Thursday, March 31, 2016

Moving Forward

T really likes this cubing material. It is definitely one of the most expensive Montessori materials we own (bells and tone-bars aside.) But the rate at which he is going to "grow-out" of this material, has me wondering if it was worth the money. Maybe the fact that he loves these puzzle pieces so much makes it worth the cost. Also, maybe the fact that this material made this set of mathematical concepts so completely and simply apparent to T makes it worth the cost.

I also wonder how the other two will fare through these lessons. I suspect they will take more time working with this material.
More cubing. But not a whole lot more cubing somehow. (Our previous cubing experience can be found here.) A note to myself and others: although these presentations reflect the KotU albums T decided to not follow the presentation. So, if I get confused about what step came next, or you can't follow my post with your album next to you, it is because T left some steps out. 

In the shot above, T is making the 8-cube with the cube of 3 and the cube of 5. He also made the 8 cube - Ninja Turtle style (purple and green) and Christmas style (white and red.)
I selected the boy and girl cube (blue and pink) cube and T set to work naming each term algebraically. Here, I pointed out that the length of the side of the first term (in this case the pink-3) is the height of the second term (in this case the blue 6 squares.)
T then labeled each term. From left to right: a2, a2b, a2b, ab2, ab2, ab2, a2b, b3.

T then organized and combined all like terms: a3, 3a2b, 3ab2, b3.
T first figured out each term on a separate blank paper ticket. Then he wrote down the equation in it's entirety.
Then T figured out how to algebraically describe the whole cube: (a+b)3.

Then we dug out our primary sensorial binomial cube material. I seriously don't know what the album introduction was, since T didn't pay any attention to what I was starting to say. Instead, he said something like, "I already KNOW MOM."

Edit: I finally really read the album page and found that the first presentation focuses on how to create the cube of (a+b) starting with the square of (a+b). It is the same production as the bead-bar exercise we did here. The point of the second part of this binomial cube lesson is to know the algebraic "names" of each piece by sight and to extrapolate a "rule" for binomials. As you can see below, T assigned algebraic "names" to each piece and now we just need to review the "rule."

After this cubing lesson we can either double back around and finish out the squaring sequence or continue on to cubing a trinomial.
Now if this were pink....
D did a little sand tray writing. He is going through our Dwyer reading folders slowly exploring the different spellings for these long-vowel sounds.
This is print not cursive. Interesting.

The other night, I got up out of bed to see why T was still awake at 11pm. He said that he had finished reading this entire book in one evening and was still sad about Charlotte. I told him to think happy thoughts and to go to sleep already. Secretly I was glad that he stayed up reading E.B. White and not something less-than-ideal like Captain Underpants.
S finished the Daily Math Word Problems Grade 2 book, and is on to the grade 3 book.
S helped D read these first readers. They do not follow the Montessori phonogram sequence so he can't read them independently quite yet. 
T got in on the Daily Math Word Problems too.
D started the addition snake game this week! I wrote more about this work here.

D was super excited to be doing a big-boy work.

Stay tuned, there is more to come soon!


  1. He can't be old enough for the snake games! Sweet little guy!

    Regarding the cubing material - it is worth it for the hands-on depth alone ;) And if you're sticking out Montessori math through the teen years, the material is used there too ;)

    1. I Knowwwwww!! He still seems like a baby to me some-times. Incidentally, he really, really liked the snake game.

      I think I am going to agree with you regarding the cubing material and the valuable hands-on experience. I doubt that these cubing concepts would have seemed as simple to T had he not had this cubing material. He just thinks these topics are so much fun. I looked ahead in the elementary album and realized that we'll be needing these for the cube root sequence too. Somehow I think that those topics are going to seem relatively simple to T too. Good to know that we could even get some use out of them through the teen years!