1, observation and induction: carefully observe the given data or graphs and try to find out the laws between them. Sometimes, the distribution of data or the shape of graphics may give hints. Through observation, you can begin to sum up a pattern or relationship.

2. Sequence analysis: When processing a series, observe the relationship between every two consecutive numbers, such as difference, multiple, factor, etc. , can help you find the pattern.

3. Function and mapping: consider the functional relationship between variables, such as y=f(x). Observing the changing trend, periodicity and symmetry of function images is helpful to find out the law.

4. Pattern recognition: for some graphics or pattern problems, find out the changing rules of the shape, color and size of the graphics. This requires careful observation and keen intuition.

5. Logical reasoning: For some topics involving logical reasoning, it is necessary to reason according to the conditions given by the topic. At this time you may need to use some basic logical rules, such as reduction to absurdity and induction.

6. Algebraic method: When solving some algebraic problems, such as solving equations or inequalities, finding the law may be finding the internal relationship or law between variables. This may require some algebraic skills, such as factorization and formulas.

7. Use assistive tools: Sometimes, using calculators, computer software or other assistive tools can help you find patterns. For example, if you draw a function image, you can intuitively see the law of function increase and decrease.

The benefits of finding laws in mathematics;

1, improve the ability to solve problems: better understand and solve mathematical problems by discovering laws. In the face of some complex problems, finding laws can help us find the internal laws and structure of the problems, so as to find more effective solutions.

2. Cultivate logical thinking: discovering laws requires us to observe, summarize, reason and judge. These processes all require logical thinking ability. By looking for rules, we can exercise our logical thinking ability and improve our ability to analyze and synthesize problems.

3. Enhance the reasoning ability: To discover laws, we need to make reasoning based on known information, and draw new conclusions or discover new laws. This process requires us to use basic logical rules and reasoning skills, thus enhancing our reasoning ability.

4. Broaden our thinking horizons: Discovering laws can not only help us solve mathematical problems, but also broaden our thinking horizons. Through the observation and analysis of different types of problems, we can find more problems and laws, so as to better understand and apply mathematical knowledge.

5. Improve interest in learning: Finding laws can help us better understand the essence and charm of mathematics, thus stimulating our interest in mathematics learning. When we discover a new law or solve a complex problem, we will feel very excited and satisfied.