8 painted wooden cubes in a wooden box with a lid. The box is
hinged and opens out to display the cubes. The lid is printed with
the binomial square pattern.
A box containing eight wooden blocks:
One red cube One blue cube
Three red and black rectangular prisms
Three blue and black rectangular prisms
All the blocks fit into a natural wood box. Each side of the cube
has the same dimensions and pattern, and represents the square of
(a + b). The faces of the small blocks are color coded: a2 is always red, b2 is always blue, and "ab" is always black.
Algebraic expression: (a + b)3 = (a + b)(a + b)(a + b) = a3+3a2b+3ab2+b3
This is an individual exercise (Note: work cycle to be observed)
The child takes the cube apart beginning with b3 and lays out the pieces as shown, according to the formula.
The child reconstructs the cube, matching red faces, black faces,
and blue faces, beginning with a3.
First Layer of the Binomial Cube: (represents a3+2a2b+ab2)
Second layer of the Binomial Cube: (represents a2b+2ab2+b3)
- The Directress shows the child how to carry the box to the table.
She sits besides the child, open up the box and lays out the blocks
in the following pattern that will make it easy for rebuilding the
cube in two layers.
- The Directress then shows the child how to rebuild the cube. The
colors printed on the lid act as a guide.
Control Of Error
The color codes.
The cube can not be built if incorrectly assembled.
Points Of Interest
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, 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.