## Wednesday, April 17, 2013

Kal-El has been working on the multiplication bead bars this week.  Doing multiplication with the bead bars is a sensorial introduction to the memorization sequence for this operation.  We started with sevens because it provides a nice variety of bead bars for the products.  If you chose something like fives there is too strong of a pattern in the products.  I don't know if you can tell, but Kal-El is smiling hugely in the picture above.  He loves multiplication.

You can find a nice summary of the procedure for this material here on the Montessori Primary Guide website.  To do the table of sevens as he is above, Kal-El "takes" the seven bars a certain number of "times" and then uses the colored bead bars to show the product as he would with the bead stairs or snake games.  Those other works make the child very fluent in reading combinations of colored and golden bead bars.  When Kal-El does "seven taken five times" (7 x 5) and sees a group of five seven-bars he doesn't know immediately how many beads he has. But, when he sees three golden ten-bars and one five-bar he knows instantly that he has 35.

Above is a photo of his completed table of eights.  He tries to stack the bars very closely and neatly together into squares and rectangles.  He knows that this work is one of the many baby steps he is taking toward building the decanomial bead square (you can see this work being done here at the blog Somewhat in the Air).  Another step toward that work that he has already taken is the sensorial building of the square of Pythagoras or "decanomial square."

A Montessori classroom might have a separate set of beads for just this work.  We are using the bead bars in our decanomial bead box to do this work.  If we run out of a color we can easily borrow from our golden beads and our snake game boxes.  In a classroom you wouldn't want to do it that way because other kids might actually be doing those works and some would be stealing beads from each other left and right.

You will want the child to take special note anytime the product makes a square.  Kal-El did this naturally as a result of all of the bead chain work he has done.  When he finishes a table he always "reads" all of the equations he made such as "one taken one time equals one" and he also likes to read the products forward and backwards as if he is doing the bead chains.

Today's post was a little mathematical break away from geology.  I will be back tomorrow with mixtures and solutions (as they pertain to geology).  Whoopee!

1. How refreshing to see one love Math so much! I have a question for you - I do not have any bead materials (insert frown) and am not sure when I will be able to begin purchasing them. I have read the great post by Montessori At Home, I believe it was, and as inspiring as that is, I know I don't have the time to make the materials at hand. Aside from the inability to replicate the cube without the beads, what would be your opinion of the 'next best way' to make a DIY set of something that would replicate the same thing that you can get from the bead bars? I have been tossing ideas around in my head for a LOOOOONG time ,and just can't settle on any one idea that would be the best I could do until we get the bead materials.

2. Amy,

You can get one in a tackle box for \$66 here: http://www.jmjpublishing.com/hm_math.html

I have a set of homemade ones that a friend made herself. It is cardboard covered with colored paper covered with packing tape. You can see them in the bottom right of this picture: