In class, Mr. Liu divides a formula into two formulas with the "clause meaning unchanged" in Chinese subject, thus drawing the concept of multiplication and division, and using the thinking method of analogical reasoning, preliminarily drawing the following conclusions;

Teacher Liu asked the students if they could find a counterexample of this kind of similar equation. After analysis, no counterexample is found, and the conclusion is that this equation is a proved law, and the mathematical thought of deductive reasoning is used in this process.

After Mr. Liu gave the actual math problem, let the students list the formulas in two ways and ask which way is simpler, using the optimization idea;

Teacher Liu came up with a practical problem with letters, and asked the students to formulate it in two ways without calculation. Then the general formula of multiplicative distribution rate is obtained, and the abstract idea is used.