First, comparative law.
By comparing the similarities and differences between mathematical conditions and problems, we study the reasons for the similarities and differences, so as to find a solution to the problem, which is the comparative method.
Example: Grade six students planted a number of trees. If everyone plants 5 trees, there are 75 trees left. If each person plants 7 trees, there will be a shortage of 15 seedlings. How many students are there in the sixth grade?
The similarities are: the number of sixth grade students remains unchanged; The difference is that the conditions in the two schemes are different.
Find a connection: the number of trees planted by each person has changed, and the total number of trees planted has also changed.
Solution: Everyone has 7-5=2 (trees), so the whole class has 75+ 15=90 (trees).
Class size is 90÷2=45.
Second, the comprehensive method.
When solving mathematical problems by comprehensive method, every known content is usually regarded as a part (or element); After analyzing the internal relationship between each part (or element) layer by layer, it is gradually deduced to the topic requirements. This method is suitable for mathematical problems with few known conditions and simple quantitative relationship.
Third, the parameter method
A method of expressing related quantities by letters or numbers that only participate in formulas and operations without solving them, and listing formulas according to the meaning of the questions is called parameter method.
Fourth, the exclusion method.
The logical principle of exclusion is that everything has its opposite. In all kinds of right and wrong results, excluding all wrong results, the rest can only be correct results.