Monday, September 30, 2013

School Days: Math

 Early last week I introduced the boys to the hierarchical material.  The next day I introduced them to the symbols.  I used the free printable file from Making Montessori Ours to make our number cards.  According to the discussion on the Keys of the Universe forum, these cards are made in the "primary" style (you will find the hierarchical presentations at the very end of AMI primary math albums for the kids who get that far).  Apparently there are some minor differences between primary and elementary hierarchical number cards.  The main difference is that the primary cards leave a big space between the heirarchical groups rather than employ the comma.  The other difference is that many people prefer the elementary cards to be in black and white.  I was fine with color cards, but I quickly grabbed a Sharpie and added the commas.

I'm actually really glad that our cards were in color.  My kid had apparently not noticed the color coding up to this point.  I believe this is the first time that a concrete material has matched the color of place-value color coding.  The other materials are all abstract.  Remember the water pump where Helen Keller made her breakthrough?  Kal-El really reminded of that as he ran around the room from material to material showing me that everything had the color coding.  He brought me wooden number cards, stamps (photo above), the small bead frame, and opened pages in his stamp game recording book (the paper has color-coded boxes).  He was so excited.  

Another neat thing about the hierarchical material was that it naturally nudged Kal-El back into bead frame work.  As soon as he knew all the symbols he announced that he was going to build some really big numbers on his bead frame.  The large one was in the storage closet and he didn't even know it existed, so of course he meant the small bead frame.  He was all upset in a few minutes and complained that his bead frame was too small!  I couldn't have asked for a better opening..."Would you like a larger one?"  We brought it out and that is when he discovered the color matching and did his little scavenger hunt.  When he had recovered he was properly introduced to the large bead frame, counted his way through the frame, and then we worked on the formation of numbers without paper.  This is where the child learns that "42 hundred" is the same as "four thousand two hundred."  

This stage can take a little while.  We don't want to move on until he can read "3 million one hundred and twenty-eight thousand five hundred and fourteen" smoothly rather than "3 millions, one hundred-thousand, two ten-thousands, 8 thousands, five hundreds, one ten, and fourteen units."  He has been reading numbers in the simple family in this way for quite some time, but it takes a while to be able to do it consistently well in the thousand family and million family on up.

Afterward he wanted to do some operations with really big numbers and remembered that the dot game included one of the larger categories (and is the other place he's seen a comma before).  I let him write his own equations for this work.  This time he wrote 69,965 x 6.  There is a little room in the margin on the left of the board and he used that to create his own 100-thousand category column.

Me Too started a new material that day as well!  He jumped into the stamp game with both feet.  It was neat because he and Kal-El  did the same work that day, just with different materials.  Like Kal-El, Me Too received an introduction to his material (comparing golden beads to stamps) and we moved on to the formation of numbers.  I have a nice stack of prewritten cards for this task.  Some of the numbers have digits in all four places, some numbers are intentionally only two- or three-digit numbers, some have zeroes in certain positions.  Me Too was unexpectedly unable to understand the place value on when the number was written on the index card.  This doesn't come up in the albums, so I had to invent a bridge activity on the fly.  I pulled out the small number cards and built the target number with those instead.  Me Too was instantly able to build the number.  So, we continued as follows:

  1. Choose an index card
  2. build the number with the wooden number cards
  3. build the number with the stamps 

He only need that bridge activity for one day.  Now he understands the place value right away when he looks at the number on the index card.  We are spending a few days building numbers before we move on to operations.  You can read about how we move through this stage and the booklets I make to record the stamp game work in this previous post.

Me Too is still working on the subtraction strip board with loose equations.  I have had the introduction to fractions ready for him for at least a week, but he hasn't chosen that work yet.  He is still choosing a bead chain once or twice a week and memorizing the skip counting and playing Speed!.

Kal-El is also working with fractions (subtraction with like-denominators), the multiplication finger boards, and he did a few packets of story problems (subtraction) last week.  I have not gotten him to choose geography yet, this week I am going to have to require it.  Like Me Too, he has been playing Speed! or counting bead chains (review).  I am hoping to switch him into the elementary album early bead chain work soon.  He has to get a little further along with his multiplication before we get too heavy into squaring and cubing work, but the early elementary activities should give us some fresh things to do without getting in over our heads.


  1. Looks like you had a fun week with math at your house.

  2. Awesome work!

    I like keeping the color too - and use a green comma - but that's us ;) It will be interesting to see where people take work like this (where it is SO wide open) now that elementary Montessori is becoming more prevalent and more materials are being offered ;)

    1. Thanks :)

      That free printable file works pretty well. If you want it in color you can print it in color, if you want it in black you could print in greyscale, there is room to add the commas in any color you wish.

      You're right...I wonder how they will eventually look when they show up as a material you can buy.

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  4. MBT,

    I also introduced the hierarchical materials last week with my 4.5 year old along for the ride. Earlier that week, I introduced her to the bead material and during the lesson she quickly related the golden bead material to the the unit, ten, and thousand in the hierarchical material. Meanwhile, while my oldest worked with the million and thousand hierarchy. He declared that the simple hierarchy was "boring" and did want anything to do with it!

  5. Love it!!!!! LOVE IT!!! I really dont know what happend here!!!! too much work, too much materials... but I dont even start this one!!!!! OMG