Tessellation Patterns

While there is no specifically AMI Montessori album page for tessellations - they are just plain fun! And when presented right, with the right materials, they fit right in with Montessori.

While we do not encourage the children to create images (we want them to explore the shape, and the function of each shape - not be focused on creating boats and flowers) - elementary children do utilize them to create images. I encourage the exploration of shape and function and steer them away from creating images until it is inevitable.

Some samples of our work:

a friend's toes

exploring different kinds of flowers

what if we just use hexagons? what would happen?
note: this particular mode teaches far more
 more than creating a flower teaches a child ;) 

she was exploring pure shape; filling in gaps with other shapes,
seeing where it would lead (this is a transition stage into
creating intentional images)

Purely exploring with shapes - and look at the beautiful pattern emerging!

Long Division - Final Results

I did the writing, because he insisted on doing it with colored
pencils, which would have been too faint for our camera.
And I wanted him to focus on the step at hand: multiplication.
He has not yet embellished this page because he wants
to do more long division problems on it first. 

My son is just at the final stages of long division - writing without the beads. It is a work we started quite a while ago; he has flown through it relatively speaking, however he will continue to utilize the beads and boards for quite a while to come. (this material starts in year 1 of the elementary Montessori mathematics album - and claims to be done by age 8 - well, that's the presentations being done at age 8 - the work will continue into upper elementary --- this expensive piece of material (approximately $100 after shipping with IFit) is worth EVERY PENNY).

This is sort of bitter-sweet! My just-turned-8-year old is doing long division on paper!

Tomorrow, we will go over the basic steps of estimating the answer, then multiplying AND checking with the beads to be sure we get each step correct.

After that, the last step is using trickier numbers and estimating.

This material is beyond amazing! Once the process is mastered, the understanding just FLOWS. I recall a woman in my primary training crying when she finally understood division - and that was the same material just doing SHORT division - as an adult she was able to comprehend how the long division would work; but as a child she had been terrorized by what is now a joyful experience for her.


I strongly encourage the use of graph paper in doing mathematics. The children can embellish their work in so many ways with graph paper, plus it keeps their numbers lined up and organized. The more complicated the operation at hand for that particular child, the more you want graph paper (ie stamp game for a 5 year old is complicated; stamp game for a 8 year old maybe not so much; long division - get the graph paper!).

Nouns: Singular and Plural

My son asked me to share a sample of his singular and plural noun booklet from last year.

With the study of the grammar boxes, there are many follow-up presentations for the article/noun box (grammar box 2), the adjective box and the verb box in particular.

For nouns, we have noun number (singular and plural), noun gender, noun classification of abstract, concrete, material, collective and the 3 types of abstract nouns. Number and gender can come just before or after presenting grammar box 2 (usually after), while noun classification comes at around 7-7.5 years old or at least a few months after presenting the other noun material, giving the child time to assimilate and an opportunity to come back and review those nouns.

As my son can attest, it is not necessary to do ALL the sets in a particular album page, let's say noun number, before moving on to noun gender, the next grammar boxes, and other language studies. Just exposure is necessary - there is plenty of time for review and follow-up. He likes to do things to completion in order, but even with these, I think we moved on to noun gender before finishing up the number cards.


Without further ado, here is something my son put together of his own accord - a booklet describing the rules for singular and plural - 1 rule per page or pair of pages. The translation (since he abbreviated) is in the caption. I tried to keep his punctuation and style - just writing out the words he abbreviated.

1: for some words add -s. (for example desk becomes desks) 

2: some words add -s. the difference is that
these words end with "e."
(for example ledge - ledges.)

Other things I've seen children do: create a chart or list of the rules; just state them aloud; explore more nouns that fit within each rule (we do NOT give them every example within a particular rule); create booklets of words; create additional card material.

For our material, I broke with the rules a bit. You are supposed to have a few sets of cards, then the remaining noun number sets are in booklet form for the child to study. I found it easier on me as a work-at-home single mom to just make cards of all the material; then my son (who loves booklets) makes his own and illustrates - so the singular is on the left side of the page and the plural is on the right side, and there might be two words and pictures on the left, with the corresponding words on the right. He then extrapolates the rule and writes it on the last page. If you make booklets, you'll make them as I just described, and still invite the child to extrapolate the rule (not necessarily the first time through, but they tend to be pretty quick with these).

How was the booklet made?
Take a regular sheet of printer paper (you don't want paper too thick for this or it won't fold right).
Fold it in half, unfold and fold it in half again the other way (making 4 section on your paper).
Now take the short side and fold it into the middle line; repeat with the other short side; unfold everything.
You should now have 8 sections - if you are holding the paper vertically (as if reading a printed letter), you will have 2 columns of 4 rectangles that are horizontal (longer than they are tall).
The tricky to describe part: see that long line you folded down the middle? On either side of that line are 4 pages; you are going cut ON that line just in the middle 2 section. So if you are still holding that paper vertically, your top row will be uncut, your bottom row will be uncut, but your middle 2 rows will be separated on the crease with a vertical cut.
Now fold the paper in half ON that line that you just cut. If done right, those middle pages want to "poof" out. Let them.

Ultimately you have 4 double-thick pages kind of in the shape of an x or a cross. Just fold them along their creases (don't create any new ones) and you have a book. I find I have to flip the pages around a couple of times to find the most "comfortable" fold so that nothing is sticking out at an odd angle.

Want a longer book? Make two or three of them, and glue them front to back. My son used two for his Singular and Plural Book.

Grammar Boxes - Objects

When doing the grammar boxes with your children, you want to have objects that match all the words in the boxes, so that the children can actually *bring* those objects - this is a movement work, not a sit-still-read-and-copy work.

Got a little boy? Legos work for a lot of the pieces!

Grammar Boxes without the Boxes

There was a time before we had the grammar boxes but my son was totally ready for them. 

I have NO images for what we did, but I can describe it! 

I took the images of the grammar boxes from photos taken when I was in classrooms. 

I then diagrammed them all onto posterboard (cardboard would have been better; covered with posterboard perhaps). I then cut little strips of cardboard to glue on as "edges". 

NOTE: the compartments were intentionally made just a bit wider than the cards, but not as tall, so that cards lay at an angle against the back edge. 

The back of each compartment was covered with an appropriately colored piece of construction paper (hint: don't use construction paper - it tends to FADE - I ultimately colored over each one with colored permanent marker). 

I then proceeded as usual with the presentations, except the cards were placed mostly flat within each "compartment" (leaning against the back "edge"). 

Interesting tidbit: the original grammar boxes as imaged in the Advanced Montessori Method book also do not have tilting insides. The compartments were vertical and the card fit in them such that they lay flat against the bottom of the box. If I were to make ours from wood, with my simple scroll saw, I would make ours similar, but with the compartments narrower from front to back, so that the cards tilt against the back of the compartment. I could have made them out of cardboard that way too - but had made the poster boards already; then was gifted with the modern style wood ones.