Shape and Space in Grade 1: Pentominoes Inquiry
Pentominoes are rectilinear shapes made from 5 connecting squares.  The squares must connect by matching side-to-side, and cannot connect just by vertexes.  The first step in the inquiry is to find all possible pentominoes (there are 12 altogether).  The first 1 or 2 could be modeled using the Area ITP: http://www.taw.org.uk/lic/itp/itps/area_2_2.swf

The 12 unique pentominoes (G1 student's recording)

Finding all possibilities type problems help learners develop persistence.  How do you know when you've found all possible pentominoes?  It is common for children to repeat the same shape in a different orientation.  This is an good teaching opportunity - a time to discuss the concept of congruence.  Sorting and classifying according to the shapes the pentominoes make is another good next step.  The set of pentominoes includes rectangle, hexagon, octagon, decagon, dodecagon.  The prefixes of these polygon words all originate in Greek....the suffix 'agon' denotes 2D ('hedron' denoting 3D).  Other inquiry routes include investigating:

• symmetry - which are symmetric which are asymmetric?
• Nets - some pentominoes are nets for open-topped cubes, some are not

Which of these pentominoes is a net for an open-topped cube?  Can you visualize which it is?

• Tessellation - Do all the pentominoes tessellate? - why/why not?

The pentominoes all link together to make rectangles of various sizes, 12 x 5, 10 x 6, 3 x 20 etc:

Another puzzle that requires trial & improvement and persistence!