Graphic analysis This is actually a simulation method.
It has strong intuition and pertinence, and is widely used in mathematics teaching. Such as engineering problems, speed problems, deployment problems, etc. It is often analyzed by drawing, and students can understand the meaning of the problem through charts, so as to set unknowns and list equations to solve according to the content of the problem.
Factorization method
Factorization is to transform a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry and trigonometry problems. There are many methods of factorization, such as extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce the use of decomposition and addition, root decomposition, exchange elements, undetermined coefficients and so on.
Personal experience method, such as sailing against the current, sailing against the current.
Many students have never been on a boat, so it is difficult for them to understand the speed of sailing with the current, against the current and against the current. In order to make students understand, I take cycling as an example (because most students ride bicycles). The students all have personal experience. Riding with the wind is easy, but riding against the wind is difficult. This is the effect of wind speed. At the same time, it is clear that sailing boat and bicycle are the same thing, and the different factors that affect it are current speed and wind speed. In this way, students can understand.
Method of substitution is a very important and widely used method to solve problems in mathematics. We usually refer to unknowns or variables as elements. The so-called method of substitution is to replace a part of the original formula with new variables in a complicated mathematical formula, thus simplifying it and making the problem easy to solve.
A careful examination of the problem
Careful examination of questions is the basis for correctly understanding the meaning of questions and solving problems correctly. In the process of doing application problems, students' unclear thinking and careless examination are the main reasons for doing wrong problems. For example, 1: The little frog said, "I eat 30 bugs every day." The big frog said, "I eat 32 more bugs than you every day." Q: How many bugs did two big frogs and a little frog eat in seven days? There are probably the following types of problem-solving errors caused by students' unclear examination. ① The direct formula of how many bugs the big frog eats is (30+32+32)×7 without careful analysis. (2) Didn't see the problem clearly. The direct expression is (30+30+32)×7. ③ There are two kinds of errors, and the formula is: (30+32)×7. These are common mistakes in solving problems caused by carelessness in exams, which are often found when solving simple application problems.
The above are the methods and skills I have compiled for you to solve the math problems in senior one.