Pollinator Week - Biology

Pollinator week is June 18-24 and we'll be doing what we can at our home. How about you?

We'll be continuing our balcony garden, as well as the gardening at our friend's home; and we'll be on a "Pollinator Hunt" all week to see what we discover. My son also wants to do some research to see what plants and insects/animals go together for pollination purposes.

He has already started our list for when we move into a house - he knows which plants he wants in order to attract certain butterflies for example ; )


Kids Discover
This great article has a list of resources for more information, as well as activities and background information.


When planning your pollinator-friendly garden, choose native plants whenever possible. The Pollinator Partnership has a native plant guide (http://pollinator.org/guides.htm) that tailors recommendations to your region. Plant a variety of species that will flower successively over the entire growing season.

Who Pollinates?

Lentils – bees and insects
Artichoke – bees
Figs – wasps
Honey – bees
Eggplant – bees
Onions – bees and flies
Garlic – bees and flies
Sesame Seed – bees, flies, wasps
Chili Peppers – bees
Sweet Potatoes – bees
Yellow Potatoes – bees
Garbanzo Beans – bees
Herbs – bees
Lettuce – bees and insects
Grapefruit – bees
Currant – bees
Avocados – bee, flies, and bats
Tomatoes – bees
Spinach – insects
Almonds – bees
Lemons – bees
Sugar Cane – bees
Cocoa – flies
Cherries – bees
Bananas – birds, bats
Vanilla – bees
Raspberries – bees
Strawberries – bees
Coffee – bees and flies
Tea – bees, insects, and flies
Cranberries – bees
Apples – bees
Tequila – bats
Oranges – bees

Find out more at Kids Discover 

Last Year in Lower Elementary - Singing the Blues

I am so happy - and so sad... My little boy is growing up!

He is entering into this last year of "lower elementary". While we use AMI albums and consider elementary a continuum from 6-12, there is a certain sense of moving forward in this next year that is the typical parental bittersweet moment ;)

For the first two years of lower elementary we have almost entirely just followed the Montessori albums, throwing in our own interests and my own requirements here and there. For the sake of our personal situation, I also have "traditional school" lesson plans on which we mark off accomplished skills and record attendance (our state only requires 180 days per school year of attendance). According to those plans, he finished 3rd grade back in January (of his normally 2nd grade year). Montessori just does that ;) And we have plenty of time to explore all his own interests! A year and a half of Ancient Egypt has been a bit much for me personally, but it has been GREAT for him!

For this third year, we'll have a bit more planning to do. I have pulled all the state standards for 3rd grade in our state. He is responsible, over the course of the next year, to ensure that he has all listed skills, knowledge and experience.

Occasionally items from this list might make it onto his weekly work plan, but mostly it will just be up to him every so often to check the list and decide how to proceed. If he knows something intuitively, he can just let it go, but knowing my son, he'll likely make a little booklet that demonstrates each skill listed on the standards. I will actually be surprised if this doesn't happen.

We're doing mathematics, language arts, science, social studies, art, and physical education (the last two only because he "wants" to - ok, fine ;) ).

Looking things over, the only areas he might be "missing" are contained within social studies, particularly local history. He will develop his own plan for going about the requirements, with my assistance. We'll head to the library for books and videos, then expand from there - he might make dioramas, art projects, timelines, charts, posters, lists, diagrams or who knows what. There are SO many ways to fulfill those requirements - and there is no one right way!

And for the record, it's not that local history is left out of the Montessori elementary albums - it is that local history MUST be developed by the local teacher and the students in conjunction with one another. Montessori history covers the framework within which to study history; and the details are left to personal research. Culture and all other aspects of social studies are covered in-depth.

As homeschoolers in our state, we do not HAVE to follow those standards; but I choose to follow the Montessori elementary albums in this regard; there is a focus on the local public school requirements in the 3rd year of lower and of upper elementary. I believe it will help to instill a sense of responsibility to and respect for local authorities, strengthen his work ethic, provide practice in a safe environment for the future when he has to do things he'd rather not do (without overwhelming him now), and set a sound pattern for a mature adulthood.


So here we are at a benchmark. Leaving behind the total freedom of primary; and the relative freedom of lower elementary; to embrace a year of outside requirements. Then we'll have two more years entirely to ourselves before we repeat at age 12 years.


