Tuesday, September 24, 2013

Montessori Math: Fitting It All In, Primary

It has been an exciting week in our homeschool as Kal-El moves out of the Montessori Primary math album and into the Montessori Elementary album.  He has finally finished everything in the primary except the division memorization work (which he will do alongside the new elementary work).
 Me Too, who has just begun his first year as a Montessori Elementary student, is still in the primary album for math.  I tried to get him through the primary work faster than his brother, but he was unable to move through the work that quickly.  Call me an amateur, but it seems to take me all of primary plus one year of elementary to finish the primary album.  I feel like we did pretty well considering we had time in the school room 3 hours a day for 3-4 days a week in our third year of primary at home and a child in a traditional Montessori school would attend for five full days every week.

What album did we use?  For primary we used the free Montessori by Hand math album and supplemented (just barely) from Montessori R&D Elementary Math, Volume One (it's identical to the Montessori R&D primary math album).  You can read all about our album choices for primary in the FAQ section of the blog (question 17) which can be found in a tab under my blog header.  If you are interested in our Elementary album choices to date, you can find them at the "Elementary" tab also located under my blog header.

I get two general types of questions when it comes to the Montessori math sequences.  The first type, particularly when one gets to elementary, is "How do you fit it all in?"  It seems like there is so much to do that your kid could do math all day, every day, and not get it done.  The second type of question is, "How do you maintain forward momentum."  It is easy to "get lost" among the various types of work and feel like you are not making progress in any kind of organized way.
The key to moving forward in the math and not feeling like you are treading water is not in the album but in the implementation.

I'm going to go out on a limb here and call my two boys' primary math experience a "success."  The secrets to that success, for my part, can be summed up in two words:  categorization and autonomy.


I divided the math up into what I call "threads."   My threads are:  linear counting, operations, memorization, fractions, and story problems/equation formats.  By the third year of primary the boys do 3-4 math works daily, each work from a different thread.  So, we don't get to every thread every day but we do get to every thread every week.

So, let's take Kal-El for example in a typical week last year.  On Monday he would choose counting a bead chain (linear counting), small bead frame (operations), fraction tickets (that cabinet I have full of numbered drawers full of equation sets), and the multiplication finger chart (memorization).  On Tuesday he would choose fraction tickets, small bead frame, multiplication finger chart, and a packet of story problems.   On Wednesday he might choose division with the stamp game, the multiplication finger chart, and a game of Speed! to practice skip counting.  And so on...  

Me Too is further behind him in the sequence.  So, on Monday he would choose counting a bead chain (linear counting.  spindle boxes, 100 board, teen boards, etc., are past works in this category), golden beads (operations), subtraction snake game (memorization).  On Tuesday Me Too might choose the subtraction finger board (memorization), counting a bead chain, and a packet of story problems.  He has not started fractions yet (he did the typical primary work, but I waited to start fraction equations until elementary).

So, you might already figured this out, but for each kid you have to be in five different places in the math album at once.  In my hard copy of the Montessori R&D math album I have eight post-it notes marking places.  Four for each kid (operations, memorization, linear counting, and story problems/equation formats) and each kid has his own post-it note in the fractions album.  When they finish a work I move their post-it note forward to the next one and I always know what to do next. I use iAnnotate on my iPad and have similar bookmarks in all of my digital albums.  You'll find  out quickly that some threads require more work than others (operations, memorization).  Those are the works you'll have your child daily.  The others can rotate.  This allows you to tell your child, "Today during our work time you need to do your addition boards and choose 2 other math works."  

It is important also to note that you don't begin every thread on "day one."  In fact, you don't begin the Montessori math album at all at the beginning of primary.  (See the Gettman periods.)  You will generally start with the  "linear counting" thread, work for a while, then add operations, work simultaneously in both threads, eventually add story problems, etc.,  The Montessori by Hand album will have tips like "start the collective exercises with the golden beads as soon as they can do X, Y, or Z."  If you are in the Montessori R&D album, I don't think they tell you.  You are on your own.  I don't know how anyone gets through those albums without another resource to tell you how to do it.


Half the battle is knowing where each kid is in the albums for each thread.  The other half is having the work set up so they can do it themselves.

You probably remember my fraction cabinet:

The drawer Kal-El is on is marked with a clothespin.  When wants to work he grabs a pencil, his fraction notebook, and the drawer of loose equations that has the clothespin on it.  He fills at least two  pages in the notebook.  Then he returns everything.  If he finishes a drawer he moves his clothespin to the next drawer.

