Cubing Material - Part Two - the REAL fun begins!

We had a fun morning exploring all of our "new" materials and it was too much for just one post ;)

After building the pink tower with the cubing material:

He finally asked me, "So what is this material for?" He has seen it at work in a classroom but it has been a while and he was not yet ready for it. He has been working with the early squaring and cubing and playing the decanomial games and calculating the values of pyramids and towers (with the bead cabinet material). So now we are on to something new.

I challenged him (before doing the actual album page) to construct one cube into its next cube.

Little secret - shhhh! Don't tell Montessori "purists" (of which I consider myself one, but with a different definition)... but Legoboy has not officially done the work with building from one square to the next square! Ahah! I have RUINED MY SON! Hahahaha - not really! I have followed an interest, in the moment of pure joy over discovering he already knew something about this material, helping me organize it - now is the perfect moment to introduce the concept!


Thus, the challenge:

Can you turn the cube of 3 into the cube of 4,
using ONLY the materials here????? 

Well, he tried all sorts of ways - some with relative success - some were just tedious and annoying (a wall of 1s) and he started figuring out where he could exchange squares of 1s for squares of larger numbers. He was presenting a series of problems (issues) to himself - knew I had an answer, so he continued to keep working, to 1) see if he could figure it out himself and 2) see if he could formulate the right question to get the answer he wanted (he knows I don't easily answer questions - that I am going to guide him in his thinking anyway, and he finds it "easier" to do as much himself first ;) ).

eh!? it was a first attempt to see what he could find
in patterning and sizes.... 

Replaced the cube with a series of squares
just to see what could be done.
he recognized patterns from the decanomial work! 

Not bad - and getting there. But what about all those squares?
isn't there something easier?
I modified the challenge to state, "build this cube of 3
into the cube of 4" (I'd reviewed my album page
in the meantime - yep, even I have to review ;) )

Back to the original cube.

A wall of ones - this got tedious - FAST. 

  

But he managed to get it. Then it all fell off. 

He thought, "what if I use the cube AND add squares?"

I didn't tell him - but this is VERY close to the actual
presentation - all the right components -
just in the wrong spots.
He built the squares at odd angles around the cube. 

It's kind of pretty from this angle ;)
But doesn't express the mathematical formula.
So I told him, "Ah, you are so close!
Is there one more easier way to rearrange just
THESE pieces???"

SUCCESS! And now the mathematics is displayed!

 Yes, I then presented him with the actual album page presentation.