Trinomial Cube

A box with:
– Three wooden cubes: red, blue, and yellow.
– Eighteen square based prisms.

  • 3 red and black, the same height as the blue cube.
  • 3 red and black, the same height as the yellow cube.
  • 3 yellow and black, the same height as the red cube.
  • 3 yellow and black, the same height as the blue cube.
  • 3 blue and black, the same height as the yellow cube.
  • 3 blue and black, the same height as the red prism.

    – Six black rectangular based prisms, whose 3 dimensions correspond to the edge of the red, blue, and yellow cubes.
    – Three wooden cubes: red, blue, and yellow.

All the pieces, once assembled, form a cube of a trinomial (a+b+c)3
The square of the trinomial 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 Trinomial 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 Trinomial Cube pulling down one side at a time

– Carefully and gently take out all of the prisms, keeping each 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 and third level in the same manner.
– Close the box, one side at a time and then replace the lid.
– Invite the child to work with the trinomial cube.


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

Exercise 2

Montessori Child working on the Trinomial CubeInvite 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 trinomial cube as in the presentation, but this time without the help of the box.

Then isolate each layer as you had done for the binomial cube. The child can isolate each layer by building one layer at a time.

Exercise 3
Repeat the building of the trinomial cube outside of the box. Then, disassemble the cube and line each prism by color: the reds together, the blues together, the yellows together, and the blacks together. Then, mix them up.

Place each cube in a row but with space between each.  Ask the child to find a prism with the same height as the red cube (it can be of any color). Line up every one in a line in front of the red cube. Find the same for the blue cube and the yellow cube (you can also use the prisms from the other lines). Notice that there are always 6 prisms left.

Last Trinomial Cube exercice

No language is given with this material.


To build the cube.

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

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


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