Fractal geometry is not a content usually addressed in basic education. This paper discusses this geometry with the purpose of disseminating and expanding knowledge about it, especially for teachers who work at this level of education. It begins with a brief history of the emergence of the fractals until its formal definition, exhibiting classic examples and a small biography of its creators. Then, we present a selection of mathematical contents of basic education that can, of course, be worked from this geometry. Some proposed activities that involve fractals and are suitable for applications at various levels of this school segment are also presented. Finally, the experience of one of the proposed activities in a 9th grade class of a public school in the city of Rio de Janeiro is portrayed. We believe that the beauty and visual appeal of fractals act as motivating and innovative elements for important themes in the basic education curriculum to be addressed in a more meaningful way.