There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing, symbolizing, and checking, and to differentiate them between linear and quadratic geometric number patterns. From the national survey results, we argue that reasoning on geometric number patterns is a proper initial activity for learning algebraic thinking in Grade 7, and the relations between the checking component and the other components appear to be different between linear and quadratic patterns. Therefore, we propose that checking can play two kinds of role in reasoning on geometric number patterns. One is to induce a strategy for generalizing, and the other is to initiate the development of symbolizing after it is integrated with generalizing. (Contains 10 tables and 2 figures.) [For complete proceedings, see ED489597.]