Algebraic Trinomial Cube

This cube goes by several names - but the most important fact is that it is NOT the trinomial cube.

As Legoboy so recently and astutely discovered:

Poorly cropped - but
1) someone skipped getting dressed
2) I wanted to include an image
 of the squaring/cubing

"It's just like the trinomial cube!" He proclaimed when he first saw it. "But the colors are different," he side-commented to me to be sure I didn't ask him about the changing colors as I did with the tower of cubes versus pink tower.

But I still had him one-upped ;) "Hmm. Different colors, alright. I'll let you explore this while I go do something else and keep myself from interrupting you!" He just smiled and proceeded to work.

When he was done, he brought it to me, and said, "Oh Mama! The colors were VERY different! They didn't even match the lid on every layer like the trinomial! This is a CRAZY cube!" (keep in mind our trinomial cube is not in our home right now - it's over at the local school building).

I told him as soon as we get our trinomial cube back into our hands, I will show him the story of the Three Kings. Of course, just to be contrary, he says, "I already know about the Three Kings! I can skip that presentation!" (sound like some adults we know? I already know it (based solely on the title or perhaps the title and the main headings, then skip the actual content, which just MIGHT actually be nuanced different, if not entirely different... and then wonder why things aren't working right;) hehe - Yep, that describes me!)

"Oh no, my son, not THOSE three kings! These are the Cubed Kings!" That got his interest up! He's been asking for a week now. Perhaps next week we'll get to it. I like to keep up some anticipation (and I do want to review a couple of other concepts before working with the Kings.).

Yeah, we had fun with this one!

Stylized version - I know how tricky the illustrations can be!
Tricky - but NECESSARY
for each and every step!

Don't know the Kings?

Pick up a Keys of the Universe mathematics album ;)

HONEST review here - from a homeschooling mom - NOT from a Montessori trainee:
There is a free elementary math album available online, with which I usually agree as to the order and general set up of presentations, but I am thoroughly perplexed by its version of the Three Kings - (this part comes from me as a trainee: and I KNOW it! And I know what is trying to get across and what comes next.) Back to being JUST a homeschooling mom: But the instructions are confusing, the story is BLECK-boring until you realize that the *actual* story comes after the presentation in the album and is actually mildly interesting but leaves some strange questions, the whole set up begs to know what pieces to move when and as a mom I want it all together so I can SEE what is going on, and I really-really want those black pieces to be the same height as their king - it just makes sense when you see the other attendants the same height as their own king. But this album has them all laid flat.    It just does not look appealing - while mathematically correct, there is another way that makes the math more clear, leaves out the strange questions and keeps the appropriate parts of the presentation together in order. I'll stick with the Keys of the Universe version ;)
Sorry! I really do LIKE that album - I just don't "love" it and I'm very honest about things these days.

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.

Cubing Material

Last week we received two large boxes of our final Montessori materials order. Turns out there will be a few more things that need replacing - sigh (my own fault for not checking!), but at least we have something for everything, in some state or another ;)

Some of the items we purchased ARE replacements; some are brand new to my son; and some are materials he has worked with elsewhere and only now has a set at home.

We had an open exploration morning with the materials - FORGET the "perfect" presentation - what better presentation than to JUST EXPLORE!?

We had SO much fun!

One of the first favorites was discovered when he was helping unpack the box of squares and cubes - it is introduced in lower elementary (around age 8) and continues into upper elementary - at least according to my albums and if a child is on top of the squaring and cubing concepts. There is obviously going to be a wider range of ages for various children - us adults in training loved these ;) But I have been astounded to hear time and again that this material isn't touched even in upper elementary - on a *routine* basis; and that many elementary teachers don't even bother getting the material because it is more appropriate to adolescence  REALLY!? Tell that to my (non-genius, totally normal) 8 year old son after our experience last week --- and all the children I've shown this work to in schools at ages 7-10. They won't tell you it's for adolescence!

As the styrofoam and bubble wraps was removed from each set of squares and cubes and put into place in the box, Legoboy suddenly said - "Wait a MINUTE! I bet this makes a PINK TOWER!" and proceeded to count how many there were ("darn! number 10 is missing! but I can make the rest of the pink tower!"), and started stacking them. I gave him a quizzical look and asked, "You're going to stack those up and it's going to become pink!? Really!?"

Note the styrofoam still all over the floor.
That stuff is a PAIN -
so we ignored it and got to work ;) 

He just looked at me, all serious, and said, "No." Then he paused. Looked at the half-done tower and said, "It looks like like the cubes from the bead cabinet. Wait.  You mean the bead cabinet cubes are the same as the pink tower, too? I didn't know that!"

Aren't those just the cutest little toes!? ;) 

(this is one of those aha! moments when a child who has already been demonstrating clear understanding of a concept for literally YEARS, suddenly "gets it" - the light bulb turns on and the child can VERBALIZE it; it makes us wonder if he didn't really get it before - but he did, it was just unconscious before - and by allowing the child the JOY of discovery, it is truly his own learning!)

He wanted to build it corner-aligned -
he likes that layout so the #1 can "fall"
down the stairs of the tower!

Music Scale Construction

I want to share this post over at Montessori Station:
Montessori Station - Music: Major Scale Construction

Having found this image over at Junk Seller (doing a Google search for C Major charts), I fell in love with this as a potential Montessori activity. The children can build this!




I am going to introduce it to my son later in the month of December - as a manipulative. I'll let you all know how it goes!

Language - An Early Book

Going through some of our previous work and found this booklet in its earliest stages - on the city of Ancient Rome:

"Hello, I am (Legoboy),
I will a(ccompany) you t(hrough) Rome."
Note the lack of spelling, thus abbreviation ;)
I did edit out his name which he had beautifully
written in all lower-case cursive ;) 

Some tracings - some free drawing

He is hiding on every page in addition to his spoken blurb. 

on the left is a helmet - he says "scary!"

This was entirely free work - not directly related to any particular school work at the time. It could have been connected and if he went to school, and did it there, it would be "school" but at home we have re-define what is school and what is home ;)   So this one was personal interest work, thus I did not critique spelling, etc - instead mentally noting what needed work during our regular school time and presenting the appropriate album pages (lesson plans) for those skills in our usual fun Montessori way :)