## Tuesday, November 5, 2013

If you saw Kal-El's Division Dance you know how excited he was to start the division memorization sequence.  Me Too is JUST as excited for him.  Check out how ridiculously closely Me Too is observing Kal-El's work.  They have even figured out a way to do this work "together."  Me Too counts out loud while Kal-El counts beads into the cup or when he distributes them on the board.

When I set the work out on the rug for the first time they couldn't keep their hands off of it.  While I was still setting up they were making patterns on the board with the green beads.

Kal-El puts the correct number of beads in the green cup to represent the dividend.  The skittles at the top of the board represent the divisor.

Then he shares the beads equally among the skittles of the divisor until he doesn't have enough left to share them all equally.  The number of rows he has (numbered along the left-hand side) are his quotient.

oops, I originally meant to write only the large 27 in the top, right corner
and the very first dividend in row one in purple
but accidentally kept writing with the purple pencil.

We started on a loose piece of division-table paper with a dividend of 27 as recommended by the albums (because it generates a relatively long list of equations that will fit on the board, some with remainders and some without).  Sometimes the quotient has a remainder, sometimes it doesn't.  When it doesn't he underlines the equation with a red pencil because that is an equation he will memorize.  The last equation on the sheet didn't fit on the board so he crossed it out.  We are only memorizing equations with a quotient of nine or smaller.

After I introduced him to the bead board on loose paper with a dividend of 27, I showed him the booklet I made for him.  The booklet has 81 pages.  He is going to record every equation that fits on the board for every dividend between one and 81.  The booklet actually starts with 81, not with one.  As he goes he will underline any equation that does not have a remainder.  When he is done I will give him another blank book of division-table paper and he will record only the equations he has underlined in red thereby making his own master book of the equations he will memorize, or his own "division tables."

You can see here how the dividend has only been written twice
by me in colored pencil and Kal-El
has filled in the rest with regular pencil.

Above is a peek at the inside of his book.  It is my slightly-adjusted version of Nienhuis' Division Tables Booklet (\$35):

I wanted to imitate how they provided the dividend twice in an outlined font, but I wanted to use a squared paper.

You can get pre-printed division table paper for free at Livable Learning.  That is where I printed my tables for the addition, subtraction, and multiplication work we did.  However, NONE of my albums use pre-printed tables for this division work.  The AMI albums all have the child "discover" the division tables they are going to memorize in the way I described above...an experience I wanted my kids to have.  The AMS albums I have skip this step altogether and go directly to using loose equations with the bead board (a step the AMI albums have you do afterward).  Also, every single album suggested a different way to "do the checks" at the end of each page.  You can use the division control chart or the first multiplication finger board.  The Montessori by Hand album suggests emphasizing the relationship between multiplication and division by using multiplication control chart one right from the beginning.  Keys of the Universe recommends using a different method for different parts of the division sequence.

image credit Nienhuis.

If you are looking for looseleaf tables to make your own booklet or to use "as is." You can buy pre-printed tables paper in a similar style from Nienhuis (100 pages for \$6.50).  Or you can print mine for free.

I created the file in Open Office because Google docs will not let you size row heights and column widths which was obviously necessary.  I set it up so that you can print double-sided and cut the paper easily into quarters.  I would have loved to put the dividend in with outline-font like Nienhuis did.  However, not only is it a pain to create an 81-table file rather than a four-table file, but it is a nightmare to set up a file like that so that the dividends stay in the right order when you print them back-to-back.  It is also a pain to print a file that way.  You'll probably spend less time writing in the dividends than you would feeding paper through to double-side it properly.

In order to share the Open Office file, I once again used Box.com:

I would really appreciate it if you would take the time to go vote for me in the Homeschool Blog Awards.  I am nominated in the Best Homeschool Method blogs category.  Thanks!

1. So glad to see them progressing happily.

One small thought. Since you are working on fractions as well - place the remainder in fraction form. It isn't a lightbulb moment when you start doing it but it is something they will come back and be excited about. I've found it really helpful for understanding both fractions and "if I just had one more this problem would be...

1. Great idea! I don't know if I have the guts to do that right away, but it certainly seems like a logical step in moving towards expressing the remainder after the decimal. I'll try and man up.

2. Ha! DJ just requested to work with the division bead boards again. He starting missing the boards when he got to division with remainders in a workbook. He loves that workbook until he gets to a problem he doesn't know how to work out. LOL. Go Montessori! Your post are always so timely whether it helps with my own children or other children I work with. Thank you for sharing.

3. Ahh, new materials. Thanks for these. We aren't there quite yet, since T isn't as fond of the memorization/exploration process. I like the boxes. Why did you do that? T's handwriting is pretty good, so that isn't something I would have thought of laying out. I did lay out our addition and subtraction booklets pretty much like Nienhuis, but in Word and saved it to PDF. That way I could get the outlined letters. I also did them back-to-back. I'll let you know if I decided to lay out our division booklets differently.

1. Hi Abbie,

As Montessori elementary children mature it seems traditional for them to keep a math notebook and they use one of those notebooks in which the pages are squared paper or graph paper. Someone once told me that in many countries other than the U.S. it is traditional for students use graph-paper notebooks for all subjects, that it is just the kind of notebook that kids get. I guess I have all of these elementary math notebooks that I've seen shots of over the years in my head and I wanted my papers to look like a page of squared notebook paper, just partly filled in as a scaffolded step. Most of the rest of the boys' math notebooks are really just squared paper or versions thereof. Plus, they do have atrocious handwriting...particularly Me Too.

Way to go having the patience to lay out all of those pages on the computer and print them double-sided. I just didn't have it in me. Open Office had the outline font, I started to fill in the forms and just said "I don't want to do this."

2. Abbie, are your files up on your blog for those? I should have checked there before I made mine... (although I guess since you haven't done division yet it wouldn't have done me any good.)

3. Nevermind, I see that addition and subtraction are indeed up on your site. I'll direct people your way for those!

4. Thanks for this. I remember using a graph paper composition book for O-Chem lab in undergrad, but I haven't seen it elsewhere. I do know montessori uses graph paper for other things besides graphing, but this is new. I haven't been doing this very long though. :). Come to think of it, I think T's number roll in primary was on squared paper. Anyway, thanks for the tip!

4. Oh I loved to see how they work together!! What a great team!!!! I just LOVE LOVE your file!!! thanks so much for share it!!!, It will be more fun to my princess!!! she start this one... and guess what??? ... "she is so tired"!!LOL and know she will love this booklet!!! thanks again!!! hugs!

5. Thanks so much for all you create and share! I really appreciate that you link up with Montessori Monday. I featured your post as the Free Printable of the Day at the Living Montessori Now Facebook page and on Pinterest. :)

6. I know I'm a little late to your post, but as we start this material this week, I am so thankful for your papers!! I am also VERY thankful for your explanation of the material!! Thanks so much!

7. Thank you!! I am so grateful for these materials.