Describes four graphical preliminary task-based models of ten Arabic-speaking children, ages 6-10, based on their interaction with the International Children's Digital Library (ICDL). Data generated from a previous study (Bilal & Bachir, 2007b) were coded and analyzed to generate the models. Seven modes of behavior characterized children's interaction: Start, Recognize, Browse, Differentiate, Read, Explore, and Finish. Each mode is associated with moves based on task characteristics. The models were constructed using the general model developed by Bilal, Sarangthem, & Bachir (2008), which was partially informed by the works of Ellis (1989), Ellis & Haugan (1997), Choo, Detlor, & Turnball (2000), and Marchionini (1995). New patterns of behavior that are missed in these works were identified (Explore and Read). The models lack a Search mode that characterized children's keyword searching. The ICDL allowed entry of Arabic script in the search box, but failed to retrieve Arabic books by keyword. Children's behavior that combined linear and non-linear progression and the core iterative processes that occurred between certain modes of behavior and varied by task provide additional perspectives for understanding information seeking behavior within the specific context of a small and well structured Web space such as the ICDL.