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Trinomial Cube

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Material

3 wooden cubes, 24 rectangular prisms, painted red, blue, yellow and black which form a cube (a+b+c)^3. The box has two hinged sides and a lid that has (a+b+c)^2 painted on top of it. 

Presentation

  1. Invite the child to the lesson. 
  2. Carefully remove the lid, and place it on the table. 
  3. Rotate the box diagonally so that both hinges are facing you. 
  4. One by one, starting with the yellow cube and taking them out left to right, front to back, top layer first, to middle layer, to bottom layer, make sure all prisms are randomized. 
  5. Place the red cube in the corner of the box where the two walls meet. 
  6. Place the thick red and black prisms on each side of the red cube. 
  7. Place a blue and black prism adjacent to the red and black prisms. 
  8. Place a thinner red and black prism on each side of the thicker red and black prisms.  
  9. Place a black prism on each side of the blue and black prism. 
  10. Place a long yellow and black prism in between the black prisms. 
  11. Place the thick red and black prism on top of the red cube. 
  12. Place the two blue and black prisms on the sides of the red and black prism. 
  13. Place the blue cube in the space where the three blue sides meet. 
  14. Place a black prism on each side of the blue and black prisms. 
  15. Place a short blue and black prism on each side of the blue cube. 
  16. Place a short yellow and black prism in the empty space between the blue and black prisms.  
  17. Place the final red and black prism on top of the red and black prism. 
  18. Place a black prism on each side of the red and black prism. 
  19. Place the final blue and black prism on top of the blue cube.  
  20. Place a long yellow and black prism on each side of the black prisms. 
  21. Place the final short yellow and black prisms on each side of the blue and black prism. 
  22. Place the yellow cube in between where the three yellow and black prisms meet. 
  23. Lift the sides of the box upwards, and place the lid on. 
  24. Invite the child to perform the exercise and explore. 

Exercises

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 different sections – separating in sections horizontally or vertically – showing the child how it is the same no matter how it is “cut.” 
Exercise 3: Three Separate Levels.
Build the separate levels of the cube outside of the box, flat on the table; the top level with the yellow cube, the middle level with the blue cube, and the bottom level with the red cube.

Language

None, other than the name of the material.

Points of Interest

Each layer needs to be flat, lay your hand on top of the layer to feel and emphasize that it is flat. 

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 trinomial cube is put together correctly.

Direct Purpose

Build the cube.

Indirect Purpose

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

Age

4

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