# Binomial cube

## Contents

- 1 Age
- 2 Materials
- 3 Preparation
- 4 Presentation
- 5 Control Of Error
- 6 Points Of Interest
- 7 Purpose
- 8 Variation
- 9 Handouts/Attachments
- 10 Government, Media Cover Up Fukushima Radiation Wave Hitting US
- 11 AP Photojournalist Blasts Obamas Press Restrictions As Orwellian Image Control
- 12 Flashback: Virtually All Mass Shootings Linked Up With Violence-Inducing Psych Drugs
- 13 Patients Stuck with The Bill When Obamacare Fails to Insure
- 14 Report: Foxconn using forced student labor to build Sonys PS4

### Age

3-6

### 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: a^{2} is always red, b^{2} is always blue, and "ab" is always black.

### Preparation

Algebraic expression: (a + b)^{3} = (a + b)(a + b)(a + b) = a^{3}+3a^{2}b+3ab^{2}+b^{3}

This is an individual exercise (Note: work cycle to be observed)

The child takes the cube apart beginning with b^{3} 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 a^{3}.

First Layer of the Binomial Cube: (represents a^{3}+2a^{2}b+ab^{2})

Second layer of the Binomial Cube: (represents a^{2}b+2ab^{2}+b^{3})

### Presentation

- 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.

The math presented above and below is provided for the teacher and is not to be presented or discussed with the child of this age. The math is presented to the children when they are older and are ready for it.

To firmly grasp the mathematical concepts behind the binomial cube, it's simplest if we start two dimensions instead of the three dimensions used by the binomial cube. .

For this example, we start with golden beads. The image below shows how we would represent (10 + 4)^{2}.

Now instead of beads, if we represent each block of beads as colored blocks as we do with the binomial cube, we get the figure below on the right. The number 10 here is represented by the variable "a", and the number 4 is represented by the variable "b".

The figure below explains the algebra behind the binomial cube.

Now if we go back to the beads, combining all blocks together, we get the following:

### Purpose

- Provide the child with tangible experience of the way in which the cube can be divided and sub-divided.
- Lay the foundations for the later study of algebra.
- The child is at the stage of the absorbent mind. The child is not asked 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.

### Variation

### Handouts/Attachments

## Government, Media Cover Up Fukushima Radiation Wave Hitting US

Radiation hot spots are popping up around the United States in the thousands of percentages higher than background radiation, mutated wildlife is being found dead on the same West Coast beaches where increased radiation levels have been documented by independent researchers, and the Fukushima TEPCO plant workers have been caught using duct tape to fix their ...

[Government, Media Cover Up Fukushima Radiation Wave Hitting US]

['.GetDomainName().' - news, stories, articles]

## AP Photojournalist Blasts Obamas Press Restrictions As Orwellian Image Control

PAUL SZOLDRA Business Insider December 12, 2013 A photojournalist for the Associated Press is pulling no punches in a scathing opinion piece published today in The New York Times, referring to the restrictions on press photographers covering the president as draconian and calling official photo releases propaganda. The article written bySantiago Lyon, vice ...

[AP Photojournalist Blasts Obamas Press Restrictions As Orwellian Image Control ]

['.GetDomainName().' - news, stories, articles]

## Flashback: Virtually All Mass Shootings Linked Up With Violence-Inducing Psych Drugs

The real cause of mass shootings such as Mondays Washington Naval Yard attack could be the psych drugs we now know Aaron Alexis was taking, and the evidence shows that the drugs are indeed a common thread throughout mass shootings. The mainstream media has long been ignoring psychiatrists and other experts who have found a link between psychiatric drugs and ...

[Flashback: Virtually All Mass Shootings Linked Up With Violence-Inducing Psych Drugs]

['.GetDomainName().' - news, stories, articles]

## Patients Stuck with The Bill When Obamacare Fails to Insure

Prison Planet.com January 4, 2013 Americans realizing Obama lied about more things than just If you like your plan you can keep it.

[Patients Stuck with The Bill When Obamacare Fails to Insure ]

['.GetDomainName().' - news, stories, articles]

## Report: Foxconn using forced student labor to build Sonys PS4

C. Custer gamesinasia.com Oct 10, 2013 Ifreports in the Chinese pressare to be believed, Sonys next-gen games console may be being assembled using some very outdated labor practices. According to Hong KongsOriental Daily, thousands of students froman IT engineering program at the Xian Institute of Technologyare being forced to work at Foxconns Yantai ...

[Report: Foxconn using forced student labor to build Sonys PS4 ]