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Three Period Lesson
Memory Games
Visual Sense
  Cylinder Blocks
  Pink Tower
  Brown Stairs
  Red Rods
  Color Tablets
  Geometric Cabinet
  Constructive Triangles
    Rectangular Triangles
    Blue Rectangular Box
    Triangular Box
    Large Hexagonal Box
    Small Hexagonal Box
  Geometrical Figures
  Sensorial Decanomial
  Knobless Cylinders
  Binomial Cube
  Trinomial Cube
  Leaf Cabinet
Tactile Sense
  Sensitizing Fingertips
  Touch Boards
  Touch Tablets
Baric Sense
  Baric Tablets
Thermic Sense
  Thermic Bottles
  Thermic Tablets
Auditory Sense
  Sound Boxes
Olfactory Sense
  Smelling Jars
Gustatory Sense
  Tasting Bottles
Stereognostic Sense
  Geometric Solids
  Sorting Trays
  Mystery Bag
  Sandpaper Globe
  Painted Globe
  Puzzle Maps
    The World
    The Continents
    The Country

Binomial Cube


A box with:
- One red cube and three red and black matching prisms.
- One blue cube and three blue and black matching prisms.

All the pieces, once assembled, form a cube of a binomial (a+b)3 
The square of the binomial is painted on the lid.

Before the presentation, check the box to make sure it has been put back correctly.


Invite the child to come and work with you. Show him the Binomial Cube box and tell him its name. Have him bring it over to the table and place it near the top left corner of the table.

- Remove the lid and place it on the diagonal of the box and so the painting is facing up.
- Pull down one side at a time.

Montessori Binomial Cube

- Carefully and gently take out all of the prisms, keeping the top level together and the bottom level together.
- Bring the child’s attention to the red cube.
- Replace it into the back left corner of the box.
- Slide it into place.
- Point to one of the red sides of the cube and then look for a prism that also has a red side.
- Place the correct prism in front of the red cube.
- Replace the first level by working your way from the back left corner to the front and then from the right side to the front.
- Replace the second level in the same manner so you are placing the blue cube in last.
- Close the box, one side at a time and then replace the lid.
- Invite the child to work with the binomial cube.


Exercise 1
The child works individually with the binomial cube as shown in the presentation.

Exercise 2
Invite the child and set up the box as done for the presentation. Remove all of the prisms and place them all together to the right of the box. Then close the box and place it to the side. Build the binomial cube as in the presentation, but this time without the help of the box. Once done, mix the prisms and have the child build it outside of the box, as you had done.

Exercise 3
Repeat the building of the binomial cube as in Exercise 2. Once it has been built outside of the box, separate the cube in half (height wise). Turn them so the child can see that they are the same. Then replace the halves together to reform the cube and carefully take off the top layer and place it next to the bottom layer to show that these too look the same. Replace the layers and have the child separate them.

Montessori Binomial Cube 2 Montessori Binomial Cube final step

No language is given with this material.


To build the cube.

Preparation for mathematics: the cube of a binomial.
Preparation for the cube root.
Introduction for algebra and preparation for the proof of the formula (a+b)3 at Elementary Level.

Control of Error
The first exercise: the box itself.
The second and third exercise: visual.

3 to 3 1/2 years   

This Montessori Video shows how to present a child with the Binomial Cube.       

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