Friday, October 31, 2014

School Days

Me Too likes to store an extra pencil between his toes "just in case."  He is recording his work with the division bead board.  He is nearly finished with that board, quite a feat since it requires that he work every possible division equation with a quotient between 1 and 81, even those with remainders.  He is also working with much larger division equations with the stamp game.  He is bogged down by the stamps though so I promised him that he could start the racks and tubes as soon as he finishes the division bead board.  Doing both in parallel is just too many tiny beads on pegboards.

Me Too did the second exercise for the notations of squares this morning.  

He told Kal-El later, "You should choose it next because it was easy peasy pumpkin squeezy."  Kal-El took his advice.

Kal-El has mastered the second exercise on the checkerboard. I decided to try to photograph an equation for you all from beginning to end.  I wasn't completely successful.  If you are doing this with your own child, please consult an album.  These photos are more so my Mom can see how this works (hi Mom!).

Kal-El's equation here is 20785 X 4769.  He has set up the multiplicand across the bottom of the board with white tiles and set up the multiplier vertically on the right-hand side with grey tiles.

At this stage on the checkerboard the child works in rows. The short explanation for what he's done here is that he has multiplied 20785 by 9.  For those of you who care about such things, I'll explain how he arrives at having the bead bars on each square.  I'll only do it for the first row.  Mom, you might want to skip this part.  I am going to bullet the steps he takes with this row so that it is legible in a feedreader.  I've noticed that all my hard returns are lost on Bloglovin' and don't know how to code my posts differently so that they'll say, so I'll bullet here.  What Kal-El does at this stage after a lot of experience with the materials is a little different than it reads in the albums.  Messier, but more economical.

  • First he multiplies each number in the multiplicand (20785) by the units of the multiplier (9). 
  • He flips over all the grey tiles in the multiplier that he is not using.
  •  He knows his facts so he thinks "5x9=45", places a five-bar in the green square and a four-bar in the blue.  A child that doesn't know his multiplication facts would place nine five-bars in the green square and add them up later.
  • Then he thinks "9x8=72".  
  • He picks up both a seven-bar and two-bar.  
  • He placed the seven-bar on the red square. 
  • He picked up the four-bar that was in the blue square up with the same hand holding the two-bar that should also go there and immediately trades them for a six-bar.  
  • Then he thinks "9x7=63".
  • He picks up a six-bar and three-bar.
  • He places the six-bar on the green square.
  • He picks up the seven-bar that's already on the red square with the same hand holding the 3-bar and immediately exchanges them for a one-bar to add to blue square.
  • At this point he could place the one-bar on the blue square, but instead then picks up the six-bar he just placed there and exchanges them both for a seven-bar.
  • Then he thinks "0x9=0" and does nothing.
  • Then he thinks "2x9=18."
  • He picks up a one-bar and eight-bar.  The one-bar is placed on the red square (far left) and the the eight-bar on the blue square next to it.
  • I really should just take a video.

Row one being finished, he moves on to row two.  He has flipped over the nine in the multiplier and revealed the six in the multiplier.  Then, he multiplies 20785 by six.

When the second row is finished, he flips over the six, reveals the seven, and multiplies 20785 by seven.


At this point my husband, who had an extra hour at home that morning, came downstairs and was amazed by this process of long multiplication.  While I was explaining it to my husband, Kal-el finished the fourth row (20785 x 4), slid all of the bead bars, added and exchanged before I had gotten a picture.  

Here is what the board looked like after that process.  The bead boards from each row are slid on the diagonal down to the bottom row.  You can see that beads in the second row consequently move one square to the left.  The beads in the third row move two squares to the left.  The bead bars stay on the same color at all times.  Each position they slide represents "adding a zero."  If you've done traditional multiplication you know you add zeroes to each row as you record your partial products.  This is the same process. 

Since I missed the photo, here is a picture of Kal-El working on a different equation.  He has just slid all of the bead bars into the bottom row and is quickly adding them and making exchanges.  It was at this point in the Montessori sequence that I truly came to appreciate fully the continuity of the Montessori math materials across the sequence.  He would not be able to do this so quickly if he hadn't been using the same colors of bead bars representing the same quantities since he was four years old.  He wouldn't be able to add them quickly and accurately except for all the work on the snake games that prepared him for this.  Various materials (golden beads, stamp game, bead frames, snake games) have been conditioning him to exchange to a higher category whenever he reaches ten.  Awesome!

Here Me Too is doing a little reading/word study work combined with grammar. The Ordinary Parent's Guide to Teaching Reading had an exercise that came up that practices all of the silent letters he has recently learned by embedding them in subjects and predicates that have to be matched.  I decided that we might as well head up the rug with the appropriate symbols from our sentence analysis materials.

Me Too loved this because it involved a lot of crawling around and inadvertently created a lot of silly wrong combinations such as "The tongue got lost in the hedge."

Speaking of grammar work, Kal-El was thrilled to pull this command card this week:

I was thrilled to add the book Animalium to our bookshelf.  GREAT zoology resource.

Me Too was so thrilled when he successfully matched his singular and plural cards from the grammar drawers that he asked me to take his picture.

He has been taking new strides in his own multiplication journey.  He started work with the LARGE bead frame.  He has counted through it several times and is practicing forming and reading large numbers on it.  

He also learned how to use the paper!


  1. I love your school days!! Oh, T is struggling it the math facts thing. He didn't get it in Primary, and we missed the boat last year because I had trouble pulling them back into repetitive I am trying all sorts of things most of which is not Montessori because I KNOW everything will be ten times easier once he knows his math facts. Meanwhile, almost done with the botany and geography cards for elementary. I feel a little silly printing these out and studying sentence analysis lessons while looking through classified cards for one that has construction site images. :)

    Oh, let me know how the bank game goes.

    1. I e-mailed you about the memorization. However, to sum up here in case anyone else sees this...

      We took the Montessori skip counting work with the chains very seriously and did a lot of practice.

      We did the full Montessori memorization sequences with the boards for each operation.

      The boys like to practice the boards they've already done on the iPad with the app for each board/operation. We also use an app called "Flash to Pass." I like it because you can limit the facts to a particular family when you want. Actual flash cards have been our least effective memorization tool.

      We played games: Speed!, Leprechan Luck, and Division 1 racing. I have tons of games like this on my Montessori Math Pinterest page.

      One of the most important things we did was to learn a song for skip counting a lot of the numbers.

      Then, finally the elementary materials themselves (checkerboard, racks and tubes, bead frames) forced the boys to skip count the facts they didn't know quickly many many times and finished off the facts so they know them quickly on sight.

  2. The songs are working. Helping them remember, and me go crazy.

    I just received the Anamalium book, and it is HUGE...your picture doesn't quite show how LARGE this book is. It is sideways in our bookcase. (It is an absolutely stunning resource.)

  3. Thanks so much for the explanation@@@!! It helps a lot!! I need to work more with the memorization boards....