# A Spatial Reasoning Task Using Pentominoes

Observing people of all ages enthusiastically engaging in mathematical tasks is what fuels my passion for the work I do.  I had such an experience recently at a K-8 elementary school on a PA Day.  Last year I had been involved in a Ministry of Education Spatial Reasoning Inquiry and now other educators had an opportunity to benefit from that work.  After briefly sharing some research and background information I got everyone into the task at hand.

Part One:  Can you find all of the possible pentominoes?

• Use 5 colour tiles to make a pentomino.  A pentomino is a shape made up of 5 squares each of which has at least one full side of another square.
• Record your pentomino.  Then make a different one.
• Keep on making and recording pentominoes until you cannot make any more that are different.

Part Two:  Which pentomino nets can be folded into an open box?

• Look at your shapes  and try to visualize which pentominoes create a net for an open box.
• Once you have completed your predictions cut out each one of them and attempt to fold them to form open boxes.

This was about my third time to implement this lesson with pentominoes over the past year.  It never ceases to amaze me how some tasks are “just right” no matter what the age of the participants.  Even better it is a high-yield task that involves very little prep and only a few materials.  Often the simplest appearing tasks have the opportunity to yield the greatest mathematical learning.  Sometimes we make it much more complicated than it needs to be!  The key is knowing why we are doing the task and what learning we want to highlight so that along with the fun and engagement, thinking moves forward.