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Exploring
Shapes in preschool, kindergarten ( Greeks, 500 BCE )
Materials: colored
stones all in one pile, arrange into shapes, one
number at a time. ( Note, this is NOT Dot-Math )
Count
aloud, rearrange stones to make the following shapes, adding one stone at a
time. Elementary geometry
is reinforced here: 1 ->point, 2 -> 2 points, required to
define a line, 3 -> 3 points required to define a plane.
Pentagons and hexagons are interesting
since these shapes show up in nature; the number 10 is a
triangle number, the sport bowling uses ten pins arranged this way!
Even-ness and Odd-ness can be immediately recognized. With
practice the student can immediately tell you if you have 9 dots or 15 dots or
12 dots ( two rectangle sixes, one above the other, or two triangle sixes, one
inverted and below the first).
Recognizing shapes and
patterns is the goal of this exercise. Once the basic shapes are known by the
student, have the student point out these shapes all around him/her. Circles
can be introduced here, especially if you start with one center stone, then
arrange all other stones so that they are the “same distance” from the first
stone (using a ruler, perhaps); the more stones you use, the better the circle
appears.
Patterns can be seen
and distinguished from one another. The Natural numbers exhibit certain
important patterns amongst themselves that can be seen, visually, with these
colored rocks! For example, squares are particularly interesting, since each
one is the sums of two smaller, adjacent triangle numbers (See Exploring Shapes
2).
History: The
Greeks thought of numbers in exactly this manner; moreover, these shapes
represented real objects found in nature. It’s no wonder that numbers were
reality to the Pythagoreans. We owe much to these Greeks for laying down rigor
and clarity of thought we take in stride (and for granted) today.
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