pentominoes

it takes a while for students to find all 12 usually

one purpose for finding these is to provide tiles to tessellate
maybe in a variety of different ways

rather than just fitting shapes together, without any regularity, it is important that students appreciate that they should be able to detect 'stripes' in their tessellations
after all, all these tessellations can all be viewed as tesselations of parallelograms
(seen by connecting corresponding corners of the pentominoes)