Ok. Reality is that the public school requirements take an average of 5 minutes per week, if that! So this is just a mommy making a mountain of a molehill ;) Hehe.

A bit of a Break

We've been taking a bit of a break from homeschooling this week - but Montessori continues ;)

I have been assisting a Catechesis of the Good Shepherd formation course (in the same building where we have our co-op class during the school year, so most of our Montessori materials are there right now).

Between some review mathematics work (yep, even older kids need to review concepts like fractions equivalency once in a while ;) ) and atrium presentations, as well as helping me organize some of the materials, I guess it's not so much of a break from Montessori or homeschooling as much as it is a break from the "work plan" - there is no work plan for this week except to enjoy it ;)

Exercises of Practical Life in Infancy

An infants' focus is almost entirely on practical life and sensorial experiences. And almost everything requires NO materials.


In our home, we had the following material-required skills for the infant years - up to 12 months old.

• toothpicks into a jar wide mouth jar, then water bottle, then mounting onto salt shaker holes
• beginning to cut with scissors - at tray on booster seat with blunt-tipped scissors and narrow strips of paper on special tray that is indicated just for cutting
• using slots and holes (balls into holes; large poker chips into a slot on a coffee can lid --- start with objects that require no force to push through, then ones with more force required)
• feeding self

Mostly we focused on movement skills, language, reading, and being together. We had the mobiles, floor bed, long mirror, and lots of loved ones to provide love and attention. No specially purchased materials here:

• couch cushions for climbing and tumbling - remove cushions from couch to create a safe climbing and tumbling game
• can or heavy jar that rolls across the floor to encourage crawling
• stairs with a gate across the 4th or so step (move it up as the child is safely climbing up and down)
• textures of various fabrics

Above all else, focus on reality - and encourage baby to participate in his own way. Talk to him with whole language (yes, high-pitched motherese is fantastic for the youngest babies!), smile, interact - all those grace and courtesy lessons coming in a few years in primary. 

Everything is practical life and sensorial at this age! 

Infant Montessori is so easy in retrospect - it really IS a minimalist approach! 

Climbing the couch cushions for the first time
(look at the happy face!)

waiting for his new friend to join him

Adolescent Montessori - Homeschool - Can it be DONE!?

I have fielded more than a few questions on this topic.

The short answer is YES.

The long answer involves a lot of discussional points with those who say "No" and have extremely valid points.

Now, I do not personally have any training or orientation for the adolescent age. NAMTA and AMI are now offering an Orientation to Adolescents course that is great time-wise, but it is frankly more expensive per day than primary and elementary AMI training combined.
OUCH.

And they don't even "have all the answers." It's not a full training - the MES Fund does not consider it a training for scholarship purposes. It is simply an orientation. And it is geared for a group setting (which I am ok studying and practicing, then adapting for homeschool purposes).

It sounds LOVELY anyhow, but I cannot afford to attend :( I need to finish paying off primary and elementary first!

In the meantime, I have started consolidating all of the resources provided in both primary and elementary, along with the required reading list for the Orientation and other resources.

I am putting together a small online discussion group specifically for this age, with reading assignments on a suggested schedule, discussion topics and sharing of ideas and resources. Everything will be from a homeschool perspective.

If you are part of our Keys of the Universe discussion board, you are already in! I will begin the official group June 21 in the adolescent section and Keys of the Universe participants have full access as part of their regular participation.

If you are not part of the Keys of the Universe discussion board, join us here:
Keys of the Universe Individual Album Support - Adolescent Montessori Discussion Group Access
One-time payment; life-time participation

We will begin June 21 in earnest; but anyone can join at any time.

The ideal participant:

• you have a child age 10-16 right now, with or without elementary Montessori experience
• you have an older child and would like to contribute from that perspective
• you have Montessori adolescent experience
• you have extensive other experience working with the adolescent group and you are familiar with Montessori principles; and want to apply those principles to the adolescent group

Anyone with any age child can be participate, but the earliest stages will be better suited for someone in the field right now or very soon; or who has been there and can provide some insight. 

