Six methods of balancing junior high school mathematics
1, least common multiple method
A, find out the atoms with more atoms on both sides of the reaction formula and a single pair, and find the least common multiple.
B, deduce the coefficient of each molecule. go home
For example:
Step 1: copper sulfate+sodium hydroxide-copper hydroxide+sodium sulfate.
Step 2: copper sulfate +2 sodium hydroxide-copper hydroxide+sodium sulfate (the balance is hydroxide)
Step 3: CuSO4+2 NaOH-Cu (OH) 2 ↓+Na2SO4 (indicate product status).
2. Observation method
Calculating the stoichiometric ratio of each reactant chemical formula and the stoichiometric ratio of the product from the product with complex chemical formula; According to the stoichiometry of the obtained chemical formula, find out the stoichiometry of other chemical formulas until it is balanced.
For example, the first step H20 (g)+Fe-Fe3O4+H2.
Step 2 4h20 (g)+3fe-Fe3O4+H2
Step 3: 4H20 (g)+3Fe-Fe3O4+4H2 (reaction condition: heating) reunion.
3. Parity balance method
See which element appears most frequently on the left and right sides of the reaction chemical equation; Starting from the odd chemical molecular formula of the element, make it even (that is, the stoichiometric number is 2); The stoichiometry obtained from it balances the stoichiometry of other chemical formulas, making the number of atoms on both sides equal.
Example: Balance
H2O(g)+ Fe ——Fe3O4+H2
Step 1: Balance oxygen atoms.
4H2O(g)+Fe——Fe3O4+H2
Step 2: Balance hydrogen and iron atoms.
4H2O(g)+3Fe——Fe3O4+4H2
Step 3: Chemical equation after balance:
4h2o (g)+3fe —— Fe3O4+4h2 = (reaction condition: heating)
4. Stoichiometric method to be determined
Different unknowns represent the stoichiometric ratio of each chemical formula in the chemical equation; According to the law of conservation of mass, the types of atoms are the same before and after the reaction, and the number of atoms is equal, and the mathematical equations are listed. Solve the equations, find any unknown number 1, and find the values of other unknown numbers; Finally, the unknown value is substituted into the original chemical equation.
For example: NH3+Cl2-NH4Cl+N2.
Let the stoichiometry of each substance be a, b, c and d in turn.
aNH3+bCl2——cNH4Cl+dN2
Equation set a=c+2d (the number of nitrogen atoms is equal)
3a=4c (equal number of hydrogen atoms)
2b=c (equal number of chlorine atoms)
Let b= 1 and the solution is: a=8/3, c=2, d= 1/3.
8nh3+3cl2-6nh4cl+N2 (A, B, C and D are all magnified by 3 times, because the coefficient cannot be decimal).
5. Price fluctuation method
First, the principle of equilibrium Due to the transfer of electrons in the redox reaction, the valence of elements is bound to rise and fall. We call elements whose valence can rise or substances containing them reducing agents. On the contrary, it is called oxidant. From the knowledge of redox reaction, we can easily draw the equilibrium principle: the total number of electrons lost by reductant = the total number of electrons gained by oxidant, that is, the total number of price increases of reductant (element) = the total number of price reductions of oxidant (element). Second, the general method and steps to balance the redox reaction equation
1, general method: from left to right.
2. Steps: convert the price, find the change, find the total amount and match the coefficient.
Namely: (1) mark the initial state and the final state of the valence of the changing elements;
⑵ Total price of initial state and final state change = change amount × coefficient
Note: It is assumed that all the above changes are expressed in positive prices, where (b-a)×(d-c) is the least common multiple.
(3) Fill the coefficients in the table before the chemical formulas of reducing agent and oxidizing agent respectively, and use them as coefficients;
(4) Balance other elements through observation;
5] Check whether the equilibrium equation conforms to the law of conservation of mass (ion equation also depends on whether it conforms to the law of conservation of charge).
6. Oxygen acquisition and oxygen loss method
For redox reaction, the oxygen loss number of oxidant is observed first, then the oxygen gain number of reductant is observed, and then the equilibrium is carried out.
For example: 3co+Fe2O3-2fe+3co2.
Oxidizer iron oxide loses three oxygen before and after the reaction, and reductant carbon monoxide gains one oxygen before and after the reaction, so it takes three carbon monoxide to take away the oxygen in iron oxide, carbon monoxide and carbon dioxide are matched with 3, and iron is matched with 2.
Through the explanation of the above chemical equation balancing method, I believe students can master the above knowledge well, and I hope students can get good grades in the exam.
Methods of learning junior high school mathematics well
How to learn junior high school mathematics well is a difficult problem for middle school students. In fact, it is not difficult to learn mathematics well, mainly depending on whether students have mastered the methods and persistently completed the mathematical tasks.
First, for textbooks, we should do three exercises: preview, practice and review.
