Mathematics, Ages 9-12

The Cubing Material is an impressive set of wooden cubes and squares designed based on the color coding of the Bead Stairs, that increase in size from 1cm to 10 cm. Using the metric system as a measuring unit will help children make connections between different combinations of cubes and squares to create harmonious cubes that they are taken apart a measure using algebraic equations! Prior to working with the Cubing Material, children will have had experience measuring the Binomial and Trinomial cubes.

I found that using Alison’s Montessori Cubing Material Task Cards increases the interactions my learners have with the materials, which would otherwise be left unused after presentations.

## Materials

- Cubing Material – Complete Set (Value Line)
- Cubing Material (Task Cards)
- Colored Counting Bars (optional)

## Cubing Material & Task Cards

Cubing Material Task Cards set consists of several cards divided into six sections. The level of complexity increases as learners go through all the sections. The **1st section** has learners revisit squaring and cubing a given number (see picture below)

The **2nd and 3rd sections** invite learners to replicate given cubes by using the Cubing Material. Section 2 offers to work with successive cubes, which means learners build a cube of only 1cm less or 1cm more than the initial cube. For instance, if learners must replicate an 8cm3 then they need to build a 7cm3 or a 9cm3 using the Cubing Material. Section 3 offers to work with non-successive cubes, which makes the work slightly more challenging.

In **Section 4**, children use the algebraic binomial cubing material to calculate a given cube. This method helps children work with expanded notation (125 –> 100 + 20 + 5) and break numbers into an algebraic form (using letters to solve equations).

In **Section 5 and 6**, learners use the algebraic binomial cubing material to calculate a given cube. This method helps children work with the expanded notation of a cube. For instance, children are asked to calculate the square of 12 or 125. They will need to use an algebraic formula: (a + b)3 =a3 + 3a2b + 3b2a + b3. To get a value for a and b, learners use expanded notation so 12 is (10 + 2), giving a = 10 and b = 2. Now, learners can calculate the formula and find the numerical value of a cube. Learners use their prior knowledge from working with the Binomial Cube and Trinomial Cube.

I believe it is more than reasonable to provide additional opportunities to work with the Cubing Materials. The Cubing Material is absolutely unique to the Montessori method and is unknown and fascinating for anyone who isn’t familiar with the Cubing Material, but who is familiar with math and what this material aims to accomplish.

I hope you enjoyed this post! I would encourage to use professional guidance to present the material: Montessori Teacher’s manuals (see below a sample of the TOC from Montessori Research and Development, Mathematics Teacher’s Manual – Volume 4 – Elementary II)