Trinomial Cube

(a+b+c)³

PRE-REQUISITE:

The child must be able to construct the binomial cube easily

before being introduced to the trinomial cube.

MATERIAL:

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             + b²  + 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

surfaces.

PURPOSE:

The child, at the period of the absorbent mind, develops a

predisposition to understand math.

CONTROL OF ERROR:

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

AGE:

4 to 6 years

EXERCISE:

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

involved.

 

 

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