All of the loose equations for the memorization work and loose equations for golden beads, stamp game, etc., are in the math cabinet:

To do memorization work, they just grab the drawer of equations they need.  They are in different operations than one another so they each have a box for equations they have finished.  When the drawer is empty is and the box is full I transfer everything back to the drawer so they can use them for the next material that needs them.    The boys have special notebooks I made to record their work for this work.  They actually each have their own special notebooks for each category (thread) of work, sometimes for each operation within that category.  You can see them in actions in a lot of posts like this one

The story problems and equation formats are in a basket you can see in the same link as above for the math cabinet.  I write their name on the envelope when they finish it so they each know which envelopes they've done.

Some works I just have to do with them, or at least set up for them.  Golden beads.  Snake game...
Some people make equation slips for the snake games (4+6+8-9+4+2-1+6=?) I just set up the snake for them or give them guidelines to set up their one (use at least 6 colored beads and 3-4 grey and white bars).  I prefer to work with them on the golden beads rather than use the equation slips because if they use equation slips they don't get place value practice from using the wooden number cards. 

Some people save a lot of work because they don't make equation slips and have the  kids write their own equations.  The equations kids write themselves are supposed to be more compelling than those provided.  I can attest to the fact that the boys prefer to solve a snake they made for themselves than one I've constructed.  However, I like to control how many positions will have dynamic exchanges or which place value positions will come to zero and such to make sure they've gotten full exposure to the types of equations they need exposure to.

I can also say that people who like the works broken down into smaller steps prefer the R&/KHT albums style (AMS) to the "big-picture style albums" such as KotU and Montessori by Hand (AMI).  I find they work well together...I work mostly from a "big picture" album but will break it down into steps with an AMS album.  I find it hard or impossible to use the AMS albums without an AMI album to guide me.

Phew!  Tomorrow I will post about how I have categorized the work for Montessori Elementary math.  Hopefully that will help those of you who are, as I am, at the beginning of that journey.

The last thing I will say is that I find it easier to keep moving forward if I have the materials to do it.  I buy a lot of materials rather than make them just so I know HOW I'm going to do the work and am ready to go.

If you are looking for elementary-level information like this you might like...
Montessori Math:  Fitting It All In, Elementary

Montessori Monday


  1. Very helpful! We will likely start golden beads next week, so this post seems like perfect timing for planning the sequence. Good luck with elementary math; I will be reading along, even though my oldest is at least two (maybe three?) years away.....

  2. I was wondering if you have any thoughts about programs like rightstart? I like how hands on Montessori is but would be overwhelmed trying to pull it all together without a guild. RightStart seems similar to what you do but has it all separated into lesson plans. Have you looked into this program at all? I feel like I am jumping off a ledge sometimes with how odd people think our math is and I have to admit to wondering if it is really going to make a difference in the long run?

    1. Danielle,

      I have not looked into the RightStart program at all because I'm super happy with the Montessori math as-is. I have heard a lot of good things about it. At the same time, I have had at least two people mention to me recently that they were abandoning RightStart and returning to pure Montessori math. Unfortunately I can't remember WHY.

      Montessori equals method plus materials. Most people seem to agree that the method is more important than the materials, but I and others believe that the materials are important as well. There are a lot of people who have found it best for their family to compromise one or the other. I don't think it is quite "Montessori" any more if you do, but there is no award or enforcement agency for that. I don't have judgmental feelings about it either way, I just think that if one is going to compromise they should have their eyes wide open about it.

      In regards to the math, I think if you study it for a few hours you will find that it is a lot simpler and more manageable than you think. However, if you really aren't going to implement it well then you should probably find another solution. If you saw my post last week on Writing with Ease you'll see that I am not above pulling in other resources when I am not implementing something well. My personal approach is to adhere as closely as I can to the METHOD when I am abandoning the MATERIALS and vice-versa.

      In your case, you would be loosening up on the METHOD and mostly maintaining the MATERIALS (albeit a simpler, less expensive, less time-consuming alternative to them). I want to make a point here...the blog Living Montessori Now does not have 25,000 followers because there are 25k families out there with Montessori homeschools. I'm guessing there are only a couple hundred of those. There are 25k families out there who like to use Montessori hands-on activities and Montessori materials in their traditional homeschools. There is nothing wrong with that. I think a successful homeschool has to fit the personality of the parent who is doing the homeschooling.

      What I think you should do is think about what kind of homeschool you want to have, what kind of teacher you want to be, and then write or just "think of" a sort of "mission statement" for your homeschool. Then your choice should be pretty clear.

      I think it is a win-win situation! Hope this helps!