Binomial Cube

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.

Materials

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.

Preparation

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)

Presentation

1. 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.
2. 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.

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Beech/Plywood.