Fractions in Lower Elementary

My Boys' Teacher over at What Did We Do All Day just posted about fractions and asked for some samples.

His chosen embellishments for this page
include math signs and the number 3 ;)
He mounted this paper onto colored paper
and inserted into a 3 ring folder as a portfolio.

I went to pull my son's math folder... and found in our recent un-organization of our home... the folder is pretty much missing. I did find the folder Lego Boy started in the co-op with some of that year's sample work.

















And he so graciously offered to create some samples on graph paper to show how he has written fractions on graph paper in the past. Unfortunately he did not go back to the basic-of-basics and instead did what "he" considers basic which is equivalency within operations. ;)

This is smaller graph paper than the first graph paper he used, but it hopefully still gets the idea across? There is no one right way...




But I did have an order of operations in fraction writing, not so much from any album but from what seemed to follow the child at the time:

• start him on blank paper - showing both ways in our culture for writing fractions (horizontal line and slanted line)
• then large large squared paper (each fraction in a square); 
• then larger graph paper, with a number, then line, then number, then space - each in their own squares ---- in order to align numerators, denominators, fractions bars, equal signs, etc. 
• regular graph paper, with the entire fraction written within a square - he can now write smaller AND this gets him ready for writing mixed number (whole numbers with a fractional portion). The whole number written big in the square and the fraction written within its own square. 
• He can write them out on lined paper as well, but true to Montessori, we try to stick with graph paper for math work. The graph paper helps with organization, mathematical principles, drawing out samples in geometry and multiplication  etc. --- it just FEEDS that MATHEMATICAL mind, where lined paper feeds the LANGUAGE of writing. 

Later, we will explore other cultures' ways of writing fractions. 

Also, I offer this file I created when my son was in primary. It is a printable file for the labeling and basic operations with fractions - I'd forgotten about this one and was about to share a funny looking one that worked and fit into our tacklebox we used - but is not "ideal" - I am so happy I found this one for you all!

Montessori Fractions: Labels and Simple Operations

I did start another file for sample elementary level problems; I will fix it up and have it included in the elementary albums at Keys of the Universe - if you're in that course and don't see it up soon, please do bug me about it ;) I am good-natured about those sort of things ;)

Last Elementary Montessori Order

I just placed our final Montessori materials order - and couldn't believe what a struggle it was to reach the free shipping level! We had all else we needed!

Wow.

One more year of lower elementary, 3 more years of upper elementary to come... and we have everything???

Ok, we'll still be purchasing and borrowing things along the way - items to correspond with interests, replacement chemicals and other supplies - but the Montessori-specific items are done.

Overall... elementary is no more expensive, Montessori-wise, than primary, perhaps cheaper (I'll look at actual numbers another day!) - and covers SIX years.

And the re-sale value canNOT be over-stated!

He was still sleeping in this photo,
but he reached out to me as I sat down next to him.
Those hands that were so tiny at birth.... 

This is a bittersweet day. It means a preparing for a closing of one area of life (browsing Montessori catalogs, determining what to make and what to buy and from whom), but it also means a true settling in. Settling in for the next 4 years. Settling into just BEing in elementary. Then on to adolescence.


Ok, scratch that last sentence. Just focus on this time. Right now. The moment we have - right now - together.




ETA: November 12: IT'S HERE!

Geometry Command Cards

Legoboy (new nickname for the blog ;) ) is working on the Geometry Command Cards, partially because he needs review on geometric concepts, partially because I need the materials checked before I offer them to others and partially so I can get some updated images to correct the incessantly annoying mathematics album files!

He is rushing through some of the work, but I thought I'd post some of it anyway :) 

Working on convergent and divergent lines: 

Reviewing the concept with the geometry sticks

parallel - the children are
neither happy nor sad

convergent - connecting of
paths - the children are SO happy!

divergent - paths are going two ways
the children are so sad!

Fast drawing the concept on paper
From a command card for "two lines"
note the opposite direction of the stick work
showing mastery of the concept in a different layout

BONUS:
ETA a link to the sample geometry command cards my son used above. These are also being added to the Keys of the Universe Geometry album, along with more advanced versions for older children. 

Homemade Vanilla

The resident child (hehe) has been studying a bit about herbs of late. And it has been on our plans to make homemade vanilla extract for quite some time. 

Obviously, not something he can do on his own... He can cut the beans, he can drain the extra fluid, he can drop in the beans, label it all and seal it up, he can store it. 

But I had to make purchase. My first alcohol purchase of my life! The things we do for our children! It does seem ironic I just purchased an alcohol for my son, though! 

(for the record, I am not opposed to alcohol, I just don't tout it or drink very much, and I have not had a reason to purchase it before now.... wait.... when I lived in Belgium, I bought some wine to bring home to family, but that was a different culture - alcohol was out with the sodas!). 

Grandma was given this kind of rum/vanilla; and we
were so happy to find it stocked at Kroger.
It has fantastic flavor, so we are excited! 

The beans we purchased from Mountain Rose Herbs: 

http://www.mountainroseherbs.com/index.php?AID=135782&Redirect=/search?page=1&q=vanilla+beans&utf8=✓

We have the "1oz Vanilla Bean organic and fair trade" and it smells right! ;) I do wonder if we got quite the driest beans (apparently you are supposed to use grade B beans - but I also wanted fair trade, etc). These seemed more most than I anticipated. So we'll see. Either way, it will work from what all sources say - it's just a nuance ;)

He has been looking at the history of the use of vanilla - and true to Montessori style, we want to look at the PEOPLE involved. Most fascinating is that a 12 year old child worked out how to hand-pollinate the vanilla so that it could be grown outside of the Latin America countries. 

Forget gold and corn and other such things - the greatest gift that the Europeans found in the Americas: VANILLA! 

Ever had chocolate without it? 

We did! Never again, thank you! 

Vanilla brought chocolate to the impoverished Europeans! And now they make the best chocolate in the world. One plant changed the world! One little boy's discovery! 

Practical Life in our Day: Mint

We are trying to be good stewards of the earth, while not letting the earth get in the way of the most important gift of human beings: relationship.

It is even better when the two are the same thing :)

In this case, we are growing mint in our living room. As it grows long, we trim it, hang it to dry, grind it up and make tea... and more... While it is drying (upside down so the oils flow back into the leaves, maximizing their potential), we have a beautiful decoration that makes our home, truly homey. Comforting. And there is a natural inclination towards being with one another in a cozy, homey home ;)

Once it is fully dried, we spend time together pulling the leaves off into a large bowl (easier to collect everything then, transfer in small quantities to the mortar and pestle). I bought a set of 3 of these on Amazon years back (affiliate link there) that have been simply fantastic!

The mint leaves are stored in a jar to use for making tea, or to add to our homemade toothpaste or anywhere else we need some mint flavoring.

That leaves the stems - which are fine for adding to the composting, but well, we have an interesting set up with our apartment management and mouse-traps get pricey when management does little to alleviate the issue. But fresh mint keeps them away.

My mother will cringe when she reads that I tuck these stems in all the places where the mice have been spotted. Despite her cringing, I can confidently report success (so far!) - ice-free and my home smells so nice! We freshen them up when we harvest new mint and THEN we compost the stems. There may be other purposes for them, but that is what we do for now :)

mint, dried, laying on the stove
because our counters were full at the time. 

grinding mint leaves with mortar and pestle