Pentominoes!!

Today was all about spatial awareness and resilience.  Before the activity started, we shared strategies with each other on how we can deal with a situation that is very hard, and when we feel in over our heads.  Students made suggestions like;

  • Walk away from it and think about something else

  • Don't pay attention to other people

  • Ask others for help

  • Sing a song while you work

  • Try and switch between using your hands and your head

  • Let your hands think, and clear your mind

  • Set a reward for yourself if you finish


With that in mind, we started what was a very difficult activity.  The subject was Pentominoes.  Pentominoes are shapes made of 5 squares, where each side of one square touches another side of one square.  Here is what we did with them;

1) Using your blocks, find out how many possible shapes you can make with 5 squares.  Flips and rotations count as 1 shape, not two.  When you have found all the possible combinations, draw them in your math journal.

2) Using the shapes you made, make a rectangle of either 3 x 20, 4 x 15, 5 x 12, or 6 x10 (what do all these have in common?).  You must use every shape and have no blank spaces of leftovers.  When finished, draw the rectangle in your math journal.

This is as far as we got today, but I am sure there are tons of extensions to go on this activity.  How many squares can you make with these shapes?  Which pentominoes tessellate?  Can you make any other images?  How about Hexaminoes (six squares)?  What if we try using triangles instead of squares?  And so on....

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