The increasing use of the Internet calls upon the need for adequate cyber security awareness to better face the risk and dangers connected with the online environment. This research presents an experiment that revealed the cyber security awareness of children at Czech primary schools. They were tested for their skills to distinguish different online risks. After the pre-testing children received training and with the time delay they filled in very similar questionnaires. The re-testing measured how well the children retained the training and their ability to use the skills in the virtual environment. The results show only a moderate level of cyber security awareness at the initial testing. The one-off training had only an insignificant impact on their online behavior. The research reveals an important finding. One-off training does not affect their responsive online behavior and is not a suitable solution for effectively improving online safety skills. The task is to involve cyber security awareness education in the whole educational process. Based on the literature and conducted research this paper provides a set of recommendations for the designers of the cyber security school curriculum.