What are the compulsory knowledge points of junior high school mathematics? One, integers and decimals.
1. The smallest number is 1 and the smallest natural number is 0.
2. Meaning of decimals: Divide the integer "1" into 10, 100, 1000 ... These fractions are one tenth, percentage and one thousandth respectively ... which can be expressed by decimals.
3. The decimal point has an integer part on the left and a decimal part on the right, followed by decimal, percentile and thousandth. ...
Integer and decimal numbers are numbers written in decimal notation.
5. Properties of decimals: Add 0 or remove 0 at the end of decimals, and the size of decimals remains unchanged.
6. Move the decimal point to the right by one, two and three places ... The original number is enlarged by 10 times, 100 times and 1000 times respectively. ...
The decimal point is shifted to the left by one place, two places and three places ... The original number is reduced by 10 times, 100 times and 1000 times respectively. ...
Second, the divisibility of numbers.
1. Factor and multiple: 20÷4=5, 20 is a multiple of 4 and 5, and 4 and 5 are factors of 20.
2. The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple.
The number of factors of a number is limited, the smallest factor is 1, and the largest factor is itself.
3. Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.
4. Prime number: If a number has only two factors: 1 and itself, it is called a prime number. Prime numbers have two factors.
Composite number: A number is called a composite number if it has other factors besides 1 and itself. A composite number has at least three factors.
The smallest prime number is 2 and the smallest composite number is 4.
The prime numbers in 1 ~ 20 are: 2,3,5,7,1,13, 17, 19.
The complex number of 1 ~ 20 is "4,6,8,9, 10, 12, 14, 15, 16, 18".
5. Features of numbers divisible by 2: Numbers of 0, 2, 4, 6 and 8 can be divisible by 2.
Features of numbers divisible by 5: Numbers with 0 or 5 bits can be divisible by 5.
The characteristics of numbers divisible by 3: the sum of the numbers in each bit of a number can be divisible by 3, and this number can also be divisible by 3.
6. Agreed factor, common multiple: the factor shared by several numbers is called the factor of these numbers; The largest one is called the greatest common factor of these numbers. The common multiple of several numbers is called the common multiple of these numbers; The smallest one is called the least common multiple of these numbers.
7. Prime numbers: Two numbers whose common factor is only 1 are called prime numbers.
Three or four operations
1. One addend = and-the other addend is minuend = difference+meiosis = minuend-difference.
One factor = product/dividend of another factor = quotient × divisor = dividend/quotient
2. Among the four operations, addition and subtraction are called primary operations, and multiplication and division are called secondary operations.
3. Operating rules:
(1) additive commutative law: Two numbers a+b=b+a are added, and the addend positions are exchanged, and the sum remains unchanged.
Multiplicative commutative law: a×b=b×a times two numbers, and the position of the commutative factor remains unchanged.
(2) Additive associative law: three numbers (a+b)+c=a+(b+c) are added, the first two numbers are added first, and then the third number is added; Or add the last two numbers first, and then add them to the first number, and their sum remains the same.
Multiplication and association law: (a×b)×c=a×(b×c) Multiply three numbers, first multiply the first two numbers and then multiply the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their products remain unchanged.
(3) Multiplicative distribution law: (a+b) × c = a× c+b× c.
Multiply the same number by the sum of two numbers, you can multiply the two addends by this number respectively, and then add the two products, and the result remains the same.
(4) The nature of subtraction: a-b-c=a-(b+c) Subtracting two numbers continuously from a number is equal to subtracting the sum of two subtractions from this number.
The nature of division: a÷b÷c=a÷(b×c) A number divided by two numbers equals the product of this number divided by two divisors.
Ways to improve primary school math scores. 1. Cultivate the habit of carefully examining questions
Careful examination of questions is the premise of correct problem solving and accurate calculation. Primary school students' lax examination of questions leads to serious mistakes, on the one hand, because students have less literacy and low understanding level; On the other hand, I am eager to succeed in doing the problem and unwilling to examine it. Therefore, in teaching, teachers should guide students to understand the importance of examining questions and enhance their awareness of examining questions. At the same time, we should also teach students the methods of examining questions and establish the basic procedures for solving problems, such as examining questions-formulas-calculation-verification-answers. And put the examination in the first place in the process of solving problems.
Second, cultivate the habit of careful inspection.
In the process of solving problems, we should cultivate the habit of careful inspection, which is the key to ensure the correctness of solving problems. Teachers should take checking calculation as one of the basic links in the process of solving problems. Strengthen training, strictly demand and urge students to do it, and explain to students what checking calculation is, as well as the method and significance of checking calculation.
Third, cultivate the habit of careful estimation.
Estimation is a shortcut to ensure the accuracy of calculation, but now many teachers think that estimation is rarely ignored as an examination content, which is very wrong. Teachers should seize every opportunity to consciously let students master the estimation method and guide them to discover some laws of sum, difference, product and quotient. For example, 2040÷40, when estimating, take 2040 as 2000 and 2040÷40 as 2000÷40, which can be used to check whether the highest digit of calculation is correct and let students understand the importance of estimation.
Fourth, cultivate the habit of finishing homework independently.
There are many homework in primary school math class, and some students with strong ability can do it quickly and accurately. After they finished, they couldn't wait to report the methods and results of solving the problem. This makes some students who are slow to do the questions copy their own results without thinking. After a long time, these students have developed the bad habit of being lazy to think. Therefore, cultivating students' habit of completing homework independently is the premise for students to learn mathematics well.
Fifth, cultivate the habit of questioning and asking difficult questions.
Students should use their brains more and be diligent in thinking. Don't be satisfied with reciting concepts, formulas, laws, etc. , but try to understand them. Questioning and asking difficult questions is a valuable learning quality, which enables students to study hard, think hard and take the initiative. Ask questions you don't understand, don't be shy to ask questions, discuss with your classmates, and never stop until you figure out the problems. When the problem is solved, students will enjoy the joy of success and improve their interest in learning mathematics.
Sixth, cultivate the habit of finding mistakes.
Students are bound to make mistakes in their studies, and teachers should not take them lightly. Because the place where students make mistakes is the weak point of their knowledge, and it may be typical and universal. Teachers should guide students to find their own mistakes and use the inspection methods they have learned to find them. Grasp the key to the problem in comparison, try to find and correct mistakes by yourself, and improve problem-solving skills.