Before each new lesson, you should preview it first, especially draw or mark the difficulties or things you don't understand with colored strokes, so that you can concentrate more in class. Preview is a prerequisite for learning every subject. Make different preparations for students' different learning abilities. Students with good grades and strong learning ability can look at examples and do classroom exercises at the end of each class, so that they can understand 70% of the new content and do 80% of the exercises. Students with poor grades just need to look at the examples and copy them well. Be familiar with the examples and the contents of this section in the book, so that they can have a good idea of the examples and listen to the lectures. This is a good learning method. Even the worst students should know something about the content and knowledge of this lesson. After learning a new lesson, we should compare and review the learned knowledge step by step according to the contents of the textbook, from easy to difficult, from simple to complicated, and summarize the concepts, theorems and formulas to deepen our understanding of the knowledge. The examples in the textbook are best done by yourself. Reasoning the concepts, theorems and formulas in the textbook to form an overall understanding of knowledge.
Second, listen carefully, take notes and think in class.
Listen to the questions in the preview in class, take notes when necessary, and consolidate them through some exercises. Mathematics is different from other subjects. It is impossible to solve practical problems by memorizing concepts, theorems and formulas. Only through practice can we reduce operational mistakes.
Third, homework should be "thinking, asking and gathering"
Homework must develop the habit of independent thinking, from different methods and angles, explore a variety of problem-solving methods from typical topics, and get association and inspiration from them. The examples in the textbook are typical, and we can find the solution from the examples. At the same time, we should also establish more mathematical problem-solving ideas, such as: equation ideas, function ideas, combination of numbers and shapes and other common methods; For difficult questions, we should ask more reasons, such as changing conditions, adding conditions, and exchanging conditions for conclusions. Is the original conclusion still valid? In addition, for the mistakes in homework and test papers, it is best to prepare a set of wrong questions for future review. Never make a second similar mistake, never make a third similar mistake.
Learning mathematics should have methods, plans and reasonable arrangements. After the new lesson, some students feel headache, so they look around and don't know what they have learned in the end. Therefore, every student should work out reasonable learning methods and goals according to his own actual situation; If there is no way, it will become a headless fly; Without goals, there will be no motivation.
After mastering some methods of learning junior high school mathematics, we should also note that junior high school is a special and crucial period in the life of middle school students. Compared with primary school mathematics learning, junior high school mathematics learning has certain differences. For example, compared with the previous courses, junior high school mathematics not only increased the amount of knowledge, but also made a qualitative leap-requiring students to master mathematical thinking methods on the basis of a deep understanding of concepts and to comprehensively use what they have learned to solve problems. Therefore, junior high school students should learn to study mathematics better now in order to successfully provoke new learning responsibilities.
In addition, we should also clearly realize that junior high school mathematics should be accompanied by a certain review process in the process of learning. In the process of review, there are many knowledge points, which can easily give students a sense of disorder. Therefore, when learning junior high school mathematics, it is necessary to establish a knowledge network system for application in review and problem solving.
We have learned a lot of knowledge points and done a lot of problems, but the impression in our minds is often vague and isolated. We must compare and sort out the connections and differences, and weave knowledge into a net, so that we can solve problems with confidence, use them freely and form the ability to solve problems. For example, what kind of quadrilateral can be determined as parallelogram, rectangle, diamond or square? There are several ideas to consider. What are the properties of their sides, corners and diagonals? What about symmetry? Let's summarize.
Learning junior high school mathematics well is an arduous and imperative task. As a math teacher, we should stand on the students' side, guide them to correct learning ideas, do a good job in reviewing and studying in junior high school, make students not afraid of learning math, and guide them to fall in love with and like math, so as to learn math well.
Practical methods of learning junior high school mathematics
First, a solid foundation of textbook knowledge.
Of course, it is essential to listen carefully in class and do homework after class. Only in this way can we learn deeper knowledge. To do this, we must study hard and not be intimidated by difficulties. This is exactly what Napoleon said: "what a person thinks and believes, he can get it."
Second, keep studying. After learning, you must practice and review.
To learn mathematics well, the most important thing is accumulation. When you usually do problems, you must do a good job in understanding and memorizing these problems. Don't be greedy for quick results, but you won't get good results. The problems you usually do should be used flexibly, and the math problems will never change without them. Some theorems, formulas and concepts should not be recited blindly, but should be recited with examples from textbooks, which will be much easier. By the way, don't do a lot of math problems on one day and do nothing on the other, which is very easy to forget, but distribute them evenly according to the daily amount. Don't do too many questions, it will work well.
Third, learn to interact, learn more and ask more questions.
Ask more teachers or classmates. Usually in the process of learning, when students encounter problems and are difficult to understand, they must remember to ask the teacher. Because, in the case of reading a book alone, it is very easy to cause you to miss or understand the knowledge incompletely, thus causing the phenomenon of not understanding some key knowledge, which will immediately affect your future study.
Fourth, be competitive and don't lose again.
Usually, in the process of learning, everyone should know a competitor to compete with him for learning. Students, perhaps between you and your opponent, success and failure will be repeated. However, as long as you stop being soft and stand up bravely every time you fall, you will always be a winner.