The Trinomial Cube

Materials:

• A box with 27 small prisms to represent the formula:

• The lid shows the square of the trinomial

Purposes:

• To observe the internal anatomy of the cube

• Introduction to algebra and proof of the formula (a+b+c)3

• Preparation for mathematics: the cube of a trinomial 

• Preparation for finding cube root

Age: 4 and up

Preparation:  The child has successfully worked with the Binomial Cube

Presentation:

• Invite the child for a lesson on the Trinomial Cube, show them how to carry the box, return it to the shelf, and have them take it to the table.    

• Remove the lid and open the box.

• Remove all the pieces from one layer at a time, grouping each layer together with the pieces in the same orientation that they were in the box.  

• Build the cube beginning with the large red cube and continuing with the pieces that are familiar and resemble the binomial cube.  Indicate where each piece will go and place it. 

• The building of the cube should be done by alternating sides with the pieces that match by color and size.

• Continue building each successive layer starting with the red prism.

• Close doors and replace the lid to verify the box will close. 

• Take off the lid and remove the pieces for the child layer by layer, separating by layers on different parts of the table.

• Invite the child to build the cube.

• Fade and observe.

Control of Error: 

• Mechanical-the box will not close if improperly assembled

• The child’s own judgment/visual discrimination of the pattern

Language: None 

Following Exercise: 

• Building the Cube on the Table 

  • Beginning with the large red cube, assemble the cube layer by layer as before in front of the child. Compare the lid to all sides.

  • Bisect the cube in several different ways to show no matter where it's bisected, it is the same. Lift the first layer off and show the underside, reset, split down the middle comparing to the lid on the table.

  • Disassemble and invite the child.

• Building the Layers Separately.

  • Beginning with the large red cube, assemble the bottom layer on the table as before.

  • Build the middle and top layer on the table to the right of the other layers, also beginning with the red piece.

  • Mix pieces and invite the child to build the layers.

• Stereognostic Building with Blindfold

  • Invite the child to take out the pieces, then build the cube wearing a blindfold.

Memory Games: None

Pedagogical Notes:

• We start with separating the layers for the child because there are so many with this exercise, it can become overwhelming.

• Start with what the child already knows by building the binomial pattern first. Place the remaining pieces with an alternating pattern evenly. This will prepare the child for a later exercise called the Decanomial Square.

• Do not let the child pull the pieces out into a heap.