Primary and Elementary Mathematics - Division

Are you planning to do elementary Montessori and already do primary?

Do this for one of the division materials and save yourself $15-ish plus shipping. Do NOT order the unit division board.

I asked my son to set this up with a sample problem so I could show you all;
he insisted that 2 divided by 1 was a "good example".
Hm-mm. :)

Order the Long Division material (Division with Racks and Tubes or Test Tube Division).

Put most of it away for most of primary; but keep out one green board, the set of green "skittles" and 100 green beads, stored in a box (the box that it comes with has 4 compartments - you could maybe use 1 for the beads, 1 for the skittles, 1 for sample problems and 1 for possible answers to match?). This will be used for unit division, 1 / 1 through 81 / 9.

Pull it out again in older primary for short division - leave three boards in storage and 3 sets of skittles. Short division work ensues (the children will do 7-digit dividends with 1-digit divisors).

Pull everything out in lower elementary for long division, which has an extensive album page - and it will be used through about age 10. Well worth the investment (if bought alone, it can be purchased from IFIT for $90-100 total, including shipping).


Already homemade the unit division material? Keep that material and add:
For Long Division, duplicate what you've done to create the remaining boards and skittles; purchase or paint the needed beads; and find racks which can be painted and that will hold 10 test tubes each (each tube needs to hold 10 beads). The bowls are easy enough to find at thrift stores or Montessori Services or other places - just paint accordingly.

It's a small thing, but on our homeschool budgets!? And perhaps space-limitation? It's worth it to buy one material and use it for a variety of purposes.



TIP 2: 

Repeat the above process for the multiplication! Don't buy the primary multiplication board - just use the red board from the Long Division material. The (red) multiplication board generally has 10 columns though, along with a slot for the number (we placed ours on top), so you'll have to adapt the presentation (we just only did through 9x9 on the board and worked on the 10s separately. It worked out fine.

Elementary Supply Area

Anyone who has followed me via Keys of the Universe or Montessori Nuggets or any of the Yahoo groups to which I belong, has probably heard me talk about the elementary difference, using the example that the primary child needs trays with everything laid out and a supply shelf to replenish as needed (but still a limited quantity). The elementary child will use that supply shelf as their go-to place, along with a stack of empty trays from which to choose the most appropriate one for their work at the moment.

Here are some photographs to visualize what I am talking about:

PRIMARY: 

Typical Primary level layout
(note the aprons hanging above)
yes, I'd like them laid out with handles to left/right
but this is the size of our shelf for now
Point: visual of all items; lots of trays;
items needed for an activity are mostly kept together

ELEMENTARY

Elementary Supplies drawers for Geography (science) -
we need about 2 more of this size!
Each drawer is labeled with contents;
should be alphabetized.
to the left, you can see the side of our large supply shelf
for boxes and bottles of safe chemicals: baking soda,
vinegar, bottles of polish, bottles of glue, etc.

Elementary Charts, with some supplies up above
(note the blue ball in upper left corner -
layers of the earth that the children helped put
together with clay - not teacher-made ;)
you can see our black timelines, seasons strips,
timezone strips, lamp,
timelines below with our impressionistic charts

The supply shelf we used.
The drawers pull out to hold larger items
than the hardware drawers on the right. 

On the clay in the one above photo: I love elementary, because I can explore WITH the children - I don't have to know everything or even have all the materials on hand! They can help put things together; go through the planning process, decision making, budgeting, etc. and then the learning is truly MUCH more their own! 

Art supplies
(we've actually rearranged this recently - I'll update soon)
This set-up could apply to both ages;
with specific intro art lessons on individual trays nearby.

This is just part of what we have done - all these images are from our co-op but each photo shows something similar or exactly to how we had it at home (850 square foot, 2 bedroom, apartment - yep, I like elementary! It fits more into a normal household.)

A Day in Elementary

Tuesday: Wood-cutting day.

I run a home-business, a portion of which includes 2D wood figures among other items. My son is the mail-boy, picker-upper, and general handy-man for the business. We go to a family friend's house for the cutting of the wood; his big part there is just taking the cut pieces (in separate bags) back out to the car and keeping things separated.

The plan for the rather unschooly-school-day:

enjoy breakfast together
morning prayers
morning chores
gather school work and games

drive to the other house: listen to "Can You Hear It?" along the half-hour drive (he's re-living the joy of first using this book in primary, having re-discovered the book/CD after about 2 years of not having it around)

When we first arrive, no-one will be home; so he will do some studying while I am tracing wood; we will have conversations during this time. He will then work independently in the living room while I am with the saw. At what work? Whatever he has chosen from his weekly contract, as well as his independent research studies. This week, it is likely he will take some of the science books we have, a magnifying glass, and a drawing pad, to see what kind of crystals he can find in various locations. They also have a piano, and until he gets his late Christmas gift from Grandma (shhh - don't tell him it's a keyboard so I can start giving him piano lessons), he will likely spend some time teaching himself (one of the children in that family uses the same books we'll be using; and he's been teaching himself for the last few weeks, but only practicing once a week...).

