Purpose: The purpose of this paper is to present an algorithm to generate story problems via controlled parameters in the domain of mathematics. The generation process is performed in the problem generation module in the context of an intelligent tutoring system suggested in this paper. Controlling the question parameters allows for adapting the generated questions according to the specific student needs. Story problems are selected since they are one of the most important types of problems in mathematics, as they help train students to apply their knowledge to real-world problems. Such problems target improving different student's skills including literacy skills through reading the problem, recognizing the embedded mathematical information, and applying the required arithmetic operators. Design/methodology/approach: Natural language generation (NLG) techniques are used to control the difficulty level of the generated story problem header in addition to effecting variations from the natural language point of view. The proposed NLG technique is based on different separated knowledge categories to provide flexibility in the generation process and allow porting the module to other contexts, domains, and to other natural languages without a complete redesign. Findings: The approach has been empirically evaluated, and the results show that the generated problems are sound, clear, and naturally readable. This is in addition to the usability of the tutoring system itself. Research limitations/implications: The generation technique is confined to the problem described using rhetorical schemas. Nevertheless, it can generate any problem provided that the rhetorical schema is available. Originality/value: Most story problems generation systems limit the variation of the story problems to formulating the sentences that describe the story problem and the associated mathematical operations. In contrast, this paper presents a story problems generation technique that allows variations in the structure of the narrative story as well as the context, sentences, wordings, and mathematical operations. This variability allows assessing different student skills along different dimensions with gradually increasing difficulty levels.