Trinomial Cube



The child must be able to construct the binomial cube easily
before being introduced to the trinomial cube.


Cube 1:

A cube composed of twenty-seven wooden blocks which fit together to
form the cube of (a + b + c). Each face that is "a2" is red, "b2" is
blue, and "c2" is yellow and all other faces are black.
a = hundreds
b = tens
c = units

Formula for the cube (a+b)3

    a + b + c
x a + b + c
    a2 + ab + ac
           ab             + b+ bc
                    ac             + bc      + c2
    a2 +2ab +2ac   +b2 +2bc       +c2
x  a  + b + c
   a3 +2a2b+2a2c  +ab2+2abc    +ac2        
______a2b           +2ab2+2abc          +b3 +2b2c    +bc2
                  +a2c            +2abc +2ac2         + b2c    +2bc2   +c3
    a3+3a2b+3a2c +3ab2+6abc +3ac2+b3 +3b2c   +3bc2    +c3

Cube 2:

Exactly like the first, but in plain wood. There are no painted


The child, at the period of the absorbent mind, develops a
predisposition to understand math.


The child matches the pieces by color. The result is a cube.


4 to 6 years


Cube 1: Colored Trinomial
The binomial and trinomial cubes come in both hinged and non-hinged boxes. If the box is not hinged, use the following proceedure:
The teacher sits next to the child at a table. Holding the lid on the box, she turns it upside down on the table. She lifts the box off the cube carefully, and looks at the different sides of the cube and with the child. The teacher removes one layer of the cube at a time and places it on the table.
If the box is hinged, the teacher may simply begin removing pieces from the hinged box and set out three layers on the table.  
Starting with the tallest layer and the red cube (a3), the teacher removes pieces in order and lays out according to the formula. She does the same with the second layer (selecting the piece with a red face "a2b" first), continuing in the sequence of the formula. She is careful
to lay pieces of the same size in front of each other. Finally, she
selects the piece with the red face, "a2c", from the third layer
and continues until the whole cube shows the formula in the
arrangement of pieces on the table.
The child and teacher spend a little time looking at the lay-out.
Then the teacher reconstructs the cube, layer by layer, beginning
with "a3", matching faces of the same color. The
teacher, by the way she handles the pieces, helps the child to
understand that she is matching faces by color. The child will realize in
time that the pieces are also matched by size. The teacher gives
help until the child is able to work alone. Most children will
need more demonstrations on subsequent days.
Cube 2: Unpainted Trinomial
When the child has had sufficient experience in working with Cube
1, he or she can use Cube 2. In most cases, the teacher will need to sit
by the child and arrange the pieces of the cube according to the
formula in an orderly way (as with the Cube 1), and reconstruct
the cube as the child watches. Here, the faces must be matched by
size alone. There is no color to guide the choice. The child,
therefore, is able to get a clearer conception of the mathematics


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