The research entitled Forms of additive thinking in third grade students (8-9 years old): an approach from the Theory of Objectification characterizes forms of additive thinking that appear, are produced, through the encounter with historical-cultural arithmetic knowledge in the joint labor that emerges between third grade students of Primary Basic Education and the teacher in the process of solving additive tasks in the naturals. These forms of thinking are produced through sensitive and material forms of perception, gestures, corporeality, symbolization, discursivity and use of artifacts.