In this paper we focused on graph tasks from Slovak Bebras Challenge with the intent to use them as a teaching and learning material. Based on qualitative categorisation of tasks together with quantitative analysis of contestants results we chose three tasks that were the most suitable for lower secondary schools Informatics in Slovakia. We used qualitative research methods to better understand what had caused the most significant problems. Based on these results we have prepared lesson plans with objective to teach pupils to understand, read, edit and to create specific graph structures. Taking Bloom taxonomy into account, worksheets were created and for each learning objective, there is at least one subtask in a worksheet. The main parts of this paper are pre-research and preliminary results of testing worksheets with pupils in the 5th and 6th year. We describe differences between groups based on gender and age. These results help us understand the reasons of contestants’ mistakes in the original tasks and of gender- and grade-specific performance in these tasks. We plan to further develop the lesson plans as we found them valuable not only as a method of research but also as proof that tasks from Bebras Challenge could be used for learning and for teaching.