I am not a big fan of traditional uses of Tangram (related to Arts or Geometry), but I find it an interesting tool to introduce fractions through visual resources. This approach seems adequate to be used after rectangular models in order to introduce the idea that the pieces not necessarily have to have the same shape. But, it has the limitation of offering only fractions with powers of 2 as denominators. This characteristics can be positive at first, but can become a limitation after some time and that is the point when this "tangram of thirds" can be useful.
The pieces in the image above are fractions (of the whole square) with multiples of 3 as denominators. I decided to share this idea because I couldn't find anything like it online and because I believe it may be useful for enthusiasts of visual resources in mathematics education. You can download files with the Tangram of thirds in the links below:
Some tasks that I think could be interesting using this resource:
Introduction: given the whole square with the pieces drawn on it and 2 of the smallest triangles, find the fraction that each piece represents of the whole.
Halves: are you able to build half using one set of pieces in three different ways?