Exploring Shapes in Preschool and Kindergarten (Greeks, 500 BC)
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 sum 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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