The main aim of this paper is to report a study that explores the thinking strategies and the most frequent errors of Hungarian grade 5-8 students in solving some problems involving arithmetical first-degree equations. The present study also aims at identifying the main arithmetical strategies attempted to solve a problem that can be solved algebraically. The analysis focuses on the shifts from arithmetic computations to algebraic thinking and procedures. Our second aim was to identify the main difficulties which students face when they have to deal with mathematical word problems. The errors made by students were categorized by stages in the problem solving process. The students' written works were analyzed seeking for patterns and regularities concerning both of the methods used by the students and the errors which occured in the problem solving process. In this paper, three prominent error types and their causes are discussed.