Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.
Showing posts with label fractions. Show all posts
Showing posts with label fractions. Show all posts

Tuesday, December 18, 2012

UPDATED past post: Fraction Materials


I recently updated this post on superfluous Montessori materials. Mostly just tweaks.

But I added the information below about the fractions materials and thought it deserved its own post because of the strong emotional response that has been sent my way when I calmly say, "This material is unnecessary." So yes, here I am a bit more emotional ;) Because I really stand behind the Montessori principles involved.


As I state in my other post, I am not intending to offend anyone, but I know this will sound that way to some people. Please consider the Montessori principles at hand; the century that has passed with consistent observations and the development of album pages appropriate to the various stages of childhood. While not everything may be solidly set in stone, the youngest ages do have a very firm foundation. It is the adolescent age where we are still playing with the details.


Fraction sets for 1/11 through 1/20 - there is a keys-based presentation for helping the children work with fraction above 1/10. If a child is given the material for fractions 1/11 and higher, he is losing out on the opportunity to explore on an abstract level. He will always be hindered in his work because he was given "the fish" when he needed directions on "using the fishing pole".

I have had 3 moms tell me their 5 or 6 year old was SO STRONGLY into fractions and since the child was SO young, this hands-on material would be appropriate for them. NO! Can I say that loud enough!? NO!!! NO! NO! NO!
(before we go on: my son at age 4 1/2 was there too - ALL things fractions! a "fraction genius" even! I really thought I had a guru on my hands - and I was ready to feed that guru-ness wherever it took us, but something happened...)


There is a reason that fractions are in the primary album for children ages 5 and 6 - BECAUSE they have an intense interest! So we are already feeding that interest! But we are feeding that interest by providing the FOUNDATION. A STRONG foundation in the basic facts and uses of fractions.

Then if your child is truly a fractions-genius and his interest hasn't yet waned (most children's intense interest in fractions wanes for a year or two, because they 1) need to consolidate and 2) are moving on to other areas of development and 3) there is just so much else to DO) - there are a series of elementary level presentations that are worked on FIRST (and the little genius can certainly do them all in 1st grade if he wants! rather than spread them across 1st-3rd), before you even get to the need for doing 1/11 and beyond. Once you get to the presentation for 1/11 and beyond - WE DON'T STOP AT 1/20! We go to 1/100 and 1/360 and BEYOND even that! So when a child is ready - he's READY! And we don't hold him back! But we lay the foundation FIRST.

Therefore the fractions materials for 1/11 through 1/20 are superfluous at best; a hindrance and a crutch at worst. Don't bother with them!


SUMMARY:
If a child is a fraction genius and it HOLDS, then he has all the primary presentations AND all the elementary work at his fingertips, before he is presented with how to address fraction smaller than 1/10 --- and at that point, a true fraction genius, will be entirely ready for that materials that are provided, or he will be genius enough to make his own material - thus consolidating and applying the fraction concepts at hand in a much more efficacious manner than just handing him the material.

:)

It all works out in the end :)


Tuesday, November 6, 2012

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 ;)