If you are looking for something totally put together with all the answers handed to you - we're not there yet! This initial group is for those who want to explore and share, together. 

Goals - Main Topics:

• establish foundation of understanding of the adolescent age
• including their needs, tendencies; how to meet them
• difference between societal expectations and reality of needs and tendencies
• What if we provide all that Montessori suggested? What will happen?
• Compare our own experiences and work through personal barriers. 
• Establish the universal principles of an adolescent Montessori homeschool
• Lend support to filling in the specifics for each individual home
• Establish collection of resources for use by homeschooling families for this age

Already part of Keys of the Universe: no cost
Join separate from Keys of the Universe: $15 - permanent access

Exercises of Practical Life in our Home - Toddler Years

Many of the simpler exercises of practical life can be done by toddlers; this frees up their primary years for deeper, more purposeful work. Included in our practical life was a lot of sensorial as well - for us the two areas overlapped a LOT in the toddler years.

In our home, we had the following for the toddler years - approximately ages 12 months to 3 years.

• continue cutting with scissors on thin strips - by age 2, using most of the primary cutting exercises
• mounting toothpicks into a mound of playdough
• continue other infant work as long as needed (see June 7 post)
• cutting banana and other very soft items with a butter-spreader
• opening and closing boxes, latches, etc. 
• twisting: caps on bottles, large nuts/bolts
• matching lids to pans (my son put this one together himself!)
• wiping up spills
• preliminary stages of getting self dressed
• how to wash hands
• walking on a wide line
• walking carrying items (such as porcelain statues)
• sweeping with a child-size broom
• safety rules (ie hold hands in parking lots)
• respect rules (ie do not touch visiting friend's keys on the table without asking)
• spooning grains (cereals in particular)
• pouring from small pitcher
• stringing large, then smaller beads
• using knobbed shape puzzles (large knobs, then smaller; all geometric shapes)
• using large eyedropper (a medicine dropper)
• matching shapes
• dressing frames as appropriate - dressing self as appropriate (shoes on)
• matching colors
• hanging loose items on a hanger
• completing work cycle of putting things away
• using spray bottles to clean windows and tables
• setting own place at the table (with an outlined place mat)
• putting away laundry and other household items

School Shopping!

School shopping season is coming up (at least in the US and Canada) and I thought I would put together a list for what items to be on the lookout for when you're stocking up:


Target Dollar Rack possibilities:

• miniature globes (for primary Montessori, get 3-6: sandpaper (land and water), continents, political, climates, oceans (you may want a larger one for the oceans), and a 6th topic I can't think of right now)
• flashcards - buy at least 2 copies of each; 2 sets creates 3-part cards with a control set and a cut set; 1 set creates flashcard games and/or classifying by type; 2 sets uncut could be matching games; 2 sets with one cut or uncut could be mounted onto cardstock and made into a booklet; you could overlap some of these ideas. 
• Flashcards for elementary - animals and plant images can be used for classification rather than hunting down and printing images or using magazines to cut up - usually one set is sufficient, unless you want to have a separate set for the information on them; or a third set so you have 2 to make a booklet and  a third set for the classification. 
• Small writing notebooks if they carry them this year

Any Back to School specials: 

• quadrille paper - either loose-leaf or in bound books - used for almost any subject in elementary (we prefer loose-leaf to create our own notebooks via binders or other binding)
• spiral notebooks for taking notes of various sorts - single subject: stock up on a lot; 3 or 5 subject, smaller quantity, but they will be used too (perhaps the whole notebook is on Ancient Egypt with each of the 5 sections being a particular theme)
• pack of loose-leaf notebook paper: wide-rule for primary and college rule for older elementary
• package of large erasers - the ones on pencils just aren't enough and the ones you add to the pencils have too much waste
• decent colored pencils in the basic colors (you might have a family set for everyone, but everyone should have their own set of basic-basic colors - prismacolor are my favorite)
• pencil pouch (better a thinner pouch than a large box - easier to transport when needed) - holds the eraser, a couple of pencils, a good sharpener (all metal is best), set of basic colored pencils, and perhaps a tiny notepad, you might have a pen in here too
• tiny notepads - they usually come in 3 packs and they are small - they are great for field notes, quick notes, short lists, and just anything that would otherwise waste a large sheet of paper -- easy to transport in a pencil pouch ;) 
• lunch bag and drink bottle - even homeschooled children can use a lunch bag and bottle for outings, trips, picnics, etc. And this is the best time to buy them. 

