The Binomial Cube

Materials:

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

  • The lid shows the square of the binomial

Purposes:

  • To observe the internal anatomy of the cube

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

  • Preparation for mathematics: the cube of a binomial

  • Preparation for cube root

Age: 3 ½ and up

Preparation: The child is successful with the visual materials (form, dimension, and color)

Presentation:

  • Invite the child for a lesson on the Binomial 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 place the top left corner where the doors will hinge and open them.

  • Remove all the pieces from the top layer one by one.  Place pieces silently on the table, keeping them in the same orientation that they were in the box.  

  • Repeat with the bottom layer.

  • Place the red cube in the back corner of the box

  • Choose a piece that will match the red side of the cube. Indicate where it will go and place it. 

  • Repeat with the remaining pieces of the bottom layer.

  • Once the bottom layer is built, repeat the process with the top layer, beginning with the red piece in the corner.

  • When all pieces are replaced, close the doors, and replace the lid to verify the box will close.

  • Remove lid, place it on the table again, open doors. 

  • Invite the child to take out and put pieces back in.

  • Fade and observe.

Language: None

Control of Error:

  • Mechanical-the box will not close if improperly assembled

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

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

    • Remove pieces from the box.

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

    • Build the top layer on the table to the right of the other layer, 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 and build the cube wearing a blindfold.

Memory Games: None

Pedagogical Notes: 

  • The patterns are reinforced as the child works with the material. This supports the mathematical mind’s ability to identify and create patterns.

  • Let the child struggle with this activity.  The control of error in the lid will encourage the child to try again, or they will put it away.

  • Representation may be necessary if a child continues to be overly challenged

Next

The Trinomial Cube