The family who lives in the house will return for lunch and the children, including my son, will go outside to work in the garden they are setting up (we have a space there this year too!). My son has responsibility for choosing the remaining "crops" to be planted (I've made my choices; and we've chosen our mutual agreements - now he has his space to fill).

They'll then play games (more in another post! these are part of my son's schooling as well) together for the rest of the afternoon; and I'll probably have them clean out the inside of my car (since the three of them are the culprits!) ;)

 We leave after supper and go to tae-kwon-do practice in the evening. We love tae-kwon-do - it's all about self-control, self-defense, mixed ages, earning rank based on effort and merit not on "privilege", NO criticism of anyone, always being helpful and considerate of others.


So this is actually a typical Tuesday - our busiest day of the week. Lots of planning; coordinating what is going to happen when; following that weekly contract, but also being able to live a real life. Both the school and life get done not in spite of one another, but by supporting one another! 

This is the sort of day that exemplifies why I chose this approach to life and school - Montessori methodology provides the framework, the initial point of departure, and life takes care of the rest. There is nothing artificial here - only joy and peace.

Colors of the Tower and Stairs

There has been much discussion over the colors of the sensorial materials of tower, stairs and rods. Isn't natural better? It has the natural grain of the wood; it doesn't chip and need repairing; it focuses on the dimension, keeping them all the same rather than looking at the colors.

Well, I went back and forth. We had colored items to start with; sold most of them when my son was in elementary and we needed the space and money. Then I opened a co-op. Alas, I ended up purchasing all-new materials. When folks have used ones for sale, they sell fast! It's just a part-time co-op, so I want that money to stretch; so we purchased natural tower and natural stairs (I still had my original homemade red rods).

Guess what gets used? The red rods.

The little-little ones (2-3 year olds) will do the tower.

When the children were more "new" they went for the stair - blocks are something familiar.

But that was it. No amount of extension presentations, language games, challenges (what I use for the elementary children to get their hands on the sensorial material) gets them being creative. It's a dud. WHAT IS GOING ON?

I did show the elementary children how to find the volume of the cubes by building up 1cm wood cubes. That gets them using the tower and parts of the stair - and they are finding similarities. But NOONE is doing extension work.

Then I saw this post at My Montessori Moments, followed the links, and wondered..... and the pieces all fell together:

Cosmic education does not "begin" in elementary - the foundations are laid in infancy and built upon in primary; and finally realized on one level in elementary (and yet another level in adolescence).

What does that have to do with the sensorial materials?????

The sensorial materials are keys to the world - sure, we want all-natural and everything I listed at the start of this post - but there is SO MUCH MORE.

Art: look at those beautiful colors:

From Pink Princess Kingdom - so beautiful!

Our materials at co-op
(can you see which cube is missing?
I'll guess you had to search for it)

Which would YOU prefer to work with!?




The focus SHOULD be on the dimensions - not the knotholes; not the grain lines. Can you really see the dimensions if both are natural? Think about it, REALLY? In this case, all-natural does not help with the appreciation of aesthetics, and deters the child from the fullest of experiences.

With this material, the children can apply the principles they see to geometry; spatial relations when carrying ANY of the materials, or living ANY aspect of their lives. These things can be further developed by the precise way we carry the sensorial materials - and using two at the same time forces the child to "think" in the moment about how to hold this one, then that one - aiding decision making and thought processes.

Chipping: We are supposed to be teaching our children to care for the materials - and sometimes that means repair them. Yes, Montessori originally said the children could knock them down. Then she spent 4 years under house arrest in India as an enemy of the state. I don't know if that caused her to change her mind; but it certainly led to an emphasis on peace education!

When my son was an infant, he attempted to knock his glass off the table. But he couldn't! Because it was a heavy glass tumbler. We started with a shot-glass, but he would insert one finger into it, with two fingers on the outside and flip it. To train him to leave it alone, I had two options if I wanted PRODUCTIVE behavior before the age I could reason with him: provide something he couldn't flip (thereby disallowing the development of the habit) or swat his hand every time. Glass tumbler it was. He never spilled a drop or broke a glass (his whole life).

So at primary, we can show them how to use the blocks without knocking them down.

Chipping happens; then we show how to make the repairs - slowly and carefully - and let it sit until it dries. Takes the fun out of that instant impulse to knock them down, when you can't use the material for a while AND you have to sit and watch it dry (yes, I've made a child wait for the paint dry due to a severe attitude issue that causing the *hurling* of the pink tower across the room). Not a punishment - just consequences. No anger on my part; just a firm "you did this; now this is what we are going to do" - no ifs, ands, or buts. Child has proven he can't handle freedom, now he stays with the adult and follows through on natural consequences.
(said child was careful with the material after that - and when chips naturally happened anyway, he was the first to volunteer to fix it up)


Now, this post was written off-the-cuff - I have much more well-thought-out posts coming up at Montessori Nuggets - this one centers on our personal experience. 4 months ago, I still would have recommended the natural cubes and prisms - but I can no longer continue that recommendation. It may work in some situations, but it's not working here - and I have children that are soaking up EVERYTHING else. This one should have been a no-brainer - it started out fine, but fizzled. The above pictures say it all.

