
The first thing that can be shown with tangrams is area. In the technical level class that I teach, we have a chapter that deals with finding the area of plane shapes. The tangrams are used to show how the "formulas" for the figures work together.
1. Using the square and two small triangle pieces, we can form a rectangle. by moving one of the triangle pieces, we can form a parallelogram. This shows the students that the area formula for a parallelogram is similar to a rectangle.
Area of Rectangle to Parallelogram
2) Using the square as 1 sq. unit, we can explore the relationship of the other pieces in the tangram puzzle.
3) The third thing that we can show using the tangram pieces are forming shapes.
There are lots of different pictures that you can form with the tangram pieces. The above were a few simple ideas of how to relate the pieces to a bigger picture.