there are several tangram interactives available
e.g. this
one (utilising geogebra)
the tangram dissection:
find how to fit all of the 7 tangram pieces into these outlines:
you could consider the perimeters
(there are 4)
[in terms of multiples of the square root of 2 and integers]
an interesting set of 3 shapes that look the same size but are not (a kind of paradox)
find outline shapes that have just one line of symmetry (using all 7 tangram pieces)
some examples (several more can be found):
find an outline shape with rotational symmetry, order 4, using all the tangram pieces
(slightly cheating, with a gap in the centre)
or the square