Wednesday 12 January 2022


Montessori Activity: Arithmetic Trinomial Cube


AGE: From 3 to 3.5 years old


1. Visually introduce the child to the concept of cubes of trinomial, while providing a fun challenge. 
2. To prepare the child for mathematics, especially algebra, through the cube’s visual representation of the following algebraic formulas:  (a+b+c)3 =  (a+b+c) * (a+b+c) * (a+b+c)  = a3+3a2b+3a2c+b3+3ab2+3b2c+c3+3ac2+3bc2+6abc


1 Arithmetic Trinomial Cube: This cube represents the equation (a+b+c)3 in concrete form and differs from the Trinomial Cube in that the component pieces are color-coded to represent hierarchical values from 1 unit to 1 million. This makes it possible for the child to equate an arithmetical value to each of the cubes and prisms.


1. Remove the lid and place it on the table with the picture facing up.

2. Take out all the prisms out carefully one layer at a time, keeping each level together.

3. Bring your child’s attention to the red cube.

4. Place it into the back left corner of the box.

5. Bring attention to one of the red sides of the cube and place a prism that also has a red side in front of the red cube.

6. Build the first layer by working your way from the back left corner to the front and then from the right side to the front.

7. Build the second and third layer in the same manner. 

8. Close the box, one side at a time and then replace the lid.

9. Invite the child to work with the trinomial cube.


1. Build the trinomial cube layer-by-layeras in the presentation without the help of the box.

2. Build the trinomial cube outside of the box.

3. Line the blocks in rows by color: a row of reds, a row of blues, a row of yellow and a row of blacks. Then build it layer-by latyer.



1. The pattern constructed compared to the pattern shown on the box.

2. The blocks fitting back into the box.


J saw the trinomial box on the shelf and was very eager to try this on 5 May 2014 (5y2m). Before I could show the presentation, he was too impatient and he had already taken all the blocks out of the box. So he built it, with a bit of help from me. I will like to repeat it again, this time, one layer at a time.

Update 16 Jan 2022:

C worked on this at the preschool. C assisted me with demonstrating this work to the kids at the Chinese class on 12 January 2022.


This is the solution showing 27 factors

28 October 2021: Show Me Day at the preschool

C assisted me with demonstrating this work to the kids at the Chinese class on 12 January 2022.

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