NOTE: For the most part, assignment books are the not best equipped to handle an elementary child's work plan or work contract; but if you find one that does work, post a link or image here!

PLEASE ADD YOUR OWN INSIGHTS HERE!

:) 

Exercises of Practical Life in Our Home - Primary

The Exercises of Practical Life are the oddest subject area in Montessori.

On the one hand, they can be entirely overlooked because it's not "academic" (it is academic and necessary for a child's development, but that's not the point to this post ;) ).

On the other hand, they are easiest to WAY OVER-DO - getting into areas that aren't, well, practical. This is where we start getting into the area of "independent learning activities" that aren't really Montessori. Useful, perhaps. Interesting, perhaps. Not going to harm your child, most likely. But NOT Montessori.
And can definitely over-burden a homeschool mom who "just wants to do it right" but sees everyone's ideas and thinks they are all necessary. No, they're not necessary - this is where you can have some creativity if you like, but it is NOT necessary!

Exercises of Practical Life: think practical. What is practical for YOUR life?

Montessori = Keys.

We actually started with old medicine droppers
at home - transitioned to glass ones later.
You can see our "supply shelf" in the back!

Home versus school = small available space.
(it could be argued that schools need to follow the same guidelines because they have more children who have less time with the materials than homeschoolers have, but I am writing about MY home right now :) ) .

Therefore, in our home, we stick with the practical exercises of the "Exercises of Practical Life" album.

At primary, that meant we had the following throughout our home - not all in one place:

Preliminary Exercises (any special materials introduced here are removed when the child is competent at the related activity)

How to Carry a Working Mat

How to Place a Pitcher

How to Carry a Tray

How to Roll a Working Mat

How to Put Down a Chair

How to Sit On a Chair at a Table

How to Fold Napkins - basic - styles added later in elementary

How to Pour Grain (dry pouring - something with weight - removed when competent with pouring)

How to Pour Water (wet pouring - removed when competent with own pitcher in the fridge)

How to Fold a Dust-cloth to Put Away (we just used the regular dust-cloths)

How to Fold a Dust-cloth to Dust (just used the regular dust-cloths) Transfer with Eyedropper - liquid from one bottle to another (related to polishing) Clothespin on edge of a jar (removed when starting to competently hang clothes in such manner)

Care of Self

How to Wash Hands

Snap Frame

Hook and Eye Frame

Button Frame

Buckle Frame

Zipper Frame

Bow Frame

Lacing Frame – V Pattern

Lacing Frame – X Pattern

Lacing Frame – Linear Pattern

Safety Pin Frame Combing Hair

Care of the Environment

How to Dust a Table

How to Use a Dustpan and Brush

How to Sweep with a Broom How to Vacuum (kid-sized vacuum)

How to Wipe Up a Spill

How to Dust Leaves

How to Polish Glass, Metal, Wood - I had separate trays, but the processes are streamlined for function within the home.

How to Care for Plants

How to Wash a Table AND counter

How to Wash Cloths

How to Iron

How to Arrange Flowers

How to Make Basic Food items (orange juice, fruit salads, pbj sandwiches)

How to Wash Fruits and Vegetables

How to Peel & Cut Various Fruits and Vegetables

How to Bake (a toaster oven is ideal; we did not, so he did everything EXCEPT when the over door was open - that part was my job) --- a primary aged child can help make almost anything from cookies and muffins to salads and sandwiches - even pizza!

