Introduction: Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences. Method: We developed a teaching experiment with a group of eight-nine years old students which shares the features of design research. It consisted of six one-hour in-class sessions, over a period of one year, in which we proposed students individual written activities, whole group discussions and individual interviews. Results: Students evidenced four different meanings of the equal sign which are here used to establish different levels in their understanding. By using these levels, we analyze the evolution of students' understanding of the sentences along the experiment. Discussion: Students evidenced the use of multiplicity of meanings of the equal sign and some displayed some instability in their understanding along the six sessions. The specific factors that explain that instability are identified and some didactical consequences are obtained. The obtained results are contrasted with those of previous studies. (Contains 2 figures, 5 tables, and 8 footnotes.)