I love using tangrams in my geometry classes but I hate having to deal with all those little pieces that get lost or broken.  Unfortunately, most of the tangram program's I've found are all designed for the user to complete a predetermined design.

After some searching I discovered a web based tangram that gives you a choice of filling in a creature or creating your own.  It does not appear to work on the iPad but it does work on my Mac. 

The Tangram Activity is a bit clunky but it does exactly what I want it to.  I have a couple activities that require students to create certain geometric shapes from certain tangrams.  One figure is a triangle like the one above that uses all the pieces.  Others might ask for a concave pentagon using pieces 2, 3, 5, and 6.  This activity has challenged my ELL students in the past.  I don't know if using a computer based version is better than the actual ones but at least they can't throw them out.

I found a second one that was originally created in 1999.  Again, it works on the computer but not on the iPad.  It does allow a person to move pieces around to create the geometric shapes without  being limited. 

I actually found a bit more information on ways to use tangrams in high school math.  Starting with Grandfather Tang’s Tangrams Go to High School (you'll have to do a search for it because it was a word document).  Its a 9 page lesson that uses tangrams to teach area and perimeter.  The activity begins by having students figure out the area of the shapes before asking students to find the perimeter of certain creations.  I like that this is a true exploration where students have to deduce much of the information themselves.

This site has excerpts of Grandfather Tang's story to read to the students before having them use the tangrams to create a variety of quadrilaterals from rectangles to rhombus to trapezoids.  Some shapes can be created while others cannot.  In addition, students can classify angles within the various pieces which provides a great review.

Finally are the two lessons found at Tom's Math Lessons over at the Math Forum which have students trace, classify each piece, and explain how they found the area.  The lessons are well done.  They come complete with objectives, materials, the lesson and extensions.  In addition, there are answer keys for both activities.

I plan to add the lessons to my repertoire because these can be done as hands on and have a geometric perspective rather than just recreating pictures.  I love finding materials such as these.