Grace and Courtesy

How to Walk Around A Mat

How to Introduce Yourself

How to Apologize

How to Observe

How to Draw Attention

How to Accept a Compliment

How to Blow Your Nose

How to Sit on Upholstered Furniture appropriately (still working on that one!) How to answer the door

Control of Movement

Walking on the Line - rolled up ball of string - stretched out when ready to use

The Silence Activity

Visual Art

Rubbings (Exploration of Texture)

Cutting - Snipping

Cutting - Lines

Advanced Cutting

Contour Drawing with Crayon (Exploration of Line)

Drawing with Colored Pencils

Cutting and Gluing (Exploration of Space)

Painting (Exploration of Color)

Sculpting (Exploration of Form)

Beginning Sewing

Sewing a Button

Advanced Sewing – Running Stitch

Basic cross-stitch Exposure to crochet Others adapted for our home:  Grating soap "Guard" when Mama makes soap (have the vinegar and water buckets ready for accidents) Safety precautions around home-made soap Holding and carrying lit candles Other candle-care Cleaning the inside of a fridge or freezer Using tweezers to pick up small items - this was a novelty experience, but taught the use of the tweezers when needed for medical purposes. Other than medical or dissections, tweezers just aren't used here.  Rock sorting within a set of tackleboxes - this was very nonchalant - his work but not on a shelf of its own within "Montessori" work.  SPUR OF THE MOMENT activities that did not become permanent in our home: washing rocks, sorting shells Chores appropriate to age and ability Using other kitchen utensils - we just taught/learned as needed, not with a specific tray activity Stringing buttons - or any other activities that are not typically done ROUTINELY in real life. Something that is done once in a great while (ie stringing popcorn for Christmas decor), is taught at the time it is needed. There is NO need for a tray activity for such activities.  Art activities - again learning what is needed in the moment after he'd all the basic art lessons from the EPL album; including play-dough, clay, painting, drawing, gluing, etc. Beyond the basics I did NOT have a tray activity for everything. He knew where the supplies were (organized in a simple, Montessori-like manner) and he knew when he had free time to create as much art as he wanted.  Other games - we like to play lots of games here - so many things that some people put on trays and use as an independent learning activity, we just used as games. Repeatable, but not necessary to have on a tray and called "school".  "Inspired" unit studies that last for a time, but are not permanently on a tray or shelf.  Cultural experiences as appropriate - related to books being read, people visiting, videos watched, people or animals met. These were not permanently on display, but cycled back into our regular life (ie chopsticks are in the utensils drawer).

We did NOT have the following - either space or philosophy:

• polishing shoes (it is in the albums, but we just don't have shoes to be polished)
• anything with those little pom-pom, warm-fuzzy things. They have NO weight, so serve little purpose when applied to real life. We used cotton balls with polishing and these needed to be replenished, so there was plenty of work to do with carrying weight-less items. Activities that others have created are cute, but when do you ever spoon or tweeze soft weightless objects in real life? These activities are novelties; not harmful, but should be kept to a minimum (and Zero is an acceptable amount ;) ). 
• trays for EVERYTHING. It's just not necessary. Many things at home can and should be done in their proper context. Yes, sometimes a preliminary presentation is needed and that might be on a tray for a while; thereafter, the materials are kept where they belong (whisks belong in the utensil drawer) and are used at appropriate times. No tray needed :) 

Montessori Materials

SOAP-BOX ALERT! This post is about me and my reactions to current materials offered by Montessori companies. It is not about my son or his education, at least directly. It's about me and my emotions.

I will not be offended if you choose not to read this. I do not intend to offend anyone with the following words, but I feel certain that someone will think I have said something offensive.

Let me say here and NOW: each family must choose for themselves and I don't judge the "extras" that you choose. We have extras too. My soap-box has to do with the impression of Montessori in the public sphere because of these "extras".

Feel free to stop reading and join us tomorrow for our regular daily reports of Montessori elementary (or previous primary or infant/toddler) experiences.

Click the next line if you don't mind reading my soap-box ;)

Amazing Myself

Sometimes I amaze myself.

I entered a giveaway with Alison's Montessori. I won! I thought I'd won a Power of Two cube - it was a crazy time in our lives that particular week, so I didn't entirely pay attention...

I recently received my new Montessori material. It's the Power of THREE cube! It is BEAUTIFUL!

18cm cube demonstrating the power of 3
Thank you Alison's Montessori!

But see, here's the kicker: my AMI Montessori albums do not have a material for this presentation! The children should be working on some level of abstraction when they receive this presentation! I have an album page - it just doesn't require a material. (so the "amazing myself" part is that I entered to win, and WON, an item I would not have purchased to begin with - however, it is SO BEAUTIFUL! have I said that yet!?) ;)

If we provide a material for *everything* (especially at upper elementary), the children's creativity will decrease, their exploratory learning will diminish, and it will be more difficult to reach abstraction. I've just seen it happen too many times.

