## Tuesday, July 24, 2012

### Trinomial Cube - LONG Life

I would like to introduce you to a long-time companion of mine - the Trinomial Cube:
 The "big" cube in primary!

 The Binomial Cube The small guy in primary
He has a few buddies:
 The Algebraic Cube - Elementary

 Power of Two Cube - Elementary

Binomial and Trinomial are beautiful puzzles in the primary environment. But the Trinomial - he goes places! While the binomial is also useful in the elementary class, the trinomial does most of the work.

(a + b + c)^3

The children are learning this sequence, sensorially at age 3 1/2, and it builds and grows from there.

The children continue to use the material sensorially in elementary, then they start doing some squaring work with the lid (the lid has (a + b + c)^2).

And one day, they hear of the Story of the Three Kings. Oh, no,  not THOSE 3 Kings - the OTHER Three Kings. These Kings: A-Cubed, B-Cubed, and C-Cubed. They were marching along happily in procession - and... there was a REVOLT! That revolt overturned the order of the procession! It was chaos! It was order! And the children learn algebra! And cubing!

And the Trinomial Cube has a new lease on life!

And the children work with the trinomial cube; then expand into the algebraic cube; finally they work with the power of two cube - it all began with the trinomial cube and his little brother the binomial cube.

But the children have moved on. And the trinomial cube appears done. A wash-out. Used up. It's all over for him.
----------------------------------------------------------------------------------

I recently read through an older NAMTA journal, on the topic of teaching geometry in adolescence, using Euclid's Book of the Elements (all 13 volumes are currently available in a set of 3 books).

Guess who makes an appearance! The trinomial cube is truly an ever-present material for the children in Montessori environments. And a credence to the AMI stance that we don't need "more" materials - we need to go DEEP with the materials!
ETA: The adolescent Algebra Album available through NAMTA - lists it as one of the necessary materials ;) NICE!

Just looking at it, consider for yourself: how deep does this material go for you? What uses could you see for your children, even if you don't have all the album pages for all the levels? What could your children experience with just this one piece of Montessori equipment?