Cute pattern!
The pattern looks as though you will construct the TeePee first, then add those larger triangles. I wouldn't do a template. Rather cut a rectangle fabric piece, then diagonally cut and those are the two pieces for the background.
The other hint ... I'd cut the rectangle larger, perhaps at 7x13, slice diagonally, then sew in place. That way you will have extra fabric, and then can easily square each block up to perfect straight edges and square corners.