Among the critical components related to the improvement of mathematics learning are the design of high cognitive demand tasks and teachers' ability to maintain these cognitive demands during their implementation of lessons. We investigate the factors affecting the maintenance and decline of cognitive demand in the implementation of a statistics lesson by two teachers who participated in a Lesson Study group for third graders (8-9 years old). The results of the investigation show notable changes in the maintenance factors associated with the teachers' questions and feedback, the scaffolding provided for the students' reasoning and the modelling of high-level performance. In terms of the decline in the level of cognitive demand, the greatest changes were found in factors corresponding to the routinization of problematic aspects of the task and to problems in lesson management. Based on the results of our collaborative work with teachers in the context of Lesson Study, we conclude that it is possible to design and implement statistical tasks in primary school classrooms that maintain high cognitive demand.