Our solution? We're going to use it in lower elementary as a sensorial exploration (kind of like having the binomial and trinomial cubes in primary); then I'll still give the presentation in upper elementary as-is according to my album page. And if my son or my co-op kids make the connection themselves, all the better. But since I only have my co-op kids a few times a month, the sensorial exploration will be PERFECTION for them!

As it stands, my son (just-turned-8) has already figured it out. He was putting it together blind-folded within 30 minutes of receiving it ;)

UPDATE 1/3/2016 After almost 4 years, an update is in order ;) I did end up selling this material (at cost for shipping) as we found it just wasn't necessary, it was an easy "puzzle" and nothing was really coming from it. Afterwards I saw that it is included in the Adolescent Mathematics album that does take it deeper. Ok, that is great, but honestly? The pieces are too big. the material is quite combersome. I have found a way to create this material from folded up cardstock that is not only smaller, but more enticing. Essentially, start with the Power of 2 Cube and add in the pieces you need from there. A post will be forthcoming in 2016 on this topic. ;)

Multiples in Mathematics

Lower elementary multiples example - this is typically first year in lower elementary if the child has had a decent amount of primary mathematics. It could happen in later first year if the child is brand new to Montessori altogether. 

each number is circled according to its multiples
see my son's key in the upper corner :)
who says Montessori children don't learn how to use legends?
right here it is - they just don't have an album page for it ;) 

my sample for how to highlight a particular number
again - using a key ;) 

Embellish your work!

Sample from other work I've seen
Borders around the page or around sections/problems
Separators between sections
Just to fill in some space

In Montessori we say, "DOODLE!"

Ok, so we don't say that. We DO say, "Embellish!"

We want the children to cherish their work, so we allow them the opportunity to personalize it, fulfilling the fundamental human needs towards vanitas: to embellish oneself and one's environment.

All Montessori parents and teachers reading this, raise your hand if you have NEVER been tempted to embellish the children's environment on some level or another - to the point of being TOO much?

Not ONE hand should be raised! ;)

We want the children to learn balance, so we allow embellishment from the beginning, integrating art and daily work, even when the subject matter is not necessarily art.

But isn't it all art? Math is art, language is art, music is art, history is full of art and those timelines are works of art, geometry is pure art in my mind, geography is an art --- all these things have grace, beauty, boundaries, creativity ---- ART.

So why isn't this information available online anywhere, on all those Montessori blogs and all those Montessori albums that provide samples!? I don't know! It's a bit frustrating, because it is so basic to Montessori, especially elementary Montessori. But it starts in primary with the stamp game in particular - embellishing the row between two problems.

My son's sample today. He chose to use markers
for the first time. Please note: Markers do not mix well with
colored pencils. Any work done in pencil should be
embellished with color pencils, NOT markers.
Use markers as a medium to themselves on their
own separate sheet of paper, if at all. 

My son has always done embellishment of some kind and he LOVES it. The work means something to him and he's perfecting his art skills.

 I will show you an example of one I'm not proud of because he rushed it. It was not meaningful and he even said so. We discussed the reality that if he doesn't WANT to embellish, he doesn't have to.

And we discussed the reality that markers and writing pencils and colored pencils don't mix well. The aesthetics are lost.

Therefore, all is not lost, because this experience prompted discussion on balance, necessity and art media usage.


What about work plans and work contracts? Well, these should generally not be embellished - perhaps very lightly (instead of a checkmark, a creative child could use another symbol) - now the work journal could be a place for art, if you use one for the child to document his or work! The work journal can be embellished in any way the situation allows. While it is not the place for the child to store finished work (only a place to record time spent and what was done; perhaps answer a follow-up question), many children prefer to draw their work into these journals or separate entries with fancy designs.

Playing with Language

You know when you've been doing Montessori very well in your home, specifically the grammar boxes and sentence analysis, when your child speaks in transposed sentences without even thinking about it - no hesitation. Just as natural as can be.

"Son, what are you doing right now?"

"Apple cutting core and it Mommy peeling an." With a big bright smile :)

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!).