1, observation method: By observing the absolute value or sign of two numbers, we can judge their size relationship. For example, of the two positive numbers, the one with larger absolute value is larger; Of the two negative numbers, the one with the larger absolute value is smaller.

2. Calculation method: For some specific numbers, we can judge their size relationship by calculating their difference or quotient. For example, for two quadratic functions, we can judge their size relationship by calculating the sign of their difference.

3. Constructor method: For some two numbers whose sizes are not easy to compare directly, you can construct a function and judge their size relationship by studying the properties of the function. For example, for two unary quadratic forms, we can judge their size relationship by constructing the function and using the monotonicity of the function.

4. Synthesis method: comprehensively use the above methods to judge the relationship between two numbers by observing, calculating and constructing functions. This method is usually suitable for more complicated situations.

The advantage of comparative size in high school mathematics;

1, improve the efficiency of solving problems: comparing sizes is one of the commonly used problem-solving methods in mathematics. Mastering this method can help students find the answers to questions faster and improve the efficiency of solving problems.

2. Enhance logical thinking ability: Comparing sizes requires students to have certain logical thinking ability. Through the training of this method, students' logical thinking ability can be enhanced and their mathematical literacy can be improved.

3. Enhance problem-solving ability: Comparing sizes requires students to comprehensively apply what they have learned and solve problems by observing, calculating and constructing functions, which can help students better master mathematical knowledge and enhance their problem-solving ability.

4. Enhance self-confidence: Mastering relatively large methods can help students better cope with math exams and improve their math scores, thus enhancing their self-confidence and learning motivation.

5. Cultivate students' interest in mathematics: by mastering relatively large methods, students can better understand the essence and function of mathematics, thus stimulating students' interest and enthusiasm in mathematics and promoting the sustainable development of mathematics learning.