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.

Thursday, May 24, 2012

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!).


  1. Woohoo!

    What a nice post :) Congratulations mom, congratulations to your son. Hurray for Montessori!

  2. I am SO not taking credit! I personally learned long division young (just a few months older than my son is now), but that is another story involving a doctor writing on a hospital pillow case while I was waiting stitches - I don't remember how he explained it, but I GOT it.

    But to see my just-turned-8-year-old doing it - I know I could not have taught it myself. Definitely hurray for Montessori ;)

  3. Good work!! I agree about the Long Division board with the graph paper. Sometimes my daughter forgets to use it, and then will quickly run to go get it. Our only problem that I had with this work was getting my daughter to overcome her fears from previously being taught how to do long division. Now it clicks:) My daughter is 12 years old, lucky for her she got to touch this material before adulthood. On the flip side my eight year old has been learning this material by observing her, if only he would slow down, then maybe he would click for him too. Your son is a hard worker and I applaud the both of you. Lots of steps, lots of concentration. You go!!

  4. Haha! Slowing down a boy! That is like stopping a freight train with one's bare hands in this household ;)

    I'll post an updated sample of his first "estimating the answer" step - probably it will post on Saturday or Monday. He ended up making a mistake with the *beads* of all things (he's previously been perfect - he checks with the large bead frame or a calculator (yes, I let him use a calculator to check his long division once in a while)).