The present study examined the behaviors in number sense and especially in computational estimation problems, of 5th and 6th grade students of Greek Primary schools, who participated in a mathematical competition. These students have not received any training in relation to computational estimation strategies nor have they been trained in expressing themselves verbally or in writing as to their way of thought while performing the set tasks. Therefore, it was examined whether these students know how to perform computational estimation, which strategies they use, and what errors they make. It was also examined whether they can write down their explanations in computational estimation problems and this ability was compared with their problem solving ability. Many researchers (Buchanan 1978; Reys 1986; Reys and Reys 1989; Dowker 2003) state that estimation plays an important role in problem solving and is very similar to it, however, no experiments have been conducted specifically on this issue.