The Hierarchical Material

Last week I gave the impressionistic Hierarchical Material presentation to my kids and our homeschool buddies.

Image from Alison’s Montessori. Link for photo credit.

The material consists of 7 solid shapes:
– a small green cube representing one unit
– a blue ten rod the size of 10 unit cubes in a line
– a red hundred square the size of 10 blue ten rods side by side
– a green thousand cube the size of 10 stacked hundred squares
– a blue ten-thousand rod the size of 10 stacked thousand cubes
– a red hundred-thousand square the size of 10 ten-thousand rods side by side.
– a large green million cube, the size of 10 stacked hundred thousand squares

I made my own material from IKEA boxes and left over Christmas tissue paper and wanted to recycle it right away, (it’s BIG) so, while my KotU albums list 4 presentations, I combined them and did two presentations in one morning. Early in the morning we looked at the material to be amazed at the size of the unit cube compared to the million cube, and added the number labels. At the end of the morning we laid the material out by shape and color and discussed how that related to the notation. Being outside, we were able to estimate the size of a billion cube too!

So, the presentations went well.

But a few days later, I’m reflecting that I feel like I suddenly understand these concepts better. Now I have an engineering degree and would claim to be quite math-y, so I’d claim that I understood these concepts pretty well beforehand. I’ve known about this material and presentation for years, but this is the first time I’ve presented it.

Layout by quantity

After the first linear layout, I feel like I can more quickly and easily relate number scale to volume. We had a great discussion comparing the unit cube to the thousand cube to the million cube and imagining what the billion cube might look like. I never did that at school! Now I feel like I can see these numbers and am better able to compare different magnitudes of numbers.

Layout by hierarchy

Laying the material out the second time, by color and size, was also an aha moment! I’m quite sure it was never explicitly pointed out to me that as we move though number groupings (simple family, thousands, millions, billions, etc.) that the unit of the family can always be represented as a cube, the tens digit of the family can always be represented by a rod, and the hundreds digit can always be represented by a square.

I also have been thinking back to the Infinity Street lesson, and place value work on the checkerboard. Presenting and guiding my children through work with these materials has certainly made reading large numbers easier for me.

The Theory of Multiple Intelligences isn’t new. It this – the visual, spacial and tactile part of the Montessori lessons and materials that makes all the difference. It doesn’t matter what type of learning you are – Montessori’s got you covered! I hope that getting the information verbally, visually, spatially, and in a tactile way will give my kids a deeper understanding, something they can “feel” in their bodies. Maybe they won’t have these “aha” moments as a grown up, because they’ll have “felt” it all along.

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