The upper kids have been hanging out in the world of geometry for quite some time. They’ve been proofing various geometry proofs – from triangle equivalencies to Pythagorean theorems to the reasons for the area formulas (most recently). So today we began shifting back into the realm of pure math.
We began cube root lessons and had a lovely Montessori moment. We beat our heads into the wall with the layout of the visual formula.
Why are certain rectangular prisms on certain levels?
Name three things you notice about the layout.
What do we know about math rules for addition? 
What do we know about math rules for multiplication?
Eventually LR and AV helped out with some concepts and began touching the materials. Even in this time when the ability to abstract is becoming easier, touching and manipulating the materials helped them understand some of the concepts.
They began to have moments of clarity that began to involve manipulating the math concepts. What if we put this here? Is it the same?
What happens if it is “mathematically wrong” but “geometrically correct?”
How much volume do the black rectangular prisms take up.
Are these like the “wings” on the square rooting work?
At lunch the other moms wanted a bit of info, Ms. JW needed to see. After we began to discuss the problem at hand, we worked backwards to easier concepts and lighted on squaring and square rooting.
Ms. JW got down the peg board and began square rooting at 625.
The Inclusive Atrium 