#32 Bring Variety
Bring Variety
Play “Imagine That!” by making silly changes to iconic quantities and groups, and telling stories of what happens. Imagine that… a teapot has two spouts! Imagine that… your hand has little hands on each fingertip! Imagine that… we have no coins or bills other than pennies! As they play, children seek out fun iconic quantities, and analyze the roles of quantities in different situations.
Pick a quantity and find many different ways to arrive at it. For example, you can draw twelve objects as two groups of six (an egg carton), as three groups of four (claws of a sloth), or as ten and two. You can arrive at sixteen by two different power paths: it’s four of fours, but also two of twos of twos of twos! Sort quantities by types of paths that lead to them. For example, you can only arrive at numbers like seven, eleven, and nineteen (primes) by addition, not by multiplication or exponentiation!
Since the ancient times, people have been designing tools and toys with subitizing in mind. Dice, dominoes, playing cards, abacus, even some number systems (Roman and Mayan, for example) use easily recognizable groups of symbols. Can you find these and other examples of groups of small quantities in everyday objects? Keep in mind that we are so used to many of these examples that we overlook them easily!
