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Binomial Cube

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2 wooden cubes, 6 rectangular prisms, painted red, blue, and black which form a cube (a+b)^3. 
The box has two hinged sides and a lid that has (a+b)^2 painted on top of it.


  1. Invite the child to the lesson and show how to carefully hold the box so that it stays together.  
  2. Invite the child to take it to the table. 
  3. Carefully remove the lid, and place it on the table. 
  4. Rotate the box diagonally so that both hinges are facing you. 
  5. Show the child how to pull the two walls of the box downwards to rest on the table. 
  6. One by one, starting with the blue cube and taking them out left to right, front to back, top layer to bottom layer, make sure all 8 prisms are randomized. 
  7. Place the red cube in the corner of the box where the two walls meet. 
  8. Place the red and black prisms on each side of the red cube. 
  9. Place a blue and black prism adjacent to the red and black prisms, so that one of the blue sides faces upwards. 
  10. Point to the red cube, and place the final red and black prism on top of it with the red side facing upwards. 
  11. Place the two blue and black prisms on the sides of the red and black prism. 
  12. Point out the three blue sides meeting, and place the blue cube in the space. 
  13. Show the child how to carefully lift the sides of the box upwards, and place the lid on. 
  14. Invite the child to perform the exercise.


Exercise 1: child performs exercise as presented.
Exercise 2: Outside of the Box.
Build the cube outside of the box, then walk around the cube to see how all the sides are the same. “Cut the cube” into two different sections – separating in half horizontally or vertically – showing the child how it is the same no matter how it is “cut.” 


None, other than name of material. 

Control of Error

The lid of the box is a visual guide, the closing of the box acts as a guide because the sides close only when the binomial cube is put together correctly.

Direct Purpose

Build the cube.

Indirect Purpose

Preparation for mathematics and the cube of the binomial.  
Prepares child for the proof of the formula at the elementary level. 
Preparation for cube root. 
Indirect preparation for algebra. 


3 1/2


The child will likely not be able to build the cube correctly the first time, but through error and exploration he will succeed.

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