I'm buying paint and painting ours - I'll update here with any changes :)

Just for kicks:

red rods on steroids - how neat is this!?

UPDATE 2016:
I never did get back to updating this! YES, PAINT THEM! After 4 years, the ongoing uptake in the work, the extensions, the art designs - WORTH IT.
And please don't have them mixed up in a basket either - have them set so they display their dimensions on the shelf or stand too. This makes an ongoing difference (any change makes a short-term difference - I am speaking of months and years here...).

Elementary Language albums - our experience and comparisons

I've been asked my opinion about language albums a lot lately, but it doesn't really fit at Montessori Nuggets, since it is more personal experience than anything else.

We originally started our at-home Montessori journey with just Montessori books and online resources available at the time (not much - but what was available was given through the hearts of the people providing it!). We (I!) had a great deal of confusion. It is amazing how long someone can be in a Montessori classroom (as an assistant, aide, sub) and not really "get it" until it is time to put it into action. I thought I "got it" on so much, until I read the books and the internet and jumped in - and WHOA. Was it an experience! Fun! But also frustrating in many ways.

Language has probably been one of the most frustrating. You can read about our Adventures in Writing here. My largest issue for elementary albums is that they be continuous - the unnatural breaks just don't cut for me or for the child. With that said, going from primary even into lower elementary, the available options didn't correspond.

Grammar was the probably the biggest gray-hair causer of them all. Some things are presented across the board, with differences for planes of development; but it was like the blind leading the blind. I could not for the life of me figure out what/how was presented when/with-which-materials; when were the grammar boxes done; why were the colors mis-matched and the numbers totally off??????? The contents didn't match the sentences! Despite having The Montessori Elementary Material in front of me, I just didn't allow the answers in front of me to sink in. It was too much, at once, while in the thick of working with the children.

AND I was trying to adapt what I'd experienced in the schools into a homeschool experience with fewer materials.

It was chaos.

I tried to create order from the chaos, but in so doing, I had been trying to pull together everyone's modifications with my own observations/experiences, and the mixture spurred a chemical reaction:

We bombed it. I totally killed grammar for my tutoring kids.

I wish I had had an album in my hands. I wished it then, but couldn't afford any. I finally got my hands on some samples and was thrown off even more. It just wasn't coming together.

Now, I look back and think, "I'm glad I did not have an album in my hands at the time."

WHY!?

Because I look at the albums that were available then, compared with what I know now - and having had primary and elementary training... and I'm not satisfied with those earlier available albums, paid for or free. Not in the slightest. They aren't much better than what I was providing at that time; and many times conflicted so badly no wonder I was thrown off by the samples I'd seen!

Now. I am happy to say that others could still use them and find joy in them. But it would not have been there for me, in our situation. Sad to say.

There is HOPE!

If I were in that past situation today!? Or if you're in the situation I was in then (starting Montessori with only a toddler with infant/toddler experience; then a slew of 2-13 year olds to care for and tutor)!? There are OPTIONS! 

There are a variety of resources available now, or more affordable now, than there were years ago. But I would recommend starting out, to get an album - with the whole kit-and-caboodle of scope and sequence.

My two favorite available albums:

• FreeMontessori.Org - Language album
• Keys of the Universe - Language album TOC and sample

These are complete, or almost so; well-organized; and cover ages 6-12 so there is an organic development of a sequence for the child, rather than unnatural breaks during a smooth plane of development. Keys of the World provides the corresponding primary level language album. 

Both are very similar - how do they differ?

• One is free; the other is what I received in training and available to you with online support.
• Free: leaves out thorough descriptions of what to do with the grammar boxes
• Keys: includes the grammar boxes in thorough detail
• Free: includes more explicit work with punctuation
• Keys: assumes it was introduced at primary; and has an informal write-up of how to informally address this area of writing
• Free: seems shorter
• There may be other differences, but these are the most key areas. 

If I could just combine those highlights right there, everything else correlates and is PERFECT! 

What do we use at home for language arts? Just the Keys of the Universe album (I did read over the punctuation in the FreeMontessori album - but I already do it all so naturally based on the informal write-up in the Keys album). My son reads a LOT so we build on what he's read; and play lots of math and language games. He does a lot of research as well so he has learned naturally about the index, glossary, table of contents, footnotes, bibliographies, and more; as well as how to re-create those things in proper context. It's not perfect yet, but he is only 7! 

If I could go back into the past and tell myself something:

Hint: You CAN provide the grammar boxes starting in primary - generally this child is a "language guru"; or has utilized ALL the primary level language materials, as well as mostly covered the rest of the materials and is hungry for additional language. This child is an avid reader and is likely (but not always) writing quite a bit - or at least composing/re-creating stories and making plays on words and phrases and plot-lines. They are already playing with language a LOT. Hence I've seen these boxes used in primary; not often, but it does happen. 

More information on the grammar boxes will be provided on Montessori Nuggets - if you're not already signed up as a follower or for a daily e-mail, I invite you to join us!