I don't know how all Tangram sets are, but ours has small, medium and large triangles, a square, and a parallelogram. Each is constructed in such a way that you can use the smaller shapes to construct the larger ones. We have 4 sets of shapes which came with our Tangram patterns, in four colors. To do this activity, you at least have to have 2 or 3 sets of shapes.
To give him a reference point for what this activity was all about, we talked about how in the past, Little Bean had figured out that two large triangles put together make a square. This was something he had figured out when doing a pattern card that required you to combine a couple shapes in order to finish the pattern. I wanted to start with the largest shape and move down in order of size. So, I asked him how we could make a large triangle using some of our smaller triangles. We discovered that two medium triangles could fit over the large triangle exactly. Then I challenged him to figure out another way to make a large triangle using some of our smaller shapes. He was at a loss, so I gave him a hint, and told him to start with the square. It soon became clear that the square and two small triangles could also make a large triangle. Next, I challenged him to use the parallelogram to make a large triangle. He figured out pretty quickly that a parallelogram combined with the two small triangles fit over the large triangle exactly.
Next, we moved on to the medium triangle. We were able to make the medium triangle by using the two smallest triangles turned on their sides.
Lastly, we looked at the parallelogram and the small square. He knew right away the square could be made with the two small triangles, and we discovered together that the parallelogram as well could be made from the small triangles.
To finish, we went back the large triangle. We constructed it again, using the parallelogram, this time constructing the parallelogram with the two small triangles on top of the triangle, making three layers. The first layer was the large triangle by itself, the second layer directly on top of that was the two small triangles and the parallelogram, and the third, top layer was another two small triangles constructing the parallelogram.
Little Bean REALLY liked this activity. His face just lit up and he'd begin to laugh each time we made a new shape in a different way. I can't wait to do this again with him. I know the more we do it, the deeper his knowledge of shapes will go. And check out Miss O--I didn't realize it at the time, but she was paying attention to this activity as well!