Binomial Cube

( a + b)3

MATERIAL:

Cube 1: A cube composed of 8 wooden blocks which fit together

in a binomial pattern, representing the cube of two numbers, (a + b),

or tens plus units. 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) or (t + u). The faces of the small

blocks are color coded: a2 is always red, b2 is always blue, and

"ab" is always black.

 

Cube 2: This cube contains blocks of the same dimensions as Cube 1,

but it is made from plain unpainted wood.

PURPOSE:

The child is at the stage of the absorbent mind. She child is

not made to understand the formula, but is using the cube in a

mathematical way. The child will build up a predisposition to

enjoy and understand mathematics later.

 

AGE:

4 to 5 years.

CONTROL OF ERROR:

Teacher control.

PRESENTATION:

Take the binomial cube to a table. The teacher sits next to the

child, and invites her to view the cube. The teacher takes the

cube apart piece by piece beginning with a3, and lays it out very

carefully.

 

The first row is set out at height "a", and the second row is set

out at height "b", according to the formula. Do not explain to the

child why you are setting the cube out in this order, or talk

about the mathematics of the cube. Simply show him. Work slowly.

 

When the formula has been set out on the table the teacher and

child view it for a minute or so. The teacher shows the child how

to rebuild the cube, starting with the cube of a, taking each

piece in order. She lets the child see that she is matching the

faces according to color. She pauses after finishing the first

layer. Then, taking a2b, she builds the second layer by taking the

pieces in order, matching the colored faces. When the teacher is

finished, she lets the child view the cube from all sides. If

necessary she may lay out the cube again and rebuild it. The child

works alone when she is ready to do so. When she has finished, the

teacher shows the child how to replace the cube in the box, beginning

by placing the smallest cube (b3) in the back of the box.

 

EXERCISE:

Cube 1: Colored Binomial

 

The child takes the cube apart beginning with a 3 and lays out the

pieces as shown, according to the formula. He reconstructs the cube,

matching red faces, black faces, and blue faces, beginning with a3.

 

Cube 2: Unpainted Binomial

 

This cube is introduced later. The teacher shows the child how to

handle the cube as cube 1, take it to pieces beginning with a3 as

before, and lay out the pieces according to the formula. The child then

rebuilds the cube. There is no color to help the child. He must build the

cube in the same way as before, but matching faces by size not color.

This, leads towards the mathematical understanding of the cube.

 

 

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