The inquiring similarity lesson is the school lesson which students construct mathematics by recognizing similarity. In this lesson, the teacher presents a mathematical entity in the first, then he (or she) presents the two entities similar and non-similar to it. At this stage, the teacher makes students inquire the similarity between the mathematical entity presented in the first and the entity presented as similar to it. After then, the teachcr presents a entity and makes students judge it to be similar or non-similar to the entity presented in the first. The teacher repeats this action. It can be said that the student constructed mathematics when he (or she) was able to recognize the similarity among the entities presented as similar in these process. In the first half of this paper, it has been clarified that it is effective in the inquiring similarity lesson to present the entities having the aliginable difference between the entities presented as similar and as non-similar. In this case, it must be taken into consideration that the significannt features for the construction of mathematics are not hidden under the ground. In the latter half of this paper, we divided the similarity required of students to recognize into the following four types and gave some means to facilitate the recognition of each type of similarity. ・objective similarity with perception ・objective similarity with no perception ・relational similarity with perception ・relational similarity with no perception
