Note:
One way that humans attempt to survive is by understanding the world
around them. The human brain is a pattern seeking organism.
So, by nature, children are interested in finding patterns,
relationships, and order. If children have worked their way
through the materials for dimension, color, and shape, they will have
found order, patterns, and relationships in those materials, and will
have developed the ability to discriminate attributes to a point where
they will enjoy the challenge of exploring the order inherent in the
binomial and trinomial cubes. For this age, 4 to 6, the purpose
of the material is not to teach math, but instead, to provide a
challenge for a child's ability to find patterns and relationships.
Therefore, the material is presented as a sensorial activity. It
is presented like a three dimensional puzzle. Anyone who likes to
do puzzles knows that in order to master a puzzle, you have to pay
attention to the relationship between the pieces. People who are
masters at puzzles will tell you that they take out, and organize,
puzzle pieces very carefully. This is what is modeled for the
child in this activity.
The math presented above and below is provided for the teacher and is
not to be presented or discussed with the child of this age. The
math is presented to the children when they are older and are ready for
it.
As mentioned above, the binomial represents two numbers represented
symbolically as (a + b). We could represent the numbers with (T +
TU) for Tens plus Tens times Units. The pattern for the binomial
squared is apparent on each of the faces of the binomial cube. It
is
represented below:
This pattern for the binomial squared can also be seen when building a
square of the number with the golden beads. For example, for the
number 13, which is (10 + 3), the pattern for the square of the number
looks like:
(10 + 3)
^{2}
a + b
x a + b
a^{2} + ab
ab + b^{2
}a^{2 }+2ab + b^{2}
or
10 + 3
x 10 +3
10^{2}+(10x3)
_
(10x3) + 3^{2}
10^{2}+2(10x3)+3^{2}