis. )
2. Three elements of the number axis: origin, positive direction and unit length.
3. Antiquities: Only two numbers with different symbols are called reciprocal. The antonym of 0 is still 0.
4. Absolute value: the absolute value of a positive number is itself, and the absolute value of a negative number is its inverse; The absolute value of 0 is 0, two negative numbers, the larger absolute value is smaller.
Addition and subtraction of rational numbers
1. Sign first, then calculate the absolute value.
2. Addition algorithm: the same sign is added, and the absolute value is added. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value. Two opposite numbers add up to 0. Add and subtract a number with 0, and you still get this number.
3. additive commutative law: a+b=b+a is added, the position of the addend is exchanged, and the sum is unchanged.
4. The law of addition and association: (a+b)+c=a+(b+c) three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged. 5.a？ b=a+(？ B) Subtracting a number is equal to adding the reciprocal of this number.
(5) rational number multiplication (first determine the sign of the product, and then determine the size of the product)
1. The same symbol is positive, different symbols are negative, and the absolute values are multiplied. Any number multiplied by 0 is 0.
2. Two numbers whose product is 1 are reciprocal.
3. Multiplicative commutative law: ab=ba
4. Multiplicative associative law: (ab)c=a(bc)
5. Multiplication and distribution law: a(b+c)=ab+ac.
(6) rational number division
1. First divide and multiply, then sign, and finally find the result.
2. dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
3. Divide two numbers, the same sign is positive and the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0, and you will get 0. (7) Power 1. The operation of finding the product of n identical factors is called power. Write one. (the result of power is called power, a is called base, and n is called exponent) 2. The odd power of a negative number is negative and the even power of a negative number is positive; Any positive integer power of 0 is 0. 3. Multiplication with the same base, constant base and exponential addition.
4. Divided by the same base, the base is constant, minus the exponent.
(8) Mixed operations of addition, subtraction, multiplication and division of rational numbers.
1. Multiply first, then multiply and divide, and finally add and subtract.
2. Operate at the same level, from left to right.
3. If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.
Mathematics learning methods and skills
1. Analysis of Common Problems in Mathematics Learning of Grade One in Junior High School
Most junior one students will accumulate some problems more or less in their studies. These problems may not be very concerned at ordinary times, so they will be highlighted after the second day of junior high school. First of all, when freshmen study mathematics, they often encounter a lack of understanding of the knowledge points and remain at the level of a little knowledge. Some junior high school students can't master the problem-solving skills when solving math problems, which shows that junior high school students lack the ability to draw inferences about mathematics.
And junior high school students' problem-solving efficiency is too low to complete the problem-solving within the specified time and can't adapt to the examination rhythm of junior high school. Some junior one students haven't developed the habit of summing up, and they won't sum up knowledge points or wrong questions. These are the reasons why junior one students can't learn math well.
2. Lay a solid mathematical foundation for Senior One.
First, pay attention to the mathematical formula of senior one. Many students are not good at math because they don't pay enough attention to concepts and formulas. Specifically, the understanding of mathematical concepts in senior one is just for display, without excavating the extended meaning and understanding the special situation of mathematical concepts. There are also some students who just memorize mathematical concepts and formulas, and junior one students lack understanding of concepts.
There are also some junior one students who don't pay attention to the memory of mathematical formulas. In fact, memory is the basis of understanding. Let's imagine, if you can't memorize mathematical formulas, how can you skillfully apply them to mathematical problems?
The second is to summarize those similar math problems. When we get into the habit of summarizing, students in Grade One will know what they are good at and what they are not good at when they solve math problems.
At the same time, if you are good at summing up, you will know which math problem-solving methods you have mastered. Only in this way can you really master the math problem-solving skills of senior one. In fact, summing up is the key to learning mathematics well. If junior one students can't do this for such a long time, they still can't do the math problems they can't do.
What are the ways to learn math well?
1. It is the key to learn math preview well before class in junior high school.
The cultivation of mathematical problem-solving thinking and ability mainly lies in the classroom, so if you want to learn junior high school mathematics well, you must pay attention to the learning efficiency of mathematics and preview it in advance. Only by previewing in advance can you know what you can't do, so that you can concentrate in class. At the same time, in junior high school math class, students should also follow the teacher's problem-solving ideas closely and pay attention to the difference between their own problem-solving ideas and teachers. Especially in the study of basic knowledge and the most basic skills, junior high school students should review in time after class after the math teacher has finished speaking, and don't let students leave any questions after the teacher has finished each class.
2. Complete junior high school math homework independently.
Junior high school students should learn to finish the homework assigned by the teacher independently. If they want to learn junior high school mathematics well, they must be diligent in thinking and never be lazy. Don't give up the problems you don't usually understand, calm down and seriously analyze and study, and try your best to solve them. I really can't think of asking my classmates or teachers. For every learning stage of junior high school mathematics, we should learn to sort out and summarize.
3. Doing more problems is the key to learning junior high school mathematics well.
If you want to learn junior high school mathematics well, you must do more math problems. Only when students master all kinds of questions can you understand the problem-solving ideas of junior high school mathematics and enrich your problem-solving ideas and thinking through accumulation. You can start with the simplest basic questions at first. Students had better focus on the exercises in the textbook, and must understand the exercises in the textbook, so as to lay a good foundation and have the best preparation for other types of questions. Then I began to do some difficult exercises after class, in order to help students develop their own ideas and improve their analytical ability.
4. Correctly treat junior high school math exam.
If junior high school students want to get high marks in mathematics, they should focus most of their energy on basic knowledge and basic skills of solving problems, because basic questions account for most of junior high school mathematics papers, so basic knowledge must be firmly remembered. In addition, we should correct our mentality and make ourselves clear when answering junior high school math questions.
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