Its main manifestations are: whole substitution, whole addition and subtraction, whole substitution, whole association, whole complement, whole transformation and so on. In junior high school mathematics, the whole idea has a good application in numbers and formulas, equations and inequalities, functions and images, geometry and graphics.
Holistic thinking
Holistic thinking is to skip the details of the problem, understand and analyze the problem as a whole, which can often simplify the problem.
Integer addition and subtraction
It is sometimes difficult or impossible to find a single object when calculating the sum and difference of multiple objects. At this time, through the whole transformation, we can combine them and add and subtract as a whole, which can simplify the problem.
Integer substitution
In the problem of algebraic expression evaluation, if the formula is complex, we can observe the characteristics of the formula, regard the same part of the complex formula as a whole, replace it with a letter, then get the value of the whole through operation, and then convert the original algebraic expression into a formula containing the whole, so as to solve the original algebraic expression.
Overall structure
When adding auxiliary lines in geometry, we should consider adding them from the overall point of view, and complete the graphics in the problem through auxiliary lines, making them become familiar basic graphics or basic models (such as isosceles triangles, handle models, etc.). ), so as to find hidden information and gather some irrelevant information together.