In this study, we extracted particles of descriptive sentences related to the concept formation of even numbers and odd numbers and clarified their relation to illustrative representations and linguistic representations. First, it was found that the frequency of use of case particles is high, regardless of academic grade. In the formation of even-numbered and oddnumbered concepts, the fact that mastering case particles leads to correct expression means that it is an issue for all grades. Second, in the formation of even and odd concepts, it was recognized that during the fifth year of elementary school and in the second year of junior high school pupils used many combinations of illustrative representations, linguistic representations, and particles, including case particles.