The purpose of this paper is to analyze in detail the process in which a 5th grade student
learned proportion and percent using double number lines and to obtain insights into how
his use of those representations supported his learning. A series of lessons were designed
and conducted in a class and the whole learning process of one student was videorecorded.
The analysis showed that he used double number lines to search for various
multiplicative relationships in problem situations and their consistent pictures, rather than
to make necessary numerical expressions systematically. The analysis also showed that
such uses of number lines made it possible for him to control his proportional reasoning
and develop his understanding of proportion and percent.