Hi David,

It sounds like the plant is a Mimosa Pudica or Sensitive Plant.

Mimosa Pudica
Sensitive Plant

Mimosa pudica or  Sensitive Plant has prickly delicate branches and feathery fronds that fold inward and droop when they are touched, shaken, or even blown on; these are called seismonic movements. The leaflets of a Sensitive Plant reopen in about half hour but fold up naturally each night. Although fun to watch, the opening and closing of the leaves weakens a Sensitive Plant if it occurs too often. Mimosa Pudica may produce tiny pink flowers that resemble little fluffy balls.

These plants are considered poisonous and should be kept away from pets and children. Read more about common houseplants that are poisonous in Don’t Feed Me To Your Cat! A Guide to Poisonous Houseplants

You can read my plant care advice for Mimosa pudica Plants in the Popular Houseplant section of the website.

http://www.houseplant411.com/houseplant/mimosa-pudica-sensitive-plant-how-to-grow-care