Thursday, May 31, 2012

Memorization of Addition: Commutative Property

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Last week Kal-El discovered the commutative property.  This work began with building all of the ways to make ten and writing them in his math notebook.  He discovered that 9+1 and 1+9 both equal ten, as do 8+2 and 2+8, etc.,  He went through his math notebook and crossed out the duplicate equations.

The next step was to use blank slips of card stock to cover the duplicate equations on control chart one.  Afterward, he was presented with control chart two.  He was really excited about the new control chart.  At least once a day he refers to control chart one and says "I don't need that one anymore."

He enjoyed this work tremendously.  He was so excited by it that he asked to borrow the camera to take some pictures afterward.  The next three photos are some that he took himself of his own work.  You can see his toes in the first shot :)

Addition strip board, control chart one, control chart 2, math notebook, and container of paper slips.

Close up of his math notebook with the duplicate equations crossed out.

The addition strip board.

I noticed over the weekend that he took the addition strip board off the shelf and re-built the equations for ten several times.

As always, if you are looking for something that will show the "big picture" of the memorization of addition sequence all in one place this post at Ecole et Cabrioles is excellent.  Also, if you need free memorization of addition materials you can find them at Livable Learning/JMJ Publishing.

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  1. Awesome photos he took!

    And great work on the math :)

  2. Great work with the Strip Board! Makes me slightly jealous as I am still waiting for my Math order to arrive from Montessori Outlet! I placed it two weeks back and my daughter is so ready to begin this work...uh!

  3. Jessica,

    Thanks! He's having a lot of fun.


    Ack! The waiting drives me nuts. I've recently been ordering from Kid Advance, they are soooo fast.

  4. Yes, I ordered at KidAdvance and Caliber Montessori a day after I ordered at Montessori Outlet, I've received both a week back, still waiting for Montessori Outlet!

  5. Please can you tell me, did you make the boards? Trying to decide whether to make (on free framers board, double layers) and strips either this board or wood.


  6. Tracey,

    I decided it was not worth making my own. JMJ publishing offers the files for free, but they are (in order to be printable) smaller than the real thing. Kal-El has trouble using such small works. Also, in my experience it is fun and satisfying to put the wooden tiles on something like the 100 board and the addition charts...doing it with little slips of paper instead, not so much.

    I was *going* to print the JMJ files, enlarge them at the copy shop and laminate them. Then, I was going to use "Woodsies" squares to make the little tiles. After looking at the cost (my ink at home, $1.75 per page for an 11x17 color copy, $3.99 to laminate an 11x17, and there are 17 charts total. Plus, I think I was going to need $20 of Woodsies.) The $100 it costs to BUY all 17 charts suddenly looked really good. It was going to cost $120 to make them myself and that wasn't even putting them on wood like you said, and they certainly weren't going to be as nice. I was going to mount on foam board and haven't even added that cost.

    If your child can handle the smaller size of the JMJ version, just print and laminate at home and be done with it. Otherwise I think you should buy it.

  7. Did you do step 11 in the addition sequence? That is the one where they do problems like ?+6=12. I was wondering if you printed your own slips or if you knew of a printable somewhere. I didn't see any at Montessori Print Shop which is where I printed out my other slips. I am all for short cuts around here. :)

    1. Yes, we did, but not in direct sequence. The Ecoile steps are AMS steps and the AMI steps are more streamlined. If you are using AMI albums my advice is to do their fewer steps and then check and see if they already have the equations memorized. If they don't, then add some AMS steps. I took these types of steps, which I call "equation formats" and separated them. We did them as filler work and happened to store them in our story problem basket. KHT Montessori provided printables for this work as part of her primary course. They aren't loose equations, but in table format.

  8. Ok, this helps a lot. I am expecting to have to do the whole sequence since the boys started Montessori late and we are doing remedial math. I am so curious how much quicker they would have memorized these equations in the "absorbent" phase. I am glad I have some younger ones coming behind so I can experience what it is like to start at the right time.